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When it is not found, a full rebuild will be done. +config: 2d7b5c0d06fd9875399c14b694147ac6 +tags: d77d1c0d9ca2f4c8421862c7c5a0d620 diff --git a/0.3/_sources/api/collectors.rst.txt b/0.3/_sources/api/collectors.rst.txt new file mode 100644 index 0000000..40c8394 --- /dev/null +++ b/0.3/_sources/api/collectors.rst.txt @@ -0,0 +1,42 @@ +Collectors & Extractors +======================= + +miplearn.classifiers.minprob +---------------------------- + +.. automodule:: miplearn.classifiers.minprob + :members: + :undoc-members: + :show-inheritance: + +miplearn.classifiers.singleclass +-------------------------------- + +.. automodule:: miplearn.classifiers.singleclass + :members: + :undoc-members: + :show-inheritance: + +miplearn.collectors.basic +------------------------- + +.. automodule:: miplearn.collectors.basic + :members: + :undoc-members: + :show-inheritance: + +miplearn.features.fields +------------------------ + +.. automodule:: miplearn.features.fields + :members: + :undoc-members: + :show-inheritance: + +miplearn.features.AlvLouWeh2017 +------------------------------- + +.. automodule:: miplearn.features.AlvLouWeh2017 + :members: + :undoc-members: + :show-inheritance: diff --git a/0.3/_sources/api/components.rst.txt b/0.3/_sources/api/components.rst.txt new file mode 100644 index 0000000..64b6c5b --- /dev/null +++ b/0.3/_sources/api/components.rst.txt @@ -0,0 +1,44 @@ +Components +========== + +miplearn.components.primal.actions +---------------------------------- + +.. automodule:: miplearn.components.primal.actions + :members: + :undoc-members: + :show-inheritance: + +miplearn.components.primal.expert +---------------------------------- + +.. automodule:: miplearn.components.primal.expert + :members: + :undoc-members: + :show-inheritance: + +miplearn.components.primal.indep +---------------------------------- + +.. automodule:: miplearn.components.primal.indep + :members: + :undoc-members: + :show-inheritance: + +miplearn.components.primal.joint +---------------------------------- + +.. automodule:: miplearn.components.primal.joint + :members: + :undoc-members: + :show-inheritance: + +miplearn.components.primal.mem +---------------------------------- + +.. automodule:: miplearn.components.primal.mem + :members: + :undoc-members: + :show-inheritance: + + \ No newline at end of file diff --git a/0.3/_sources/api/helpers.rst.txt b/0.3/_sources/api/helpers.rst.txt new file mode 100644 index 0000000..d83450f --- /dev/null +++ b/0.3/_sources/api/helpers.rst.txt @@ -0,0 +1,18 @@ +Helpers +======= + +miplearn.io +----------- + +.. automodule:: miplearn.io + :members: + :undoc-members: + :show-inheritance: + +miplearn.h5 +----------- + +.. automodule:: miplearn.h5 + :members: + :undoc-members: + :show-inheritance: diff --git a/0.3/_sources/api/problems.rst.txt b/0.3/_sources/api/problems.rst.txt new file mode 100644 index 0000000..a60a968 --- /dev/null +++ b/0.3/_sources/api/problems.rst.txt @@ -0,0 +1,57 @@ +Benchmark Problems +================== + +miplearn.problems.binpack +------------------------- + +.. automodule:: miplearn.problems.binpack + :members: + +miplearn.problems.multiknapsack +------------------------------- + +.. automodule:: miplearn.problems.multiknapsack + :members: + +miplearn.problems.pmedian +------------------------- + +.. automodule:: miplearn.problems.pmedian + :members: + +miplearn.problems.setcover +-------------------------- + +.. automodule:: miplearn.problems.setcover + :members: + +miplearn.problems.setpack +------------------------- + +.. automodule:: miplearn.problems.setpack + :members: + +miplearn.problems.stab +---------------------- + +.. automodule:: miplearn.problems.stab + :members: + +miplearn.problems.tsp +--------------------- + +.. automodule:: miplearn.problems.tsp + :members: + +miplearn.problems.uc +-------------------- + +.. automodule:: miplearn.problems.uc + :members: + +miplearn.problems.vertexcover +----------------------------- + +.. automodule:: miplearn.problems.vertexcover + :members: + diff --git a/0.3/_sources/api/solvers.rst.txt b/0.3/_sources/api/solvers.rst.txt new file mode 100644 index 0000000..2337d92 --- /dev/null +++ b/0.3/_sources/api/solvers.rst.txt @@ -0,0 +1,26 @@ +Solvers +======= + +miplearn.solvers.abstract +------------------------- + +.. automodule:: miplearn.solvers.abstract + :members: + :undoc-members: + :show-inheritance: + +miplearn.solvers.gurobi +------------------------- + +.. automodule:: miplearn.solvers.gurobi + :members: + :undoc-members: + :show-inheritance: + +miplearn.solvers.learning +------------------------- + +.. automodule:: miplearn.solvers.learning + :members: + :undoc-members: + :show-inheritance: diff --git a/0.3/_sources/guide/collectors.ipynb.txt b/0.3/_sources/guide/collectors.ipynb.txt new file mode 100644 index 0000000..0d90c7b --- /dev/null +++ b/0.3/_sources/guide/collectors.ipynb.txt @@ -0,0 +1,278 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "id": "505cea0b-5f5d-478a-9107-42bb5515937d", + "metadata": {}, + "source": [ + "# Training Data Collectors\n", + "The first step in solving mixed-integer optimization problems with the assistance of supervised machine learning methods is solving a large set of training instances and collecting the raw training data. In this section, we describe the various training data collectors included in MIPLearn. Additionally, the framework follows the convention of storing all training data in files with a specific data format (namely, HDF5). In this section, we briefly describe this format and the rationale for choosing it.\n", + "\n", + "## Overview\n", + "\n", + "In MIPLearn, a **collector** is a class that solves or analyzes the problem and collects raw data which may be later useful for machine learning methods. Collectors, by convention, take as input: (i) a list of problem data filenames, in gzipped pickle format, ending with `.pkl.gz`; (ii) a function that builds the optimization model, such as `build_tsp_model`. After processing is done, collectors store the training data in a HDF5 file located alongside with the problem data. For example, if the problem data is stored in file `problem.pkl.gz`, then the collector writes to `problem.h5`. Collectors are, in general, very time consuming, as they may need to solve the problem to optimality, potentially multiple times.\n", + "\n", + "## HDF5 Format\n", + "\n", + "MIPLearn stores all training data in [HDF5](HDF5) (Hierarchical Data Format, Version 5) files. The HDF format was originally developed by the [National Center for Supercomputing Applications][NCSA] (NCSA) for storing and organizing large amounts of data, and supports a variety of data types, including integers, floating-point numbers, strings, and arrays. Compared to other formats, such as CSV, JSON or SQLite, the HDF5 format provides several advantages for MIPLearn, including:\n", + "\n", + "- *Storage of multiple scalars, vectors and matrices in a single file* --- This allows MIPLearn to store all training data related to a given problem instance in a single file, which makes training data easier to store, organize and transfer.\n", + "- *High-performance partial I/O* --- Partial I/O allows MIPLearn to read a single element from the training data (e.g. value of the optimal solution) without loading the entire file to memory or reading it from beginning to end, which dramatically improves performance and reduces memory requirements. This is especially important when processing a large number of training data files.\n", + "- *On-the-fly compression* --- HDF5 files can be transparently compressed, using the gzip method, which reduces storage requirements and accelerates network transfers.\n", + "- *Stable, portable and well-supported data format* --- Training data files are typically expensive to generate. Having a stable and well supported data format ensures that these files remain usable in the future, potentially even by other non-Python MIP/ML frameworks.\n", + "\n", + "MIPLearn currently uses HDF5 as simple key-value storage for numerical data; more advanced features of the format, such as metadata, are not currently used. Although files generated by MIPLearn can be read with any HDF5 library, such as [h5py][h5py], some convenience functions are provided to make the access more simple and less error-prone. Specifically, the class [H5File][H5File], which is built on top of h5py, provides the methods [put_scalar][put_scalar], [put_array][put_array], [put_sparse][put_sparse], [put_bytes][put_bytes] to store, respectively, scalar values, dense multi-dimensional arrays, sparse multi-dimensional arrays and arbitrary binary data. The corresponding *get* methods are also provided. Compared to pure h5py methods, these methods automatically perform type-checking and gzip compression. The example below shows their usage.\n", + "\n", + "[HDF5]: https://en.wikipedia.org/wiki/Hierarchical_Data_Format\n", + "[NCSA]: https://en.wikipedia.org/wiki/National_Center_for_Supercomputing_Applications\n", + "[h5py]: https://www.h5py.org/\n", + "[H5File]: ../../api/helpers/#miplearn.h5.H5File\n", + "[put_scalar]: ../../api/helpers/#miplearn.h5.H5File.put_scalar\n", + "[put_array]: ../../api/helpers/#miplearn.h5.H5File.put_scalar\n", + "[put_sparse]: ../../api/helpers/#miplearn.h5.H5File.put_scalar\n", + "[put_bytes]: ../../api/helpers/#miplearn.h5.H5File.put_scalar\n", + "\n", + "\n", + "### Example" + ] + }, + { + "cell_type": "code", + "execution_count": 1, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "x1 = 1\n", + "x2 = hello world\n", + "x3 = [1 2 3]\n", + "x4 = [[0.37454012 0.9507143 0.7319939 ]\n", + " [0.5986585 0.15601864 0.15599452]\n", + " [0.05808361 0.8661761 0.601115 ]]\n", + "x5 = (2, 3)\t0.68030757\n", + " (3, 2)\t0.45049927\n", + " (4, 0)\t0.013264962\n", + " (0, 2)\t0.94220173\n", + " (4, 2)\t0.5632882\n", + " (2, 1)\t0.3854165\n", + " (1, 1)\t0.015966251\n", + " (3, 0)\t0.23089382\n", + " (4, 4)\t0.24102546\n", + " (1, 3)\t0.68326354\n", + " (3, 1)\t0.6099967\n", + " (0, 3)\t0.8331949\n" + ] + } + ], + "source": [ + "import numpy as np\n", + "import scipy.sparse\n", + "\n", + "from miplearn.h5 import H5File\n", + "\n", + "# Set random seed to make example reproducible\n", + "np.random.seed(42)\n", + "\n", + "# Create a new empty HDF5 file\n", + "with H5File(\"test.h5\", \"w\") as h5:\n", + " # Store a scalar\n", + " h5.put_scalar(\"x1\", 1)\n", + " h5.put_scalar(\"x2\", \"hello world\")\n", + "\n", + " # Store a dense array and a dense matrix\n", + " h5.put_array(\"x3\", np.array([1, 2, 3]))\n", + " h5.put_array(\"x4\", np.random.rand(3, 3))\n", + "\n", + " # Store a sparse matrix\n", + " h5.put_sparse(\"x5\", scipy.sparse.random(5, 5, 0.5))\n", + "\n", + "# Re-open the file we just created and print\n", + "# previously-stored data\n", + "with H5File(\"test.h5\", \"r\") as h5:\n", + " print(\"x1 =\", h5.get_scalar(\"x1\"))\n", + " print(\"x2 =\", h5.get_scalar(\"x2\"))\n", + " print(\"x3 =\", h5.get_array(\"x3\"))\n", + " print(\"x4 =\", h5.get_array(\"x4\"))\n", + " print(\"x5 =\", h5.get_sparse(\"x5\"))" + ], + "metadata": { + "collapsed": false + } + }, + { + "cell_type": "markdown", + "source": [], + "metadata": { + "collapsed": false + } + }, + { + "cell_type": "markdown", + "source": [ + "## Basic collector\n", + "\n", + "[BasicCollector][BasicCollector] is the most fundamental collector, and performs the following steps:\n", + "\n", + "1. Extracts all model data, such as objective function and constraint right-hand sides into numpy arrays, which can later be easily and efficiently accessed without rebuilding the model or invoking the solver;\n", + "2. Solves the linear relaxation of the problem and stores its optimal solution, basis status and sensitivity information, among other information;\n", + "3. Solves the original mixed-integer optimization problem to optimality and stores its optimal solution, along with solve statistics, such as number of explored nodes and wallclock time.\n", + "\n", + "Data extracted in Phases 1, 2 and 3 above are prefixed, respectively as `static_`, `lp_` and `mip_`. The entire set of fields is shown in the table below.\n", + "\n", + "[BasicCollector]: ../../api/collectors/#miplearn.collectors.basic.BasicCollector\n" + ], + "metadata": { + "collapsed": false + } + }, + { + "cell_type": "markdown", + "source": [ + "### Data fields\n", + "\n", + "| Field | Type | Description |\n", + "|-----------------------------------|---------------------|---------------------------------------------------------------------------------------------------------------------------------------------|\n", + "| `static_constr_lhs` | `(nconstrs, nvars)` | Constraint left-hand sides, in sparse matrix format |\n", + "| `static_constr_names` | `(nconstrs,)` | Constraint names |\n", + "| `static_constr_rhs` | `(nconstrs,)` | Constraint right-hand sides |\n", + "| `static_constr_sense` | `(nconstrs,)` | Constraint senses (`\"<\"`, `\">\"` or `\"=\"`) |\n", + "| `static_obj_offset` | `float` | Constant value added to the objective function |\n", + "| `static_sense` | `str` | `\"min\"` if minimization problem or `\"max\"` otherwise |\n", + "| `static_var_lower_bounds` | `(nvars,)` | Variable lower bounds |\n", + "| `static_var_names` | `(nvars,)` | Variable names |\n", + "| `static_var_obj_coeffs` | `(nvars,)` | Objective coefficients |\n", + "| `static_var_types` | `(nvars,)` | Types of the decision variables (`\"C\"`, `\"B\"` and `\"I\"` for continuous, binary and integer, respectively) |\n", + "| `static_var_upper_bounds` | `(nvars,)` | Variable upper bounds |\n", + "| `lp_constr_basis_status` | `(nconstr,)` | Constraint basis status (`0` for basic, `-1` for non-basic) |\n", + "| `lp_constr_dual_values` | `(nconstr,)` | Constraint dual value (or shadow price) |\n", + "| `lp_constr_sa_rhs_{up,down}` | `(nconstr,)` | Sensitivity information for the constraint RHS |\n", + "| `lp_constr_slacks` | `(nconstr,)` | Constraint slack in the solution to the LP relaxation |\n", + "| `lp_obj_value` | `float` | Optimal value of the LP relaxation |\n", + "| `lp_var_basis_status` | `(nvars,)` | Variable basis status (`0`, `-1`, `-2` or `-3` for basic, non-basic at lower bound, non-basic at upper bound, and superbasic, respectively) |\n", + "| `lp_var_reduced_costs` | `(nvars,)` | Variable reduced costs |\n", + "| `lp_var_sa_{obj,ub,lb}_{up,down}` | `(nvars,)` | Sensitivity information for the variable objective coefficient, lower and upper bound. |\n", + "| `lp_var_values` | `(nvars,)` | Optimal solution to the LP relaxation |\n", + "| `lp_wallclock_time` | `float` | Time taken to solve the LP relaxation (in seconds) |\n", + "| `mip_constr_slacks` | `(nconstrs,)` | Constraint slacks in the best MIP solution |\n", + "| `mip_gap` | `float` | Relative MIP optimality gap |\n", + "| `mip_node_count` | `float` | Number of explored branch-and-bound nodes |\n", + "| `mip_obj_bound` | `float` | Dual bound |\n", + "| `mip_obj_value` | `float` | Value of the best MIP solution |\n", + "| `mip_var_values` | `(nvars,)` | Best MIP solution |\n", + "| `mip_wallclock_time` | `float` | Time taken to solve the MIP (in seconds) |" + ], + "metadata": { + "collapsed": false + } + }, + { + "cell_type": "markdown", + "source": [ + "### Example\n", + "\n", + "The example below shows how to generate a few random instances of the traveling salesman problem, store its problem data, run the collector and print some of the training data to screen." + ], + "metadata": { + "collapsed": false + } + }, + { + "cell_type": "code", + "execution_count": 2, + "outputs": [ + { + "name": "stderr", + "output_type": "stream", + "text": [ + "/home/axavier/Software/anaconda3/envs/miplearn/lib/python3.8/site-packages/tqdm/auto.py:22: TqdmWarning: IProgress not found. Please update jupyter and ipywidgets. See https://ipywidgets.readthedocs.io/en/stable/user_install.html\n", + " from .autonotebook import tqdm as notebook_tqdm\n" + ] + }, + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Removing empty/corrupted h5 file: data/tsp/00000.h5\n", + "lp_obj_value = 2909.0\n", + "mip_obj_value = 2921.0\n" + ] + } + ], + "source": [ + "import random\n", + "import numpy as np\n", + "from scipy.stats import uniform, randint\n", + "from glob import glob\n", + "\n", + "from miplearn.problems.tsp import (\n", + " TravelingSalesmanGenerator,\n", + " build_tsp_model,\n", + ")\n", + "from miplearn.io import save\n", + "from miplearn.h5 import H5File\n", + "from miplearn.collectors.basic import BasicCollector\n", + "\n", + "# Set random seed to make example reproducible.\n", + "random.seed(42)\n", + "np.random.seed(42)\n", + "\n", + "# Generate a few instances of the traveling salesman problem.\n", + "data = TravelingSalesmanGenerator(\n", + " n=randint(low=10, high=11),\n", + " x=uniform(loc=0.0, scale=1000.0),\n", + " y=uniform(loc=0.0, scale=1000.0),\n", + " gamma=uniform(loc=0.90, scale=0.20),\n", + " fix_cities=True,\n", + " round=True,\n", + ").generate(10)\n", + "\n", + "# Save instance data to data/tsp/00000.pkl.gz, data/tsp/00001.pkl.gz, ...\n", + "save(data, \"data/tsp\")\n", + "\n", + "# Solve all instances and collect basic solution information. Process at most four\n", + "# instances in parallel, with a per-instance time limit of one hour.\n", + "bc = BasicCollector(time_limit_sec=3600)\n", + "bc.collect(glob(\"data/tsp/*.pkl.gz\"), build_tsp_model, n_jobs=4)\n", + "\n", + "# Read and print some training data for the first instance.\n", + "with H5File(\"data/tsp/00000.h5\", \"r\") as h5:\n", + " print(\"lp_obj_value = \", h5.get_scalar(\"lp_obj_value\"))\n", + " print(\"mip_obj_value = \", h5.get_scalar(\"mip_obj_value\"))" + ], + "metadata": { + "collapsed": false + } + }, + { + "cell_type": "code", + "execution_count": 2, + "outputs": [], + "source": [], + "metadata": { + "collapsed": false + } + } + ], + "metadata": { + "kernelspec": { + "display_name": "Python 3", + "language": "python", + "name": "python3" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.8.13" + } + }, + "nbformat": 4, + "nbformat_minor": 5 +} diff --git a/0.3/_sources/guide/features.ipynb.txt b/0.3/_sources/guide/features.ipynb.txt new file mode 100644 index 0000000..70e937c --- /dev/null +++ b/0.3/_sources/guide/features.ipynb.txt @@ -0,0 +1,334 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "id": "cdc6ebe9-d1d4-4de1-9b5a-4fc8ef57b11b", + "metadata": {}, + "source": [ + "# Feature Extractors\n", + "\n", + "In the previous page, we introduced *training data collectors*, which solve the optimization problem and collect raw training data, such as the optimal solution. In this page, we introduce **feature extractors**, which take the raw training data, stored in HDF5 files, and extract relevant information in order to train a machine learning model. We describe the extractors readily available in MIPLearn." + ] + }, + { + "cell_type": "markdown", + "source": [ + "\n", + "## Overview\n", + "\n", + "Feature extraction is an important step of the process of building a machine learning model because it helps to reduce the complexity of the data and convert it into a format that is more easily processed. Previous research has proposed converting absolute variable coefficients, for example, into relative values which are invariant to various transformations, such as problem scaling, making them more amenable to learning. Various other transformations have also been described.\n", + "\n", + "In the framework, we treat data collection and feature extraction as two separate steps to accelerate the model development cycle. Specifically, collectors are typically time-consuming, as they often need to solve the problem to optimality, and therefore focus on collecting and storing all data that may or may not be relevant, in its raw format. Feature extractors, on the other hand, focus entirely on filtering the data and improving its representation, and are therefore much faster to run. Experimenting with new data representations, therefore, can be done without resolving the instances.\n", + "\n", + "In MIPLearn, extractors implement the abstract class [FeatureExtractor][FeatureExtractor], which has methods that take as input an [H5File][H5File] and produce either: (i) instance features, which describe the entire instances; (ii) variable features, which describe a particular decision variables; or (iii) constraint features, which describe a particular constraint. The extractor is free to implement only a subset of these methods, if it is known that it will not be used with a machine learning component that requires the other types of features.\n", + "\n", + "[FeatureExtractor]: ../../api/collectors/#miplearn.features.fields.FeaturesExtractor\n", + "[H5File]: ../../api/helpers/#miplearn.h5.H5File" + ], + "metadata": { + "collapsed": false + } + }, + { + "cell_type": "markdown", + "source": [ + "\n", + "## H5FieldsExtractor\n", + "\n", + "[H5FieldsExtractor][H5FieldsExtractor], the most simple extractor in MIPLearn, simple extracts data that is already available in the HDF5 file, assembles it into a matrix and returns it as-is. The fields used to build instance, variable and constraint features are user-specified. The class also performs checks to ensure that the shapes of the returned matrices make sense." + ], + "metadata": { + "collapsed": false + } + }, + { + "cell_type": "markdown", + "source": [ + "### Example\n", + "\n", + "The example below demonstrates the usage of H5FieldsExtractor in a randomly generated instance of the multi-dimensional knapsack problem." + ], + "metadata": { + "collapsed": false + } + }, + { + "cell_type": "code", + "execution_count": 1, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "instance features (11,) \n", + " [-1531.24308771 -350. -692. -454.\n", + " -709. -605. -543. -321.\n", + " -674. -571. -341. ]\n", + "variable features (10, 4) \n", + " [[-1.53124309e+03 -3.50000000e+02 0.00000000e+00 9.43468018e+01]\n", + " [-1.53124309e+03 -6.92000000e+02 2.51703322e-01 0.00000000e+00]\n", + " [-1.53124309e+03 -4.54000000e+02 0.00000000e+00 8.25504150e+01]\n", + " [-1.53124309e+03 -7.09000000e+02 1.11373022e-01 0.00000000e+00]\n", + " [-1.53124309e+03 -6.05000000e+02 1.00000000e+00 -1.26055283e+02]\n", + " [-1.53124309e+03 -5.43000000e+02 0.00000000e+00 1.68693771e+02]\n", + " [-1.53124309e+03 -3.21000000e+02 1.07488781e-01 0.00000000e+00]\n", + " [-1.53124309e+03 -6.74000000e+02 8.82293701e-01 0.00000000e+00]\n", + " [-1.53124309e+03 -5.71000000e+02 0.00000000e+00 1.41129074e+02]\n", + " [-1.53124309e+03 -3.41000000e+02 1.28830120e-01 0.00000000e+00]]\n", + "constraint features (5, 3) \n", + " [[ 1.3100000e+03 -1.5978307e-01 0.0000000e+00]\n", + " [ 9.8800000e+02 -3.2881632e-01 0.0000000e+00]\n", + " [ 1.0040000e+03 -4.0601316e-01 0.0000000e+00]\n", + " [ 1.2690000e+03 -1.3659772e-01 0.0000000e+00]\n", + " [ 1.0070000e+03 -2.8800571e-01 0.0000000e+00]]\n" + ] + } + ], + "source": [ + "from glob import glob\n", + "from shutil import rmtree\n", + "\n", + "import numpy as np\n", + "from scipy.stats import uniform, randint\n", + "\n", + "from miplearn.collectors.basic import BasicCollector\n", + "from miplearn.features.fields import H5FieldsExtractor\n", + "from miplearn.h5 import H5File\n", + "from miplearn.io import save\n", + "from miplearn.problems.multiknapsack import (\n", + " MultiKnapsackGenerator,\n", + " build_multiknapsack_model\n", + ")\n", + "\n", + "# Set random seed to make example reproducible\n", + "np.random.seed(42)\n", + "\n", + "# Generate some random multiknapsack instances\n", + "rmtree(\"data/multiknapsack/\", ignore_errors=True)\n", + "save(\n", + " MultiKnapsackGenerator(\n", + " n=randint(low=10, high=11),\n", + " m=randint(low=5, high=6),\n", + " w=uniform(loc=0, scale=1000),\n", + " K=uniform(loc=100, scale=0),\n", + " u=uniform(loc=1, scale=0),\n", + " alpha=uniform(loc=0.25, scale=0),\n", + " w_jitter=uniform(loc=0.95, scale=0.1),\n", + " p_jitter=uniform(loc=0.75, scale=0.5),\n", + " fix_w=True,\n", + " ).generate(10),\n", + " \"data/multiknapsack\"\n", + ")\n", + "\n", + "# Run the basic collector\n", + "BasicCollector().collect(\n", + " glob(\"data/multiknapsack/*\"),\n", + " build_multiknapsack_model,\n", + " n_jobs=4,\n", + ")\n", + "\n", + "ext = H5FieldsExtractor(\n", + " # Use as instance features the value of the LP relaxation and the\n", + " # vector of objective coefficients.\n", + " instance_fields=[\n", + " \"lp_obj_value\",\n", + " \"static_var_obj_coeffs\",\n", + " ],\n", + " # For each variable, use as features the optimal value of the LP\n", + " # relaxation, the variable objective coefficient, the variable's\n", + " # value its reduced cost.\n", + " var_fields=[\n", + " \"lp_obj_value\",\n", + " \"static_var_obj_coeffs\",\n", + " \"lp_var_values\",\n", + " \"lp_var_reduced_costs\",\n", + " ],\n", + " # For each constraint, use as features the RHS, dual value and slack.\n", + " constr_fields=[\n", + " \"static_constr_rhs\",\n", + " \"lp_constr_dual_values\",\n", + " \"lp_constr_slacks\",\n", + " ]\n", + ")\n", + "\n", + "with H5File(\"data/multiknapsack/00000.h5\") as h5:\n", + " # Extract and print instance features\n", + " x1 = ext.get_instance_features(h5)\n", + " print(\"instance features\", x1.shape, \"\\n\", x1)\n", + "\n", + " # Extract and print variable features\n", + " x2 = ext.get_var_features(h5)\n", + " print(\"variable features\", x2.shape, \"\\n\", x2)\n", + "\n", + " # Extract and print constraint features\n", + " x3 = ext.get_constr_features(h5)\n", + " print(\"constraint features\", x3.shape, \"\\n\", x3)\n" + ], + "metadata": { + "collapsed": false + } + }, + { + "cell_type": "markdown", + "source": [ + "\n", + "[H5FieldsExtractor]: ../../api/collectors/#miplearn.features.fields.H5FieldsExtractor" + ], + "metadata": { + "collapsed": false + } + }, + { + "cell_type": "markdown", + "source": [ + "
\n", + "Warning\n", + "\n", + "You should ensure that the number of features remains the same for all relevant HDF5 files. In the previous example, to illustrate this issue, we used variable objective coefficients as instance features. While this is allowed, note that this requires all problem instances to have the same number of variables; otherwise the number of features would vary from instance to instance and MIPLearn would be unable to concatenate the matrices.\n", + "
" + ], + "metadata": { + "collapsed": false + } + }, + { + "cell_type": "markdown", + "source": [ + "## AlvLouWeh2017Extractor\n", + "\n", + "Alvarez, Louveaux and Wehenkel (2017) proposed a set features to describe a particular decision variable in a given node of the branch-and-bound tree, and applied it to the problem of mimicking strong branching decisions. The class [AlvLouWeh2017Extractor][] implements a subset of these features (40 out of 64), which are available outside of the branch-and-bound tree. Some features are derived from the static defintion of the problem (i.e. from objective function and constraint data), while some features are derived from the solution to the LP relaxation. The features have been designed to be: (i) independent of the size of the problem; (ii) invariant with respect to irrelevant problem transformations, such as row and column permutation; and (iii) independent of the scale of the problem. We refer to the paper for a more complete description.\n", + "\n", + "### Example" + ], + "metadata": { + "collapsed": false + } + }, + { + "cell_type": "code", + "execution_count": 5, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "x1 (10, 40) \n", + " [[-1.00e+00 1.00e+20 1.00e-01 1.00e+00 0.00e+00 1.00e+00 6.00e-01\n", + " 0.00e+00 0.00e+00 0.00e+00 0.00e+00 0.00e+00 0.00e+00 0.00e+00\n", + " 0.00e+00 1.00e+00 6.00e-01 1.00e+00 1.75e+01 1.00e+00 2.00e-01\n", + " 1.00e+00 0.00e+00 0.00e+00 0.00e+00 0.00e+00 0.00e+00 0.00e+00\n", + " 0.00e+00 0.00e+00 0.00e+00 0.00e+00 0.00e+00 0.00e+00 0.00e+00\n", + " 0.00e+00 1.00e+00 -1.00e+00 0.00e+00 1.00e+20]\n", + " [-1.00e+00 1.00e+20 1.00e-01 1.00e+00 1.00e-01 1.00e+00 1.00e+00\n", + " 0.00e+00 0.00e+00 0.00e+00 0.00e+00 0.00e+00 0.00e+00 0.00e+00\n", + " 0.00e+00 1.00e+00 7.00e-01 1.00e+00 5.10e+00 1.00e+00 2.00e-01\n", + " 1.00e+00 0.00e+00 0.00e+00 0.00e+00 0.00e+00 0.00e+00 0.00e+00\n", + " 0.00e+00 0.00e+00 0.00e+00 0.00e+00 0.00e+00 0.00e+00 0.00e+00\n", + " 3.00e-01 -1.00e+00 -1.00e+00 0.00e+00 0.00e+00]\n", + " [-1.00e+00 1.00e+20 1.00e-01 1.00e+00 0.00e+00 1.00e+00 9.00e-01\n", + " 0.00e+00 0.00e+00 0.00e+00 0.00e+00 0.00e+00 0.00e+00 0.00e+00\n", + " 0.00e+00 1.00e+00 5.00e-01 1.00e+00 1.30e+01 1.00e+00 2.00e-01\n", + " 1.00e+00 0.00e+00 0.00e+00 0.00e+00 0.00e+00 0.00e+00 0.00e+00\n", + " 0.00e+00 0.00e+00 0.00e+00 0.00e+00 0.00e+00 0.00e+00 0.00e+00\n", + " 0.00e+00 1.00e+00 -1.00e+00 0.00e+00 1.00e+20]\n", + " [-1.00e+00 1.00e+20 1.00e-01 1.00e+00 2.00e-01 1.00e+00 9.00e-01\n", + " 0.00e+00 0.00e+00 0.00e+00 0.00e+00 0.00e+00 0.00e+00 0.00e+00\n", + " 0.00e+00 1.00e+00 8.00e-01 1.00e+00 3.40e+00 1.00e+00 2.00e-01\n", + " 1.00e+00 1.00e-01 0.00e+00 0.00e+00 0.00e+00 0.00e+00 0.00e+00\n", + " 0.00e+00 0.00e+00 0.00e+00 0.00e+00 0.00e+00 0.00e+00 0.00e+00\n", + " 1.00e-01 -1.00e+00 -1.00e+00 0.00e+00 0.00e+00]\n", + " [-1.00e+00 1.00e+20 1.00e-01 1.00e+00 1.00e-01 1.00e+00 7.00e-01\n", + " 0.00e+00 0.00e+00 0.00e+00 0.00e+00 0.00e+00 0.00e+00 0.00e+00\n", + " 0.00e+00 1.00e+00 6.00e-01 1.00e+00 3.80e+00 1.00e+00 2.00e-01\n", + " 1.00e+00 0.00e+00 0.00e+00 0.00e+00 0.00e+00 0.00e+00 0.00e+00\n", + " 0.00e+00 0.00e+00 0.00e+00 0.00e+00 0.00e+00 0.00e+00 0.00e+00\n", + " 0.00e+00 -1.00e+00 -1.00e+00 0.00e+00 0.00e+00]\n", + " [-1.00e+00 1.00e+20 1.00e-01 1.00e+00 1.00e-01 1.00e+00 8.00e-01\n", + " 0.00e+00 0.00e+00 0.00e+00 0.00e+00 0.00e+00 0.00e+00 0.00e+00\n", + " 0.00e+00 1.00e+00 7.00e-01 1.00e+00 3.30e+00 1.00e+00 2.00e-01\n", + " 1.00e+00 0.00e+00 0.00e+00 0.00e+00 0.00e+00 0.00e+00 0.00e+00\n", + " 0.00e+00 0.00e+00 0.00e+00 0.00e+00 0.00e+00 0.00e+00 0.00e+00\n", + " 0.00e+00 1.00e+00 -1.00e+00 0.00e+00 1.00e+20]\n", + " [-1.00e+00 1.00e+20 1.00e-01 1.00e+00 0.00e+00 1.00e+00 3.00e-01\n", + " 0.00e+00 0.00e+00 0.00e+00 0.00e+00 0.00e+00 0.00e+00 0.00e+00\n", + " 0.00e+00 1.00e+00 1.00e+00 1.00e+00 5.70e+00 1.00e+00 1.00e-01\n", + " 1.00e+00 0.00e+00 0.00e+00 0.00e+00 0.00e+00 0.00e+00 0.00e+00\n", + " 0.00e+00 0.00e+00 0.00e+00 0.00e+00 0.00e+00 0.00e+00 0.00e+00\n", + " 1.00e-01 -1.00e+00 -1.00e+00 0.00e+00 0.00e+00]\n", + " [-1.00e+00 1.00e+20 1.00e-01 1.00e+00 1.00e-01 1.00e+00 6.00e-01\n", + " 0.00e+00 0.00e+00 0.00e+00 0.00e+00 0.00e+00 0.00e+00 0.00e+00\n", + " 0.00e+00 1.00e+00 8.00e-01 1.00e+00 6.80e+00 1.00e+00 2.00e-01\n", + " 1.00e+00 0.00e+00 0.00e+00 0.00e+00 0.00e+00 0.00e+00 0.00e+00\n", + " 0.00e+00 0.00e+00 0.00e+00 0.00e+00 0.00e+00 0.00e+00 0.00e+00\n", + " 1.00e-01 -1.00e+00 -1.00e+00 0.00e+00 0.00e+00]\n", + " [-1.00e+00 1.00e+20 1.00e-01 1.00e+00 4.00e-01 1.00e+00 6.00e-01\n", + " 0.00e+00 0.00e+00 0.00e+00 0.00e+00 0.00e+00 0.00e+00 0.00e+00\n", + " 0.00e+00 1.00e+00 8.00e-01 1.00e+00 1.40e+00 1.00e+00 1.00e-01\n", + " 1.00e+00 1.00e-01 0.00e+00 0.00e+00 0.00e+00 0.00e+00 0.00e+00\n", + " 0.00e+00 0.00e+00 0.00e+00 0.00e+00 0.00e+00 0.00e+00 0.00e+00\n", + " 0.00e+00 1.00e+00 -1.00e+00 0.00e+00 1.00e+20]\n", + " [-1.00e+00 1.00e+20 1.00e-01 1.00e+00 0.00e+00 1.00e+00 5.00e-01\n", + " 0.00e+00 0.00e+00 0.00e+00 0.00e+00 0.00e+00 0.00e+00 0.00e+00\n", + " 0.00e+00 1.00e+00 5.00e-01 1.00e+00 7.60e+00 1.00e+00 1.00e-01\n", + " 1.00e+00 0.00e+00 0.00e+00 0.00e+00 0.00e+00 0.00e+00 0.00e+00\n", + " 0.00e+00 0.00e+00 0.00e+00 0.00e+00 0.00e+00 0.00e+00 0.00e+00\n", + " 1.00e-01 -1.00e+00 -1.00e+00 0.00e+00 0.00e+00]]\n" + ] + } + ], + "source": [ + "from miplearn.features.AlvLouWeh2017 import AlvLouWeh2017Extractor\n", + "from miplearn.h5 import H5File\n", + "\n", + "# Build the extractor\n", + "ext = AlvLouWeh2017Extractor()\n", + "\n", + "# Open previously-created multiknapsack training data\n", + "with H5File(\"data/multiknapsack/00000.h5\") as h5:\n", + "\n", + " # Extract and print variable features\n", + " x1 = ext.get_var_features(h5)\n", + " print(\"x1\", x1.shape, \"\\n\", x1.round(1))" + ], + "metadata": { + "collapsed": false + } + }, + { + "cell_type": "markdown", + "source": [ + "
\n", + "References\n", + "\n", + "* **Alvarez, Alejandro Marcos.** *Computational and theoretical synergies between linear optimization and supervised machine learning.* (2016). University of Liège.\n", + "* **Alvarez, Alejandro Marcos, Quentin Louveaux, and Louis Wehenkel.** *A machine learning-based approximation of strong branching.* INFORMS Journal on Computing 29.1 (2017): 185-195.\n", + "\n", + "
" + ], + "metadata": { + "collapsed": false + } + } + ], + "metadata": { + "kernelspec": { + "display_name": "Python 3", + "language": "python", + "name": "python3" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.8.13" + } + }, + "nbformat": 4, + "nbformat_minor": 5 +} diff --git a/0.3/_sources/guide/primal.ipynb.txt b/0.3/_sources/guide/primal.ipynb.txt new file mode 100644 index 0000000..e9d8f45 --- /dev/null +++ b/0.3/_sources/guide/primal.ipynb.txt @@ -0,0 +1,283 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "id": "880cf4c7-d3c4-4b92-85c7-04a32264cdae", + "metadata": {}, + "source": [ + "# Primal Components\n", + "\n", + "In MIPLearn, a **primal component** is class that uses machine learning to predict a (potentially partial) assignment of values to the decision variables of the problem. Predicting high-quality primal solutions may be beneficial, as they allow the MIP solver to prune potentially large portions of the search space. Alternatively, if proof of optimality is not required, the MIP solver can be used to complete the partial solution generated by the machine learning model and and double-check its feasibility. MIPLearn allows both of these usage patterns.\n", + "\n", + "In this page, we describe the four primal components currently included in MIPLearn, which employ machine learning in different ways. Each component is highly configurable, and accepts an user-provided machine learning model, which it uses for all predictions. Each component can also be configured to provide the solution to the solver in multiple ways, depending on whether proof of optimality is required.\n", + "\n", + "## Primal component actions\n", + "\n", + "Before presenting the primal components themselves, we briefly discuss the three ways a solution may be provided to the solver. Each approach has benefits and limitations, which we also discuss in this section. All primal components can be configured to use any of the following approaches.\n", + "\n", + "The first approach is to provide the solution to the solver as a **warm start**. This is implemented by the class [SetWarmStart](SetWarmStart). The main advantage is that this method maintains all optimality and feasibility guarantees of the MIP solver, while still providing significant performance benefits for various classes of problems. If the machine learning model is able to predict multiple solutions, it is also possible to set multiple warm starts. In this case, the solver evaluates each warm start, discards the infeasible ones, then proceeds with the one that has the best objective value. The main disadvantage of this approach, compared to the next two, is that it provides relatively modest speedups for most problem classes, and no speedup at all for many others, even when the machine learning predictions are 100% accurate.\n", + "\n", + "[SetWarmStart]: ../../api/components/#miplearn.components.primal.actions.SetWarmStart\n", + "\n", + "The second approach is to **fix the decision variables** to their predicted values, then solve a restricted optimization problem on the remaining variables. This approach is implemented by the class `FixVariables`. The main advantage is its potential speedup: if machine learning can accurately predict values for a significant portion of the decision variables, then the MIP solver can typically complete the solution in a small fraction of the time it would take to find the same solution from scratch. The main disadvantage of this approach is that it loses optimality guarantees; that is, the complete solution found by the MIP solver may no longer be globally optimal. Also, if the machine learning predictions are not sufficiently accurate, there might not even be a feasible assignment for the variables that were left free.\n", + "\n", + "Finally, the third approach, which tries to strike a balance between the two previous ones, is to **enforce proximity** to a given solution. This strategy is implemented by the class `EnforceProximity`. More precisely, given values $\\bar{x}_1,\\ldots,\\bar{x}_n$ for a subset of binary decision variables $x_1,\\ldots,x_n$, this approach adds the constraint\n", + "\n", + "$$\n", + "\\sum_{i : \\bar{x}_i=0} x_i + \\sum_{i : \\bar{x}_i=1} \\left(1 - x_i\\right) \\leq k,\n", + "$$\n", + "to the problem, where $k$ is a user-defined parameter, which indicates how many of the predicted variables are allowed to deviate from the machine learning suggestion. The main advantage of this approach, compared to fixing variables, is its tolerance to lower-quality machine learning predictions. Its main disadvantage is that it typically leads to smaller speedups, especially for larger values of $k$. This approach also loses optimality guarantees.\n", + "\n", + "## Memorizing primal component\n", + "\n", + "A simple machine learning strategy for the prediction of primal solutions is to memorize all distinct solutions seen during training, then try to predict, during inference time, which of those memorized solutions are most likely to be feasible and to provide a good objective value for the current instance. The most promising solutions may alternatively be combined into a single partial solution, which is then provided to the MIP solver. Both variations of this strategy are implemented by the `MemorizingPrimalComponent` class. Note that it is only applicable if the problem size, and in fact if the meaning of the decision variables, remains the same across problem instances.\n", + "\n", + "More precisely, let $I_1,\\ldots,I_n$ be the training instances, and let $\\bar{x}^1,\\ldots,\\bar{x}^n$ be their respective optimal solutions. Given a new instance $I_{n+1}$, `MemorizingPrimalComponent` expects a user-provided binary classifier that assigns (through the `predict_proba` method, following scikit-learn's conventions) a score $\\delta_i$ to each solution $\\bar{x}^i$, such that solutions with higher score are more likely to be good solutions for $I_{n+1}$. The features provided to the classifier are the instance features computed by an user-provided extractor. Given these scores, the component then performs one of the following to actions, as decided by the user:\n", + "\n", + "1. Selects the top $k$ solutions with the highest scores and provides them to the solver; this is implemented by `SelectTopSolutions`, and it is typically used with the `SetWarmStart` action.\n", + "\n", + "2. Merges the top $k$ solutions into a single partial solution, then provides it to the solver. This is implemented by `MergeTopSolutions`. More precisely, suppose that the machine learning regressor ordered the solutions in the sequence $\\bar{x}^{i_1},\\ldots,\\bar{x}^{i_n}$, with the most promising solutions appearing first, and with ties being broken arbitrarily. The component starts by keeping only the $k$ most promising solutions $\\bar{x}^{i_1},\\ldots,\\bar{x}^{i_k}$. Then it computes, for each binary decision variable $x_l$, its average assigned value $\\tilde{x}_l$:\n", + "$$\n", + " \\tilde{x}_l = \\frac{1}{k} \\sum_{j=1}^k \\bar{x}^{i_j}_l.\n", + "$$\n", + " Finally, the component constructs a merged solution $y$, defined as:\n", + "$$\n", + " y_j = \\begin{cases}\n", + " 0 & \\text{ if } \\tilde{x}_l \\le \\theta_0 \\\\\n", + " 1 & \\text{ if } \\tilde{x}_l \\ge \\theta_1 \\\\\n", + " \\square & \\text{otherwise,}\n", + " \\end{cases}\n", + "$$\n", + " where $\\theta_0$ and $\\theta_1$ are user-specified parameters, and where $\\square$ indicates that the variable is left undefined. The solution $y$ is then provided by the solver using any of the three approaches defined in the previous section.\n", + "\n", + "The above specification of `MemorizingPrimalComponent` is meant to be as general as possible. Simpler strategies can be implemented by configuring this component in specific ways. For example, a simpler approach employed in the literature is to collect all optimal solutions, then provide the entire list of solutions to the solver as warm starts, without any filtering or post-processing. This strategy can be implemented with `MemorizingPrimalComponent` by using a model that returns a constant value for all solutions (e.g. [scikit-learn's DummyClassifier][DummyClassifier]), then selecting the top $n$ (instead of $k$) solutions. See example below. Another simple approach is taking the solution to the most similar instance, and using it, by itself, as a warm start. This can be implemented by using a model that computes distances between the current instance and the training ones (e.g. [scikit-learn's KNeighborsClassifier][KNeighborsClassifier]), then select the solution to the nearest one. See also example below. More complex strategies, of course, can also be configured.\n", + "\n", + "[DummyClassifier]: https://scikit-learn.org/stable/modules/generated/sklearn.dummy.DummyClassifier.html\n", + "[KNeighborsClassifier]: https://scikit-learn.org/stable/modules/generated/sklearn.neighbors.KNeighborsClassifier.html\n", + "\n", + "### Examples" + ] + }, + { + "cell_type": "code", + "execution_count": 3, + "outputs": [], + "source": [ + "\n", + "from sklearn.dummy import DummyClassifier\n", + "from sklearn.neighbors import KNeighborsClassifier\n", + "\n", + "from miplearn.components.primal.actions import (\n", + " SetWarmStart,\n", + " FixVariables,\n", + " EnforceProximity,\n", + ")\n", + "from miplearn.components.primal.mem import (\n", + " MemorizingPrimalComponent,\n", + " SelectTopSolutions,\n", + " MergeTopSolutions,\n", + ")\n", + "from miplearn.extractors.dummy import DummyExtractor\n", + "from miplearn.extractors.fields import H5FieldsExtractor\n", + "\n", + "# Configures a memorizing primal component that collects\n", + "# all distinct solutions seen during training and provides\n", + "# them to the solver without any filtering or post-processing.\n", + "comp1 = MemorizingPrimalComponent(\n", + " clf=DummyClassifier(),\n", + " extractor=DummyExtractor(),\n", + " constructor=SelectTopSolutions(1_000_000),\n", + " action=SetWarmStart(),\n", + ")\n", + "\n", + "# Configures a memorizing primal component that finds the\n", + "# training instance with the closest objective function, then\n", + "# fixes the decision variables to the values they assumed\n", + "# at the optimal solution for that instance.\n", + "comp2 = MemorizingPrimalComponent(\n", + " clf=KNeighborsClassifier(n_neighbors=1),\n", + " extractor=H5FieldsExtractor(\n", + " instance_fields=[\"static_var_obj_coeffs\"],\n", + " ),\n", + " constructor=SelectTopSolutions(1),\n", + " action=FixVariables(),\n", + ")\n", + "\n", + "# Configures a memorizing primal component that finds the distinct\n", + "# solutions to the 10 most similar training problem instances,\n", + "# selects the 3 solutions that were most often optimal to these\n", + "# training instances, combines them into a single partial solution,\n", + "# then enforces proximity, allowing at most 3 variables to deviate\n", + "# from the machine learning suggestion.\n", + "comp3 = MemorizingPrimalComponent(\n", + " clf=KNeighborsClassifier(n_neighbors=10),\n", + " extractor=H5FieldsExtractor(instance_fields=[\"static_var_obj_coeffs\"]),\n", + " constructor=MergeTopSolutions(k=3, thresholds=[0.25, 0.75]),\n", + " action=EnforceProximity(3),\n", + ")" + ], + "metadata": { + "collapsed": false + } + }, + { + "cell_type": "markdown", + "source": [ + "## Independent vars primal component\n", + "\n", + "Instead of memorizing previously-seen primal solutions, it is also natural to use machine learning models to directly predict the values of the decision variables, constructing a solution from scratch. This approach has the benefit of potentially constructing novel high-quality solutions, never observed in the training data. Two variations of this strategy are supported by MIPLearn: (i) predicting the values of the decision variables independently, using multiple ML models; or (ii) predicting the values jointly, with a single model. We describe the first variation in this section, and the second variation in the next section.\n", + "\n", + "Let $I_1,\\ldots,I_n$ be the training instances, and let $\\bar{x}^1,\\ldots,\\bar{x}^n$ be their respective optimal solutions. For each binary decision variable $x_j$, the component `IndependentVarsPrimalComponent` creates a copy of a user-provided binary classifier and trains it to predict the optimal value of $x_j$, given $\\bar{x}^1_j,\\ldots,\\bar{x}^n_j$ as training labels. The features provided to the model are the variable features computed by an user-provided extractor. During inference time, the component uses these $n$ binary classifiers to construct a solution and provides it to the solver using one of the available actions.\n", + "\n", + "Three issues often arise in practice when using this approach:\n", + "\n", + " 1. For certain binary variables $x_j$, it is frequently the case that its optimal value is either always zero or always one in the training dataset, which poses problems to some standard scikit-learn classifiers, since they do not expect a single class. The wrapper `SingleClassFix` can be used to fix this issue (see example below).\n", + "2. It is also frequently the case that machine learning classifier can only reliably predict the values of some variables with high accuracy, not all of them. In this situation, instead of computing a complete primal solution, it may be more beneficial to construct a partial solution containing values only for the variables for which the ML made a high-confidence prediction. The meta-classifier `MinProbabilityClassifier` can be used for this purpose. It asks the base classifier for the probability of the value being zero or one (using the `predict_proba` method) and erases from the primal solution all values whose probabilities are below a given threshold.\n", + "3. To make multiple copies of the provided ML classifier, MIPLearn uses the standard `sklearn.base.clone` method, which may not be suitable for classifiers from other frameworks. To handle this, it is possible to override the clone function using the `clone_fn` constructor argument.\n", + "\n", + "### Examples" + ], + "metadata": { + "collapsed": false + } + }, + { + "cell_type": "code", + "execution_count": 4, + "outputs": [], + "source": [ + "from sklearn.linear_model import LogisticRegression\n", + "from miplearn.classifiers.minprob import MinProbabilityClassifier\n", + "from miplearn.classifiers.singleclass import SingleClassFix\n", + "from miplearn.components.primal.indep import IndependentVarsPrimalComponent\n", + "from miplearn.extractors.AlvLouWeh2017 import AlvLouWeh2017Extractor\n", + "from miplearn.solvers.learning import LearningSolver\n", + "from miplearn.components.primal.actions import SetWarmStart\n", + "\n", + "# Configures a primal component that independently predicts the value of each\n", + "# binary variable using logistic regression and provides it to the solver as\n", + "# warm start. Erases predictions with probability less than 99%; applies\n", + "# single-class fix; and uses AlvLouWeh2017 features.\n", + "comp = IndependentVarsPrimalComponent(\n", + " base_clf=SingleClassFix(\n", + " MinProbabilityClassifier(\n", + " base_clf=LogisticRegression(),\n", + " thresholds=[0.99, 0.99],\n", + " ),\n", + " ),\n", + " extractor=AlvLouWeh2017Extractor(),\n", + " action=SetWarmStart(),\n", + ")" + ], + "metadata": { + "collapsed": false + } + }, + { + "cell_type": "markdown", + "source": [ + "## Joint vars primal component\n", + "In the previous subsection, we used multiple machine learning models to independently predict the values of the binary decision variables. When these values are correlated, an alternative approach is to jointly predict the values of all binary variables using a single machine learning model. This strategy is implemented by `JointVarsPrimalComponent`. Compared to the previous ones, this component is much more straightforwad. It simply extracts instance features, using the user-provided feature extractor, then directly trains the user-provided binary classifier (using the `fit` method), without making any copies. The trained classifier is then used to predict entire solutions (using the `predict` method), which are given to the solver using one of the previously discussed methods. In the example below, we illustrate the usage of this component with a simple feed-forward neural network.\n", + "\n", + "`JointVarsPrimalComponent` can also be used to implement strategies that use multiple machine learning models, but not indepedently. For example, a common strategy in multioutput prediction is building a *classifier chain*. In this approach, the first decision variable is predicted using the instance features alone; but the $n$-th decision variable is predicted using the instance features plus the predicted values of the $n-1$ previous variables. This can be easily implemented using scikit-learn's `ClassifierChain` estimator, as shown in the example below.\n", + "\n", + "### Examples" + ], + "metadata": { + "collapsed": false + } + }, + { + "cell_type": "code", + "execution_count": 5, + "outputs": [], + "source": [ + "from sklearn.multioutput import ClassifierChain\n", + "from sklearn.neural_network import MLPClassifier\n", + "from miplearn.components.primal.joint import JointVarsPrimalComponent\n", + "from miplearn.extractors.fields import H5FieldsExtractor\n", + "from miplearn.solvers.learning import LearningSolver\n", + "from miplearn.components.primal.actions import SetWarmStart\n", + "\n", + "# Configures a primal component that uses a feedforward neural network\n", + "# to jointly predict the values of the binary variables, based on the\n", + "# objective cost function, and provides the solution to the solver as\n", + "# a warm start.\n", + "comp = JointVarsPrimalComponent(\n", + " clf=MLPClassifier(),\n", + " extractor=H5FieldsExtractor(\n", + " instance_fields=['static_var_obj_coeffs'],\n", + " ),\n", + " action=SetWarmStart(),\n", + ")\n", + "\n", + "# Configures a primal component that uses a chain of logistic regression\n", + "# models to jointly predict the values of the binary variables, based on\n", + "# the objective function.\n", + "comp = JointVarsPrimalComponent(\n", + " clf=ClassifierChain(SingleClassFix(LogisticRegression())),\n", + " extractor=H5FieldsExtractor(\n", + " instance_fields=['static_var_obj_coeffs'],\n", + " ),\n", + " action=SetWarmStart(),\n", + ")" + ], + "metadata": { + "collapsed": false + } + }, + { + "cell_type": "markdown", + "source": [ + "## Expert primal component\n", + "\n", + "Before spending time and effort choosing a machine learning strategy and tweaking its parameters, it is usually a good idea to evaluate what would be the performance impact of the model if its predictions were 100% accurate. This is especially important for the prediction of warm starts, since they are not always very beneficial. To simplify this task, MIPLearn provides `ExpertPrimalComponent`, a component which simply loads the optimal solution from the HDF5 file, assuming that it has already been computed, then directly provides it to the solver using one of the available methods. This component is useful in benchmarks, to evaluate how close to the best theoretical performance the machine learning components are.\n", + "\n", + "### Example" + ], + "metadata": { + "collapsed": false + } + }, + { + "cell_type": "code", + "execution_count": 4, + "outputs": [], + "source": [ + "from miplearn.components.primal.expert import ExpertPrimalComponent\n", + "from miplearn.components.primal.actions import SetWarmStart\n", + "\n", + "# Configures an expert primal component, which reads a pre-computed\n", + "# optimal solution from the HDF5 file and provides it to the solver\n", + "# as warm start.\n", + "comp = ExpertPrimalComponent(\n", + " action=SetWarmStart()\n", + ")" + ], + "metadata": { + "collapsed": false + } + } + ], + "metadata": { + "kernelspec": { + "display_name": "Python 3", + "language": "python", + "name": "python3" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.8.13" + } + }, + "nbformat": 4, + "nbformat_minor": 5 +} diff --git a/0.3/_sources/guide/problems.ipynb.txt b/0.3/_sources/guide/problems.ipynb.txt new file mode 100644 index 0000000..e91b0d3 --- /dev/null +++ b/0.3/_sources/guide/problems.ipynb.txt @@ -0,0 +1,1536 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "id": "f89436b4-5bc5-4ae3-a20a-522a2cd65274", + "metadata": {}, + "source": [ + "# Benchmark Problems\n", + "\n", + "## Overview\n", + "\n", + "Benchmark sets such as [MIPLIB](https://miplib.zib.de/) or [TSPLIB](http://comopt.ifi.uni-heidelberg.de/software/TSPLIB95/) are usually employed to evaluate the performance of conventional MIP solvers. Two shortcomings, unfortunately, make existing benchmark sets less than ideal for evaluating the performance of learning-enhanced MIP solvers: (i) while existing benchmark sets typically contain hundreds or thousands of instances, machine learning (ML) methods typically benefit from having orders of magnitude more instances available for training; (ii) current machine learning methods typically provide best performance on sets of homogeneous instances, buch general-purpose benchmark sets contain relatively few examples of each problem type.\n", + "\n", + "To tackle this challenge, MIPLearn provides random instance generators for a wide variety of classical optimization problems, covering applications from different fields, that can be used to evaluate new learning-enhanced MIP techniques in a measurable and reproducible way. As of MIPLearn 0.3, nine problem generators are available, each customizable with user-provided probability distribution and flexible parameters. The generators can be configured, for example, to produce large sets of very similar instances of same size, where only the objective function changes, or more diverse sets of instances, with various sizes and characteristics, belonging to a particular problem class.\n", + "\n", + "In the following, we describe the problems included in the library, their MIP formulation and the generation algorithm." + ] + }, + { + "cell_type": "markdown", + "source": [ + "
\n", + "Warning\n", + "\n", + "The random instance generators and formulations shown below are subject to change. If you use them in your research, for reproducibility, you should specify the MIPLearn version and all parameters.\n", + "
\n", + "\n", + "
\n", + "Note\n", + "\n", + "- To make the instances easier to process, all formulations are written as a minimization problem.\n", + "- Some problem formulations, such as the one for the *traveling salesman problem*, contain an exponential number of constraints, which are enforced through constraint generation. The MPS files for these problems contain only the constraints that were generated during a trial run, not the entire set of constraints. Resolving the MPS file, therefore, may not generate a feasible primal solution for the problem.\n", + "
" + ], + "metadata": { + "collapsed": false + } + }, + { + "cell_type": "markdown", + "id": "830f3784-a3fc-4e2f-a484-e7808841ffe8", + "metadata": { + "jp-MarkdownHeadingCollapsed": true, + "tags": [] + }, + "source": [ + "## Bin Packing\n", + "\n", + "**Bin packing** is a combinatorial optimization problem that asks for the optimal way to pack a given set of items into a finite number of containers (or bins) of fixed capacity. More specifically, the problem is to assign indivisible items of different sizes to identical bins, while minimizing the number of bins used. The problem is NP-hard and has many practical applications, including logistics and warehouse management, where it is used to determine how to best store and transport goods using a limited amount of space." + ] + }, + { + "cell_type": "markdown", + "id": "af933298-92a9-4c5d-8d07-0d4918dedbb8", + "metadata": { + "tags": [] + }, + "source": [ + "### Formulation\n", + "\n", + "Let $n$ be the number of items, and $s_i$ the size of the $i$-th item. Also let $B$ be the size of the bins. For each bin $j$, let $y_j$ be a binary decision variable which equals one if the bin is used. For every item-bin pair $(i,j)$, let $x_{ij}$ be a binary decision variable which equals one if item $i$ is assigned to bin $j$. The bin packing problem is formulated as:" + ] + }, + { + "cell_type": "markdown", + "source": [ + "\n", + "$$\n", + "\\begin{align*}\n", + "\\text{minimize} \\;\\;\\;\n", + " & \\sum_{j=1}^n y_j \\\\\n", + "\\text{subject to} \\;\\;\\;\n", + " & \\sum_{i=1}^n s_i x_{ij} \\leq B y_j & \\forall j=1,\\ldots,n \\\\\n", + " & \\sum_{j=1}^n x_{ij} = 1 & \\forall i=1,\\ldots,n \\\\\n", + " & y_i \\in \\{0,1\\} & \\forall i=1,\\ldots,n \\\\\n", + " & x_{ij} \\in \\{0,1\\} & \\forall i,j=1,\\ldots,n \\\\\n", + "\\end{align*}\n", + "$$" + ], + "metadata": { + "collapsed": false + } + }, + { + "cell_type": "markdown", + "source": [ + "### Random instance generator\n", + "\n", + "Random instances of the bin packing problem can be generated using the class [BinPackGenerator][BinPackGenerator].\n", + "\n", + "If `fix_items=False`, the class samples the user-provided probability distributions `n`, `sizes` and `capacity` to decide, respectively, the number of items, the sizes of the items and capacity of the bin. All values are sampled independently.\n", + "\n", + "If `fix_items=True`, the class creates a reference instance, using the method previously described, then generates additional instances by perturbing its item sizes and bin capacity. More specifically, the sizes of the items are set to $s_i \\gamma_i$, where $s_i$ is the size of the $i$-th item in the reference instance and $\\gamma_i$ is sampled from `sizes_jitter`. Similarly, the bin size is set to $B \\beta$, where $B$ is the reference bin size and $\\beta$ is sampled from `capacity_jitter`. The number of items remains the same across all generated instances.\n", + "\n", + "[BinPackGenerator]: ../../api/problems/#miplearn.problems.binpack.BinPackGenerator" + ], + "metadata": { + "collapsed": false + } + }, + { + "cell_type": "markdown", + "source": [ + "### Example" + ], + "metadata": { + "collapsed": false + } + }, + { + "cell_type": "code", + "execution_count": 1, + "id": "f14e560c-ef9f-4c48-8467-72d6acce5f9f", + "metadata": { + "tags": [] + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "0 [ 8.47 26. 19.52 14.11 3.65 3.65 1.4 21.76 14.82 16.96] 102.24\n", + "1 [ 8.69 22.78 17.81 14.83 4.12 3.67 1.46 22.05 13.66 18.08] 93.41\n", + "2 [ 8.55 25.9 20. 15.89 3.75 3.59 1.51 21.4 13.89 17.68] 90.69\n", + "3 [10.13 22.62 18.89 14.4 3.92 3.94 1.36 23.69 15.85 19.26] 107.9\n", + "4 [ 9.55 25.77 16.79 14.06 3.55 3.76 1.42 20.66 16.02 17.19] 95.62\n", + "5 [ 9.44 22.06 19.41 13.69 4.28 4.11 1.36 19.51 15.98 18.43] 104.58\n", + "6 [ 9.87 21.74 17.78 13.82 4.18 4. 1.4 19.76 14.46 17.08] 104.59\n", + "7 [ 9.62 25.61 18.2 13.83 4.07 4.1 1.47 22.83 15.01 17.78] 98.55\n", + "8 [ 8.47 21.9 16.58 15.37 3.76 3.91 1.57 20.57 14.76 18.61] 94.58\n", + "9 [ 8.57 22.77 17.06 16.25 4.14 4. 1.56 22.97 14.09 19.09] 100.79\n", + "\n", + "Restricted license - for non-production use only - expires 2023-10-25\n", + "Gurobi Optimizer version 9.5.2 build v9.5.2rc0 (linux64)\n", + "Thread count: 16 physical cores, 32 logical processors, using up to 32 threads\n", + "Optimize a model with 20 rows, 110 columns and 210 nonzeros\n", + "Model fingerprint: 0x1ff9913f\n", + "Variable types: 0 continuous, 110 integer (110 binary)\n", + "Coefficient statistics:\n", + " Matrix range [1e+00, 1e+02]\n", + " Objective range [1e+00, 1e+00]\n", + " Bounds range [1e+00, 1e+00]\n", + " RHS range [1e+00, 1e+00]\n", + "Found heuristic solution: objective 5.0000000\n", + "Presolve time: 0.00s\n", + "Presolved: 20 rows, 110 columns, 210 nonzeros\n", + "Variable types: 0 continuous, 110 integer (110 binary)\n", + "\n", + "Root relaxation: objective 1.274844e+00, 38 iterations, 0.00 seconds (0.00 work units)\n", + "\n", + " Nodes | Current Node | Objective Bounds | Work\n", + " Expl Unexpl | Obj Depth IntInf | Incumbent BestBd Gap | It/Node Time\n", + "\n", + " 0 0 1.27484 0 4 5.00000 1.27484 74.5% - 0s\n", + "H 0 0 4.0000000 1.27484 68.1% - 0s\n", + "H 0 0 2.0000000 1.27484 36.3% - 0s\n", + " 0 0 1.27484 0 4 2.00000 1.27484 36.3% - 0s\n", + "\n", + "Explored 1 nodes (38 simplex iterations) in 0.00 seconds (0.00 work units)\n", + "Thread count was 32 (of 32 available processors)\n", + "\n", + "Solution count 3: 2 4 5 \n", + "\n", + "Optimal solution found (tolerance 1.00e-04)\n", + "Best objective 2.000000000000e+00, best bound 2.000000000000e+00, gap 0.0000%\n" + ] + } + ], + "source": [ + "import numpy as np\n", + "from scipy.stats import uniform, randint\n", + "from miplearn.problems.binpack import BinPackGenerator, build_binpack_model\n", + "\n", + "# Set random seed, to make example reproducible\n", + "np.random.seed(42)\n", + "\n", + "# Generate random instances of the binpack problem with ten items\n", + "data = BinPackGenerator(\n", + " n=randint(low=10, high=11),\n", + " sizes=uniform(loc=0, scale=25),\n", + " capacity=uniform(loc=100, scale=0),\n", + " sizes_jitter=uniform(loc=0.9, scale=0.2),\n", + " capacity_jitter=uniform(loc=0.9, scale=0.2),\n", + " fix_items=True,\n", + ").generate(10)\n", + "\n", + "# Print sizes and capacities\n", + "for i in range(10):\n", + " print(i, data[i].sizes, data[i].capacity)\n", + "print()\n", + "\n", + "# Optimize first instance\n", + "model = build_binpack_model(data[0])\n", + "model.optimize()" + ] + }, + { + "cell_type": "markdown", + "id": "9a3df608-4faf-444b-b5c2-18d3e90cbb5a", + "metadata": { + "tags": [] + }, + "source": [ + "## Multi-Dimensional Knapsack\n", + "\n", + "The **multi-dimensional knapsack problem** is a generalization of the classic knapsack problem, which involves selecting a subset of items to be placed in a knapsack such that the total value of the items is maximized without exceeding a maximum weight. In this generalization, items have multiple weights (representing multiple resources), and multiple weight constraints must be satisfied." + ] + }, + { + "cell_type": "markdown", + "id": "8d989002-d837-4ccf-a224-0504a6d66473", + "metadata": { + "tags": [] + }, + "source": [ + "### Formulation\n", + "\n", + "Let $n$ be the number of items and $m$ be the number of resources. For each item $j$ and resource $i$, let $p_j$ be the price of the item, let $w_{ij}$ be the amount of resource $j$ item $i$ consumes (i.e. the $j$-th weight of the item), and let $b_i$ be the total amount of resource $i$ available (or the size of the $j$-th knapsack). The formulation is given by:" + ] + }, + { + "cell_type": "markdown", + "source": [ + "\n", + "$$\n", + "\\begin{align*}\n", + " \\text{minimize}\\;\\;\\;\n", + " & - \\sum_{j=1}^n p_j x_j\n", + " \\\\\n", + " \\text{subject to}\\;\\;\\;\n", + " & \\sum_{j=1}^n w_{ij} x_j \\leq b_i\n", + " & \\forall i=1,\\ldots,m \\\\\n", + " & x_j \\in \\{0,1\\}\n", + " & \\forall j=1,\\ldots,n\n", + "\\end{align*}\n", + "$$" + ], + "metadata": { + "collapsed": false + } + }, + { + "cell_type": "markdown", + "id": "81b5b085-cfa9-45ce-9682-3aeb9be96cba", + "metadata": {}, + "source": [ + "### Random instance generator\n", + "\n", + "The class [MultiKnapsackGenerator][MultiKnapsackGenerator] can be used to generate random instances of this problem. The number of items $n$ and knapsacks $m$ are sampled from the user-provided probability distributions `n` and `m`. The weights $w_{ij}$ are sampled independently from the provided distribution `w`. The capacity of knapsack $i$ is set to\n", + "\n", + "[MultiKnapsackGenerator]: ../../api/problems/#miplearn.problems.multiknapsack.MultiKnapsackGenerator\n", + "\n", + "$$\n", + " b_i = \\alpha_i \\sum_{j=1}^n w_{ij}\n", + "$$\n", + "\n", + "where $\\alpha_i$, the tightness ratio, is sampled from the provided probability\n", + "distribution `alpha`. To make the instances more challenging, the costs of the items\n", + "are linearly correlated to their average weights. More specifically, the price of each\n", + "item $j$ is set to:\n", + "\n", + "$$\n", + " p_j = \\sum_{i=1}^m \\frac{w_{ij}}{m} + K u_j,\n", + "$$\n", + "\n", + "where $K$, the correlation coefficient, and $u_j$, the correlation multiplier, are sampled\n", + "from the provided probability distributions `K` and `u`.\n", + "\n", + "If `fix_w=True` is provided, then $w_{ij}$ are kept the same in all generated instances. This also implies that $n$ and $m$ are kept fixed. Although the prices and capacities are derived from $w_{ij}$, as long as `u` and `K` are not constants, the generated instances will still not be completely identical.\n", + "\n", + "\n", + "If a probability distribution `w_jitter` is provided, then item weights will be set to $w_{ij} \\gamma_{ij}$ where $\\gamma_{ij}$ is sampled from `w_jitter`. When combined with `fix_w=True`, this argument may be used to generate instances where the weight of each item is roughly the same, but not exactly identical, across all instances. The prices of the items and the capacities of the knapsacks will be calculated as above, but using these perturbed weights instead.\n", + "\n", + "By default, all generated prices, weights and capacities are rounded to the nearest integer number. If `round=False` is provided, this rounding will be disabled." + ] + }, + { + "cell_type": "markdown", + "id": "f92135b8-67e7-4ec5-aeff-2fc17ad5e46d", + "metadata": {}, + "source": [ + "
\n", + "References\n", + "\n", + "* **Freville, Arnaud, and Gérard Plateau.** *An efficient preprocessing procedure for the multidimensional 0–1 knapsack problem.* Discrete applied mathematics 49.1-3 (1994): 189-212.\n", + "* **Fréville, Arnaud.** *The multidimensional 0–1 knapsack problem: An overview.* European Journal of Operational Research 155.1 (2004): 1-21.\n", + "
" + ] + }, + { + "cell_type": "markdown", + "source": [ + "### Example" + ], + "metadata": { + "collapsed": false + } + }, + { + "cell_type": "code", + "execution_count": 2, + "id": "1ce5f8fb-2769-4fbd-a40c-fd62b897690a", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "prices\n", + " [350. 692. 454. 709. 605. 543. 321. 674. 571. 341.]\n", + "weights\n", + " [[392. 977. 764. 622. 158. 163. 56. 840. 574. 696.]\n", + " [ 20. 948. 860. 209. 178. 184. 293. 541. 414. 305.]\n", + " [629. 135. 278. 378. 466. 803. 205. 492. 584. 45.]\n", + " [630. 173. 64. 907. 947. 794. 312. 99. 711. 439.]\n", + " [117. 506. 35. 915. 266. 662. 312. 516. 521. 178.]]\n", + "capacities\n", + " [1310. 988. 1004. 1269. 1007.]\n", + "\n", + "Gurobi Optimizer version 9.5.2 build v9.5.2rc0 (linux64)\n", + "Thread count: 16 physical cores, 32 logical processors, using up to 32 threads\n", + "Optimize a model with 5 rows, 10 columns and 50 nonzeros\n", + "Model fingerprint: 0xaf3ac15e\n", + "Variable types: 0 continuous, 10 integer (10 binary)\n", + "Coefficient statistics:\n", + " Matrix range [2e+01, 1e+03]\n", + " Objective range [3e+02, 7e+02]\n", + " Bounds range [1e+00, 1e+00]\n", + " RHS range [1e+03, 1e+03]\n", + "Found heuristic solution: objective -804.0000000\n", + "Presolve removed 0 rows and 3 columns\n", + "Presolve time: 0.00s\n", + "Presolved: 5 rows, 7 columns, 34 nonzeros\n", + "Variable types: 0 continuous, 7 integer (7 binary)\n", + "\n", + "Root relaxation: objective -1.428726e+03, 4 iterations, 0.00 seconds (0.00 work units)\n", + "\n", + " Nodes | Current Node | Objective Bounds | Work\n", + " Expl Unexpl | Obj Depth IntInf | Incumbent BestBd Gap | It/Node Time\n", + "\n", + " 0 0 -1428.7265 0 4 -804.00000 -1428.7265 77.7% - 0s\n", + "H 0 0 -1279.000000 -1428.7265 11.7% - 0s\n", + "\n", + "Cutting planes:\n", + " Cover: 1\n", + "\n", + "Explored 1 nodes (4 simplex iterations) in 0.00 seconds (0.00 work units)\n", + "Thread count was 32 (of 32 available processors)\n", + "\n", + "Solution count 2: -1279 -804 \n", + "No other solutions better than -1279\n", + "\n", + "Optimal solution found (tolerance 1.00e-04)\n", + "Best objective -1.279000000000e+03, best bound -1.279000000000e+03, gap 0.0000%\n" + ] + } + ], + "source": [ + "import numpy as np\n", + "from scipy.stats import uniform, randint\n", + "from miplearn.problems.multiknapsack import (\n", + " MultiKnapsackGenerator,\n", + " build_multiknapsack_model,\n", + ")\n", + "\n", + "# Set random seed, to make example reproducible\n", + "np.random.seed(42)\n", + "\n", + "# Generate ten similar random instances of the multiknapsack problem with\n", + "# ten items, five resources and weights around [0, 1000].\n", + "data = MultiKnapsackGenerator(\n", + " n=randint(low=10, high=11),\n", + " m=randint(low=5, high=6),\n", + " w=uniform(loc=0, scale=1000),\n", + " K=uniform(loc=100, scale=0),\n", + " u=uniform(loc=1, scale=0),\n", + " alpha=uniform(loc=0.25, scale=0),\n", + " w_jitter=uniform(loc=0.95, scale=0.1),\n", + " p_jitter=uniform(loc=0.75, scale=0.5),\n", + " fix_w=True,\n", + ").generate(10)\n", + "\n", + "# Print data for one of the instances\n", + "print(\"prices\\n\", data[0].prices)\n", + "print(\"weights\\n\", data[0].weights)\n", + "print(\"capacities\\n\", data[0].capacities)\n", + "print()\n", + "\n", + "# Build model and optimize\n", + "model = build_multiknapsack_model(data[0])\n", + "model.optimize()" + ] + }, + { + "cell_type": "markdown", + "id": "e20376b0-0781-4bfa-968f-ded5fa47e176", + "metadata": { + "tags": [] + }, + "source": [ + "## Capacitated P-Median\n", + "\n", + "The **capacitated p-median** problem is a variation of the classic $p$-median problem, in which a set of customers must be served by a set of facilities. In the capacitated $p$-Median problem, each facility has a fixed capacity, and the goal is to minimize the total cost of serving the customers while ensuring that the capacity of each facility is not exceeded. Variations of problem are often used in logistics and supply chain management to determine the most efficient locations for warehouses or distribution centers." + ] + }, + { + "cell_type": "markdown", + "id": "2af65137-109e-4ca0-8753-bd999825204f", + "metadata": { + "tags": [] + }, + "source": [ + "### Formulation\n", + "\n", + "Let $I=\\{1,\\ldots,n\\}$ be the set of customers. For each customer $i \\in I$, let $d_i$ be its demand and let $y_i$ be a binary decision variable that equals one if we decide to open a facility at that customer's location. For each pair $(i,j) \\in I \\times I$, let $x_{ij}$ be a binary decision variable that equals one if customer $i$ is assigned to facility $j$. Furthermore, let $w_{ij}$ be the cost of serving customer $i$ from facility $j$, let $p$ be the number of facilities we must open, and let $c_j$ be the capacity of facility $j$. The problem is formulated as:" + ] + }, + { + "cell_type": "markdown", + "id": "a2494ab1-d306-4db7-a100-8f1dfd4a55d7", + "metadata": { + "tags": [] + }, + "source": [ + "$$\n", + "\\begin{align*}\n", + " \\text{minimize}\\;\\;\\;\n", + " & \\sum_{i \\in I} \\sum_{j \\in I} w_{ij} x_{ij}\n", + " \\\\\n", + " \\text{subject to}\\;\\;\\;\n", + " & \\sum_{j \\in I} x_{ij} = 1 & \\forall i \\in I \\\\\n", + " & \\sum_{j \\in I} y_j = p \\\\\n", + " & \\sum_{i \\in I} d_i x_{ij} \\leq c_j y_j & \\forall j \\in I \\\\\n", + " & x_{ij} \\in \\{0, 1\\} & \\forall i, j \\in I \\\\\n", + " & y_j \\in \\{0, 1\\} & \\forall j \\in I\n", + "\\end{align*}\n", + "$$" + ] + }, + { + "cell_type": "markdown", + "id": "9dddf0d6-1f86-40d4-93a8-ccfe93d38e0d", + "metadata": {}, + "source": [ + "### Random instance generator\n", + "\n", + "The class [PMedianGenerator][PMedianGenerator] can be used to generate random instances of this problem. First, it decides the number of customers and the parameter $p$ by sampling the provided `n` and `p` distributions, respectively. Then, for each customer $i$, the class builds its geographical location $(x_i, y_i)$ by sampling the provided `x` and `y` distributions. For each $i$, the demand for customer $i$ and the capacity of facility $i$ are decided by sampling the provided distributions `demands` and `capacities`, respectively. Finally, the costs $w_{ij}$ are set to the Euclidean distance between the locations of customers $i$ and $j$.\n", + "\n", + "If `fixed=True`, then the number of customers, their locations, the parameter $p$, the demands and the capacities are only sampled from their respective distributions exactly once, to build a reference instance which is then randomly perturbed. Specifically, in each perturbation, the distances, demands and capacities are multiplied by random scaling factors sampled from the distributions `distances_jitter`, `demands_jitter` and `capacities_jitter`, respectively. The result is a list of instances that have the same set of customers, but slightly different demands, capacities and distances.\n", + "\n", + "[PMedianGenerator]: ../../api/problems/#miplearn.problems.pmedian.PMedianGenerator" + ] + }, + { + "cell_type": "markdown", + "source": [ + "### Example" + ], + "metadata": { + "collapsed": false + } + }, + { + "cell_type": "code", + "execution_count": 3, + "id": "4e0e4223-b4e0-4962-a157-82a23a86e37d", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "p = 5\n", + "distances =\n", + " [[ 0. 50.17 82.42 32.76 33.2 35.45 86.88 79.11 43.17 66.2 ]\n", + " [ 50.17 0. 72.64 72.51 17.06 80.25 39.92 68.93 43.41 42.96]\n", + " [ 82.42 72.64 0. 71.69 70.92 82.51 67.88 3.76 39.74 30.73]\n", + " [ 32.76 72.51 71.69 0. 56.56 11.03 101.35 69.39 42.09 68.58]\n", + " [ 33.2 17.06 70.92 56.56 0. 63.68 54.71 67.16 34.89 44.99]\n", + " [ 35.45 80.25 82.51 11.03 63.68 0. 111.04 80.29 52.78 79.36]\n", + " [ 86.88 39.92 67.88 101.35 54.71 111.04 0. 65.13 61.37 40.82]\n", + " [ 79.11 68.93 3.76 69.39 67.16 80.29 65.13 0. 36.26 27.24]\n", + " [ 43.17 43.41 39.74 42.09 34.89 52.78 61.37 36.26 0. 26.62]\n", + " [ 66.2 42.96 30.73 68.58 44.99 79.36 40.82 27.24 26.62 0. ]]\n", + "demands = [6.12 1.39 2.92 3.66 4.56 7.85 2. 5.14 5.92 0.46]\n", + "capacities = [151.89 42.63 16.26 237.22 241.41 202.1 76.15 24.42 171.06 110.04]\n", + "\n", + "Gurobi Optimizer version 9.5.2 build v9.5.2rc0 (linux64)\n", + "Thread count: 16 physical cores, 32 logical processors, using up to 32 threads\n", + "Optimize a model with 21 rows, 110 columns and 220 nonzeros\n", + "Model fingerprint: 0x8d8d9346\n", + "Variable types: 0 continuous, 110 integer (110 binary)\n", + "Coefficient statistics:\n", + " Matrix range [5e-01, 2e+02]\n", + " Objective range [4e+00, 1e+02]\n", + " Bounds range [1e+00, 1e+00]\n", + " RHS range [1e+00, 5e+00]\n", + "Found heuristic solution: objective 368.7900000\n", + "Presolve time: 0.00s\n", + "Presolved: 21 rows, 110 columns, 220 nonzeros\n", + "Variable types: 0 continuous, 110 integer (110 binary)\n", + "Found heuristic solution: objective 245.6400000\n", + "\n", + "Root relaxation: objective 0.000000e+00, 18 iterations, 0.00 seconds (0.00 work units)\n", + "\n", + " Nodes | Current Node | Objective Bounds | Work\n", + " Expl Unexpl | Obj Depth IntInf | Incumbent BestBd Gap | It/Node Time\n", + "\n", + " 0 0 0.00000 0 6 245.64000 0.00000 100% - 0s\n", + "H 0 0 185.1900000 0.00000 100% - 0s\n", + "H 0 0 148.6300000 17.14595 88.5% - 0s\n", + "H 0 0 113.1800000 17.14595 84.9% - 0s\n", + " 0 0 17.14595 0 10 113.18000 17.14595 84.9% - 0s\n", + "H 0 0 99.5000000 17.14595 82.8% - 0s\n", + "H 0 0 98.3900000 17.14595 82.6% - 0s\n", + "H 0 0 93.9800000 64.28872 31.6% - 0s\n", + " 0 0 64.28872 0 15 93.98000 64.28872 31.6% - 0s\n", + "H 0 0 93.9200000 64.28872 31.5% - 0s\n", + " 0 0 86.06884 0 15 93.92000 86.06884 8.36% - 0s\n", + "* 0 0 0 91.2300000 91.23000 0.00% - 0s\n", + "\n", + "Explored 1 nodes (60 simplex iterations) in 0.01 seconds (0.00 work units)\n", + "Thread count was 32 (of 32 available processors)\n", + "\n", + "Solution count 10: 91.23 93.92 93.98 ... 368.79\n", + "\n", + "Optimal solution found (tolerance 1.00e-04)\n", + "Best objective 9.123000000000e+01, best bound 9.123000000000e+01, gap 0.0000%\n" + ] + } + ], + "source": [ + "import numpy as np\n", + "from scipy.stats import uniform, randint\n", + "from miplearn.problems.pmedian import PMedianGenerator, build_pmedian_model\n", + "\n", + "# Set random seed, to make example reproducible\n", + "np.random.seed(42)\n", + "\n", + "# Generate random instances with ten customers located in a\n", + "# 100x100 square, with demands in [0,10], capacities in [0, 250].\n", + "data = PMedianGenerator(\n", + " x=uniform(loc=0.0, scale=100.0),\n", + " y=uniform(loc=0.0, scale=100.0),\n", + " n=randint(low=10, high=11),\n", + " p=randint(low=5, high=6),\n", + " demands=uniform(loc=0, scale=10),\n", + " capacities=uniform(loc=0, scale=250),\n", + " distances_jitter=uniform(loc=0.9, scale=0.2),\n", + " demands_jitter=uniform(loc=0.9, scale=0.2),\n", + " capacities_jitter=uniform(loc=0.9, scale=0.2),\n", + " fixed=True,\n", + ").generate(10)\n", + "\n", + "# Print data for one of the instances\n", + "print(\"p =\", data[0].p)\n", + "print(\"distances =\\n\", data[0].distances)\n", + "print(\"demands =\", data[0].demands)\n", + "print(\"capacities =\", data[0].capacities)\n", + "print()\n", + "\n", + "# Build and optimize model\n", + "model = build_pmedian_model(data[0])\n", + "model.optimize()" + ] + }, + { + "cell_type": "markdown", + "id": "36129dbf-ecba-4026-ad4d-f2356bad4a26", + "metadata": {}, + "source": [ + "## Set cover\n", + "\n", + "The **set cover problem** is a classical NP-hard optimization problem which aims to minimize the number of sets needed to cover all elements in a given universe. Each set may contain a different number of elements, and sets may overlap with each other. This problem can be useful in various real-world scenarios such as scheduling, resource allocation, and network design." + ] + }, + { + "cell_type": "markdown", + "source": [ + "### Formulation\n", + "\n", + "Let $U = \\{1,\\ldots,n\\}$ be a given universe set, and let $S=\\{S_1,\\ldots,S_m\\}$ be a collection of sets whose union equal $U$. For each $j \\in \\{1,\\ldots,m\\}$, let $w_j$ be the weight of set $S_j$, and let $x_j$ be a binary decision variable that equals one if set $S_j$ is chosen. The set cover problem is formulated as:" + ], + "metadata": { + "collapsed": false + } + }, + { + "cell_type": "markdown", + "id": "5062d606-678c-45ba-9a45-d3c8b7401ad1", + "metadata": {}, + "source": [ + "$$\n", + "\\begin{align*}\n", + " \\text{minimize}\\;\\;\\;\n", + " & \\sum_{j=1}^m w_j x_j\n", + " \\\\\n", + " \\text{subject to}\\;\\;\\;\n", + " & \\sum_{j : i \\in S_j} x_j \\geq 1 & \\forall i \\in \\{1,\\ldots,n\\} \\\\\n", + " & x_j \\in \\{0, 1\\} & \\forall j \\in \\{1,\\ldots,m\\}\n", + "\\end{align*}\n", + "$$" + ] + }, + { + "cell_type": "markdown", + "id": "2732c050-2e11-44fc-bdd1-1b804a60f166", + "metadata": {}, + "source": [ + "### Random instance generator\n", + "\n", + "The class [SetCoverGenerator] can generate random instances of this problem. The class first decides the number of elements and sets by sampling the provided distributions `n_elements` and `n_sets`, respectively. Then it generates a random incidence matrix $M$, as follows:\n", + "\n", + "1. The density $d$ of $M$ is decided by sampling the provided probability distribution `density`.\n", + "2. Each entry of $M$ is then sampled from the Bernoulli distribution, with probability $d$.\n", + "3. To ensure that each element belongs to at least one set, the class identifies elements that are not contained in any set, then assigns them to a random set (chosen uniformly).\n", + "4. Similarly, to ensure that each set contains at least one element, the class identifies empty sets, then modifies them to include one random element (chosen uniformly).\n", + "\n", + "Finally, the weight of set $j$ is set to $w_j + K | S_j |$, where $w_j$ and $k$ are sampled from `costs` and `K`, respectively, and where $|S_j|$ denotes the size of set $S_j$. The parameter $K$ is used to introduce some correlation between the size of the set and its weight, making the instance more challenging. Note that `K` is only sampled once for the entire instance.\n", + "\n", + "If `fix_sets=True`, then all generated instances have exactly the same sets and elements. The costs of the sets, however, are multiplied by random scaling factors sampled from the provided probability distribution `costs_jitter`.\n", + "\n", + "[SetCoverGenerator]: ../../api/problems/#miplearn.problems.setcover.SetCoverGenerator" + ] + }, + { + "cell_type": "markdown", + "id": "569aa5ec-d475-41fa-a5d9-0b1a675fdf95", + "metadata": {}, + "source": [ + "### Example" + ] + }, + { + "cell_type": "code", + "execution_count": 4, + "id": "3224845b-9afd-463e-abf4-e0e93d304859", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "matrix\n", + " [[1 0 0 0 1 1 1 0 0 0]\n", + " [1 0 0 1 1 1 1 0 1 1]\n", + " [0 1 1 1 1 0 1 0 0 1]\n", + " [0 1 1 0 0 0 1 1 0 1]\n", + " [1 1 1 0 1 0 1 0 0 1]]\n", + "costs [1044.58 850.13 1014.5 944.83 697.9 971.87 213.49 220.98 70.23\n", + " 425.33]\n", + "\n", + "Gurobi Optimizer version 9.5.2 build v9.5.2rc0 (linux64)\n", + "Thread count: 16 physical cores, 32 logical processors, using up to 32 threads\n", + "Optimize a model with 5 rows, 10 columns and 28 nonzeros\n", + "Model fingerprint: 0xe5c2d4fa\n", + "Variable types: 0 continuous, 10 integer (10 binary)\n", + "Coefficient statistics:\n", + " Matrix range [1e+00, 1e+00]\n", + " Objective range [7e+01, 1e+03]\n", + " Bounds range [1e+00, 1e+00]\n", + " RHS range [1e+00, 1e+00]\n", + "Found heuristic solution: objective 213.4900000\n", + "Presolve removed 5 rows and 10 columns\n", + "Presolve time: 0.00s\n", + "Presolve: All rows and columns removed\n", + "\n", + "Explored 0 nodes (0 simplex iterations) in 0.00 seconds (0.00 work units)\n", + "Thread count was 1 (of 32 available processors)\n", + "\n", + "Solution count 1: 213.49 \n", + "\n", + "Optimal solution found (tolerance 1.00e-04)\n", + "Best objective 2.134900000000e+02, best bound 2.134900000000e+02, gap 0.0000%\n" + ] + } + ], + "source": [ + "import numpy as np\n", + "from scipy.stats import uniform, randint\n", + "from miplearn.problems.setcover import SetCoverGenerator, build_setcover_model\n", + "\n", + "# Set random seed, to make example reproducible\n", + "np.random.seed(42)\n", + "\n", + "# Build random instances with five elements, ten sets and costs\n", + "# in the [0, 1000] interval, with a correlation factor of 25 and\n", + "# an incidence matrix with 25% density.\n", + "data = SetCoverGenerator(\n", + " n_elements=randint(low=5, high=6),\n", + " n_sets=randint(low=10, high=11),\n", + " costs=uniform(loc=0.0, scale=1000.0),\n", + " costs_jitter=uniform(loc=0.90, scale=0.20),\n", + " density=uniform(loc=0.5, scale=0.00),\n", + " K=uniform(loc=25.0, scale=0.0),\n", + " fix_sets=True,\n", + ").generate(10)\n", + "\n", + "# Print problem data for one instance\n", + "print(\"matrix\\n\", data[0].incidence_matrix)\n", + "print(\"costs\", data[0].costs)\n", + "print()\n", + "\n", + "# Build and optimize model\n", + "model = build_setcover_model(data[0])\n", + "model.optimize()" + ] + }, + { + "cell_type": "markdown", + "id": "255a4e88-2e38-4a1b-ba2e-806b6bd4c815", + "metadata": {}, + "source": [ + "## Set Packing\n", + "\n", + "**Set packing** is a classical optimization problem that asks for the maximum number of disjoint sets within a given list. This problem often arises in real-world situations where a finite number of resources need to be allocated to tasks, such as airline flight crew scheduling." + ] + }, + { + "cell_type": "markdown", + "source": [ + "### Formulation\n", + "\n", + "Let $U=\\{1,\\ldots,n\\}$ be a given universe set, and let $S = \\{S_1, \\ldots, S_m\\}$ be a collection of subsets of $U$. For each subset $j \\in \\{1, \\ldots, m\\}$, let $w_j$ be the weight of $S_j$ and let $x_j$ be a binary decision variable which equals one if set $S_j$ is chosen. The problem is formulated as:" + ], + "metadata": { + "collapsed": false + } + }, + { + "cell_type": "markdown", + "source": [ + "$$\n", + "\\begin{align*}\n", + " \\text{minimize}\\;\\;\\;\n", + " & -\\sum_{j=1}^m w_j x_j\n", + " \\\\\n", + " \\text{subject to}\\;\\;\\;\n", + " & \\sum_{j : i \\in S_j} x_j \\leq 1 & \\forall i \\in \\{1,\\ldots,n\\} \\\\\n", + " & x_j \\in \\{0, 1\\} & \\forall j \\in \\{1,\\ldots,m\\}\n", + "\\end{align*}\n", + "$$" + ], + "metadata": { + "collapsed": false + } + }, + { + "cell_type": "markdown", + "source": [ + "### Random instance generator\n", + "\n", + "The class [SetPackGenerator][SetPackGenerator] can generate random instances of this problem. It accepts exactly the same arguments, and generates instance data in exactly the same way as [SetCoverGenerator][SetCoverGenerator]. For more details, please see the documentation for that class.\n", + "\n", + "[SetPackGenerator]: ../../api/problems/#miplearn.problems.setpack.SetPackGenerator\n", + "[SetCoverGenerator]: ../../api/problems/#miplearn.problems.setcover.SetCoverGenerator\n", + "\n", + "### Example" + ], + "metadata": { + "collapsed": false + } + }, + { + "cell_type": "code", + "execution_count": 5, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "matrix\n", + " [[1 0 0 0 1 1 1 0 0 0]\n", + " [1 0 0 1 1 1 1 0 1 1]\n", + " [0 1 1 1 1 0 1 0 0 1]\n", + " [0 1 1 0 0 0 1 1 0 1]\n", + " [1 1 1 0 1 0 1 0 0 1]]\n", + "costs [1044.58 850.13 1014.5 944.83 697.9 971.87 213.49 220.98 70.23\n", + " 425.33]\n", + "\n", + "Gurobi Optimizer version 9.5.2 build v9.5.2rc0 (linux64)\n", + "Thread count: 16 physical cores, 32 logical processors, using up to 32 threads\n", + "Optimize a model with 5 rows, 10 columns and 28 nonzeros\n", + "Model fingerprint: 0x4ee91388\n", + "Variable types: 0 continuous, 10 integer (10 binary)\n", + "Coefficient statistics:\n", + " Matrix range [1e+00, 1e+00]\n", + " Objective range [7e+01, 1e+03]\n", + " Bounds range [1e+00, 1e+00]\n", + " RHS range [1e+00, 1e+00]\n", + "Found heuristic solution: objective -1265.560000\n", + "Presolve removed 5 rows and 10 columns\n", + "Presolve time: 0.00s\n", + "Presolve: All rows and columns removed\n", + "\n", + "Explored 0 nodes (0 simplex iterations) in 0.00 seconds (0.00 work units)\n", + "Thread count was 1 (of 32 available processors)\n", + "\n", + "Solution count 2: -1986.37 -1265.56 \n", + "No other solutions better than -1986.37\n", + "\n", + "Optimal solution found (tolerance 1.00e-04)\n", + "Best objective -1.986370000000e+03, best bound -1.986370000000e+03, gap 0.0000%\n" + ] + } + ], + "source": [ + "import numpy as np\n", + "from scipy.stats import uniform, randint\n", + "from miplearn.problems.setpack import SetPackGenerator, build_setpack_model\n", + "\n", + "# Set random seed, to make example reproducible\n", + "np.random.seed(42)\n", + "\n", + "# Build random instances with five elements, ten sets and costs\n", + "# in the [0, 1000] interval, with a correlation factor of 25 and\n", + "# an incidence matrix with 25% density.\n", + "data = SetPackGenerator(\n", + " n_elements=randint(low=5, high=6),\n", + " n_sets=randint(low=10, high=11),\n", + " costs=uniform(loc=0.0, scale=1000.0),\n", + " costs_jitter=uniform(loc=0.90, scale=0.20),\n", + " density=uniform(loc=0.5, scale=0.00),\n", + " K=uniform(loc=25.0, scale=0.0),\n", + " fix_sets=True,\n", + ").generate(10)\n", + "\n", + "# Print problem data for one instance\n", + "print(\"matrix\\n\", data[0].incidence_matrix)\n", + "print(\"costs\", data[0].costs)\n", + "print()\n", + "\n", + "# Build and optimize model\n", + "model = build_setpack_model(data[0])\n", + "model.optimize()" + ], + "metadata": { + "collapsed": false + } + }, + { + "cell_type": "markdown", + "id": "373e450c-8f8b-4b59-bf73-251bdd6ff67e", + "metadata": {}, + "source": [ + "## Stable Set\n", + "\n", + "The **maximum-weight stable set problem** is a classical optimization problem in graph theory which asks for the maximum-weight subset of vertices in a graph such that no two vertices in the subset are adjacent. The problem often arises in real-world scheduling or resource allocation situations, where stable sets represent tasks or resources that can be chosen simultaneously without conflicts.\n", + "\n", + "### Formulation\n", + "\n", + "Let $G=(V,E)$ be a simple undirected graph, and for each vertex $v \\in V$, let $w_v$ be its weight. The problem is formulated as:" + ] + }, + { + "cell_type": "markdown", + "source": [ + "$$\n", + "\\begin{align*}\n", + "\\text{minimize} \\;\\;\\; & -\\sum_{v \\in V} w_v x_v \\\\\n", + "\\text{such that} \\;\\;\\; & \\sum_{v \\in C} x_v \\leq 1 & \\forall C \\in \\mathcal{C} \\\\\n", + "& x_v \\in \\{0, 1\\} & \\forall v \\in V\n", + "\\end{align*}\n", + "$$\n", + "where $\\mathcal{C}$ is the set of cliques in $G$. We recall that a clique is a subset of vertices in which every pair of vertices is adjacent." + ], + "metadata": { + "collapsed": false + } + }, + { + "cell_type": "markdown", + "source": [ + "\n", + "### Random instance generator\n", + "\n", + "The class [MaxWeightStableSetGenerator][MaxWeightStableSetGenerator] can be used to generate random instances of this problem. The class first samples the user-provided probability distributions `n` and `p` to decide the number of vertices and the density of the graph. Then, it generates a random Erdős-Rényi graph $G_{n,p}$. We recall that, in such a graph, each potential edge is included with probabilty $p$, independently for each other. The class then samples the provided probability distribution `w` to decide the vertex weights.\n", + "\n", + "[MaxWeightStableSetGenerator]: ../../api/problems/#miplearn.problems.stab.MaxWeightStableSetGenerator\n", + "\n", + "If `fix_graph=True`, then all generated instances have the same random graph. For each instance, the weights are decided by sampling `w`, as described above.\n", + "\n", + "### Example" + ], + "metadata": { + "collapsed": false + } + }, + { + "cell_type": "code", + "execution_count": 24, + "id": "0f996e99-0ec9-472b-be8a-30c9b8556931", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "graph [(0, 2), (0, 4), (0, 8), (1, 2), (1, 3), (1, 5), (1, 6), (1, 9), (2, 5), (2, 9), (3, 6), (3, 7), (6, 9), (7, 8), (8, 9)]\n", + "weights[0] [37.45 95.07 73.2 59.87 15.6 15.6 5.81 86.62 60.11 70.81]\n", + "weights[1] [ 2.06 96.99 83.24 21.23 18.18 18.34 30.42 52.48 43.19 29.12]\n", + "\n", + "Gurobi Optimizer version 9.5.2 build v9.5.2rc0 (linux64)\n", + "Thread count: 16 physical cores, 32 logical processors, using up to 32 threads\n", + "Optimize a model with 10 rows, 10 columns and 24 nonzeros\n", + "Model fingerprint: 0xf4c21689\n", + "Variable types: 0 continuous, 10 integer (10 binary)\n", + "Coefficient statistics:\n", + " Matrix range [1e+00, 1e+00]\n", + " Objective range [6e+00, 1e+02]\n", + " Bounds range [1e+00, 1e+00]\n", + " RHS range [1e+00, 1e+00]\n", + "Found heuristic solution: objective -219.1400000\n", + "Presolve removed 2 rows and 2 columns\n", + "Presolve time: 0.00s\n", + "Presolved: 8 rows, 8 columns, 19 nonzeros\n", + "Variable types: 0 continuous, 8 integer (8 binary)\n", + "\n", + "Root relaxation: objective -2.205650e+02, 4 iterations, 0.00 seconds (0.00 work units)\n", + "\n", + " Nodes | Current Node | Objective Bounds | Work\n", + " Expl Unexpl | Obj Depth IntInf | Incumbent BestBd Gap | It/Node Time\n", + "\n", + " 0 0 infeasible 0 -219.14000 -219.14000 0.00% - 0s\n", + "\n", + "Explored 1 nodes (4 simplex iterations) in 0.00 seconds (0.00 work units)\n", + "Thread count was 32 (of 32 available processors)\n", + "\n", + "Solution count 1: -219.14 \n", + "No other solutions better than -219.14\n", + "\n", + "Optimal solution found (tolerance 1.00e-04)\n", + "Best objective -2.191400000000e+02, best bound -2.191400000000e+02, gap 0.0000%\n" + ] + } + ], + "source": [ + "import random\n", + "import numpy as np\n", + "from scipy.stats import uniform, randint\n", + "from miplearn.problems.stab import MaxWeightStableSetGenerator, build_stab_model\n", + "\n", + "# Set random seed to make example reproducible\n", + "random.seed(42)\n", + "np.random.seed(42)\n", + "\n", + "# Generate random instances with a fixed 10-node graph,\n", + "# 25% density and random weights in the [0, 100] interval.\n", + "data = MaxWeightStableSetGenerator(\n", + " w=uniform(loc=0.0, scale=100.0),\n", + " n=randint(low=10, high=11),\n", + " p=uniform(loc=0.25, scale=0.0),\n", + " fix_graph=True,\n", + ").generate(10)\n", + "\n", + "# Print the graph and weights for two instances\n", + "print(\"graph\", data[0].graph.edges)\n", + "print(\"weights[0]\", data[0].weights)\n", + "print(\"weights[1]\", data[1].weights)\n", + "print()\n", + "\n", + "# Load and optimize the first instance\n", + "model = build_stab_model(data[0])\n", + "model.optimize()" + ] + }, + { + "cell_type": "markdown", + "id": "444d1092-fd83-4957-b691-a198d56ba066", + "metadata": {}, + "source": [ + "## Traveling Salesman\n", + "\n", + "Given a list of cities and the distances between them, the **traveling salesman problem** asks for the shortest route starting at the first city, visiting each other city exactly once, then returning to the first city. This problem is a generalization of the Hamiltonian path problem, one of Karp's 21 NP-complete problems, and has many practical applications, including routing delivery trucks and scheduling airline routes." + ] + }, + { + "cell_type": "markdown", + "source": [ + "### Formulation\n", + "\n", + "Let $G=(V,E)$ be a simple undirected graph. For each edge $e \\in E$, let $d_e$ be its weight (or distance) and let $x_e$ be a binary decision variable which equals one if $e$ is included in the route. The problem is formulated as:" + ], + "metadata": { + "collapsed": false + } + }, + { + "cell_type": "markdown", + "source": [ + "$$\n", + "\\begin{align*}\n", + "\\text{minimize} \\;\\;\\;\n", + " & \\sum_{e \\in E} d_e x_e \\\\\n", + "\\text{such that} \\;\\;\\;\n", + " & \\sum_{e : \\delta(v)} x_e = 2 & \\forall v \\in V, \\\\\n", + " & \\sum_{e \\in \\delta(S)} x_e \\geq 2 & \\forall S \\subsetneq V, |S| \\neq \\emptyset, \\\\\n", + " & x_e \\in \\{0, 1\\} & \\forall e \\in E,\n", + "\\end{align*}\n", + "$$\n", + "where $\\delta(v)$ denotes the set of edges adjacent to vertex $v$, and $\\delta(S)$ denotes the set of edges that have one extremity in $S$ and one in $V \\setminus S$. Because of its exponential size, we enforce the second set of inequalities as lazy constraints." + ], + "metadata": { + "collapsed": false + } + }, + { + "cell_type": "markdown", + "source": [ + "### Random instance generator\n", + "\n", + "The class [TravelingSalesmanGenerator][TravelingSalesmanGenerator] can be used to generate random instances of this problem. Initially, the class samples the user-provided probability distribution `n` to decide how many cities to generate. Then, for each city $i$, the class generates its geographical location $(x_i, y_i)$ by sampling the provided distributions `x` and `y`. The distance $d_{ij}$ between cities $i$ and $j$ is then set to\n", + "$$\n", + "\\gamma_{ij} \\sqrt{(x_i - x_j)^2 + (y_i - y_j)^2},\n", + "$$\n", + "where $\\gamma$ is a random scaling factor sampled from the provided probability distribution `gamma`.\n", + "\n", + "If `fix_cities=True`, then the list of cities is kept the same for all generated instances. The $\\gamma$ values, however, and therefore also the distances, are still different. By default, all distances $d_{ij}$ are rounded to the nearest integer. If `round=False` is provided, this rounding will be disabled.\n", + "\n", + "[TravelingSalesmanGenerator]: ../../api/problems/#miplearn.problems.tsp.TravelingSalesmanGenerator" + ], + "metadata": { + "collapsed": false + } + }, + { + "cell_type": "markdown", + "source": [ + "### Example" + ], + "metadata": { + "collapsed": false + } + }, + { + "cell_type": "code", + "execution_count": 32, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "distances[0]\n", + " [[ 0. 513. 762. 358. 325. 374. 932. 731. 391. 634.]\n", + " [ 513. 0. 726. 765. 163. 754. 409. 719. 446. 400.]\n", + " [ 762. 726. 0. 780. 756. 744. 656. 40. 383. 334.]\n", + " [ 358. 765. 780. 0. 549. 117. 925. 702. 422. 728.]\n", + " [ 325. 163. 756. 549. 0. 663. 526. 708. 377. 462.]\n", + " [ 374. 754. 744. 117. 663. 0. 1072. 802. 501. 853.]\n", + " [ 932. 409. 656. 925. 526. 1072. 0. 654. 603. 433.]\n", + " [ 731. 719. 40. 702. 708. 802. 654. 0. 381. 255.]\n", + " [ 391. 446. 383. 422. 377. 501. 603. 381. 0. 287.]\n", + " [ 634. 400. 334. 728. 462. 853. 433. 255. 287. 0.]]\n", + "distances[1]\n", + " [[ 0. 493. 900. 354. 323. 367. 841. 727. 444. 668.]\n", + " [ 493. 0. 690. 687. 175. 725. 368. 744. 398. 446.]\n", + " [ 900. 690. 0. 666. 728. 827. 736. 41. 371. 317.]\n", + " [ 354. 687. 666. 0. 570. 104. 1090. 712. 454. 648.]\n", + " [ 323. 175. 728. 570. 0. 655. 521. 650. 356. 469.]\n", + " [ 367. 725. 827. 104. 655. 0. 1146. 779. 476. 752.]\n", + " [ 841. 368. 736. 1090. 521. 1146. 0. 681. 565. 394.]\n", + " [ 727. 744. 41. 712. 650. 779. 681. 0. 374. 286.]\n", + " [ 444. 398. 371. 454. 356. 476. 565. 374. 0. 274.]\n", + " [ 668. 446. 317. 648. 469. 752. 394. 286. 274. 0.]]\n", + "\n", + "Set parameter LazyConstraints to value 1\n", + "Gurobi Optimizer version 9.5.2 build v9.5.2rc0 (linux64)\n", + "Thread count: 16 physical cores, 32 logical processors, using up to 32 threads\n", + "Optimize a model with 10 rows, 45 columns and 90 nonzeros\n", + "Model fingerprint: 0x719675e5\n", + "Variable types: 0 continuous, 45 integer (45 binary)\n", + "Coefficient statistics:\n", + " Matrix range [1e+00, 1e+00]\n", + " Objective range [4e+01, 1e+03]\n", + " Bounds range [1e+00, 1e+00]\n", + " RHS range [2e+00, 2e+00]\n", + "Presolve time: 0.00s\n", + "Presolved: 10 rows, 45 columns, 90 nonzeros\n", + "Variable types: 0 continuous, 45 integer (45 binary)\n", + "\n", + "Root relaxation: objective 2.921000e+03, 17 iterations, 0.00 seconds (0.00 work units)\n", + "\n", + " Nodes | Current Node | Objective Bounds | Work\n", + " Expl Unexpl | Obj Depth IntInf | Incumbent BestBd Gap | It/Node Time\n", + "\n", + "* 0 0 0 2921.0000000 2921.00000 0.00% - 0s\n", + "\n", + "Cutting planes:\n", + " Lazy constraints: 3\n", + "\n", + "Explored 1 nodes (17 simplex iterations) in 0.01 seconds (0.00 work units)\n", + "Thread count was 32 (of 32 available processors)\n", + "\n", + "Solution count 1: 2921 \n", + "\n", + "Optimal solution found (tolerance 1.00e-04)\n", + "Best objective 2.921000000000e+03, best bound 2.921000000000e+03, gap 0.0000%\n", + "\n", + "User-callback calls 100, time in user-callback 0.00 sec\n" + ] + } + ], + "source": [ + "import random\n", + "import numpy as np\n", + "from scipy.stats import uniform, randint\n", + "from miplearn.problems.tsp import TravelingSalesmanGenerator, build_tsp_model\n", + "\n", + "# Set random seed to make example reproducible\n", + "random.seed(42)\n", + "np.random.seed(42)\n", + "\n", + "# Generate random instances with a fixed ten cities in the 1000x1000 box\n", + "# and random distance scaling factors in the [0.90, 1.10] interval.\n", + "data = TravelingSalesmanGenerator(\n", + " n=randint(low=10, high=11),\n", + " x=uniform(loc=0.0, scale=1000.0),\n", + " y=uniform(loc=0.0, scale=1000.0),\n", + " gamma=uniform(loc=0.90, scale=0.20),\n", + " fix_cities=True,\n", + " round=True,\n", + ").generate(10)\n", + "\n", + "# Print distance matrices for the first two instances\n", + "print(\"distances[0]\\n\", data[0].distances)\n", + "print(\"distances[1]\\n\", data[1].distances)\n", + "print()\n", + "\n", + "# Load and optimize the first instance\n", + "model = build_tsp_model(data[0])\n", + "model.optimize()" + ], + "metadata": { + "collapsed": false + } + }, + { + "cell_type": "markdown", + "id": "26dfc157-11f4-4564-b368-95ee8200875e", + "metadata": {}, + "source": [ + "## Unit Commitment\n", + "\n", + "The **unit commitment problem** is a mixed-integer optimization problem which asks which power generation units should be turned on and off, at what time, and at what capacity, in order to meet the demand for electricity generation at the lowest cost. Numerous operational constraints are typically enforced, such as *ramping constraints*, which prevent generation units from changing power output levels too quickly from one time step to the next, and *minimum-up* and *minimum-down* constraints, which prevent units from switching on and off too frequently. The unit commitment problem is widely used in power systems planning and operations." + ] + }, + { + "cell_type": "markdown", + "source": [ + "\n", + "
\n", + "Note\n", + "\n", + "MIPLearn includes a simple formulation for the unit commitment problem, which enforces only minimum and maximum power production, as well as minimum-up and minimum-down constraints. The formulation does not enforce, for example, ramping trajectories, piecewise-linear cost curves, start-up costs or transmission and n-1 security constraints. For a more complete set of formulations, solution methods and realistic benchmark instances for the problem, see [UnitCommitment.jl](https://github.com/ANL-CEEESA/UnitCommitment.jl).\n", + "
\n", + "\n", + "### Formulation\n", + "\n", + "Let $T$ be the number of time steps, $G$ be the number of generation units, and let $D_t$ be the power demand (in MW) at time $t$. For each generating unit $g$, let $P^\\max_g$ and $P^\\min_g$ be the maximum and minimum amount of power the unit is able to produce when switched on; let $L_g$ and $l_g$ be the minimum up- and down-time for unit $g$; let $C^\\text{fixed}$ be the cost to keep unit $g$ on for one time step, regardless of its power output level; let $C^\\text{start}$ be the cost to switch unit $g$ on; and let $C^\\text{var}$ be the cost for generator $g$ to produce 1 MW of power. In this formulation, we assume linear production costs. For each generator $g$ and time $t$, let $x_{gt}$ be a binary variable which equals one if unit $g$ is on at time $t$, let $w_{gt}$ be a binary variable which equals one if unit $g$ switches from being off at time $t-1$ to being on at time $t$, and let $p_{gt}$ be a continuous variable which indicates the amount of power generated. The formulation is given by:" + ], + "metadata": { + "collapsed": false + } + }, + { + "cell_type": "markdown", + "source": [ + "\n", + "$$\n", + "\\begin{align*}\n", + "\\text{minimize} \\;\\;\\;\n", + " & \\sum_{t=1}^T \\sum_{g=1}^G \\left(\n", + " x_{gt} C^\\text{fixed}_g\n", + " + w_{gt} C^\\text{start}_g\n", + " + p_{gt} C^\\text{var}_g\n", + " \\right)\n", + " \\\\\n", + "\\text{such that} \\;\\;\\;\n", + " & \\sum_{k=t-L_g+1}^t w_{gk} \\leq x_{gt}\n", + " & \\forall g\\; \\forall t=L_g-1,\\ldots,T-1 \\\\\n", + " & \\sum_{k=g-l_g+1}^T w_{gt} \\leq 1 - x_{g,t-l_g+1}\n", + " & \\forall g \\forall t=l_g-1,\\ldots,T-1 \\\\\n", + " & w_{gt} \\geq x_{gt} - x_{g,t-1}\n", + " & \\forall g \\forall t=1,\\ldots,T-1 \\\\\n", + " & \\sum_{g=1}^G p_{gt} \\geq D_t\n", + " & \\forall t \\\\\n", + " & P^\\text{min}_g x_{gt} \\leq p_{gt}\n", + " & \\forall g, t \\\\\n", + " & p_{gt} \\leq P^\\text{max}_g x_{gt}\n", + " & \\forall g, t \\\\\n", + " & x_{gt} \\in \\{0, 1\\}\n", + " & \\forall g, t.\n", + "\\end{align*}\n", + "$$" + ], + "metadata": { + "collapsed": false + } + }, + { + "cell_type": "markdown", + "source": [ + "\n", + "The first set of inequalities enforces minimum up-time constraints: if unit $g$ is down at time $t$, then it cannot start up during the previous $L_g$ time steps. The second set of inequalities enforces minimum down-time constraints, and is symmetrical to the previous one. The third set ensures that if unit $g$ starts up at time $t$, then the start up variable must be one. The fourth set ensures that demand is satisfied at each time period. The fifth and sixth sets enforce bounds to the quantity of power generated by each unit.\n", + "\n", + "
\n", + "References\n", + "\n", + "- *Bendotti, P., Fouilhoux, P. & Rottner, C.* **The min-up/min-down unit commitment polytope.** J Comb Optim 36, 1024-1058 (2018). https://doi.org/10.1007/s10878-018-0273-y\n", + "
" + ], + "metadata": { + "collapsed": false + } + }, + { + "cell_type": "markdown", + "source": [ + "\n", + "### Random instance generator\n", + "\n", + "The class `UnitCommitmentGenerator` can be used to generate random instances of this problem.\n", + "\n", + "First, the user-provided probability distributions `n_units` and `n_periods` are sampled to determine the number of generating units and the number of time steps, respectively. Then, for each unit, the probabilities `max_power` and `min_power` are sampled to determine the unit's maximum and minimum power output. To make it easier to generate valid ranges, `min_power` is not specified as the absolute power level in MW, but rather as a multiplier of `max_power`; for example, if `max_power` samples to 100 and `min_power` samples to 0.5, then the unit's power range is set to `[50,100]`. Then, the distributions `cost_startup`, `cost_prod` and `cost_fixed` are sampled to determine the unit's startup, variable and fixed costs, while the distributions `min_uptime` and `min_downtime` are sampled to determine its minimum up/down-time.\n", + "\n", + "After parameters for the units have been generated, the class then generates a periodic demand curve, with a peak every 12 time steps, in the range $(0.4C, 0.8C)$, where $C$ is the sum of all units' maximum power output. Finally, all costs and demand values are perturbed by random scaling factors independently sampled from the distributions `cost_jitter` and `demand_jitter`, respectively.\n", + "\n", + "If `fix_units=True`, then the list of generators (with their respective parameters) is kept the same for all generated instances. If `cost_jitter` and `demand_jitter` are provided, the instances will still have slightly different costs and demands." + ], + "metadata": { + "collapsed": false + } + }, + { + "cell_type": "markdown", + "source": [ + "### Example" + ], + "metadata": { + "collapsed": false + } + }, + { + "cell_type": "code", + "execution_count": 8, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "min_power[0] [117.79 245.85 271.85 207.7 81.38]\n", + "max_power[0] [218.54 477.82 379.4 319.4 120.21]\n", + "min_uptime[0] [7 6 3 5 7]\n", + "min_downtime[0] [7 3 5 6 2]\n", + "min_power[0] [117.79 245.85 271.85 207.7 81.38]\n", + "cost_startup[0] [3042.42 5247.56 4319.45 2912.29 6118.53]\n", + "cost_prod[0] [ 6.97 14.61 18.32 22.8 39.26]\n", + "cost_fixed[0] [199.67 514.23 592.41 46.45 607.54]\n", + "demand[0]\n", + " [ 905.06 915.41 1166.52 1212.29 1127.81 953.52 905.06 796.21 783.78\n", + " 866.23 768.62 899.59 905.06 946.23 1087.61 1004.24 1048.36 992.03\n", + " 905.06 750.82 691.48 606.15 658.5 809.95]\n", + "\n", + "min_power[1] [117.79 245.85 271.85 207.7 81.38]\n", + "max_power[1] [218.54 477.82 379.4 319.4 120.21]\n", + "min_uptime[1] [7 6 3 5 7]\n", + "min_downtime[1] [7 3 5 6 2]\n", + "min_power[1] [117.79 245.85 271.85 207.7 81.38]\n", + "cost_startup[1] [2458.08 6200.26 4585.74 2666.05 4783.34]\n", + "cost_prod[1] [ 6.31 13.33 20.42 24.37 46.86]\n", + "cost_fixed[1] [196.9 416.42 655.57 52.51 626.15]\n", + "demand[1]\n", + " [ 981.42 840.07 1095.59 1102.03 1088.41 932.29 863.67 848.56 761.33\n", + " 828.28 775.18 834.99 959.76 865.72 1193.52 1058.92 985.19 893.92\n", + " 962.16 781.88 723.15 639.04 602.4 787.02]\n", + "\n", + "Gurobi Optimizer version 9.5.2 build v9.5.2rc0 (linux64)\n", + "Thread count: 6 physical cores, 12 logical processors, using up to 12 threads\n", + "Optimize a model with 578 rows, 360 columns and 2128 nonzeros\n", + "Model fingerprint: 0x4dc1c661\n", + "Variable types: 120 continuous, 240 integer (240 binary)\n", + "Coefficient statistics:\n", + " Matrix range [1e+00, 5e+02]\n", + " Objective range [7e+00, 6e+03]\n", + " Bounds range [1e+00, 1e+00]\n", + " RHS range [1e+00, 1e+03]\n", + "Presolve removed 244 rows and 131 columns\n", + "Presolve time: 0.01s\n", + "Presolved: 334 rows, 229 columns, 842 nonzeros\n", + "Variable types: 116 continuous, 113 integer (113 binary)\n", + "Found heuristic solution: objective 441426.66550\n", + "Found heuristic solution: objective 429461.97680\n", + "Found heuristic solution: objective 374043.64040\n", + "\n", + "Root relaxation: objective 3.361348e+05, 139 iterations, 0.00 seconds (0.00 work units)\n", + "\n", + " Nodes | Current Node | Objective Bounds | Work\n", + " Expl Unexpl | Obj Depth IntInf | Incumbent BestBd Gap | It/Node Time\n", + "\n", + " 0 0 336134.820 0 18 374043.640 336134.820 10.1% - 0s\n", + "H 0 0 368600.14450 336134.820 8.81% - 0s\n", + "H 0 0 364721.76610 364721.766 0.00% - 0s\n", + " 0 0 - 0 364721.766 364721.766 0.00% - 0s\n", + "\n", + "Cutting planes:\n", + " Gomory: 3\n", + " Cover: 8\n", + " Implied bound: 29\n", + " Clique: 222\n", + " MIR: 7\n", + " Flow cover: 7\n", + " RLT: 1\n", + " Relax-and-lift: 7\n", + "\n", + "Explored 1 nodes (232 simplex iterations) in 0.04 seconds (0.02 work units)\n", + "Thread count was 12 (of 12 available processors)\n", + "\n", + "Solution count 5: 364722 368600 374044 ... 441427\n", + "\n", + "Optimal solution found (tolerance 1.00e-04)\n", + "Best objective 3.647217661000e+05, best bound 3.647217661000e+05, gap 0.0000%\n" + ] + } + ], + "source": [ + "import random\n", + "import numpy as np\n", + "from scipy.stats import uniform, randint\n", + "from miplearn.problems.uc import UnitCommitmentGenerator, build_uc_model\n", + "\n", + "# Set random seed to make example reproducible\n", + "random.seed(42)\n", + "np.random.seed(42)\n", + "\n", + "# Generate a random instance with 5 generators and 24 time steps\n", + "data = UnitCommitmentGenerator(\n", + " n_units=randint(low=5, high=6),\n", + " n_periods=randint(low=24, high=25),\n", + " max_power=uniform(loc=50, scale=450),\n", + " min_power=uniform(loc=0.5, scale=0.25),\n", + " cost_startup=uniform(loc=0, scale=10_000),\n", + " cost_prod=uniform(loc=0, scale=50),\n", + " cost_fixed=uniform(loc=0, scale=1_000),\n", + " min_uptime=randint(low=2, high=8),\n", + " min_downtime=randint(low=2, high=8),\n", + " cost_jitter=uniform(loc=0.75, scale=0.5),\n", + " demand_jitter=uniform(loc=0.9, scale=0.2),\n", + " fix_units=True,\n", + ").generate(10)\n", + "\n", + "# Print problem data for the two first instances\n", + "for i in range(2):\n", + " print(f\"min_power[{i}]\", data[i].min_power)\n", + " print(f\"max_power[{i}]\", data[i].max_power)\n", + " print(f\"min_uptime[{i}]\", data[i].min_uptime)\n", + " print(f\"min_downtime[{i}]\", data[i].min_downtime)\n", + " print(f\"min_power[{i}]\", data[i].min_power)\n", + " print(f\"cost_startup[{i}]\", data[i].cost_startup)\n", + " print(f\"cost_prod[{i}]\", data[i].cost_prod)\n", + " print(f\"cost_fixed[{i}]\", data[i].cost_fixed)\n", + " print(f\"demand[{i}]\\n\", data[i].demand)\n", + " print()\n", + "\n", + "# Load and optimize the first instance\n", + "model = build_uc_model(data[0])\n", + "model.optimize()" + ], + "metadata": { + "collapsed": false + } + }, + { + "cell_type": "markdown", + "id": "169293c7-33e1-4d28-8d39-9982776251d7", + "metadata": {}, + "source": [ + "## Vertex Cover\n", + "\n", + "**Minimum weight vertex cover** is a classical optimization problem in graph theory where the goal is to find the minimum-weight set of vertices that are connected to all of the edges in the graph. The problem generalizes one of Karp's 21 NP-complete problems and has applications in various fields, including bioinformatics and machine learning." + ] + }, + { + "cell_type": "markdown", + "source": [ + "\n", + "### Formulation\n", + "\n", + "Let $G=(V,E)$ be a simple graph. For each vertex $v \\in V$, let $w_g$ be its weight, and let $x_v$ be a binary decision variable which equals one if $v$ is included in the cover. The mixed-integer linear formulation for the problem is given by:" + ], + "metadata": { + "collapsed": false + } + }, + { + "cell_type": "markdown", + "source": [ + " $$\n", + "\\begin{align*}\n", + "\\text{minimize} \\;\\;\\;\n", + " & \\sum_{v \\in V} w_v \\\\\n", + "\\text{such that} \\;\\;\\;\n", + " & x_i + x_j \\ge 1 & \\forall \\{i, j\\} \\in E, \\\\\n", + " & x_{i,j} \\in \\{0, 1\\}\n", + " & \\forall \\{i,j\\} \\in E.\n", + "\\end{align*}\n", + "$$" + ], + "metadata": { + "collapsed": false + } + }, + { + "cell_type": "markdown", + "source": [ + "### Random instance generator\n", + "\n", + "The class [MinWeightVertexCoverGenerator][MinWeightVertexCoverGenerator] can be used to generate random instances of this problem. The class accepts exactly the same parameters and behaves exactly in the same way as [MaxWeightStableSetGenerator][MaxWeightStableSetGenerator]. See the [stable set section](#Stable-Set) for more details.\n", + "\n", + "[MinWeightVertexCoverGenerator]: ../../api/problems/#module-miplearn.problems.vertexcover\n", + "[MaxWeightStableSetGenerator]: ../../api/problems/#miplearn.problems.stab.MaxWeightStableSetGenerator\n", + "\n", + "### Example" + ], + "metadata": { + "collapsed": false + } + }, + { + "cell_type": "code", + "execution_count": 9, + "id": "5fff7afe-5b7a-4889-a502-66751ec979bf", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "graph [(0, 2), (0, 4), (0, 8), (1, 2), (1, 3), (1, 5), (1, 6), (1, 9), (2, 5), (2, 9), (3, 6), (3, 7), (6, 9), (7, 8), (8, 9)]\n", + "weights[0] [37.45 95.07 73.2 59.87 15.6 15.6 5.81 86.62 60.11 70.81]\n", + "weights[1] [ 2.06 96.99 83.24 21.23 18.18 18.34 30.42 52.48 43.19 29.12]\n", + "\n", + "Gurobi Optimizer version 9.5.2 build v9.5.2rc0 (linux64)\n", + "Thread count: 6 physical cores, 12 logical processors, using up to 12 threads\n", + "Optimize a model with 15 rows, 10 columns and 30 nonzeros\n", + "Model fingerprint: 0x2d2d1390\n", + "Variable types: 0 continuous, 10 integer (10 binary)\n", + "Coefficient statistics:\n", + " Matrix range [1e+00, 1e+00]\n", + " Objective range [6e+00, 1e+02]\n", + " Bounds range [1e+00, 1e+00]\n", + " RHS range [1e+00, 1e+00]\n", + "Found heuristic solution: objective 301.0000000\n", + "Presolve removed 7 rows and 2 columns\n", + "Presolve time: 0.00s\n", + "Presolved: 8 rows, 8 columns, 19 nonzeros\n", + "Variable types: 0 continuous, 8 integer (8 binary)\n", + "\n", + "Root relaxation: objective 2.995750e+02, 8 iterations, 0.00 seconds (0.00 work units)\n", + "\n", + " Nodes | Current Node | Objective Bounds | Work\n", + " Expl Unexpl | Obj Depth IntInf | Incumbent BestBd Gap | It/Node Time\n", + "\n", + " 0 0 infeasible 0 301.00000 301.00000 0.00% - 0s\n", + "\n", + "Explored 1 nodes (8 simplex iterations) in 0.01 seconds (0.00 work units)\n", + "Thread count was 12 (of 12 available processors)\n", + "\n", + "Solution count 1: 301 \n", + "\n", + "Optimal solution found (tolerance 1.00e-04)\n", + "Best objective 3.010000000000e+02, best bound 3.010000000000e+02, gap 0.0000%\n" + ] + } + ], + "source": [ + "import random\n", + "import numpy as np\n", + "from scipy.stats import uniform, randint\n", + "from miplearn.problems.vertexcover import MinWeightVertexCoverGenerator, build_vertexcover_model\n", + "\n", + "# Set random seed to make example reproducible\n", + "random.seed(42)\n", + "np.random.seed(42)\n", + "\n", + "# Generate random instances with a fixed 10-node graph,\n", + "# 25% density and random weights in the [0, 100] interval.\n", + "data = MinWeightVertexCoverGenerator(\n", + " w=uniform(loc=0.0, scale=100.0),\n", + " n=randint(low=10, high=11),\n", + " p=uniform(loc=0.25, scale=0.0),\n", + " fix_graph=True,\n", + ").generate(10)\n", + "\n", + "# Print the graph and weights for two instances\n", + "print(\"graph\", data[0].graph.edges)\n", + "print(\"weights[0]\", data[0].weights)\n", + "print(\"weights[1]\", data[1].weights)\n", + "print()\n", + "\n", + "# Load and optimize the first instance\n", + "model = build_vertexcover_model(data[0])\n", + "model.optimize()\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "outputs": [], + "source": [], + "metadata": { + "collapsed": false + } + } + ], + "metadata": { + "kernelspec": { + "display_name": "Python 3", + "language": "python", + "name": "python3" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.8.13" + } + }, + "nbformat": 4, + "nbformat_minor": 5 +} diff --git a/0.3/_sources/guide/solvers.ipynb.txt b/0.3/_sources/guide/solvers.ipynb.txt new file mode 100644 index 0000000..40d1709 --- /dev/null +++ b/0.3/_sources/guide/solvers.ipynb.txt @@ -0,0 +1,210 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "id": "3371f072-be1e-4c47-b765-b5d30fdbfae6", + "metadata": {}, + "source": [ + "# Solvers\n", + "\n", + "## LearningSolver\n", + "\n", + "### Example" + ] + }, + { + "cell_type": "code", + "execution_count": 3, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Gurobi Optimizer version 9.5.2 build v9.5.2rc0 (linux64)\n", + "Thread count: 6 physical cores, 12 logical processors, using up to 12 threads\n", + "Optimize a model with 10 rows, 45 columns and 90 nonzeros\n", + "Model fingerprint: 0x6ddcd141\n", + "Coefficient statistics:\n", + " Matrix range [1e+00, 1e+00]\n", + " Objective range [4e+01, 1e+03]\n", + " Bounds range [1e+00, 1e+00]\n", + " RHS range [2e+00, 2e+00]\n", + "Presolve time: 0.00s\n", + "Presolved: 10 rows, 45 columns, 90 nonzeros\n", + "\n", + "Iteration Objective Primal Inf. Dual Inf. Time\n", + " 0 6.3600000e+02 1.700000e+01 0.000000e+00 0s\n", + " 15 2.7610000e+03 0.000000e+00 0.000000e+00 0s\n", + "\n", + "Solved in 15 iterations and 0.01 seconds (0.00 work units)\n", + "Optimal objective 2.761000000e+03\n", + "Set parameter LazyConstraints to value 1\n", + "Gurobi Optimizer version 9.5.2 build v9.5.2rc0 (linux64)\n", + "Thread count: 6 physical cores, 12 logical processors, using up to 12 threads\n", + "Optimize a model with 10 rows, 45 columns and 90 nonzeros\n", + "Model fingerprint: 0x74ca3d0a\n", + "Variable types: 0 continuous, 45 integer (45 binary)\n", + "Coefficient statistics:\n", + " Matrix range [1e+00, 1e+00]\n", + " Objective range [4e+01, 1e+03]\n", + " Bounds range [1e+00, 1e+00]\n", + " RHS range [2e+00, 2e+00]\n", + "\n", + "User MIP start produced solution with objective 2796 (0.01s)\n", + "Loaded user MIP start with objective 2796\n", + "\n", + "Presolve time: 0.00s\n", + "Presolved: 10 rows, 45 columns, 90 nonzeros\n", + "Variable types: 0 continuous, 45 integer (45 binary)\n", + "\n", + "Root relaxation: objective 2.761000e+03, 14 iterations, 0.00 seconds (0.00 work units)\n", + "\n", + " Nodes | Current Node | Objective Bounds | Work\n", + " Expl Unexpl | Obj Depth IntInf | Incumbent BestBd Gap | It/Node Time\n", + "\n", + " 0 0 cutoff 0 2796.00000 2796.00000 0.00% - 0s\n", + "\n", + "Cutting planes:\n", + " Lazy constraints: 3\n", + "\n", + "Explored 1 nodes (15 simplex iterations) in 0.02 seconds (0.00 work units)\n", + "Thread count was 12 (of 12 available processors)\n", + "\n", + "Solution count 1: 2796 \n", + "\n", + "Optimal solution found (tolerance 1.00e-04)\n", + "Best objective 2.796000000000e+03, best bound 2.796000000000e+03, gap 0.0000%\n", + "\n", + "User-callback calls 103, time in user-callback 0.00 sec\n", + "Gurobi Optimizer version 9.5.2 build v9.5.2rc0 (linux64)\n", + "Thread count: 6 physical cores, 12 logical processors, using up to 12 threads\n", + "Optimize a model with 10 rows, 45 columns and 90 nonzeros\n", + "Model fingerprint: 0x74ca3d0a\n", + "Variable types: 0 continuous, 45 integer (45 binary)\n", + "Coefficient statistics:\n", + " Matrix range [1e+00, 1e+00]\n", + " Objective range [4e+01, 1e+03]\n", + " Bounds range [1e+00, 1e+00]\n", + " RHS range [2e+00, 2e+00]\n", + "Presolved: 10 rows, 45 columns, 90 nonzeros\n", + "\n", + "Continuing optimization...\n", + "\n", + "\n", + "Cutting planes:\n", + " Lazy constraints: 3\n", + "\n", + "Explored 1 nodes (15 simplex iterations) in 0.01 seconds (0.00 work units)\n", + "Thread count was 12 (of 12 available processors)\n", + "\n", + "Solution count 1: 2796 \n", + "\n", + "Optimal solution found (tolerance 1.00e-04)\n", + "Best objective 2.796000000000e+03, best bound 2.796000000000e+03, gap 0.0000%\n", + "\n", + "User-callback calls 27, time in user-callback 0.00 sec\n" + ] + } + ], + "source": [ + "import random\n", + "\n", + "import numpy as np\n", + "from scipy.stats import uniform, randint\n", + "from sklearn.linear_model import LogisticRegression\n", + "\n", + "from miplearn.classifiers.minprob import MinProbabilityClassifier\n", + "from miplearn.classifiers.singleclass import SingleClassFix\n", + "from miplearn.collectors.basic import BasicCollector\n", + "from miplearn.components.primal.actions import SetWarmStart\n", + "from miplearn.components.primal.indep import IndependentVarsPrimalComponent\n", + "from miplearn.extractors.AlvLouWeh2017 import AlvLouWeh2017Extractor\n", + "from miplearn.io import save\n", + "from miplearn.problems.tsp import (\n", + " TravelingSalesmanGenerator,\n", + " build_tsp_model,\n", + ")\n", + "from miplearn.solvers.learning import LearningSolver\n", + "\n", + "# Set random seed to make example reproducible.\n", + "random.seed(42)\n", + "np.random.seed(42)\n", + "\n", + "# Generate a few instances of the traveling salesman problem.\n", + "data = TravelingSalesmanGenerator(\n", + " n=randint(low=10, high=11),\n", + " x=uniform(loc=0.0, scale=1000.0),\n", + " y=uniform(loc=0.0, scale=1000.0),\n", + " gamma=uniform(loc=0.90, scale=0.20),\n", + " fix_cities=True,\n", + " round=True,\n", + ").generate(50)\n", + "\n", + "# Save instance data to data/tsp/00000.pkl.gz, data/tsp/00001.pkl.gz, ...\n", + "all_data = save(data, \"data/tsp\")\n", + "\n", + "# Split train/test data\n", + "train_data = all_data[:40]\n", + "test_data = all_data[40:]\n", + "\n", + "# Collect training data\n", + "bc = BasicCollector(time_limit_sec=3600)\n", + "bc.collect(train_data, build_tsp_model, n_jobs=4)\n", + "\n", + "# Build learning solver\n", + "solver = LearningSolver(\n", + " components=[\n", + " IndependentVarsPrimalComponent(\n", + " base_clf=SingleClassFix(\n", + " MinProbabilityClassifier(\n", + " base_clf=LogisticRegression(),\n", + " thresholds=[0.95, 0.95],\n", + " ),\n", + " ),\n", + " extractor=AlvLouWeh2017Extractor(),\n", + " action=SetWarmStart(),\n", + " )\n", + " ]\n", + ")\n", + "\n", + "# Train ML models\n", + "solver.fit(train_data)\n", + "\n", + "# Solve a test instance\n", + "solver.optimize(test_data[0], build_tsp_model);" + ], + "metadata": { + "collapsed": false + } + }, + { + "cell_type": "code", + "execution_count": 2, + "id": "e27d2cbd-5341-461d-bbc1-8131aee8d949", + "metadata": {}, + "outputs": [], + "source": [] + } + ], + "metadata": { + "kernelspec": { + "display_name": "Python 3", + "language": "python", + "name": "python3" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.8.13" + } + }, + "nbformat": 4, + "nbformat_minor": 5 +} diff --git a/0.3/_sources/index.rst.txt b/0.3/_sources/index.rst.txt new file mode 100644 index 0000000..92c13f8 --- /dev/null +++ b/0.3/_sources/index.rst.txt @@ -0,0 +1,31 @@ +MIPLearn +======== +**MIPLearn** is an extensible framework for solving discrete optimization problems using a combination of Mixed-Integer Linear Programming (MIP) and Machine Learning (ML). MIPLearn uses ML methods to automatically identify patterns in previously solved instances of the problem, then uses these patterns to accelerate the performance of conventional state-of-the-art MIP solvers such as CPLEX, Gurobi or XPRESS. + +Unlike pure ML methods, MIPLearn is not only able to find high-quality solutions to discrete optimization problems, but it can also prove the optimality and feasibility of these solutions. Unlike conventional MIP solvers, MIPLearn can take full advantage of very specific observations that happen to be true in a particular family of instances (such as the observation that a particular constraint is typically redundant, or that a particular variable typically assumes a certain value). For certain classes of problems, this approach has been shown to provide significant performance benefits (see benchmarks and references). + + +Contents +-------- + +.. toctree:: + :maxdepth: 10 + :caption: User Guide + :numbered: 2 + + guide/problems + guide/collectors + guide/features + guide/primal + guide/solvers + +.. toctree:: + :maxdepth: 10 + :caption: API Reference + :numbered: 2 + + api/problems + api/collectors + api/components + api/solvers + api/helpers diff --git a/0.3/_sources/tutorials/getting-started-jl.ipynb.txt b/0.3/_sources/tutorials/getting-started-jl.ipynb.txt new file mode 100644 index 0000000..5b3ee60 --- /dev/null +++ b/0.3/_sources/tutorials/getting-started-jl.ipynb.txt @@ -0,0 +1,625 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "id": "6b8983b1", + "metadata": { + "tags": [] + }, + "source": [ + "# Getting started (JuMP)\n", + "\n", + "## Introduction\n", + "\n", + "**MIPLearn** is an open source framework that uses machine learning (ML) to accelerate the performance of both commercial and open source mixed-integer programming solvers (e.g. Gurobi, CPLEX, XPRESS, Cbc or SCIP). In this tutorial, we will:\n", + "\n", + "1. Install the Python/Pyomo version of MIPLearn\n", + "2. Model a simple optimization problem using JuMP\n", + "3. Generate training data and train the ML models\n", + "4. Use the ML models together Gurobi to solve new instances\n", + "\n", + "
\n", + "Note\n", + " \n", + "The Python/Pyomo version of MIPLearn is currently only compatible with with Gurobi, CPLEX and XPRESS. For broader solver compatibility, see the Julia/JuMP version of the package.\n", + "
\n", + "\n", + "
\n", + "Warning\n", + " \n", + "MIPLearn is still in early development stage. If run into any bugs or issues, please submit a bug report in our GitHub repository. Comments, suggestions and pull requests are also very welcome!\n", + " \n", + "
\n" + ] + }, + { + "cell_type": "markdown", + "id": "02f0a927", + "metadata": {}, + "source": [ + "## Installation\n", + "\n", + "MIPLearn is available in two versions:\n", + "\n", + "- Python version, compatible with the Pyomo modeling language,\n", + "- Julia version, compatible with the JuMP modeling language.\n", + "\n", + "In this tutorial, we will demonstrate how to use and install the Python/Pyomo version of the package. The first step is to install Python 3.8+ in your computer. See the [official Python website for more instructions](https://www.python.org/downloads/). After Python is installed, we proceed to install MIPLearn using `pip`:" + ] + }, + { + "cell_type": "code", + "execution_count": 1, + "id": "cd8a69c1", + "metadata": {}, + "outputs": [], + "source": [ + "# !pip install MIPLearn==0.2.0.dev13" + ] + }, + { + "cell_type": "markdown", + "id": "e8274543", + "metadata": {}, + "source": [ + "In addition to MIPLearn itself, we will also install Gurobi 9.5, a state-of-the-art commercial MILP solver. This step also install a demo license for Gurobi, which should able to solve the small optimization problems in this tutorial. A paid license is required for solving large-scale problems." + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "id": "dcc8756c", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Looking in indexes: https://pypi.gurobi.com\n", + "Requirement already satisfied: gurobipy<9.6,>=9.5 in /opt/anaconda3/envs/miplearn/lib/python3.8/site-packages (9.5.1)\n" + ] + } + ], + "source": [ + "!pip install --upgrade -i https://pypi.gurobi.com 'gurobipy>=9.5,<9.6'" + ] + }, + { + "cell_type": "markdown", + "id": "a14e4550", + "metadata": {}, + "source": [ + "
\n", + " \n", + "Note\n", + " \n", + "In the code above, we install specific version of all packages to ensure that this tutorial keeps running in the future, even when newer (and possibly incompatible) versions of the packages are released. This is usually a recommended practice for all Python projects.\n", + " \n", + "
" + ] + }, + { + "cell_type": "markdown", + "id": "16b86823", + "metadata": {}, + "source": [ + "## Modeling a simple optimization problem\n", + "\n", + "To illustrate how can MIPLearn be used, we will model and solve a small optimization problem related to power systems optimization. The problem we discuss below is a simplification of the **unit commitment problem,** a practical optimization problem solved daily by electric grid operators around the world. \n", + "\n", + "Suppose that you work at a utility company, and that it is your job to decide which electrical generators should be online at a certain hour of the day, as well as how much power should each generator produce. More specifically, assume that your company owns $n$ generators, denoted by $g_1, \\ldots, g_n$. Each generator can either be online or offline. An online generator $g_i$ can produce between $p^\\text{min}_i$ to $p^\\text{max}_i$ megawatts of power, and it costs your company $c^\\text{fix}_i + c^\\text{var}_i y_i$, where $y_i$ is the amount of power produced. An offline generator produces nothing and costs nothing. You also know that the total amount of power to be produced needs to be exactly equal to the total demand $d$ (in megawatts). To minimize the costs to your company, which generators should be online, and how much power should they produce?\n", + "\n", + "This simple problem can be modeled as a *mixed-integer linear optimization* problem as follows. For each generator $g_i$, let $x_i \\in \\{0,1\\}$ be a decision variable indicating whether $g_i$ is online, and let $y_i \\geq 0$ be a decision variable indicating how much power does $g_i$ produce. The problem is then given by:\n", + "\n", + "$$\n", + "\\begin{align}\n", + "\\text{minimize } \\quad & \\sum_{i=1}^n \\left( c^\\text{fix}_i x_i + c^\\text{var}_i y_i \\right) \\\\\n", + "\\text{subject to } \\quad & y_i \\leq p^\\text{max}_i x_i & i=1,\\ldots,n \\\\\n", + "& y_i \\geq p^\\text{min}_i x_i & i=1,\\ldots,n \\\\\n", + "& \\sum_{i=1}^n y_i = d \\\\\n", + "& x_i \\in \\{0,1\\} & i=1,\\ldots,n \\\\\n", + "& y_i \\geq 0 & i=1,\\ldots,n\n", + "\\end{align}\n", + "$$\n", + "\n", + "
\n", + " \n", + "Note\n", + " \n", + "We use a simplified version of the unit commitment problem in this tutorial just to make it easier to follow. MIPLearn can also handle realistic, large-scale versions of this problem. See benchmarks for more details.\n", + " \n", + "
\n", + "\n", + "Next, let us convert this abstract mathematical formulation into a concrete optimization model, using Python and Pyomo. We start by defining a data class `UnitCommitmentData`, which holds all the input data." + ] + }, + { + "cell_type": "code", + "execution_count": 3, + "id": "22a67170-10b4-43d3-8708-014d91141e73", + "metadata": { + "tags": [] + }, + "outputs": [], + "source": [ + "from dataclasses import dataclass\n", + "import numpy as np\n", + "\n", + "@dataclass\n", + "class UnitCommitmentData:\n", + " demand: float\n", + " pmin: np.ndarray\n", + " pmax: np.ndarray\n", + " cfix: np.ndarray\n", + " cvar: np.ndarray" + ] + }, + { + "cell_type": "markdown", + "id": "29f55efa-0751-465a-9b0a-a821d46a3d40", + "metadata": {}, + "source": [ + "Next, we write a `build_uc_model` function, which converts the input data into a concrete Pyomo model." + ] + }, + { + "cell_type": "code", + "execution_count": 4, + "id": "2f67032f-0d74-4317-b45c-19da0ec859e9", + "metadata": {}, + "outputs": [], + "source": [ + "import pyomo.environ as pe\n", + "\n", + "def build_uc_model(data: UnitCommitmentData) -> pe.ConcreteModel:\n", + " model = pe.ConcreteModel()\n", + " n = len(data.pmin)\n", + " model.x = pe.Var(range(n), domain=pe.Binary)\n", + " model.y = pe.Var(range(n), domain=pe.NonNegativeReals)\n", + " model.obj = pe.Objective(\n", + " expr=sum(\n", + " data.cfix[i] * model.x[i] +\n", + " data.cvar[i] * model.y[i]\n", + " for i in range(n)\n", + " )\n", + " )\n", + " model.eq_max_power = pe.ConstraintList()\n", + " model.eq_min_power = pe.ConstraintList()\n", + " for i in range(n):\n", + " model.eq_max_power.add(model.y[i] <= data.pmax[i] * model.x[i])\n", + " model.eq_min_power.add(model.y[i] >= data.pmin[i] * model.x[i])\n", + " model.eq_demand = pe.Constraint(\n", + " expr=sum(model.y[i] for i in range(n)) == data.demand,\n", + " )\n", + " return model" + ] + }, + { + "cell_type": "markdown", + "id": "c22714a3", + "metadata": {}, + "source": [ + "At this point, we can already use Pyomo and any mixed-integer linear programming solver to find optimal solutions to any instance of this problem. To illustrate this, let us solve a small instance with three generators:" + ] + }, + { + "cell_type": "code", + "execution_count": 5, + "id": "2a896f47", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Set parameter Threads to value 1\n", + "Set parameter Seed to value 42\n", + "Restricted license - for non-production use only - expires 2023-10-25\n", + "obj = 1320.0\n", + "x = [-0.0, 1.0, 1.0]\n", + "y = [0.0, 60.0, 40.0]\n" + ] + } + ], + "source": [ + "model = build_uc_model(\n", + " UnitCommitmentData(\n", + " demand = 100.0,\n", + " pmin = [10, 20, 30],\n", + " pmax = [50, 60, 70],\n", + " cfix = [700, 600, 500],\n", + " cvar = [1.5, 2.0, 2.5],\n", + " )\n", + ")\n", + "\n", + "solver = pe.SolverFactory(\"gurobi_persistent\")\n", + "solver.set_instance(model)\n", + "solver.solve()\n", + "print(\"obj =\", model.obj())\n", + "print(\"x =\", [model.x[i].value for i in range(3)])\n", + "print(\"y =\", [model.y[i].value for i in range(3)])" + ] + }, + { + "cell_type": "markdown", + "id": "41b03bbc", + "metadata": {}, + "source": [ + "Running the code above, we found that the optimal solution for our small problem instance costs \\$1320. It is achieve by keeping generators 2 and 3 online and producing, respectively, 60 MW and 40 MW of power." + ] + }, + { + "cell_type": "markdown", + "id": "cf60c1dd", + "metadata": {}, + "source": [ + "## Generating training data\n", + "\n", + "Although Gurobi could solve the small example above in a fraction of a second, it gets slower for larger and more complex versions of the problem. If this is a problem that needs to be solved frequently, as it is often the case in practice, it could make sense to spend some time upfront generating a **trained** version of Gurobi, which can solve new instances (similar to the ones it was trained on) faster.\n", + "\n", + "In the following, we will use MIPLearn to train machine learning models that is able to predict the optimal solution for instances that follow a given probability distribution, then it will provide this predicted solution to Gurobi as a warm start. Before we can train the model, we need to collect training data by solving a large number of instances. In real-world situations, we may construct these training instances based on historical data. In this tutorial, we will construct them using a random instance generator:" + ] + }, + { + "cell_type": "code", + "execution_count": 6, + "id": "5eb09fab", + "metadata": {}, + "outputs": [], + "source": [ + "from scipy.stats import uniform\n", + "from typing import List\n", + "import random\n", + "\n", + "def random_uc_data(samples: int, n: int, seed: int = 42) -> List[UnitCommitmentData]:\n", + " random.seed(seed)\n", + " np.random.seed(seed)\n", + " pmin = uniform(loc=100_000.0, scale=400_000.0).rvs(n)\n", + " pmax = pmin * uniform(loc=2.0, scale=2.5).rvs(n)\n", + " cfix = pmin * uniform(loc=100.0, scale=25.0).rvs(n)\n", + " cvar = uniform(loc=1.25, scale=0.25).rvs(n)\n", + " return [\n", + " UnitCommitmentData(\n", + " demand = pmax.sum() * uniform(loc=0.5, scale=0.25).rvs(),\n", + " pmin = pmin,\n", + " pmax = pmax,\n", + " cfix = cfix,\n", + " cvar = cvar,\n", + " )\n", + " for i in range(samples)\n", + " ]" + ] + }, + { + "cell_type": "markdown", + "id": "3a03a7ac", + "metadata": {}, + "source": [ + "In this example, for simplicity, only the demands change from one instance to the next. We could also have randomized the costs, production limits or even the number of units. The more randomization we have in the training data, however, the more challenging it is for the machine learning models to learn solution patterns.\n", + "\n", + "Now we generate 500 instances of this problem, each one with 50 generators, and we use 450 of these instances for training. After generating the instances, we write them to individual files. MIPLearn uses files during the training process because, for large-scale optimization problems, it is often impractical to hold in memory the entire training data, as well as the concrete Pyomo models. Files also make it much easier to solve multiple instances simultaneously, potentially even on multiple machines. We will cover parallel and distributed computing in a future tutorial. The code below generates the files `uc/train/00000.pkl.gz`, `uc/train/00001.pkl.gz`, etc., which contain the input data in compressed (gzipped) pickle format." + ] + }, + { + "cell_type": "code", + "execution_count": 7, + "id": "6156752c", + "metadata": {}, + "outputs": [], + "source": [ + "from miplearn import save\n", + "data = random_uc_data(samples=500, n=50)\n", + "train_files = save(data[0:450], \"uc/train/\")\n", + "test_files = save(data[450:500], \"uc/test/\")" + ] + }, + { + "cell_type": "markdown", + "id": "b17af877", + "metadata": {}, + "source": [ + "Finally, we use `LearningSolver` to solve all the training instances. `LearningSolver` is the main component provided by MIPLearn, which integrates MIP solvers and ML. The optimal solutions, along with other useful training data, are stored in HDF5 files `uc/train/00000.h5`, `uc/train/00001.h5`, etc." + ] + }, + { + "cell_type": "code", + "execution_count": 12, + "id": "7623f002", + "metadata": {}, + "outputs": [], + "source": [ + "from miplearn import LearningSolver\n", + "solver = LearningSolver()\n", + "solver.solve(train_files, build_uc_model);" + ] + }, + { + "cell_type": "markdown", + "id": "2f24ee83", + "metadata": {}, + "source": [ + "## Solving test instances\n", + "\n", + "With training data in hand, we can now fit the ML models, using the `LearningSolver.fit` method, then solve the test instances with `LearningSolver.solve`, as shown below. The `tee=True` parameter asks MIPLearn to print the solver log to the screen." + ] + }, + { + "cell_type": "code", + "execution_count": 9, + "id": "c8385030", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Set parameter LogFile to value \"/tmp/tmpvbaqbyty.log\"\n", + "Set parameter QCPDual to value 1\n", + "Gurobi Optimizer version 9.5.1 build v9.5.1rc2 (linux64)\n", + "Thread count: 16 physical cores, 32 logical processors, using up to 1 threads\n", + "Optimize a model with 101 rows, 100 columns and 250 nonzeros\n", + "Model fingerprint: 0x8de73876\n", + "Coefficient statistics:\n", + " Matrix range [1e+00, 2e+06]\n", + " Objective range [1e+00, 6e+07]\n", + " Bounds range [1e+00, 1e+00]\n", + " RHS range [2e+07, 2e+07]\n", + "Presolve removed 100 rows and 50 columns\n", + "Presolve time: 0.00s\n", + "Presolved: 1 rows, 50 columns, 50 nonzeros\n", + "\n", + "Iteration Objective Primal Inf. Dual Inf. Time\n", + " 0 5.7349081e+08 1.044003e+04 0.000000e+00 0s\n", + " 1 6.8268465e+08 0.000000e+00 0.000000e+00 0s\n", + "\n", + "Solved in 1 iterations and 0.00 seconds (0.00 work units)\n", + "Optimal objective 6.826846503e+08\n", + "Set parameter LogFile to value \"\"\n", + "Set parameter LogFile to value \"/tmp/tmp48j6n35b.log\"\n", + "Gurobi Optimizer version 9.5.1 build v9.5.1rc2 (linux64)\n", + "Thread count: 16 physical cores, 32 logical processors, using up to 1 threads\n", + "Optimize a model with 101 rows, 100 columns and 250 nonzeros\n", + "Model fingerprint: 0x200d64ba\n", + "Variable types: 50 continuous, 50 integer (50 binary)\n", + "Coefficient statistics:\n", + " Matrix range [1e+00, 2e+06]\n", + " Objective range [1e+00, 6e+07]\n", + " Bounds range [1e+00, 1e+00]\n", + " RHS range [2e+07, 2e+07]\n", + "\n", + "User MIP start produced solution with objective 6.84841e+08 (0.00s)\n", + "Loaded user MIP start with objective 6.84841e+08\n", + "\n", + "Presolve time: 0.00s\n", + "Presolved: 101 rows, 100 columns, 250 nonzeros\n", + "Variable types: 50 continuous, 50 integer (50 binary)\n", + "\n", + "Root relaxation: objective 6.826847e+08, 56 iterations, 0.00 seconds (0.00 work units)\n", + "\n", + " Nodes | Current Node | Objective Bounds | Work\n", + " Expl Unexpl | Obj Depth IntInf | Incumbent BestBd Gap | It/Node Time\n", + "\n", + " 0 0 6.8268e+08 0 1 6.8484e+08 6.8268e+08 0.31% - 0s\n", + " 0 0 6.8315e+08 0 3 6.8484e+08 6.8315e+08 0.25% - 0s\n", + " 0 0 6.8315e+08 0 1 6.8484e+08 6.8315e+08 0.25% - 0s\n", + " 0 0 6.8315e+08 0 3 6.8484e+08 6.8315e+08 0.25% - 0s\n", + " 0 0 6.8315e+08 0 4 6.8484e+08 6.8315e+08 0.25% - 0s\n", + " 0 0 6.8315e+08 0 4 6.8484e+08 6.8315e+08 0.25% - 0s\n", + " 0 2 6.8327e+08 0 4 6.8484e+08 6.8327e+08 0.23% - 0s\n", + "\n", + "Cutting planes:\n", + " Flow cover: 3\n", + "\n", + "Explored 32 nodes (155 simplex iterations) in 0.02 seconds (0.00 work units)\n", + "Thread count was 1 (of 32 available processors)\n", + "\n", + "Solution count 1: 6.84841e+08 \n", + "\n", + "Optimal solution found (tolerance 1.00e-04)\n", + "Best objective 6.848411655488e+08, best bound 6.848411655488e+08, gap 0.0000%\n", + "Set parameter LogFile to value \"\"\n", + "WARNING: Cannot get reduced costs for MIP.\n", + "WARNING: Cannot get duals for MIP.\n" + ] + } + ], + "source": [ + "solver_ml = LearningSolver()\n", + "solver_ml.fit(train_files, build_uc_model)\n", + "solver_ml.solve(test_files[0:1], build_uc_model, tee=True);" + ] + }, + { + "cell_type": "markdown", + "id": "61da6dad-7f56-4edb-aa26-c00eb5f946c0", + "metadata": {}, + "source": [ + "By examining the solve log above, specifically the line `Loaded user MIP start with objective...`, we can see that MIPLearn was able to construct an initial solution which turned out to be the optimal solution to the problem. Now let us repeat the code above, but using an untrained solver. Note that the `fit` line is omitted." + ] + }, + { + "cell_type": "code", + "execution_count": 10, + "id": "33d15d6c-6db4-477f-bd4b-fe8e84e5f023", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Set parameter LogFile to value \"/tmp/tmp3uhhdurw.log\"\n", + "Set parameter QCPDual to value 1\n", + "Gurobi Optimizer version 9.5.1 build v9.5.1rc2 (linux64)\n", + "Thread count: 16 physical cores, 32 logical processors, using up to 1 threads\n", + "Optimize a model with 101 rows, 100 columns and 250 nonzeros\n", + "Model fingerprint: 0x8de73876\n", + "Coefficient statistics:\n", + " Matrix range [1e+00, 2e+06]\n", + " Objective range [1e+00, 6e+07]\n", + " Bounds range [1e+00, 1e+00]\n", + " RHS range [2e+07, 2e+07]\n", + "Presolve removed 100 rows and 50 columns\n", + "Presolve time: 0.00s\n", + "Presolved: 1 rows, 50 columns, 50 nonzeros\n", + "\n", + "Iteration Objective Primal Inf. Dual Inf. Time\n", + " 0 5.7349081e+08 1.044003e+04 0.000000e+00 0s\n", + " 1 6.8268465e+08 0.000000e+00 0.000000e+00 0s\n", + "\n", + "Solved in 1 iterations and 0.01 seconds (0.00 work units)\n", + "Optimal objective 6.826846503e+08\n", + "Set parameter LogFile to value \"\"\n", + "Set parameter LogFile to value \"/tmp/tmp18aqg2ic.log\"\n", + "Gurobi Optimizer version 9.5.1 build v9.5.1rc2 (linux64)\n", + "Thread count: 16 physical cores, 32 logical processors, using up to 1 threads\n", + "Optimize a model with 101 rows, 100 columns and 250 nonzeros\n", + "Model fingerprint: 0xb90d1075\n", + "Variable types: 50 continuous, 50 integer (50 binary)\n", + "Coefficient statistics:\n", + " Matrix range [1e+00, 2e+06]\n", + " Objective range [1e+00, 6e+07]\n", + " Bounds range [1e+00, 1e+00]\n", + " RHS range [2e+07, 2e+07]\n", + "Found heuristic solution: objective 8.056576e+08\n", + "Presolve time: 0.00s\n", + "Presolved: 101 rows, 100 columns, 250 nonzeros\n", + "Variable types: 50 continuous, 50 integer (50 binary)\n", + "\n", + "Root relaxation: objective 6.826847e+08, 56 iterations, 0.00 seconds (0.00 work units)\n", + "\n", + " Nodes | Current Node | Objective Bounds | Work\n", + " Expl Unexpl | Obj Depth IntInf | Incumbent BestBd Gap | It/Node Time\n", + "\n", + " 0 0 6.8268e+08 0 1 8.0566e+08 6.8268e+08 15.3% - 0s\n", + "H 0 0 7.099498e+08 6.8268e+08 3.84% - 0s\n", + " 0 0 6.8315e+08 0 3 7.0995e+08 6.8315e+08 3.78% - 0s\n", + "H 0 0 6.883227e+08 6.8315e+08 0.75% - 0s\n", + " 0 0 6.8352e+08 0 4 6.8832e+08 6.8352e+08 0.70% - 0s\n", + " 0 0 6.8352e+08 0 4 6.8832e+08 6.8352e+08 0.70% - 0s\n", + " 0 0 6.8352e+08 0 1 6.8832e+08 6.8352e+08 0.70% - 0s\n", + "H 0 0 6.862582e+08 6.8352e+08 0.40% - 0s\n", + " 0 0 6.8352e+08 0 4 6.8626e+08 6.8352e+08 0.40% - 0s\n", + " 0 0 6.8352e+08 0 4 6.8626e+08 6.8352e+08 0.40% - 0s\n", + " 0 0 6.8352e+08 0 1 6.8626e+08 6.8352e+08 0.40% - 0s\n", + " 0 0 6.8352e+08 0 3 6.8626e+08 6.8352e+08 0.40% - 0s\n", + " 0 0 6.8352e+08 0 4 6.8626e+08 6.8352e+08 0.40% - 0s\n", + " 0 0 6.8352e+08 0 4 6.8626e+08 6.8352e+08 0.40% - 0s\n", + " 0 2 6.8354e+08 0 4 6.8626e+08 6.8354e+08 0.40% - 0s\n", + "* 18 5 6 6.849018e+08 6.8413e+08 0.11% 3.1 0s\n", + "H 24 1 6.848412e+08 6.8426e+08 0.09% 3.2 0s\n", + "\n", + "Cutting planes:\n", + " Gomory: 1\n", + " Flow cover: 2\n", + "\n", + "Explored 30 nodes (217 simplex iterations) in 0.02 seconds (0.00 work units)\n", + "Thread count was 1 (of 32 available processors)\n", + "\n", + "Solution count 6: 6.84841e+08 6.84902e+08 6.86258e+08 ... 8.05658e+08\n", + "\n", + "Optimal solution found (tolerance 1.00e-04)\n", + "Best objective 6.848411655488e+08, best bound 6.848411655488e+08, gap 0.0000%\n", + "Set parameter LogFile to value \"\"\n", + "WARNING: Cannot get reduced costs for MIP.\n", + "WARNING: Cannot get duals for MIP.\n" + ] + } + ], + "source": [ + "solver_baseline = LearningSolver()\n", + "solver_baseline.solve(test_files[0:1], build_uc_model, tee=True);" + ] + }, + { + "cell_type": "markdown", + "id": "b6d37b88-9fcc-43ee-ac1e-2a7b1e51a266", + "metadata": {}, + "source": [ + "In the log above, the `MIP start` line is missing, and Gurobi had to start with a significantly inferior initial solution. The solver was still able to find the optimal solution at the end, but it required using its own internal heuristic procedures. In this example, because we solve very small optimization problems, there was almost no difference in terms of running time. For larger problems, however, the difference can be significant. See benchmarks for more details.\n", + "\n", + "
\n", + "Note\n", + " \n", + "In addition to partial initial solutions, MIPLearn is also able to predict lazy constraints, cutting planes and branching priorities. See the next tutorials for more details.\n", + "
\n", + "\n", + "
\n", + "Note\n", + " \n", + "It is not necessary to specify what ML models to use. MIPLearn, by default, will try a number of classical ML models and will choose the one that performs the best, based on k-fold cross validation. MIPLearn is also able to automatically collect features based on the MIP formulation of the problem and the solution to the LP relaxation, among other things, so it does not require handcrafted features. If you do want to customize the models and features, however, that is also possible, as we will see in a later tutorial.\n", + "
" + ] + }, + { + "cell_type": "markdown", + "id": "eec97f06", + "metadata": { + "tags": [] + }, + "source": [ + "## Accessing the solution\n", + "\n", + "In the example above, we used `LearningSolver.solve` together with data files to solve both the training and the test instances. The optimal solutions were saved to HDF5 files in the train/test folders, and could be retrieved by reading theses files, but that is not very convenient. In the following example, we show how to build and solve a Pyomo model entirely in-memory, using our trained solver." + ] + }, + { + "cell_type": "code", + "execution_count": 11, + "id": "67a6cd18", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "obj = 903865807.3536932\n", + " x = [1.0, 1.0, 1.0, 1.0, 1.0]\n", + " y = [1105176.593734543, 1891284.5155055337, 1708177.4224033852, 1438329.610189608, 535496.3347187206]\n" + ] + } + ], + "source": [ + "# Construct model using previously defined functions\n", + "data = random_uc_data(samples=1, n=50)[0]\n", + "model = build_uc_model(data)\n", + "\n", + "# Solve model using ML + Gurobi\n", + "solver_ml.solve(model)\n", + "\n", + "# Print part of the optimal solution\n", + "print(\"obj =\", model.obj())\n", + "print(\" x =\", [model.x[i].value for i in range(5)])\n", + "print(\" y =\", [model.y[i].value for i in range(5)])" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "5593d23a-83bd-4e16-8253-6300f5e3f63b", + "metadata": {}, + "outputs": [], + "source": [] + } + ], + "metadata": { + "kernelspec": { + "display_name": "Python 3", + "language": "python", + "name": "python3" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.8.13" + } + }, + "nbformat": 4, + "nbformat_minor": 5 +} diff --git a/0.3/_sources/tutorials/getting-started-pyomo.ipynb.txt b/0.3/_sources/tutorials/getting-started-pyomo.ipynb.txt new file mode 100644 index 0000000..55c5830 --- /dev/null +++ b/0.3/_sources/tutorials/getting-started-pyomo.ipynb.txt @@ -0,0 +1,625 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "id": "6b8983b1", + "metadata": { + "tags": [] + }, + "source": [ + "# Getting started (Pyomo)\n", + "\n", + "## Introduction\n", + "\n", + "**MIPLearn** is an open source framework that uses machine learning (ML) to accelerate the performance of both commercial and open source mixed-integer programming solvers (e.g. Gurobi, CPLEX, XPRESS, Cbc or SCIP). In this tutorial, we will:\n", + "\n", + "1. Install the Python/Pyomo version of MIPLearn\n", + "2. Model a simple optimization problem using JuMP\n", + "3. Generate training data and train the ML models\n", + "4. Use the ML models together Gurobi to solve new instances\n", + "\n", + "
\n", + "Note\n", + " \n", + "The Python/Pyomo version of MIPLearn is currently only compatible with with Gurobi, CPLEX and XPRESS. For broader solver compatibility, see the Julia/JuMP version of the package.\n", + "
\n", + "\n", + "
\n", + "Warning\n", + " \n", + "MIPLearn is still in early development stage. If run into any bugs or issues, please submit a bug report in our GitHub repository. Comments, suggestions and pull requests are also very welcome!\n", + " \n", + "
\n" + ] + }, + { + "cell_type": "markdown", + "id": "02f0a927", + "metadata": {}, + "source": [ + "## Installation\n", + "\n", + "MIPLearn is available in two versions:\n", + "\n", + "- Python version, compatible with the Pyomo modeling language,\n", + "- Julia version, compatible with the JuMP modeling language.\n", + "\n", + "In this tutorial, we will demonstrate how to use and install the Python/Pyomo version of the package. The first step is to install Python 3.8+ in your computer. See the [official Python website for more instructions](https://www.python.org/downloads/). After Python is installed, we proceed to install MIPLearn using `pip`:" + ] + }, + { + "cell_type": "code", + "execution_count": 1, + "id": "cd8a69c1", + "metadata": {}, + "outputs": [], + "source": [ + "# !pip install MIPLearn==0.2.0.dev13" + ] + }, + { + "cell_type": "markdown", + "id": "e8274543", + "metadata": {}, + "source": [ + "In addition to MIPLearn itself, we will also install Gurobi 9.5, a state-of-the-art commercial MILP solver. This step also install a demo license for Gurobi, which should able to solve the small optimization problems in this tutorial. A paid license is required for solving large-scale problems." + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "id": "dcc8756c", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Looking in indexes: https://pypi.gurobi.com\n", + "Requirement already satisfied: gurobipy<9.6,>=9.5 in /opt/anaconda3/envs/miplearn/lib/python3.8/site-packages (9.5.1)\n" + ] + } + ], + "source": [ + "!pip install --upgrade -i https://pypi.gurobi.com 'gurobipy>=9.5,<9.6'" + ] + }, + { + "cell_type": "markdown", + "id": "a14e4550", + "metadata": {}, + "source": [ + "
\n", + " \n", + "Note\n", + " \n", + "In the code above, we install specific version of all packages to ensure that this tutorial keeps running in the future, even when newer (and possibly incompatible) versions of the packages are released. This is usually a recommended practice for all Python projects.\n", + " \n", + "
" + ] + }, + { + "cell_type": "markdown", + "id": "16b86823", + "metadata": {}, + "source": [ + "## Modeling a simple optimization problem\n", + "\n", + "To illustrate how can MIPLearn be used, we will model and solve a small optimization problem related to power systems optimization. The problem we discuss below is a simplification of the **unit commitment problem,** a practical optimization problem solved daily by electric grid operators around the world. \n", + "\n", + "Suppose that you work at a utility company, and that it is your job to decide which electrical generators should be online at a certain hour of the day, as well as how much power should each generator produce. More specifically, assume that your company owns $n$ generators, denoted by $g_1, \\ldots, g_n$. Each generator can either be online or offline. An online generator $g_i$ can produce between $p^\\text{min}_i$ to $p^\\text{max}_i$ megawatts of power, and it costs your company $c^\\text{fix}_i + c^\\text{var}_i y_i$, where $y_i$ is the amount of power produced. An offline generator produces nothing and costs nothing. You also know that the total amount of power to be produced needs to be exactly equal to the total demand $d$ (in megawatts). To minimize the costs to your company, which generators should be online, and how much power should they produce?\n", + "\n", + "This simple problem can be modeled as a *mixed-integer linear optimization* problem as follows. For each generator $g_i$, let $x_i \\in \\{0,1\\}$ be a decision variable indicating whether $g_i$ is online, and let $y_i \\geq 0$ be a decision variable indicating how much power does $g_i$ produce. The problem is then given by:\n", + "\n", + "$$\n", + "\\begin{align}\n", + "\\text{minimize } \\quad & \\sum_{i=1}^n \\left( c^\\text{fix}_i x_i + c^\\text{var}_i y_i \\right) \\\\\n", + "\\text{subject to } \\quad & y_i \\leq p^\\text{max}_i x_i & i=1,\\ldots,n \\\\\n", + "& y_i \\geq p^\\text{min}_i x_i & i=1,\\ldots,n \\\\\n", + "& \\sum_{i=1}^n y_i = d \\\\\n", + "& x_i \\in \\{0,1\\} & i=1,\\ldots,n \\\\\n", + "& y_i \\geq 0 & i=1,\\ldots,n\n", + "\\end{align}\n", + "$$\n", + "\n", + "
\n", + " \n", + "Note\n", + " \n", + "We use a simplified version of the unit commitment problem in this tutorial just to make it easier to follow. MIPLearn can also handle realistic, large-scale versions of this problem. See benchmarks for more details.\n", + " \n", + "
\n", + "\n", + "Next, let us convert this abstract mathematical formulation into a concrete optimization model, using Python and Pyomo. We start by defining a data class `UnitCommitmentData`, which holds all the input data." + ] + }, + { + "cell_type": "code", + "execution_count": 3, + "id": "22a67170-10b4-43d3-8708-014d91141e73", + "metadata": { + "tags": [] + }, + "outputs": [], + "source": [ + "from dataclasses import dataclass\n", + "import numpy as np\n", + "\n", + "@dataclass\n", + "class UnitCommitmentData:\n", + " demand: float\n", + " pmin: np.ndarray\n", + " pmax: np.ndarray\n", + " cfix: np.ndarray\n", + " cvar: np.ndarray" + ] + }, + { + "cell_type": "markdown", + "id": "29f55efa-0751-465a-9b0a-a821d46a3d40", + "metadata": {}, + "source": [ + "Next, we write a `build_uc_model` function, which converts the input data into a concrete Pyomo model." + ] + }, + { + "cell_type": "code", + "execution_count": 4, + "id": "2f67032f-0d74-4317-b45c-19da0ec859e9", + "metadata": {}, + "outputs": [], + "source": [ + "import pyomo.environ as pe\n", + "\n", + "def build_uc_model(data: UnitCommitmentData) -> pe.ConcreteModel:\n", + " model = pe.ConcreteModel()\n", + " n = len(data.pmin)\n", + " model.x = pe.Var(range(n), domain=pe.Binary)\n", + " model.y = pe.Var(range(n), domain=pe.NonNegativeReals)\n", + " model.obj = pe.Objective(\n", + " expr=sum(\n", + " data.cfix[i] * model.x[i] +\n", + " data.cvar[i] * model.y[i]\n", + " for i in range(n)\n", + " )\n", + " )\n", + " model.eq_max_power = pe.ConstraintList()\n", + " model.eq_min_power = pe.ConstraintList()\n", + " for i in range(n):\n", + " model.eq_max_power.add(model.y[i] <= data.pmax[i] * model.x[i])\n", + " model.eq_min_power.add(model.y[i] >= data.pmin[i] * model.x[i])\n", + " model.eq_demand = pe.Constraint(\n", + " expr=sum(model.y[i] for i in range(n)) == data.demand,\n", + " )\n", + " return model" + ] + }, + { + "cell_type": "markdown", + "id": "c22714a3", + "metadata": {}, + "source": [ + "At this point, we can already use Pyomo and any mixed-integer linear programming solver to find optimal solutions to any instance of this problem. To illustrate this, let us solve a small instance with three generators:" + ] + }, + { + "cell_type": "code", + "execution_count": 5, + "id": "2a896f47", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Set parameter Threads to value 1\n", + "Set parameter Seed to value 42\n", + "Restricted license - for non-production use only - expires 2023-10-25\n", + "obj = 1320.0\n", + "x = [-0.0, 1.0, 1.0]\n", + "y = [0.0, 60.0, 40.0]\n" + ] + } + ], + "source": [ + "model = build_uc_model(\n", + " UnitCommitmentData(\n", + " demand = 100.0,\n", + " pmin = [10, 20, 30],\n", + " pmax = [50, 60, 70],\n", + " cfix = [700, 600, 500],\n", + " cvar = [1.5, 2.0, 2.5],\n", + " )\n", + ")\n", + "\n", + "solver = pe.SolverFactory(\"gurobi_persistent\")\n", + "solver.set_instance(model)\n", + "solver.solve()\n", + "print(\"obj =\", model.obj())\n", + "print(\"x =\", [model.x[i].value for i in range(3)])\n", + "print(\"y =\", [model.y[i].value for i in range(3)])" + ] + }, + { + "cell_type": "markdown", + "id": "41b03bbc", + "metadata": {}, + "source": [ + "Running the code above, we found that the optimal solution for our small problem instance costs \\$1320. It is achieve by keeping generators 2 and 3 online and producing, respectively, 60 MW and 40 MW of power." + ] + }, + { + "cell_type": "markdown", + "id": "cf60c1dd", + "metadata": {}, + "source": [ + "## Generating training data\n", + "\n", + "Although Gurobi could solve the small example above in a fraction of a second, it gets slower for larger and more complex versions of the problem. If this is a problem that needs to be solved frequently, as it is often the case in practice, it could make sense to spend some time upfront generating a **trained** version of Gurobi, which can solve new instances (similar to the ones it was trained on) faster.\n", + "\n", + "In the following, we will use MIPLearn to train machine learning models that is able to predict the optimal solution for instances that follow a given probability distribution, then it will provide this predicted solution to Gurobi as a warm start. Before we can train the model, we need to collect training data by solving a large number of instances. In real-world situations, we may construct these training instances based on historical data. In this tutorial, we will construct them using a random instance generator:" + ] + }, + { + "cell_type": "code", + "execution_count": 6, + "id": "5eb09fab", + "metadata": {}, + "outputs": [], + "source": [ + "from scipy.stats import uniform\n", + "from typing import List\n", + "import random\n", + "\n", + "def random_uc_data(samples: int, n: int, seed: int = 42) -> List[UnitCommitmentData]:\n", + " random.seed(seed)\n", + " np.random.seed(seed)\n", + " pmin = uniform(loc=100_000.0, scale=400_000.0).rvs(n)\n", + " pmax = pmin * uniform(loc=2.0, scale=2.5).rvs(n)\n", + " cfix = pmin * uniform(loc=100.0, scale=25.0).rvs(n)\n", + " cvar = uniform(loc=1.25, scale=0.25).rvs(n)\n", + " return [\n", + " UnitCommitmentData(\n", + " demand = pmax.sum() * uniform(loc=0.5, scale=0.25).rvs(),\n", + " pmin = pmin,\n", + " pmax = pmax,\n", + " cfix = cfix,\n", + " cvar = cvar,\n", + " )\n", + " for i in range(samples)\n", + " ]" + ] + }, + { + "cell_type": "markdown", + "id": "3a03a7ac", + "metadata": {}, + "source": [ + "In this example, for simplicity, only the demands change from one instance to the next. We could also have randomized the costs, production limits or even the number of units. The more randomization we have in the training data, however, the more challenging it is for the machine learning models to learn solution patterns.\n", + "\n", + "Now we generate 500 instances of this problem, each one with 50 generators, and we use 450 of these instances for training. After generating the instances, we write them to individual files. MIPLearn uses files during the training process because, for large-scale optimization problems, it is often impractical to hold in memory the entire training data, as well as the concrete Pyomo models. Files also make it much easier to solve multiple instances simultaneously, potentially even on multiple machines. We will cover parallel and distributed computing in a future tutorial. The code below generates the files `uc/train/00000.pkl.gz`, `uc/train/00001.pkl.gz`, etc., which contain the input data in compressed (gzipped) pickle format." + ] + }, + { + "cell_type": "code", + "execution_count": 7, + "id": "6156752c", + "metadata": {}, + "outputs": [], + "source": [ + "from miplearn import save\n", + "data = random_uc_data(samples=500, n=50)\n", + "train_files = save(data[0:450], \"uc/train/\")\n", + "test_files = save(data[450:500], \"uc/test/\")" + ] + }, + { + "cell_type": "markdown", + "id": "b17af877", + "metadata": {}, + "source": [ + "Finally, we use `LearningSolver` to solve all the training instances. `LearningSolver` is the main component provided by MIPLearn, which integrates MIP solvers and ML. The optimal solutions, along with other useful training data, are stored in HDF5 files `uc/train/00000.h5`, `uc/train/00001.h5`, etc." + ] + }, + { + "cell_type": "code", + "execution_count": 12, + "id": "7623f002", + "metadata": {}, + "outputs": [], + "source": [ + "from miplearn import LearningSolver\n", + "solver = LearningSolver()\n", + "solver.solve(train_files, build_uc_model);" + ] + }, + { + "cell_type": "markdown", + "id": "2f24ee83", + "metadata": {}, + "source": [ + "## Solving test instances\n", + "\n", + "With training data in hand, we can now fit the ML models, using the `LearningSolver.fit` method, then solve the test instances with `LearningSolver.solve`, as shown below. The `tee=True` parameter asks MIPLearn to print the solver log to the screen." + ] + }, + { + "cell_type": "code", + "execution_count": 9, + "id": "c8385030", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Set parameter LogFile to value \"/tmp/tmpvbaqbyty.log\"\n", + "Set parameter QCPDual to value 1\n", + "Gurobi Optimizer version 9.5.1 build v9.5.1rc2 (linux64)\n", + "Thread count: 16 physical cores, 32 logical processors, using up to 1 threads\n", + "Optimize a model with 101 rows, 100 columns and 250 nonzeros\n", + "Model fingerprint: 0x8de73876\n", + "Coefficient statistics:\n", + " Matrix range [1e+00, 2e+06]\n", + " Objective range [1e+00, 6e+07]\n", + " Bounds range [1e+00, 1e+00]\n", + " RHS range [2e+07, 2e+07]\n", + "Presolve removed 100 rows and 50 columns\n", + "Presolve time: 0.00s\n", + "Presolved: 1 rows, 50 columns, 50 nonzeros\n", + "\n", + "Iteration Objective Primal Inf. Dual Inf. Time\n", + " 0 5.7349081e+08 1.044003e+04 0.000000e+00 0s\n", + " 1 6.8268465e+08 0.000000e+00 0.000000e+00 0s\n", + "\n", + "Solved in 1 iterations and 0.00 seconds (0.00 work units)\n", + "Optimal objective 6.826846503e+08\n", + "Set parameter LogFile to value \"\"\n", + "Set parameter LogFile to value \"/tmp/tmp48j6n35b.log\"\n", + "Gurobi Optimizer version 9.5.1 build v9.5.1rc2 (linux64)\n", + "Thread count: 16 physical cores, 32 logical processors, using up to 1 threads\n", + "Optimize a model with 101 rows, 100 columns and 250 nonzeros\n", + "Model fingerprint: 0x200d64ba\n", + "Variable types: 50 continuous, 50 integer (50 binary)\n", + "Coefficient statistics:\n", + " Matrix range [1e+00, 2e+06]\n", + " Objective range [1e+00, 6e+07]\n", + " Bounds range [1e+00, 1e+00]\n", + " RHS range [2e+07, 2e+07]\n", + "\n", + "User MIP start produced solution with objective 6.84841e+08 (0.00s)\n", + "Loaded user MIP start with objective 6.84841e+08\n", + "\n", + "Presolve time: 0.00s\n", + "Presolved: 101 rows, 100 columns, 250 nonzeros\n", + "Variable types: 50 continuous, 50 integer (50 binary)\n", + "\n", + "Root relaxation: objective 6.826847e+08, 56 iterations, 0.00 seconds (0.00 work units)\n", + "\n", + " Nodes | Current Node | Objective Bounds | Work\n", + " Expl Unexpl | Obj Depth IntInf | Incumbent BestBd Gap | It/Node Time\n", + "\n", + " 0 0 6.8268e+08 0 1 6.8484e+08 6.8268e+08 0.31% - 0s\n", + " 0 0 6.8315e+08 0 3 6.8484e+08 6.8315e+08 0.25% - 0s\n", + " 0 0 6.8315e+08 0 1 6.8484e+08 6.8315e+08 0.25% - 0s\n", + " 0 0 6.8315e+08 0 3 6.8484e+08 6.8315e+08 0.25% - 0s\n", + " 0 0 6.8315e+08 0 4 6.8484e+08 6.8315e+08 0.25% - 0s\n", + " 0 0 6.8315e+08 0 4 6.8484e+08 6.8315e+08 0.25% - 0s\n", + " 0 2 6.8327e+08 0 4 6.8484e+08 6.8327e+08 0.23% - 0s\n", + "\n", + "Cutting planes:\n", + " Flow cover: 3\n", + "\n", + "Explored 32 nodes (155 simplex iterations) in 0.02 seconds (0.00 work units)\n", + "Thread count was 1 (of 32 available processors)\n", + "\n", + "Solution count 1: 6.84841e+08 \n", + "\n", + "Optimal solution found (tolerance 1.00e-04)\n", + "Best objective 6.848411655488e+08, best bound 6.848411655488e+08, gap 0.0000%\n", + "Set parameter LogFile to value \"\"\n", + "WARNING: Cannot get reduced costs for MIP.\n", + "WARNING: Cannot get duals for MIP.\n" + ] + } + ], + "source": [ + "solver_ml = LearningSolver()\n", + "solver_ml.fit(train_files, build_uc_model)\n", + "solver_ml.solve(test_files[0:1], build_uc_model, tee=True);" + ] + }, + { + "cell_type": "markdown", + "id": "61da6dad-7f56-4edb-aa26-c00eb5f946c0", + "metadata": {}, + "source": [ + "By examining the solve log above, specifically the line `Loaded user MIP start with objective...`, we can see that MIPLearn was able to construct an initial solution which turned out to be the optimal solution to the problem. Now let us repeat the code above, but using an untrained solver. Note that the `fit` line is omitted." + ] + }, + { + "cell_type": "code", + "execution_count": 10, + "id": "33d15d6c-6db4-477f-bd4b-fe8e84e5f023", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Set parameter LogFile to value \"/tmp/tmp3uhhdurw.log\"\n", + "Set parameter QCPDual to value 1\n", + "Gurobi Optimizer version 9.5.1 build v9.5.1rc2 (linux64)\n", + "Thread count: 16 physical cores, 32 logical processors, using up to 1 threads\n", + "Optimize a model with 101 rows, 100 columns and 250 nonzeros\n", + "Model fingerprint: 0x8de73876\n", + "Coefficient statistics:\n", + " Matrix range [1e+00, 2e+06]\n", + " Objective range [1e+00, 6e+07]\n", + " Bounds range [1e+00, 1e+00]\n", + " RHS range [2e+07, 2e+07]\n", + "Presolve removed 100 rows and 50 columns\n", + "Presolve time: 0.00s\n", + "Presolved: 1 rows, 50 columns, 50 nonzeros\n", + "\n", + "Iteration Objective Primal Inf. Dual Inf. Time\n", + " 0 5.7349081e+08 1.044003e+04 0.000000e+00 0s\n", + " 1 6.8268465e+08 0.000000e+00 0.000000e+00 0s\n", + "\n", + "Solved in 1 iterations and 0.01 seconds (0.00 work units)\n", + "Optimal objective 6.826846503e+08\n", + "Set parameter LogFile to value \"\"\n", + "Set parameter LogFile to value \"/tmp/tmp18aqg2ic.log\"\n", + "Gurobi Optimizer version 9.5.1 build v9.5.1rc2 (linux64)\n", + "Thread count: 16 physical cores, 32 logical processors, using up to 1 threads\n", + "Optimize a model with 101 rows, 100 columns and 250 nonzeros\n", + "Model fingerprint: 0xb90d1075\n", + "Variable types: 50 continuous, 50 integer (50 binary)\n", + "Coefficient statistics:\n", + " Matrix range [1e+00, 2e+06]\n", + " Objective range [1e+00, 6e+07]\n", + " Bounds range [1e+00, 1e+00]\n", + " RHS range [2e+07, 2e+07]\n", + "Found heuristic solution: objective 8.056576e+08\n", + "Presolve time: 0.00s\n", + "Presolved: 101 rows, 100 columns, 250 nonzeros\n", + "Variable types: 50 continuous, 50 integer (50 binary)\n", + "\n", + "Root relaxation: objective 6.826847e+08, 56 iterations, 0.00 seconds (0.00 work units)\n", + "\n", + " Nodes | Current Node | Objective Bounds | Work\n", + " Expl Unexpl | Obj Depth IntInf | Incumbent BestBd Gap | It/Node Time\n", + "\n", + " 0 0 6.8268e+08 0 1 8.0566e+08 6.8268e+08 15.3% - 0s\n", + "H 0 0 7.099498e+08 6.8268e+08 3.84% - 0s\n", + " 0 0 6.8315e+08 0 3 7.0995e+08 6.8315e+08 3.78% - 0s\n", + "H 0 0 6.883227e+08 6.8315e+08 0.75% - 0s\n", + " 0 0 6.8352e+08 0 4 6.8832e+08 6.8352e+08 0.70% - 0s\n", + " 0 0 6.8352e+08 0 4 6.8832e+08 6.8352e+08 0.70% - 0s\n", + " 0 0 6.8352e+08 0 1 6.8832e+08 6.8352e+08 0.70% - 0s\n", + "H 0 0 6.862582e+08 6.8352e+08 0.40% - 0s\n", + " 0 0 6.8352e+08 0 4 6.8626e+08 6.8352e+08 0.40% - 0s\n", + " 0 0 6.8352e+08 0 4 6.8626e+08 6.8352e+08 0.40% - 0s\n", + " 0 0 6.8352e+08 0 1 6.8626e+08 6.8352e+08 0.40% - 0s\n", + " 0 0 6.8352e+08 0 3 6.8626e+08 6.8352e+08 0.40% - 0s\n", + " 0 0 6.8352e+08 0 4 6.8626e+08 6.8352e+08 0.40% - 0s\n", + " 0 0 6.8352e+08 0 4 6.8626e+08 6.8352e+08 0.40% - 0s\n", + " 0 2 6.8354e+08 0 4 6.8626e+08 6.8354e+08 0.40% - 0s\n", + "* 18 5 6 6.849018e+08 6.8413e+08 0.11% 3.1 0s\n", + "H 24 1 6.848412e+08 6.8426e+08 0.09% 3.2 0s\n", + "\n", + "Cutting planes:\n", + " Gomory: 1\n", + " Flow cover: 2\n", + "\n", + "Explored 30 nodes (217 simplex iterations) in 0.02 seconds (0.00 work units)\n", + "Thread count was 1 (of 32 available processors)\n", + "\n", + "Solution count 6: 6.84841e+08 6.84902e+08 6.86258e+08 ... 8.05658e+08\n", + "\n", + "Optimal solution found (tolerance 1.00e-04)\n", + "Best objective 6.848411655488e+08, best bound 6.848411655488e+08, gap 0.0000%\n", + "Set parameter LogFile to value \"\"\n", + "WARNING: Cannot get reduced costs for MIP.\n", + "WARNING: Cannot get duals for MIP.\n" + ] + } + ], + "source": [ + "solver_baseline = LearningSolver()\n", + "solver_baseline.solve(test_files[0:1], build_uc_model, tee=True);" + ] + }, + { + "cell_type": "markdown", + "id": "b6d37b88-9fcc-43ee-ac1e-2a7b1e51a266", + "metadata": {}, + "source": [ + "In the log above, the `MIP start` line is missing, and Gurobi had to start with a significantly inferior initial solution. The solver was still able to find the optimal solution at the end, but it required using its own internal heuristic procedures. In this example, because we solve very small optimization problems, there was almost no difference in terms of running time. For larger problems, however, the difference can be significant. See benchmarks for more details.\n", + "\n", + "
\n", + "Note\n", + " \n", + "In addition to partial initial solutions, MIPLearn is also able to predict lazy constraints, cutting planes and branching priorities. See the next tutorials for more details.\n", + "
\n", + "\n", + "
\n", + "Note\n", + " \n", + "It is not necessary to specify what ML models to use. MIPLearn, by default, will try a number of classical ML models and will choose the one that performs the best, based on k-fold cross validation. MIPLearn is also able to automatically collect features based on the MIP formulation of the problem and the solution to the LP relaxation, among other things, so it does not require handcrafted features. If you do want to customize the models and features, however, that is also possible, as we will see in a later tutorial.\n", + "
" + ] + }, + { + "cell_type": "markdown", + "id": "eec97f06", + "metadata": { + "tags": [] + }, + "source": [ + "## Accessing the solution\n", + "\n", + "In the example above, we used `LearningSolver.solve` together with data files to solve both the training and the test instances. The optimal solutions were saved to HDF5 files in the train/test folders, and could be retrieved by reading theses files, but that is not very convenient. In the following example, we show how to build and solve a Pyomo model entirely in-memory, using our trained solver." + ] + }, + { + "cell_type": "code", + "execution_count": 11, + "id": "67a6cd18", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "obj = 903865807.3536932\n", + " x = [1.0, 1.0, 1.0, 1.0, 1.0]\n", + " y = [1105176.593734543, 1891284.5155055337, 1708177.4224033852, 1438329.610189608, 535496.3347187206]\n" + ] + } + ], + "source": [ + "# Construct model using previously defined functions\n", + "data = random_uc_data(samples=1, n=50)[0]\n", + "model = build_uc_model(data)\n", + "\n", + "# Solve model using ML + Gurobi\n", + "solver_ml.solve(model)\n", + "\n", + "# Print part of the optimal solution\n", + "print(\"obj =\", model.obj())\n", + "print(\" x =\", [model.x[i].value for i in range(5)])\n", + "print(\" y =\", [model.y[i].value for i in range(5)])" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": 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(min-width:1200px){.toc-entry a{padding-right:0}}.toc-entry a:hover{color:rgba(var(--pst-color-toc-link-hover),1);text-decoration:none}.bd-sidebar{padding-top:1em}@media (min-width:720px){.bd-sidebar{border-right:1px solid rgba(0,0,0,.1)}@supports (position:-webkit-sticky) or (position:sticky){.bd-sidebar{position:-webkit-sticky;position:sticky;top:calc(var(--pst-header-height) + 20px);z-index:1000;height:calc(100vh - var(--pst-header-height) - 20px)}}}.bd-sidebar.no-sidebar{border-right:0}.bd-links{padding-top:1rem;padding-bottom:1rem;margin-right:-15px;margin-left:-15px}@media (min-width:720px){.bd-links{display:block!important}@supports (position:-webkit-sticky) or (position:sticky){.bd-links{max-height:calc(100vh - 11rem);overflow-y:auto}}}.bd-sidenav{display:none}.bd-content{padding-top:20px}.bd-content .section{max-width:100%}.bd-content .section table{display:block;overflow:auto}.bd-toc-link{display:block;padding:.25rem 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li>a:hover{color:rgba(var(--pst-color-sidebar-link-hover),1);text-decoration:none;background-color:transparent}.bd-sidebar .nav li>a.reference.external:after{font-family:Font Awesome\ 5 Free;font-weight:900;content:"\f35d";font-size:.75em;margin-left:.3em}.bd-sidebar .nav .active:hover>a,.bd-sidebar .nav .active>a{font-weight:600;color:rgba(var(--pst-color-sidebar-link-active),1)}.toc-h2{font-size:.85rem}.toc-h3{font-size:.75rem}.toc-h4{font-size:.65rem}.toc-entry>.nav-link.active{font-weight:600;color:#130654;color:rgba(var(--pst-color-toc-link-active),1);background-color:transparent;border-left:2px solid rgba(var(--pst-color-toc-link-active),1)}.nav-link:hover{border-style:none}#navbar-main-elements li.nav-item i{font-size:.7rem;padding-left:2px;vertical-align:middle}.bd-toc .nav .nav{display:none}.bd-toc .nav .nav.visible,.bd-toc .nav>.active>ul{display:block}.prev-next-bottom{margin:20px 0}.prev-next-bottom a.left-prev,.prev-next-bottom a.right-next{padding:10px;border:1px solid rgba(0,0,0,.2);max-width:45%;overflow-x:hidden;color:rgba(0,0,0,.65)}.prev-next-bottom a.left-prev{float:left}.prev-next-bottom a.left-prev:before{content:"<< "}.prev-next-bottom a.right-next{float:right}.prev-next-bottom a.right-next:after{content:" >>"}.alert{padding-bottom:0}.alert-info a{color:#e83e8c}#navbar-icon-links i.fa,#navbar-icon-links i.fab,#navbar-icon-links i.far,#navbar-icon-links i.fas{vertical-align:middle;font-style:normal;font-size:1.5rem;line-height:1.25}#navbar-icon-links i.fa-github-square:before{color:#333}#navbar-icon-links i.fa-twitter-square:before{color:#55acee}#navbar-icon-links i.fa-gitlab:before{color:#548}#navbar-icon-links i.fa-bitbucket:before{color:#0052cc}.tocsection{border-left:1px solid #eee;padding:.3rem 1.5rem}.tocsection i{padding-right:.5rem}.editthispage{padding-top:2rem}.editthispage a{color:#130754}.xr-wrap[hidden]{display:block!important}.toctree-checkbox{position:absolute;display:none}.toctree-checkbox~ul{display:none}.toctree-checkbox~label i{transform:rotate(0deg)}.toctree-checkbox:checked~ul{display:block}.toctree-checkbox:checked~label i{transform:rotate(180deg)}.bd-sidebar li{position:relative}.bd-sidebar label{position:absolute;top:0;right:0;height:30px;width:30px;cursor:pointer;display:flex;justify-content:center;align-items:center}.bd-sidebar label:hover{background:rgba(var(--pst-color-sidebar-expander-background-hover),1)}.bd-sidebar label i{display:inline-block;font-size:.75rem;text-align:center}.bd-sidebar label i:hover{color:rgba(var(--pst-color-sidebar-link-hover),1)}.bd-sidebar li.has-children>.reference{padding-right:30px}div.doctest>div.highlight span.gp,span.linenos,table.highlighttable td.linenos{user-select:none!important;-webkit-user-select:text!important;-webkit-user-select:none!important;-moz-user-select:none!important;-ms-user-select:none!important} \ No newline at end of file diff --git a/0.3/_static/css/theme.css b/0.3/_static/css/theme.css new file mode 100644 index 0000000..3f6e79d --- /dev/null +++ b/0.3/_static/css/theme.css @@ -0,0 +1,117 @@ +:root { + /***************************************************************************** + * Theme config + **/ + --pst-header-height: 60px; + + /***************************************************************************** + * Font size + **/ + --pst-font-size-base: 15px; /* base font size - applied at body / html level */ + + /* heading font sizes */ + --pst-font-size-h1: 36px; + --pst-font-size-h2: 32px; + --pst-font-size-h3: 26px; + --pst-font-size-h4: 21px; + --pst-font-size-h5: 18px; + --pst-font-size-h6: 16px; + + /* smaller then heading font sizes*/ + --pst-font-size-milli: 12px; + + --pst-sidebar-font-size: .9em; + --pst-sidebar-caption-font-size: .9em; + + /***************************************************************************** + * Font family + **/ + /* These are adapted from https://systemfontstack.com/ */ + --pst-font-family-base-system: -apple-system, BlinkMacSystemFont, Segoe UI, "Helvetica Neue", + Arial, sans-serif, Apple Color Emoji, Segoe UI Emoji, Segoe UI Symbol; + --pst-font-family-monospace-system: "SFMono-Regular", Menlo, Consolas, Monaco, + Liberation Mono, Lucida Console, monospace; + + --pst-font-family-base: var(--pst-font-family-base-system); + --pst-font-family-heading: var(--pst-font-family-base); + --pst-font-family-monospace: var(--pst-font-family-monospace-system); + + /***************************************************************************** + * Color + * + * Colors are defined in rgb string way, "red, green, blue" + **/ + --pst-color-primary: 19, 6, 84; + --pst-color-success: 40, 167, 69; + --pst-color-info: 0, 123, 255; /*23, 162, 184;*/ + --pst-color-warning: 255, 193, 7; + --pst-color-danger: 220, 53, 69; + --pst-color-text-base: 51, 51, 51; + + --pst-color-h1: var(--pst-color-primary); + --pst-color-h2: var(--pst-color-primary); + --pst-color-h3: var(--pst-color-text-base); + --pst-color-h4: var(--pst-color-text-base); + --pst-color-h5: var(--pst-color-text-base); + --pst-color-h6: var(--pst-color-text-base); + --pst-color-paragraph: var(--pst-color-text-base); + --pst-color-link: 0, 91, 129; + --pst-color-link-hover: 227, 46, 0; + --pst-color-headerlink: 198, 15, 15; + --pst-color-headerlink-hover: 255, 255, 255; + --pst-color-preformatted-text: 34, 34, 34; + --pst-color-preformatted-background: 250, 250, 250; + --pst-color-inline-code: 232, 62, 140; + + --pst-color-active-navigation: 19, 6, 84; + --pst-color-navbar-link: 77, 77, 77; + --pst-color-navbar-link-hover: var(--pst-color-active-navigation); + --pst-color-navbar-link-active: var(--pst-color-active-navigation); + --pst-color-sidebar-link: 77, 77, 77; + --pst-color-sidebar-link-hover: var(--pst-color-active-navigation); + --pst-color-sidebar-link-active: var(--pst-color-active-navigation); + --pst-color-sidebar-expander-background-hover: 244, 244, 244; + --pst-color-sidebar-caption: 77, 77, 77; + --pst-color-toc-link: 119, 117, 122; + --pst-color-toc-link-hover: var(--pst-color-active-navigation); + --pst-color-toc-link-active: var(--pst-color-active-navigation); + + /***************************************************************************** + * Icon + **/ + + /* font awesome icons*/ + --pst-icon-check-circle: '\f058'; + --pst-icon-info-circle: '\f05a'; + --pst-icon-exclamation-triangle: '\f071'; + --pst-icon-exclamation-circle: '\f06a'; + --pst-icon-times-circle: '\f057'; + --pst-icon-lightbulb: '\f0eb'; + + /***************************************************************************** + * Admonitions + **/ + + --pst-color-admonition-default: var(--pst-color-info); + --pst-color-admonition-note: var(--pst-color-info); + --pst-color-admonition-attention: var(--pst-color-warning); + --pst-color-admonition-caution: var(--pst-color-warning); + --pst-color-admonition-warning: var(--pst-color-warning); + --pst-color-admonition-danger: var(--pst-color-danger); + --pst-color-admonition-error: var(--pst-color-danger); + --pst-color-admonition-hint: var(--pst-color-success); + --pst-color-admonition-tip: var(--pst-color-success); + --pst-color-admonition-important: var(--pst-color-success); + + --pst-icon-admonition-default: var(--pst-icon-info-circle); + --pst-icon-admonition-note: var(--pst-icon-info-circle); + --pst-icon-admonition-attention: var(--pst-icon-exclamation-circle); + --pst-icon-admonition-caution: var(--pst-icon-exclamation-triangle); + --pst-icon-admonition-warning: var(--pst-icon-exclamation-triangle); + --pst-icon-admonition-danger: var(--pst-icon-exclamation-triangle); + --pst-icon-admonition-error: var(--pst-icon-times-circle); + --pst-icon-admonition-hint: var(--pst-icon-lightbulb); + --pst-icon-admonition-tip: var(--pst-icon-lightbulb); + --pst-icon-admonition-important: var(--pst-icon-exclamation-circle); + +} diff --git a/0.3/_static/custom.css b/0.3/_static/custom.css new file mode 100644 index 0000000..668b842 --- /dev/null +++ b/0.3/_static/custom.css @@ -0,0 +1,120 @@ +h1.site-logo { + font-size: 30px !important; +} + +h1.site-logo small { + font-size: 20px !important; +} + +code { + display: inline-block; + border-radius: 4px; + padding: 0 4px; + background-color: #eee; + color: rgb(232, 62, 140); +} + +.right-next, .left-prev { + border-radius: 8px; + border-width: 0px !important; + box-shadow: 2px 2px 6px rgba(0, 0, 0, 0.2); +} + +.right-next:hover, .left-prev:hover { + text-decoration: none; +} + +.admonition { + border-radius: 8px; + border-width: 0; + box-shadow: 0 0 0 !important; +} + +.note { background-color: rgba(0, 123, 255, 0.1); } +.note * { color: rgb(69 94 121); } + +.warning { background-color: rgb(220 150 40 / 10%); } +.warning * { color: rgb(105 72 28); } + +.input_area, .output_area, .output_area img { + border-radius: 8px !important; + border-width: 0 !important; + margin: 8px 0 8px 0; +} + +.output_area { + padding: 4px; + background-color: hsl(227 60% 11% / 0.7) !important; +} + +.output_area pre { + color: #fff; + line-height: 20px !important; +} + +.input_area pre { + background-color: rgba(0 0 0 / 3%) !important; + padding: 12px !important; + line-height: 20px; +} + +.ansi-green-intense-fg { + color: #64d88b !important; +} + +#site-navigation { + background-color: #fafafa; +} + +.container, .container-lg, .container-md, .container-sm, .container-xl { + max-width: inherit !important; +} + +h1, h2 { + font-weight: bold !important; +} + +#main-content .section { + max-width: 900px !important; + margin: 0 auto !important; + font-size: 16px; +} + +p.caption { + font-weight: bold; +} + +h2 { + padding-bottom: 5px; + border-bottom: 1px solid #ccc; +} + +h3 { + margin-top: 1.5rem; +} + +tbody, thead, pre { + border: 1px solid rgba(0, 0, 0, 0.25); +} + +table td, th { + padding: 8px; +} + +table p { + margin-bottom: 0; +} + +table td code { + white-space: nowrap; +} + +table tr, +table th { + border-bottom: 1px solid rgba(0, 0, 0, 0.1); +} + +table tr:last-child { + border-bottom: 0; +} + diff --git a/0.3/_static/doctools.js b/0.3/_static/doctools.js new file mode 100644 index 0000000..61ac9d2 --- /dev/null +++ b/0.3/_static/doctools.js @@ -0,0 +1,321 @@ +/* + * doctools.js + * ~~~~~~~~~~~ + * + * Sphinx JavaScript utilities for all documentation. + * + * :copyright: Copyright 2007-2021 by the Sphinx team, see AUTHORS. + * :license: BSD, see LICENSE for details. + * + */ + +/** + * select a different prefix for underscore + */ +$u = _.noConflict(); + +/** + * make the code below compatible with browsers without + * an installed firebug like debugger +if (!window.console || !console.firebug) { + var names = ["log", "debug", "info", "warn", "error", "assert", "dir", + "dirxml", "group", "groupEnd", "time", "timeEnd", "count", "trace", + "profile", "profileEnd"]; + window.console = {}; + for (var i = 0; i < names.length; ++i) + window.console[names[i]] = function() {}; +} + */ + +/** + * small helper function to urldecode strings + * + * See https://developer.mozilla.org/en-US/docs/Web/JavaScript/Reference/Global_Objects/decodeURIComponent#Decoding_query_parameters_from_a_URL + */ +jQuery.urldecode = function(x) { + if (!x) { + return x + } + return decodeURIComponent(x.replace(/\+/g, ' ')); +}; + +/** + * small helper function to urlencode strings + */ +jQuery.urlencode = encodeURIComponent; + +/** + * This function returns the parsed url parameters of the + * current request. Multiple values per key are supported, + * it will always return arrays of strings for the value parts. + */ +jQuery.getQueryParameters = function(s) { + if (typeof s === 'undefined') + s = document.location.search; + var parts = s.substr(s.indexOf('?') + 1).split('&'); + var result = {}; + for (var i = 0; i < parts.length; i++) { + var tmp = parts[i].split('=', 2); + var key = jQuery.urldecode(tmp[0]); + var value = jQuery.urldecode(tmp[1]); + if (key in result) + result[key].push(value); + else + result[key] = [value]; + } + return result; +}; + +/** + * highlight a given string on a jquery object by wrapping it in + * span elements with the given class name. + */ +jQuery.fn.highlightText = function(text, className) { + function highlight(node, addItems) { + if (node.nodeType === 3) { + var val = node.nodeValue; + var pos = val.toLowerCase().indexOf(text); + if (pos >= 0 && + !jQuery(node.parentNode).hasClass(className) && + !jQuery(node.parentNode).hasClass("nohighlight")) { + var span; + var isInSVG = jQuery(node).closest("body, svg, foreignObject").is("svg"); + if (isInSVG) { + span = document.createElementNS("http://www.w3.org/2000/svg", "tspan"); + } else { + span = document.createElement("span"); + span.className = className; + } + span.appendChild(document.createTextNode(val.substr(pos, text.length))); + node.parentNode.insertBefore(span, node.parentNode.insertBefore( + document.createTextNode(val.substr(pos + text.length)), + node.nextSibling)); + node.nodeValue = val.substr(0, pos); + if (isInSVG) { + var rect = document.createElementNS("http://www.w3.org/2000/svg", "rect"); + var bbox = node.parentElement.getBBox(); + rect.x.baseVal.value = bbox.x; + rect.y.baseVal.value = bbox.y; + rect.width.baseVal.value = bbox.width; + rect.height.baseVal.value = bbox.height; + rect.setAttribute('class', className); + addItems.push({ + "parent": node.parentNode, + "target": rect}); + } + } + } + else if (!jQuery(node).is("button, select, textarea")) { + jQuery.each(node.childNodes, function() { + highlight(this, addItems); + }); + } + } + var addItems = []; + var result = this.each(function() { + highlight(this, addItems); + }); + for (var i = 0; i < addItems.length; ++i) { + jQuery(addItems[i].parent).before(addItems[i].target); + } + return result; +}; + +/* + * backward compatibility for jQuery.browser + * This will be supported until firefox bug is fixed. + */ +if (!jQuery.browser) { + jQuery.uaMatch = function(ua) { + ua = ua.toLowerCase(); + + var match = /(chrome)[ \/]([\w.]+)/.exec(ua) || + /(webkit)[ \/]([\w.]+)/.exec(ua) || + /(opera)(?:.*version|)[ \/]([\w.]+)/.exec(ua) || + /(msie) ([\w.]+)/.exec(ua) || + ua.indexOf("compatible") < 0 && /(mozilla)(?:.*? rv:([\w.]+)|)/.exec(ua) || + []; + + return { + browser: match[ 1 ] || "", + version: match[ 2 ] || "0" + }; + }; + jQuery.browser = {}; + jQuery.browser[jQuery.uaMatch(navigator.userAgent).browser] = true; +} + +/** + * Small JavaScript module for the documentation. + */ +var Documentation = { + + init : function() { + this.fixFirefoxAnchorBug(); + this.highlightSearchWords(); + this.initIndexTable(); + if (DOCUMENTATION_OPTIONS.NAVIGATION_WITH_KEYS) { + this.initOnKeyListeners(); + } + }, + + /** + * i18n support + */ + TRANSLATIONS : {}, + PLURAL_EXPR : function(n) { return n === 1 ? 0 : 1; }, + LOCALE : 'unknown', + + // gettext and ngettext don't access this so that the functions + // can safely bound to a different name (_ = Documentation.gettext) + gettext : function(string) { + var translated = Documentation.TRANSLATIONS[string]; + if (typeof translated === 'undefined') + return string; + return (typeof translated === 'string') ? translated : translated[0]; + }, + + ngettext : function(singular, plural, n) { + var translated = Documentation.TRANSLATIONS[singular]; + if (typeof translated === 'undefined') + return (n == 1) ? singular : plural; + return translated[Documentation.PLURALEXPR(n)]; + }, + + addTranslations : function(catalog) { + for (var key in catalog.messages) + this.TRANSLATIONS[key] = catalog.messages[key]; + this.PLURAL_EXPR = new Function('n', 'return +(' + catalog.plural_expr + ')'); + this.LOCALE = catalog.locale; + }, + + /** + * add context elements like header anchor links + */ + addContextElements : function() { + $('div[id] > :header:first').each(function() { + $('\u00B6'). + attr('href', '#' + this.id). + attr('title', _('Permalink to this headline')). + appendTo(this); + }); + $('dt[id]').each(function() { + $('\u00B6'). + attr('href', '#' + this.id). + attr('title', _('Permalink to this definition')). + appendTo(this); + }); + }, + + /** + * workaround a firefox stupidity + * see: https://bugzilla.mozilla.org/show_bug.cgi?id=645075 + */ + fixFirefoxAnchorBug : function() { + if (document.location.hash && $.browser.mozilla) + window.setTimeout(function() { + document.location.href += ''; + }, 10); + }, + + /** + * highlight the search words provided in the url in the text + */ + highlightSearchWords : function() { + var params = $.getQueryParameters(); + var terms = (params.highlight) ? params.highlight[0].split(/\s+/) : []; + if (terms.length) { + var body = $('div.body'); + if (!body.length) { + body = $('body'); + } + window.setTimeout(function() { + $.each(terms, function() { + body.highlightText(this.toLowerCase(), 'highlighted'); + }); + }, 10); + $('

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b/0.3/_static/jquery-3.5.1.js new file mode 100644 index 0000000..5093733 --- /dev/null +++ b/0.3/_static/jquery-3.5.1.js @@ -0,0 +1,10872 @@ +/*! + * jQuery JavaScript Library v3.5.1 + * https://jquery.com/ + * + * Includes Sizzle.js + * https://sizzlejs.com/ + * + * Copyright JS Foundation and other contributors + * Released under the MIT license + * https://jquery.org/license + * + * Date: 2020-05-04T22:49Z + */ +( function( global, factory ) { + + "use strict"; + + if ( typeof module === "object" && typeof module.exports === "object" ) { + + // For CommonJS and CommonJS-like environments where a proper `window` + // is present, execute the factory and get jQuery. + // For environments that do not have a `window` with a `document` + // (such as Node.js), expose a factory as module.exports. + // This accentuates the need for the creation of a real `window`. + // e.g. var jQuery = require("jquery")(window); + // See ticket #14549 for more info. + module.exports = global.document ? + factory( global, true ) : + function( w ) { + if ( !w.document ) { + throw new Error( "jQuery requires a window with a document" ); + } + return factory( w ); + }; + } else { + factory( global ); + } + +// Pass this if window is not defined yet +} )( typeof window !== "undefined" ? window : this, function( window, noGlobal ) { + +// Edge <= 12 - 13+, Firefox <=18 - 45+, IE 10 - 11, Safari 5.1 - 9+, iOS 6 - 9.1 +// throw exceptions when non-strict code (e.g., ASP.NET 4.5) accesses strict mode +// arguments.callee.caller (trac-13335). But as of jQuery 3.0 (2016), strict mode should be common +// enough that all such attempts are guarded in a try block. +"use strict"; + +var arr = []; + +var getProto = Object.getPrototypeOf; + +var slice = arr.slice; + +var flat = arr.flat ? function( array ) { + return arr.flat.call( array ); +} : function( array ) { + return arr.concat.apply( [], array ); +}; + + +var push = arr.push; + +var indexOf = arr.indexOf; + +var class2type = {}; + +var toString = class2type.toString; + +var hasOwn = class2type.hasOwnProperty; + +var fnToString = hasOwn.toString; + +var ObjectFunctionString = fnToString.call( Object ); + +var support = {}; + +var isFunction = function isFunction( obj ) { + + // Support: Chrome <=57, Firefox <=52 + // In some browsers, typeof returns "function" for HTML elements + // (i.e., `typeof document.createElement( "object" ) === "function"`). + // We don't want to classify *any* DOM node as a function. + return typeof obj === "function" && typeof obj.nodeType !== "number"; + }; + + +var isWindow = function isWindow( obj ) { + return obj != null && obj === obj.window; + }; + + +var document = window.document; + + + + var preservedScriptAttributes = { + type: true, + src: true, + nonce: true, + noModule: true + }; + + function DOMEval( code, node, doc ) { + doc = doc || document; + + var i, val, + script = doc.createElement( "script" ); + + script.text = code; + if ( node ) { + for ( i in preservedScriptAttributes ) { + + // Support: Firefox 64+, Edge 18+ + // Some browsers don't support the "nonce" property on scripts. + // On the other hand, just using `getAttribute` is not enough as + // the `nonce` attribute is reset to an empty string whenever it + // becomes browsing-context connected. + // See https://github.com/whatwg/html/issues/2369 + // See https://html.spec.whatwg.org/#nonce-attributes + // The `node.getAttribute` check was added for the sake of + // `jQuery.globalEval` so that it can fake a nonce-containing node + // via an object. + val = node[ i ] || node.getAttribute && node.getAttribute( i ); + if ( val ) { + script.setAttribute( i, val ); + } + } + } + doc.head.appendChild( script ).parentNode.removeChild( script ); + } + + +function toType( obj ) { + if ( obj == null ) { + return obj + ""; + } + + // Support: Android <=2.3 only (functionish RegExp) + return typeof obj === "object" || typeof obj === "function" ? + class2type[ toString.call( obj ) ] || "object" : + typeof obj; +} +/* global Symbol */ +// Defining this global in .eslintrc.json would create a danger of using the global +// unguarded in another place, it seems safer to define global only for this module + + + +var + version = "3.5.1", + + // Define a local copy of jQuery + jQuery = function( selector, context ) { + + // The jQuery object is actually just the init constructor 'enhanced' + // Need init if jQuery is called (just allow error to be thrown if not included) + return new jQuery.fn.init( selector, context ); + }; + +jQuery.fn = jQuery.prototype = { + + // The current version of jQuery being used + jquery: version, + + constructor: jQuery, + + // The default length of a jQuery object is 0 + length: 0, + + toArray: function() { + return slice.call( this ); + }, + + // Get the Nth element in the matched element set OR + // Get the whole matched element set as a clean array + get: function( num ) { + + // Return all the elements in a clean array + if ( num == null ) { + return slice.call( this ); + } + + // Return just the one element from the set + return num < 0 ? this[ num + this.length ] : this[ num ]; + }, + + // Take an array of elements and push it onto the stack + // (returning the new matched element set) + pushStack: function( elems ) { + + // Build a new jQuery matched element set + var ret = jQuery.merge( this.constructor(), elems ); + + // Add the old object onto the stack (as a reference) + ret.prevObject = this; + + // Return the newly-formed element set + return ret; + }, + + // Execute a callback for every element in the matched set. + each: function( callback ) { + return jQuery.each( this, callback ); + }, + + map: function( callback ) { + return this.pushStack( jQuery.map( this, function( elem, i ) { + return callback.call( elem, i, elem ); + } ) ); + }, + + slice: function() { + return this.pushStack( slice.apply( this, arguments ) ); + }, + + first: function() { + return this.eq( 0 ); + }, + + last: function() { + return this.eq( -1 ); + }, + + even: function() { + return this.pushStack( jQuery.grep( this, function( _elem, i ) { + return ( i + 1 ) % 2; + } ) ); + }, + + odd: function() { + return this.pushStack( jQuery.grep( this, function( _elem, i ) { + return i % 2; + } ) ); + }, + + eq: function( i ) { + var len = this.length, + j = +i + ( i < 0 ? len : 0 ); + return this.pushStack( j >= 0 && j < len ? [ this[ j ] ] : [] ); + }, + + end: function() { + return this.prevObject || this.constructor(); + }, + + // For internal use only. + // Behaves like an Array's method, not like a jQuery method. + push: push, + sort: arr.sort, + splice: arr.splice +}; + +jQuery.extend = jQuery.fn.extend = function() { + var options, name, src, copy, copyIsArray, clone, + target = arguments[ 0 ] || {}, + i = 1, + length = arguments.length, + deep = false; + + // Handle a deep copy situation + if ( typeof target === "boolean" ) { + deep = target; + + // Skip the boolean and the target + target = arguments[ i ] || {}; + i++; + } + + // Handle case when target is a string or something (possible in deep copy) + if ( typeof target !== "object" && !isFunction( target ) ) { + target = {}; + } + + // Extend jQuery itself if only one argument is passed + if ( i === length ) { + target = this; + i--; + } + + for ( ; i < length; i++ ) { + + // Only deal with non-null/undefined values + if ( ( options = arguments[ i ] ) != null ) { + + // Extend the base object + for ( name in options ) { + copy = options[ name ]; + + // Prevent Object.prototype pollution + // Prevent never-ending loop + if ( name === "__proto__" || target === copy ) { + continue; + } + + // Recurse if we're merging plain objects or arrays + if ( deep && copy && ( jQuery.isPlainObject( copy ) || + ( copyIsArray = Array.isArray( copy ) ) ) ) { + src = target[ name ]; + + // Ensure proper type for the source value + if ( copyIsArray && !Array.isArray( src ) ) { + clone = []; + } else if ( !copyIsArray && !jQuery.isPlainObject( src ) ) { + clone = {}; + } else { + clone = src; + } + copyIsArray = false; + + // Never move original objects, clone them + target[ name ] = jQuery.extend( deep, clone, copy ); + + // Don't bring in undefined values + } else if ( copy !== undefined ) { + target[ name ] = copy; + } + } + } + } + + // Return the modified object + return target; +}; + +jQuery.extend( { + + // Unique for each copy of jQuery on the page + expando: "jQuery" + ( version + Math.random() ).replace( /\D/g, "" ), + + // Assume jQuery is ready without the ready module + isReady: true, + + error: function( msg ) { + throw new Error( msg ); + }, + + noop: function() {}, + + isPlainObject: function( obj ) { + var proto, Ctor; + + // Detect obvious negatives + // Use toString instead of jQuery.type to catch host objects + if ( !obj || toString.call( obj ) !== "[object Object]" ) { + return false; + } + + proto = getProto( obj ); + + // Objects with no prototype (e.g., `Object.create( null )`) are plain + if ( !proto ) { + return true; + } + + // Objects with prototype are plain iff they were constructed by a global Object function + Ctor = hasOwn.call( proto, "constructor" ) && proto.constructor; + return typeof Ctor === "function" && fnToString.call( Ctor ) === ObjectFunctionString; + }, + + isEmptyObject: function( obj ) { + var name; + + for ( name in obj ) { + return false; + } + return true; + }, + + // Evaluates a script in a provided context; falls back to the global one + // if not specified. + globalEval: function( code, options, doc ) { + DOMEval( code, { nonce: options && options.nonce }, doc ); + }, + + each: function( obj, callback ) { + var length, i = 0; + + if ( isArrayLike( obj ) ) { + length = obj.length; + for ( ; i < length; i++ ) { + if ( callback.call( obj[ i ], i, obj[ i ] ) === false ) { + break; + } + } + } else { + for ( i in obj ) { + if ( callback.call( obj[ i ], i, obj[ i ] ) === false ) { + break; + } + } + } + + return obj; + }, + + // results is for internal usage only + makeArray: function( arr, results ) { + var ret = results || []; + + if ( arr != null ) { + if ( isArrayLike( Object( arr ) ) ) { + jQuery.merge( ret, + typeof arr === "string" ? + [ arr ] : arr + ); + } else { + push.call( ret, arr ); + } + } + + return ret; + }, + + inArray: function( elem, arr, i ) { + return arr == null ? -1 : indexOf.call( arr, elem, i ); + }, + + // Support: Android <=4.0 only, PhantomJS 1 only + // push.apply(_, arraylike) throws on ancient WebKit + merge: function( first, second ) { + var len = +second.length, + j = 0, + i = first.length; + + for ( ; j < len; j++ ) { + first[ i++ ] = second[ j ]; + } + + first.length = i; + + return first; + }, + + grep: function( elems, callback, invert ) { + var callbackInverse, + matches = [], + i = 0, + length = elems.length, + callbackExpect = !invert; + + // Go through the array, only saving the items + // that pass the validator function + for ( ; i < length; i++ ) { + callbackInverse = !callback( elems[ i ], i ); + if ( callbackInverse !== callbackExpect ) { + matches.push( elems[ i ] ); + } + } + + return matches; + }, + + // arg is for internal usage only + map: function( elems, callback, arg ) { + var length, value, + i = 0, + ret = []; + + // Go through the array, translating each of the items to their new values + if ( isArrayLike( elems ) ) { + length = elems.length; + for ( ; i < length; i++ ) { + value = callback( elems[ i ], i, arg ); + + if ( value != null ) { + ret.push( value ); + } + } + + // Go through every key on the object, + } else { + for ( i in elems ) { + value = callback( elems[ i ], i, arg ); + + if ( value != null ) { + ret.push( value ); + } + } + } + + // Flatten any nested arrays + return flat( ret ); + }, + + // A global GUID counter for objects + guid: 1, + + // jQuery.support is not used in Core but other projects attach their + // properties to it so it needs to exist. + support: support +} ); + +if ( typeof Symbol === "function" ) { + jQuery.fn[ Symbol.iterator ] = arr[ Symbol.iterator ]; +} + +// Populate the class2type map +jQuery.each( "Boolean Number String Function Array Date RegExp Object Error Symbol".split( " " ), +function( _i, name ) { + class2type[ "[object " + name + "]" ] = name.toLowerCase(); +} ); + +function isArrayLike( obj ) { + + // Support: real iOS 8.2 only (not reproducible in simulator) + // `in` check used to prevent JIT error (gh-2145) + // hasOwn isn't used here due to false negatives + // regarding Nodelist length in IE + var length = !!obj && "length" in obj && obj.length, + type = toType( obj ); + + if ( isFunction( obj ) || isWindow( obj ) ) { + return false; + } + + return type === "array" || length === 0 || + typeof length === "number" && length > 0 && ( length - 1 ) in obj; +} +var Sizzle = +/*! + * Sizzle CSS Selector Engine v2.3.5 + * https://sizzlejs.com/ + * + * Copyright JS Foundation and other contributors + * Released under the MIT license + * https://js.foundation/ + * + * Date: 2020-03-14 + */ +( function( window ) { +var i, + support, + Expr, + getText, + isXML, + tokenize, + compile, + select, + outermostContext, + sortInput, + hasDuplicate, + + // Local document vars + setDocument, + document, + docElem, + documentIsHTML, + rbuggyQSA, + rbuggyMatches, + matches, + contains, + + // Instance-specific data + expando = "sizzle" + 1 * new Date(), + preferredDoc = window.document, + dirruns = 0, + done = 0, + classCache = createCache(), + tokenCache = createCache(), + compilerCache = createCache(), + nonnativeSelectorCache = createCache(), + sortOrder = function( a, b ) { + if ( a === b ) { + hasDuplicate = true; + } + return 0; + }, + + // Instance methods + hasOwn = ( {} ).hasOwnProperty, + arr = [], + pop = arr.pop, + pushNative = arr.push, + push = arr.push, + slice = arr.slice, + + // Use a stripped-down indexOf as it's faster than native + // https://jsperf.com/thor-indexof-vs-for/5 + indexOf = function( list, elem ) { + var i = 0, + len = list.length; + for ( ; i < len; i++ ) { + if ( list[ i ] === elem ) { + return i; + } + } + return -1; + }, + + booleans = "checked|selected|async|autofocus|autoplay|controls|defer|disabled|hidden|" + + "ismap|loop|multiple|open|readonly|required|scoped", + + // Regular expressions + + // http://www.w3.org/TR/css3-selectors/#whitespace + whitespace = "[\\x20\\t\\r\\n\\f]", + + // https://www.w3.org/TR/css-syntax-3/#ident-token-diagram + identifier = "(?:\\\\[\\da-fA-F]{1,6}" + whitespace + + "?|\\\\[^\\r\\n\\f]|[\\w-]|[^\0-\\x7f])+", + + // Attribute selectors: http://www.w3.org/TR/selectors/#attribute-selectors + attributes = "\\[" + whitespace + "*(" + identifier + ")(?:" + whitespace + + + // Operator (capture 2) + "*([*^$|!~]?=)" + whitespace + + + // "Attribute values must be CSS identifiers [capture 5] + // or strings [capture 3 or capture 4]" + "*(?:'((?:\\\\.|[^\\\\'])*)'|\"((?:\\\\.|[^\\\\\"])*)\"|(" + identifier + "))|)" + + whitespace + "*\\]", + + pseudos = ":(" + identifier + ")(?:\\((" + + + // To reduce the number of selectors needing tokenize in the preFilter, prefer arguments: + // 1. quoted (capture 3; capture 4 or capture 5) + "('((?:\\\\.|[^\\\\'])*)'|\"((?:\\\\.|[^\\\\\"])*)\")|" + + + // 2. simple (capture 6) + "((?:\\\\.|[^\\\\()[\\]]|" + attributes + ")*)|" + + + // 3. anything else (capture 2) + ".*" + + ")\\)|)", + + // Leading and non-escaped trailing whitespace, capturing some non-whitespace characters preceding the latter + rwhitespace = new RegExp( whitespace + "+", "g" ), + rtrim = new RegExp( "^" + whitespace + "+|((?:^|[^\\\\])(?:\\\\.)*)" + + whitespace + "+$", "g" ), + + rcomma = new RegExp( "^" + whitespace + "*," + whitespace + "*" ), + rcombinators = new RegExp( "^" + whitespace + "*([>+~]|" + whitespace + ")" + whitespace + + "*" ), + rdescend = new RegExp( whitespace + "|>" ), + + rpseudo = new RegExp( pseudos ), + ridentifier = new RegExp( "^" + identifier + "$" ), + + matchExpr = { + "ID": new RegExp( "^#(" + identifier + ")" ), + "CLASS": new RegExp( "^\\.(" + identifier + ")" ), + "TAG": new RegExp( "^(" + identifier + "|[*])" ), + "ATTR": new RegExp( "^" + attributes ), + "PSEUDO": new RegExp( "^" + pseudos ), + "CHILD": new RegExp( "^:(only|first|last|nth|nth-last)-(child|of-type)(?:\\(" + + whitespace + "*(even|odd|(([+-]|)(\\d*)n|)" + whitespace + "*(?:([+-]|)" + + whitespace + "*(\\d+)|))" + whitespace + "*\\)|)", "i" ), + "bool": new RegExp( "^(?:" + booleans + ")$", "i" ), + + // For use in libraries implementing .is() + // We use this for POS matching in `select` + "needsContext": new RegExp( "^" + whitespace + + "*[>+~]|:(even|odd|eq|gt|lt|nth|first|last)(?:\\(" + whitespace + + "*((?:-\\d)?\\d*)" + whitespace + "*\\)|)(?=[^-]|$)", "i" ) + }, + + rhtml = /HTML$/i, + rinputs = /^(?:input|select|textarea|button)$/i, + rheader = /^h\d$/i, + + rnative = /^[^{]+\{\s*\[native \w/, + + // Easily-parseable/retrievable ID or TAG or CLASS selectors + rquickExpr = /^(?:#([\w-]+)|(\w+)|\.([\w-]+))$/, + + rsibling = /[+~]/, + + // CSS escapes + // http://www.w3.org/TR/CSS21/syndata.html#escaped-characters + runescape = new RegExp( "\\\\[\\da-fA-F]{1,6}" + whitespace + "?|\\\\([^\\r\\n\\f])", "g" ), + funescape = function( escape, nonHex ) { + var high = "0x" + escape.slice( 1 ) - 0x10000; + + return nonHex ? + + // Strip the backslash prefix from a non-hex escape sequence + nonHex : + + // Replace a hexadecimal escape sequence with the encoded Unicode code point + // Support: IE <=11+ + // For values outside the Basic Multilingual Plane (BMP), manually construct a + // surrogate pair + high < 0 ? + String.fromCharCode( high + 0x10000 ) : + String.fromCharCode( high >> 10 | 0xD800, high & 0x3FF | 0xDC00 ); + }, + + // CSS string/identifier serialization + // https://drafts.csswg.org/cssom/#common-serializing-idioms + rcssescape = /([\0-\x1f\x7f]|^-?\d)|^-$|[^\0-\x1f\x7f-\uFFFF\w-]/g, + fcssescape = function( ch, asCodePoint ) { + if ( asCodePoint ) { + + // U+0000 NULL becomes U+FFFD REPLACEMENT CHARACTER + if ( ch === "\0" ) { + return "\uFFFD"; + } + + // Control characters and (dependent upon position) numbers get escaped as code points + return ch.slice( 0, -1 ) + "\\" + + ch.charCodeAt( ch.length - 1 ).toString( 16 ) + " "; + } + + // Other potentially-special ASCII characters get backslash-escaped + return "\\" + ch; + }, + + // Used for iframes + // See setDocument() + // Removing the function wrapper causes a "Permission Denied" + // error in IE + unloadHandler = function() { + setDocument(); + }, + + inDisabledFieldset = addCombinator( + function( elem ) { + return elem.disabled === true && elem.nodeName.toLowerCase() === "fieldset"; + }, + { dir: "parentNode", next: "legend" } + ); + +// Optimize for push.apply( _, NodeList ) +try { + push.apply( + ( arr = slice.call( preferredDoc.childNodes ) ), + preferredDoc.childNodes + ); + + // Support: Android<4.0 + // Detect silently failing push.apply + // eslint-disable-next-line no-unused-expressions + arr[ preferredDoc.childNodes.length ].nodeType; +} catch ( e ) { + push = { apply: arr.length ? + + // Leverage slice if possible + function( target, els ) { + pushNative.apply( target, slice.call( els ) ); + } : + + // Support: IE<9 + // Otherwise append directly + function( target, els ) { + var j = target.length, + i = 0; + + // Can't trust NodeList.length + while ( ( target[ j++ ] = els[ i++ ] ) ) {} + target.length = j - 1; + } + }; +} + +function Sizzle( selector, context, results, seed ) { + var m, i, elem, nid, match, groups, newSelector, + newContext = context && context.ownerDocument, + + // nodeType defaults to 9, since context defaults to document + nodeType = context ? context.nodeType : 9; + + results = results || []; + + // Return early from calls with invalid selector or context + if ( typeof selector !== "string" || !selector || + nodeType !== 1 && nodeType !== 9 && nodeType !== 11 ) { + + return results; + } + + // Try to shortcut find operations (as opposed to filters) in HTML documents + if ( !seed ) { + setDocument( context ); + context = context || document; + + if ( documentIsHTML ) { + + // If the selector is sufficiently simple, try using a "get*By*" DOM method + // (excepting DocumentFragment context, where the methods don't exist) + if ( nodeType !== 11 && ( match = rquickExpr.exec( selector ) ) ) { + + // ID selector + if ( ( m = match[ 1 ] ) ) { + + // Document context + if ( nodeType === 9 ) { + if ( ( elem = context.getElementById( m ) ) ) { + + // Support: IE, Opera, Webkit + // TODO: identify versions + // getElementById can match elements by name instead of ID + if ( elem.id === m ) { + results.push( elem ); + return results; + } + } else { + return results; + } + + // Element context + } else { + + // Support: IE, Opera, Webkit + // TODO: identify versions + // getElementById can match elements by name instead of ID + if ( newContext && ( elem = newContext.getElementById( m ) ) && + contains( context, elem ) && + elem.id === m ) { + + results.push( elem ); + return results; + } + } + + // Type selector + } else if ( match[ 2 ] ) { + push.apply( results, context.getElementsByTagName( selector ) ); + return results; + + // Class selector + } else if ( ( m = match[ 3 ] ) && support.getElementsByClassName && + context.getElementsByClassName ) { + + push.apply( results, context.getElementsByClassName( m ) ); + return results; + } + } + + // Take advantage of querySelectorAll + if ( support.qsa && + !nonnativeSelectorCache[ selector + " " ] && + ( !rbuggyQSA || !rbuggyQSA.test( selector ) ) && + + // Support: IE 8 only + // Exclude object elements + ( nodeType !== 1 || context.nodeName.toLowerCase() !== "object" ) ) { + + newSelector = selector; + newContext = context; + + // qSA considers elements outside a scoping root when evaluating child or + // descendant combinators, which is not what we want. + // In such cases, we work around the behavior by prefixing every selector in the + // list with an ID selector referencing the scope context. + // The technique has to be used as well when a leading combinator is used + // as such selectors are not recognized by querySelectorAll. + // Thanks to Andrew Dupont for this technique. + if ( nodeType === 1 && + ( rdescend.test( selector ) || rcombinators.test( selector ) ) ) { + + // Expand context for sibling selectors + newContext = rsibling.test( selector ) && testContext( context.parentNode ) || + context; + + // We can use :scope instead of the ID hack if the browser + // supports it & if we're not changing the context. + if ( newContext !== context || !support.scope ) { + + // Capture the context ID, setting it first if necessary + if ( ( nid = context.getAttribute( "id" ) ) ) { + nid = nid.replace( rcssescape, fcssescape ); + } else { + context.setAttribute( "id", ( nid = expando ) ); + } + } + + // Prefix every selector in the list + groups = tokenize( selector ); + i = groups.length; + while ( i-- ) { + groups[ i ] = ( nid ? "#" + nid : ":scope" ) + " " + + toSelector( groups[ i ] ); + } + newSelector = groups.join( "," ); + } + + try { + push.apply( results, + newContext.querySelectorAll( newSelector ) + ); + return results; + } catch ( qsaError ) { + nonnativeSelectorCache( selector, true ); + } finally { + if ( nid === expando ) { + context.removeAttribute( "id" ); + } + } + } + } + } + + // All others + return select( selector.replace( rtrim, "$1" ), context, results, seed ); +} + +/** + * Create key-value caches of limited size + * @returns {function(string, object)} Returns the Object data after storing it on itself with + * property name the (space-suffixed) string and (if the cache is larger than Expr.cacheLength) + * deleting the oldest entry + */ +function createCache() { + var keys = []; + + function cache( key, value ) { + + // Use (key + " ") to avoid collision with native prototype properties (see Issue #157) + if ( keys.push( key + " " ) > Expr.cacheLength ) { + + // Only keep the most recent entries + delete cache[ keys.shift() ]; + } + return ( cache[ key + " " ] = value ); + } + return cache; +} + +/** + * Mark a function for special use by Sizzle + * @param {Function} fn The function to mark + */ +function markFunction( fn ) { + fn[ expando ] = true; + return fn; +} + +/** + * Support testing using an element + * @param {Function} fn Passed the created element and returns a boolean result + */ +function assert( fn ) { + var el = document.createElement( "fieldset" ); + + try { + return !!fn( el ); + } catch ( e ) { + return false; + } finally { + + // Remove from its parent by default + if ( el.parentNode ) { + el.parentNode.removeChild( el ); + } + + // release memory in IE + el = null; + } +} + +/** + * Adds the same handler for all of the specified attrs + * @param {String} attrs Pipe-separated list of attributes + * @param {Function} handler The method that will be applied + */ +function addHandle( attrs, handler ) { + var arr = attrs.split( "|" ), + i = arr.length; + + while ( i-- ) { + Expr.attrHandle[ arr[ i ] ] = handler; + } +} + +/** + * Checks document order of two siblings + * @param {Element} a + * @param {Element} b + * @returns {Number} Returns less than 0 if a precedes b, greater than 0 if a follows b + */ +function siblingCheck( a, b ) { + var cur = b && a, + diff = cur && a.nodeType === 1 && b.nodeType === 1 && + a.sourceIndex - b.sourceIndex; + + // Use IE sourceIndex if available on both nodes + if ( diff ) { + return diff; + } + + // Check if b follows a + if ( cur ) { + while ( ( cur = cur.nextSibling ) ) { + if ( cur === b ) { + return -1; + } + } + } + + return a ? 1 : -1; +} + +/** + * Returns a function to use in pseudos for input types + * @param {String} type + */ +function createInputPseudo( type ) { + return function( elem ) { + var name = elem.nodeName.toLowerCase(); + return name === "input" && elem.type === type; + }; +} + +/** + * Returns a function to use in pseudos for buttons + * @param {String} type + */ +function createButtonPseudo( type ) { + return function( elem ) { + var name = elem.nodeName.toLowerCase(); + return ( name === "input" || name === "button" ) && elem.type === type; + }; +} + +/** + * Returns a function to use in pseudos for :enabled/:disabled + * @param {Boolean} disabled true for :disabled; false for :enabled + */ +function createDisabledPseudo( disabled ) { + + // Known :disabled false positives: fieldset[disabled] > legend:nth-of-type(n+2) :can-disable + return function( elem ) { + + // Only certain elements can match :enabled or :disabled + // https://html.spec.whatwg.org/multipage/scripting.html#selector-enabled + // https://html.spec.whatwg.org/multipage/scripting.html#selector-disabled + if ( "form" in elem ) { + + // Check for inherited disabledness on relevant non-disabled elements: + // * listed form-associated elements in a disabled fieldset + // https://html.spec.whatwg.org/multipage/forms.html#category-listed + // https://html.spec.whatwg.org/multipage/forms.html#concept-fe-disabled + // * option elements in a disabled optgroup + // https://html.spec.whatwg.org/multipage/forms.html#concept-option-disabled + // All such elements have a "form" property. + if ( elem.parentNode && elem.disabled === false ) { + + // Option elements defer to a parent optgroup if present + if ( "label" in elem ) { + if ( "label" in elem.parentNode ) { + return elem.parentNode.disabled === disabled; + } else { + return elem.disabled === disabled; + } + } + + // Support: IE 6 - 11 + // Use the isDisabled shortcut property to check for disabled fieldset ancestors + return elem.isDisabled === disabled || + + // Where there is no isDisabled, check manually + /* jshint -W018 */ + elem.isDisabled !== !disabled && + inDisabledFieldset( elem ) === disabled; + } + + return elem.disabled === disabled; + + // Try to winnow out elements that can't be disabled before trusting the disabled property. + // Some victims get caught in our net (label, legend, menu, track), but it shouldn't + // even exist on them, let alone have a boolean value. + } else if ( "label" in elem ) { + return elem.disabled === disabled; + } + + // Remaining elements are neither :enabled nor :disabled + return false; + }; +} + +/** + * Returns a function to use in pseudos for positionals + * @param {Function} fn + */ +function createPositionalPseudo( fn ) { + return markFunction( function( argument ) { + argument = +argument; + return markFunction( function( seed, matches ) { + var j, + matchIndexes = fn( [], seed.length, argument ), + i = matchIndexes.length; + + // Match elements found at the specified indexes + while ( i-- ) { + if ( seed[ ( j = matchIndexes[ i ] ) ] ) { + seed[ j ] = !( matches[ j ] = seed[ j ] ); + } + } + } ); + } ); +} + +/** + * Checks a node for validity as a Sizzle context + * @param {Element|Object=} context + * @returns {Element|Object|Boolean} The input node if acceptable, otherwise a falsy value + */ +function testContext( context ) { + return context && typeof context.getElementsByTagName !== "undefined" && context; +} + +// Expose support vars for convenience +support = Sizzle.support = {}; + +/** + * Detects XML nodes + * @param {Element|Object} elem An element or a document + * @returns {Boolean} True iff elem is a non-HTML XML node + */ +isXML = Sizzle.isXML = function( elem ) { + var namespace = elem.namespaceURI, + docElem = ( elem.ownerDocument || elem ).documentElement; + + // Support: IE <=8 + // Assume HTML when documentElement doesn't yet exist, such as inside loading iframes + // https://bugs.jquery.com/ticket/4833 + return !rhtml.test( namespace || docElem && docElem.nodeName || "HTML" ); +}; + +/** + * Sets document-related variables once based on the current document + * @param {Element|Object} [doc] An element or document object to use to set the document + * @returns {Object} Returns the current document + */ +setDocument = Sizzle.setDocument = function( node ) { + var hasCompare, subWindow, + doc = node ? node.ownerDocument || node : preferredDoc; + + // Return early if doc is invalid or already selected + // Support: IE 11+, Edge 17 - 18+ + // IE/Edge sometimes throw a "Permission denied" error when strict-comparing + // two documents; shallow comparisons work. + // eslint-disable-next-line eqeqeq + if ( doc == document || doc.nodeType !== 9 || !doc.documentElement ) { + return document; + } + + // Update global variables + document = doc; + docElem = document.documentElement; + documentIsHTML = !isXML( document ); + + // Support: IE 9 - 11+, Edge 12 - 18+ + // Accessing iframe documents after unload throws "permission denied" errors (jQuery #13936) + // Support: IE 11+, Edge 17 - 18+ + // IE/Edge sometimes throw a "Permission denied" error when strict-comparing + // two documents; shallow comparisons work. + // eslint-disable-next-line eqeqeq + if ( preferredDoc != document && + ( subWindow = document.defaultView ) && subWindow.top !== subWindow ) { + + // Support: IE 11, Edge + if ( subWindow.addEventListener ) { + subWindow.addEventListener( "unload", unloadHandler, false ); + + // Support: IE 9 - 10 only + } else if ( subWindow.attachEvent ) { + subWindow.attachEvent( "onunload", unloadHandler ); + } + } + + // Support: IE 8 - 11+, Edge 12 - 18+, Chrome <=16 - 25 only, Firefox <=3.6 - 31 only, + // Safari 4 - 5 only, Opera <=11.6 - 12.x only + // IE/Edge & older browsers don't support the :scope pseudo-class. + // Support: Safari 6.0 only + // Safari 6.0 supports :scope but it's an alias of :root there. + support.scope = assert( function( el ) { + docElem.appendChild( el ).appendChild( document.createElement( "div" ) ); + return typeof el.querySelectorAll !== "undefined" && + !el.querySelectorAll( ":scope fieldset div" ).length; + } ); + + /* Attributes + ---------------------------------------------------------------------- */ + + // Support: IE<8 + // Verify that getAttribute really returns attributes and not properties + // (excepting IE8 booleans) + support.attributes = assert( function( el ) { + el.className = "i"; + return !el.getAttribute( "className" ); + } ); + + /* getElement(s)By* + ---------------------------------------------------------------------- */ + + // Check if getElementsByTagName("*") returns only elements + support.getElementsByTagName = assert( function( el ) { + el.appendChild( document.createComment( "" ) ); + return !el.getElementsByTagName( "*" ).length; + } ); + + // Support: IE<9 + support.getElementsByClassName = rnative.test( document.getElementsByClassName ); + + // Support: IE<10 + // Check if getElementById returns elements by name + // The broken getElementById methods don't pick up programmatically-set names, + // so use a roundabout getElementsByName test + support.getById = assert( function( el ) { + docElem.appendChild( el ).id = expando; + return !document.getElementsByName || !document.getElementsByName( expando ).length; + } ); + + // ID filter and find + if ( support.getById ) { + Expr.filter[ "ID" ] = function( id ) { + var attrId = id.replace( runescape, funescape ); + return function( elem ) { + return elem.getAttribute( "id" ) === attrId; + }; + }; + Expr.find[ "ID" ] = function( id, context ) { + if ( typeof context.getElementById !== "undefined" && documentIsHTML ) { + var elem = context.getElementById( id ); + return elem ? [ elem ] : []; + } + }; + } else { + Expr.filter[ "ID" ] = function( id ) { + var attrId = id.replace( runescape, funescape ); + return function( elem ) { + var node = typeof elem.getAttributeNode !== "undefined" && + elem.getAttributeNode( "id" ); + return node && node.value === attrId; + }; + }; + + // Support: IE 6 - 7 only + // getElementById is not reliable as a find shortcut + Expr.find[ "ID" ] = function( id, context ) { + if ( typeof context.getElementById !== "undefined" && documentIsHTML ) { + var node, i, elems, + elem = context.getElementById( id ); + + if ( elem ) { + + // Verify the id attribute + node = elem.getAttributeNode( "id" ); + if ( node && node.value === id ) { + return [ elem ]; + } + + // Fall back on getElementsByName + elems = context.getElementsByName( id ); + i = 0; + while ( ( elem = elems[ i++ ] ) ) { + node = elem.getAttributeNode( "id" ); + if ( node && node.value === id ) { + return [ elem ]; + } + } + } + + return []; + } + }; + } + + // Tag + Expr.find[ "TAG" ] = support.getElementsByTagName ? + function( tag, context ) { + if ( typeof context.getElementsByTagName !== "undefined" ) { + return context.getElementsByTagName( tag ); + + // DocumentFragment nodes don't have gEBTN + } else if ( support.qsa ) { + return context.querySelectorAll( tag ); + } + } : + + function( tag, context ) { + var elem, + tmp = [], + i = 0, + + // By happy coincidence, a (broken) gEBTN appears on DocumentFragment nodes too + results = context.getElementsByTagName( tag ); + + // Filter out possible comments + if ( tag === "*" ) { + while ( ( elem = results[ i++ ] ) ) { + if ( elem.nodeType === 1 ) { + tmp.push( elem ); + } + } + + return tmp; + } + return results; + }; + + // Class + Expr.find[ "CLASS" ] = support.getElementsByClassName && function( className, context ) { + if ( typeof context.getElementsByClassName !== "undefined" && documentIsHTML ) { + return context.getElementsByClassName( className ); + } + }; + + /* QSA/matchesSelector + ---------------------------------------------------------------------- */ + + // QSA and matchesSelector support + + // matchesSelector(:active) reports false when true (IE9/Opera 11.5) + rbuggyMatches = []; + + // qSa(:focus) reports false when true (Chrome 21) + // We allow this because of a bug in IE8/9 that throws an error + // whenever `document.activeElement` is accessed on an iframe + // So, we allow :focus to pass through QSA all the time to avoid the IE error + // See https://bugs.jquery.com/ticket/13378 + rbuggyQSA = []; + + if ( ( support.qsa = rnative.test( document.querySelectorAll ) ) ) { + + // Build QSA regex + // Regex strategy adopted from Diego Perini + assert( function( el ) { + + var input; + + // Select is set to empty string on purpose + // This is to test IE's treatment of not explicitly + // setting a boolean content attribute, + // since its presence should be enough + // https://bugs.jquery.com/ticket/12359 + docElem.appendChild( el ).innerHTML = "" + + ""; + + // Support: IE8, Opera 11-12.16 + // Nothing should be selected when empty strings follow ^= or $= or *= + // The test attribute must be unknown in Opera but "safe" for WinRT + // https://msdn.microsoft.com/en-us/library/ie/hh465388.aspx#attribute_section + if ( el.querySelectorAll( "[msallowcapture^='']" ).length ) { + rbuggyQSA.push( "[*^$]=" + whitespace + "*(?:''|\"\")" ); + } + + // Support: IE8 + // Boolean attributes and "value" are not treated correctly + if ( !el.querySelectorAll( "[selected]" ).length ) { + rbuggyQSA.push( "\\[" + whitespace + "*(?:value|" + booleans + ")" ); + } + + // Support: Chrome<29, Android<4.4, Safari<7.0+, iOS<7.0+, PhantomJS<1.9.8+ + if ( !el.querySelectorAll( "[id~=" + expando + "-]" ).length ) { + rbuggyQSA.push( "~=" ); + } + + // Support: IE 11+, Edge 15 - 18+ + // IE 11/Edge don't find elements on a `[name='']` query in some cases. + // Adding a temporary attribute to the document before the selection works + // around the issue. + // Interestingly, IE 10 & older don't seem to have the issue. + input = document.createElement( "input" ); + input.setAttribute( "name", "" ); + el.appendChild( input ); + if ( !el.querySelectorAll( "[name='']" ).length ) { + rbuggyQSA.push( "\\[" + whitespace + "*name" + whitespace + "*=" + + whitespace + "*(?:''|\"\")" ); + } + + // Webkit/Opera - :checked should return selected option elements + // http://www.w3.org/TR/2011/REC-css3-selectors-20110929/#checked + // IE8 throws error here and will not see later tests + if ( !el.querySelectorAll( ":checked" ).length ) { + rbuggyQSA.push( ":checked" ); + } + + // Support: Safari 8+, iOS 8+ + // https://bugs.webkit.org/show_bug.cgi?id=136851 + // In-page `selector#id sibling-combinator selector` fails + if ( !el.querySelectorAll( "a#" + expando + "+*" ).length ) { + rbuggyQSA.push( ".#.+[+~]" ); + } + + // Support: Firefox <=3.6 - 5 only + // Old Firefox doesn't throw on a badly-escaped identifier. + el.querySelectorAll( "\\\f" ); + rbuggyQSA.push( "[\\r\\n\\f]" ); + } ); + + assert( function( el ) { + el.innerHTML = "" + + ""; + + // Support: Windows 8 Native Apps + // The type and name attributes are restricted during .innerHTML assignment + var input = document.createElement( "input" ); + input.setAttribute( "type", "hidden" ); + el.appendChild( input ).setAttribute( "name", "D" ); + + // Support: IE8 + // Enforce case-sensitivity of name attribute + if ( el.querySelectorAll( "[name=d]" ).length ) { + rbuggyQSA.push( "name" + whitespace + "*[*^$|!~]?=" ); + } + + // FF 3.5 - :enabled/:disabled and hidden elements (hidden elements are still enabled) + // IE8 throws error here and will not see later tests + if ( el.querySelectorAll( ":enabled" ).length !== 2 ) { + rbuggyQSA.push( ":enabled", ":disabled" ); + } + + // Support: IE9-11+ + // IE's :disabled selector does not pick up the children of disabled fieldsets + docElem.appendChild( el ).disabled = true; + if ( el.querySelectorAll( ":disabled" ).length !== 2 ) { + rbuggyQSA.push( ":enabled", ":disabled" ); + } + + // Support: Opera 10 - 11 only + // Opera 10-11 does not throw on post-comma invalid pseudos + el.querySelectorAll( "*,:x" ); + rbuggyQSA.push( ",.*:" ); + } ); + } + + if ( ( support.matchesSelector = rnative.test( ( matches = docElem.matches || + docElem.webkitMatchesSelector || + docElem.mozMatchesSelector || + docElem.oMatchesSelector || + docElem.msMatchesSelector ) ) ) ) { + + assert( function( el ) { + + // Check to see if it's possible to do matchesSelector + // on a disconnected node (IE 9) + support.disconnectedMatch = matches.call( el, "*" ); + + // This should fail with an exception + // Gecko does not error, returns false instead + matches.call( el, "[s!='']:x" ); + rbuggyMatches.push( "!=", pseudos ); + } ); + } + + rbuggyQSA = rbuggyQSA.length && new RegExp( rbuggyQSA.join( "|" ) ); + rbuggyMatches = rbuggyMatches.length && new RegExp( rbuggyMatches.join( "|" ) ); + + /* Contains + ---------------------------------------------------------------------- */ + hasCompare = rnative.test( docElem.compareDocumentPosition ); + + // Element contains another + // Purposefully self-exclusive + // As in, an element does not contain itself + contains = hasCompare || rnative.test( docElem.contains ) ? + function( a, b ) { + var adown = a.nodeType === 9 ? a.documentElement : a, + bup = b && b.parentNode; + return a === bup || !!( bup && bup.nodeType === 1 && ( + adown.contains ? + adown.contains( bup ) : + a.compareDocumentPosition && a.compareDocumentPosition( bup ) & 16 + ) ); + } : + function( a, b ) { + if ( b ) { + while ( ( b = b.parentNode ) ) { + if ( b === a ) { + return true; + } + } + } + return false; + }; + + /* Sorting + ---------------------------------------------------------------------- */ + + // Document order sorting + sortOrder = hasCompare ? + function( a, b ) { + + // Flag for duplicate removal + if ( a === b ) { + hasDuplicate = true; + return 0; + } + + // Sort on method existence if only one input has compareDocumentPosition + var compare = !a.compareDocumentPosition - !b.compareDocumentPosition; + if ( compare ) { + return compare; + } + + // Calculate position if both inputs belong to the same document + // Support: IE 11+, Edge 17 - 18+ + // IE/Edge sometimes throw a "Permission denied" error when strict-comparing + // two documents; shallow comparisons work. + // eslint-disable-next-line eqeqeq + compare = ( a.ownerDocument || a ) == ( b.ownerDocument || b ) ? + a.compareDocumentPosition( b ) : + + // Otherwise we know they are disconnected + 1; + + // Disconnected nodes + if ( compare & 1 || + ( !support.sortDetached && b.compareDocumentPosition( a ) === compare ) ) { + + // Choose the first element that is related to our preferred document + // Support: IE 11+, Edge 17 - 18+ + // IE/Edge sometimes throw a "Permission denied" error when strict-comparing + // two documents; shallow comparisons work. + // eslint-disable-next-line eqeqeq + if ( a == document || a.ownerDocument == preferredDoc && + contains( preferredDoc, a ) ) { + return -1; + } + + // Support: IE 11+, Edge 17 - 18+ + // IE/Edge sometimes throw a "Permission denied" error when strict-comparing + // two documents; shallow comparisons work. + // eslint-disable-next-line eqeqeq + if ( b == document || b.ownerDocument == preferredDoc && + contains( preferredDoc, b ) ) { + return 1; + } + + // Maintain original order + return sortInput ? + ( indexOf( sortInput, a ) - indexOf( sortInput, b ) ) : + 0; + } + + return compare & 4 ? -1 : 1; + } : + function( a, b ) { + + // Exit early if the nodes are identical + if ( a === b ) { + hasDuplicate = true; + return 0; + } + + var cur, + i = 0, + aup = a.parentNode, + bup = b.parentNode, + ap = [ a ], + bp = [ b ]; + + // Parentless nodes are either documents or disconnected + if ( !aup || !bup ) { + + // Support: IE 11+, Edge 17 - 18+ + // IE/Edge sometimes throw a "Permission denied" error when strict-comparing + // two documents; shallow comparisons work. + /* eslint-disable eqeqeq */ + return a == document ? -1 : + b == document ? 1 : + /* eslint-enable eqeqeq */ + aup ? -1 : + bup ? 1 : + sortInput ? + ( indexOf( sortInput, a ) - indexOf( sortInput, b ) ) : + 0; + + // If the nodes are siblings, we can do a quick check + } else if ( aup === bup ) { + return siblingCheck( a, b ); + } + + // Otherwise we need full lists of their ancestors for comparison + cur = a; + while ( ( cur = cur.parentNode ) ) { + ap.unshift( cur ); + } + cur = b; + while ( ( cur = cur.parentNode ) ) { + bp.unshift( cur ); + } + + // Walk down the tree looking for a discrepancy + while ( ap[ i ] === bp[ i ] ) { + i++; + } + + return i ? + + // Do a sibling check if the nodes have a common ancestor + siblingCheck( ap[ i ], bp[ i ] ) : + + // Otherwise nodes in our document sort first + // Support: IE 11+, Edge 17 - 18+ + // IE/Edge sometimes throw a "Permission denied" error when strict-comparing + // two documents; shallow comparisons work. + /* eslint-disable eqeqeq */ + ap[ i ] == preferredDoc ? -1 : + bp[ i ] == preferredDoc ? 1 : + /* eslint-enable eqeqeq */ + 0; + }; + + return document; +}; + +Sizzle.matches = function( expr, elements ) { + return Sizzle( expr, null, null, elements ); +}; + +Sizzle.matchesSelector = function( elem, expr ) { + setDocument( elem ); + + if ( support.matchesSelector && documentIsHTML && + !nonnativeSelectorCache[ expr + " " ] && + ( !rbuggyMatches || !rbuggyMatches.test( expr ) ) && + ( !rbuggyQSA || !rbuggyQSA.test( expr ) ) ) { + + try { + var ret = matches.call( elem, expr ); + + // IE 9's matchesSelector returns false on disconnected nodes + if ( ret || support.disconnectedMatch || + + // As well, disconnected nodes are said to be in a document + // fragment in IE 9 + elem.document && elem.document.nodeType !== 11 ) { + return ret; + } + } catch ( e ) { + nonnativeSelectorCache( expr, true ); + } + } + + return Sizzle( expr, document, null, [ elem ] ).length > 0; +}; + +Sizzle.contains = function( context, elem ) { + + // Set document vars if needed + // Support: IE 11+, Edge 17 - 18+ + // IE/Edge sometimes throw a "Permission denied" error when strict-comparing + // two documents; shallow comparisons work. + // eslint-disable-next-line eqeqeq + if ( ( context.ownerDocument || context ) != document ) { + setDocument( context ); + } + return contains( context, elem ); +}; + +Sizzle.attr = function( elem, name ) { + + // Set document vars if needed + // Support: IE 11+, Edge 17 - 18+ + // IE/Edge sometimes throw a "Permission denied" error when strict-comparing + // two documents; shallow comparisons work. + // eslint-disable-next-line eqeqeq + if ( ( elem.ownerDocument || elem ) != document ) { + setDocument( elem ); + } + + var fn = Expr.attrHandle[ name.toLowerCase() ], + + // Don't get fooled by Object.prototype properties (jQuery #13807) + val = fn && hasOwn.call( Expr.attrHandle, name.toLowerCase() ) ? + fn( elem, name, !documentIsHTML ) : + undefined; + + return val !== undefined ? + val : + support.attributes || !documentIsHTML ? + elem.getAttribute( name ) : + ( val = elem.getAttributeNode( name ) ) && val.specified ? + val.value : + null; +}; + +Sizzle.escape = function( sel ) { + return ( sel + "" ).replace( rcssescape, fcssescape ); +}; + +Sizzle.error = function( msg ) { + throw new Error( "Syntax error, unrecognized expression: " + msg ); +}; + +/** + * Document sorting and removing duplicates + * @param {ArrayLike} results + */ +Sizzle.uniqueSort = function( results ) { + var elem, + duplicates = [], + j = 0, + i = 0; + + // Unless we *know* we can detect duplicates, assume their presence + hasDuplicate = !support.detectDuplicates; + sortInput = !support.sortStable && results.slice( 0 ); + results.sort( sortOrder ); + + if ( hasDuplicate ) { + while ( ( elem = results[ i++ ] ) ) { + if ( elem === results[ i ] ) { + j = duplicates.push( i ); + } + } + while ( j-- ) { + results.splice( duplicates[ j ], 1 ); + } + } + + // Clear input after sorting to release objects + // See https://github.com/jquery/sizzle/pull/225 + sortInput = null; + + return results; +}; + +/** + * Utility function for retrieving the text value of an array of DOM nodes + * @param {Array|Element} elem + */ +getText = Sizzle.getText = function( elem ) { + var node, + ret = "", + i = 0, + nodeType = elem.nodeType; + + if ( !nodeType ) { + + // If no nodeType, this is expected to be an array + while ( ( node = elem[ i++ ] ) ) { + + // Do not traverse comment nodes + ret += getText( node ); + } + } else if ( nodeType === 1 || nodeType === 9 || nodeType === 11 ) { + + // Use textContent for elements + // innerText usage removed for consistency of new lines (jQuery #11153) + if ( typeof elem.textContent === "string" ) { + return elem.textContent; + } else { + + // Traverse its children + for ( elem = elem.firstChild; elem; elem = elem.nextSibling ) { + ret += getText( elem ); + } + } + } else if ( nodeType === 3 || nodeType === 4 ) { + return elem.nodeValue; + } + + // Do not include comment or processing instruction nodes + + return ret; +}; + +Expr = Sizzle.selectors = { + + // Can be adjusted by the user + cacheLength: 50, + + createPseudo: markFunction, + + match: matchExpr, + + attrHandle: {}, + + find: {}, + + relative: { + ">": { dir: "parentNode", first: true }, + " ": { dir: "parentNode" }, + "+": { dir: "previousSibling", first: true }, + "~": { dir: "previousSibling" } + }, + + preFilter: { + "ATTR": function( match ) { + match[ 1 ] = match[ 1 ].replace( runescape, funescape ); + + // Move the given value to match[3] whether quoted or unquoted + match[ 3 ] = ( match[ 3 ] || match[ 4 ] || + match[ 5 ] || "" ).replace( runescape, funescape ); + + if ( match[ 2 ] === "~=" ) { + match[ 3 ] = " " + match[ 3 ] + " "; + } + + return match.slice( 0, 4 ); + }, + + "CHILD": function( match ) { + + /* matches from matchExpr["CHILD"] + 1 type (only|nth|...) + 2 what (child|of-type) + 3 argument (even|odd|\d*|\d*n([+-]\d+)?|...) + 4 xn-component of xn+y argument ([+-]?\d*n|) + 5 sign of xn-component + 6 x of xn-component + 7 sign of y-component + 8 y of y-component + */ + match[ 1 ] = match[ 1 ].toLowerCase(); + + if ( match[ 1 ].slice( 0, 3 ) === "nth" ) { + + // nth-* requires argument + if ( !match[ 3 ] ) { + Sizzle.error( match[ 0 ] ); + } + + // numeric x and y parameters for Expr.filter.CHILD + // remember that false/true cast respectively to 0/1 + match[ 4 ] = +( match[ 4 ] ? + match[ 5 ] + ( match[ 6 ] || 1 ) : + 2 * ( match[ 3 ] === "even" || match[ 3 ] === "odd" ) ); + match[ 5 ] = +( ( match[ 7 ] + match[ 8 ] ) || match[ 3 ] === "odd" ); + + // other types prohibit arguments + } else if ( match[ 3 ] ) { + Sizzle.error( match[ 0 ] ); + } + + return match; + }, + + "PSEUDO": function( match ) { + var excess, + unquoted = !match[ 6 ] && match[ 2 ]; + + if ( matchExpr[ "CHILD" ].test( match[ 0 ] ) ) { + return null; + } + + // Accept quoted arguments as-is + if ( match[ 3 ] ) { + match[ 2 ] = match[ 4 ] || match[ 5 ] || ""; + + // Strip excess characters from unquoted arguments + } else if ( unquoted && rpseudo.test( unquoted ) && + + // Get excess from tokenize (recursively) + ( excess = tokenize( unquoted, true ) ) && + + // advance to the next closing parenthesis + ( excess = unquoted.indexOf( ")", unquoted.length - excess ) - unquoted.length ) ) { + + // excess is a negative index + match[ 0 ] = match[ 0 ].slice( 0, excess ); + match[ 2 ] = unquoted.slice( 0, excess ); + } + + // Return only captures needed by the pseudo filter method (type and argument) + return match.slice( 0, 3 ); + } + }, + + filter: { + + "TAG": function( nodeNameSelector ) { + var nodeName = nodeNameSelector.replace( runescape, funescape ).toLowerCase(); + return nodeNameSelector === "*" ? + function() { + return true; + } : + function( elem ) { + return elem.nodeName && elem.nodeName.toLowerCase() === nodeName; + }; + }, + + "CLASS": function( className ) { + var pattern = classCache[ className + " " ]; + + return pattern || + ( pattern = new RegExp( "(^|" + whitespace + + ")" + className + "(" + whitespace + "|$)" ) ) && classCache( + className, function( elem ) { + return pattern.test( + typeof elem.className === "string" && elem.className || + typeof elem.getAttribute !== "undefined" && + elem.getAttribute( "class" ) || + "" + ); + } ); + }, + + "ATTR": function( name, operator, check ) { + return function( elem ) { + var result = Sizzle.attr( elem, name ); + + if ( result == null ) { + return operator === "!="; + } + if ( !operator ) { + return true; + } + + result += ""; + + /* eslint-disable max-len */ + + return operator === "=" ? result === check : + operator === "!=" ? result !== check : + operator === "^=" ? check && result.indexOf( check ) === 0 : + operator === "*=" ? check && result.indexOf( check ) > -1 : + operator === "$=" ? check && result.slice( -check.length ) === check : + operator === "~=" ? ( " " + result.replace( rwhitespace, " " ) + " " ).indexOf( check ) > -1 : + operator === "|=" ? result === check || result.slice( 0, check.length + 1 ) === check + "-" : + false; + /* eslint-enable max-len */ + + }; + }, + + "CHILD": function( type, what, _argument, first, last ) { + var simple = type.slice( 0, 3 ) !== "nth", + forward = type.slice( -4 ) !== "last", + ofType = what === "of-type"; + + return first === 1 && last === 0 ? + + // Shortcut for :nth-*(n) + function( elem ) { + return !!elem.parentNode; + } : + + function( elem, _context, xml ) { + var cache, uniqueCache, outerCache, node, nodeIndex, start, + dir = simple !== forward ? "nextSibling" : "previousSibling", + parent = elem.parentNode, + name = ofType && elem.nodeName.toLowerCase(), + useCache = !xml && !ofType, + diff = false; + + if ( parent ) { + + // :(first|last|only)-(child|of-type) + if ( simple ) { + while ( dir ) { + node = elem; + while ( ( node = node[ dir ] ) ) { + if ( ofType ? + node.nodeName.toLowerCase() === name : + node.nodeType === 1 ) { + + return false; + } + } + + // Reverse direction for :only-* (if we haven't yet done so) + start = dir = type === "only" && !start && "nextSibling"; + } + return true; + } + + start = [ forward ? parent.firstChild : parent.lastChild ]; + + // non-xml :nth-child(...) stores cache data on `parent` + if ( forward && useCache ) { + + // Seek `elem` from a previously-cached index + + // ...in a gzip-friendly way + node = parent; + outerCache = node[ expando ] || ( node[ expando ] = {} ); + + // Support: IE <9 only + // Defend against cloned attroperties (jQuery gh-1709) + uniqueCache = outerCache[ node.uniqueID ] || + ( outerCache[ node.uniqueID ] = {} ); + + cache = uniqueCache[ type ] || []; + nodeIndex = cache[ 0 ] === dirruns && cache[ 1 ]; + diff = nodeIndex && cache[ 2 ]; + node = nodeIndex && parent.childNodes[ nodeIndex ]; + + while ( ( node = ++nodeIndex && node && node[ dir ] || + + // Fallback to seeking `elem` from the start + ( diff = nodeIndex = 0 ) || start.pop() ) ) { + + // When found, cache indexes on `parent` and break + if ( node.nodeType === 1 && ++diff && node === elem ) { + uniqueCache[ type ] = [ dirruns, nodeIndex, diff ]; + break; + } + } + + } else { + + // Use previously-cached element index if available + if ( useCache ) { + + // ...in a gzip-friendly way + node = elem; + outerCache = node[ expando ] || ( node[ expando ] = {} ); + + // Support: IE <9 only + // Defend against cloned attroperties (jQuery gh-1709) + uniqueCache = outerCache[ node.uniqueID ] || + ( outerCache[ node.uniqueID ] = {} ); + + cache = uniqueCache[ type ] || []; + nodeIndex = cache[ 0 ] === dirruns && cache[ 1 ]; + diff = nodeIndex; + } + + // xml :nth-child(...) + // or :nth-last-child(...) or :nth(-last)?-of-type(...) + if ( diff === false ) { + + // Use the same loop as above to seek `elem` from the start + while ( ( node = ++nodeIndex && node && node[ dir ] || + ( diff = nodeIndex = 0 ) || start.pop() ) ) { + + if ( ( ofType ? + node.nodeName.toLowerCase() === name : + node.nodeType === 1 ) && + ++diff ) { + + // Cache the index of each encountered element + if ( useCache ) { + outerCache = node[ expando ] || + ( node[ expando ] = {} ); + + // Support: IE <9 only + // Defend against cloned attroperties (jQuery gh-1709) + uniqueCache = outerCache[ node.uniqueID ] || + ( outerCache[ node.uniqueID ] = {} ); + + uniqueCache[ type ] = [ dirruns, diff ]; + } + + if ( node === elem ) { + break; + } + } + } + } + } + + // Incorporate the offset, then check against cycle size + diff -= last; + return diff === first || ( diff % first === 0 && diff / first >= 0 ); + } + }; + }, + + "PSEUDO": function( pseudo, argument ) { + + // pseudo-class names are case-insensitive + // http://www.w3.org/TR/selectors/#pseudo-classes + // Prioritize by case sensitivity in case custom pseudos are added with uppercase letters + // Remember that setFilters inherits from pseudos + var args, + fn = Expr.pseudos[ pseudo ] || Expr.setFilters[ pseudo.toLowerCase() ] || + Sizzle.error( "unsupported pseudo: " + pseudo ); + + // The user may use createPseudo to indicate that + // arguments are needed to create the filter function + // just as Sizzle does + if ( fn[ expando ] ) { + return fn( argument ); + } + + // But maintain support for old signatures + if ( fn.length > 1 ) { + args = [ pseudo, pseudo, "", argument ]; + return Expr.setFilters.hasOwnProperty( pseudo.toLowerCase() ) ? + markFunction( function( seed, matches ) { + var idx, + matched = fn( seed, argument ), + i = matched.length; + while ( i-- ) { + idx = indexOf( seed, matched[ i ] ); + seed[ idx ] = !( matches[ idx ] = matched[ i ] ); + } + } ) : + function( elem ) { + return fn( elem, 0, args ); + }; + } + + return fn; + } + }, + + pseudos: { + + // Potentially complex pseudos + "not": markFunction( function( selector ) { + + // Trim the selector passed to compile + // to avoid treating leading and trailing + // spaces as combinators + var input = [], + results = [], + matcher = compile( selector.replace( rtrim, "$1" ) ); + + return matcher[ expando ] ? + markFunction( function( seed, matches, _context, xml ) { + var elem, + unmatched = matcher( seed, null, xml, [] ), + i = seed.length; + + // Match elements unmatched by `matcher` + while ( i-- ) { + if ( ( elem = unmatched[ i ] ) ) { + seed[ i ] = !( matches[ i ] = elem ); + } + } + } ) : + function( elem, _context, xml ) { + input[ 0 ] = elem; + matcher( input, null, xml, results ); + + // Don't keep the element (issue #299) + input[ 0 ] = null; + return !results.pop(); + }; + } ), + + "has": markFunction( function( selector ) { + return function( elem ) { + return Sizzle( selector, elem ).length > 0; + }; + } ), + + "contains": markFunction( function( text ) { + text = text.replace( runescape, funescape ); + return function( elem ) { + return ( elem.textContent || getText( elem ) ).indexOf( text ) > -1; + }; + } ), + + // "Whether an element is represented by a :lang() selector + // is based solely on the element's language value + // being equal to the identifier C, + // or beginning with the identifier C immediately followed by "-". + // The matching of C against the element's language value is performed case-insensitively. + // The identifier C does not have to be a valid language name." + // http://www.w3.org/TR/selectors/#lang-pseudo + "lang": markFunction( function( lang ) { + + // lang value must be a valid identifier + if ( !ridentifier.test( lang || "" ) ) { + Sizzle.error( "unsupported lang: " + lang ); + } + lang = lang.replace( runescape, funescape ).toLowerCase(); + return function( elem ) { + var elemLang; + do { + if ( ( elemLang = documentIsHTML ? + elem.lang : + elem.getAttribute( "xml:lang" ) || elem.getAttribute( "lang" ) ) ) { + + elemLang = elemLang.toLowerCase(); + return elemLang === lang || elemLang.indexOf( lang + "-" ) === 0; + } + } while ( ( elem = elem.parentNode ) && elem.nodeType === 1 ); + return false; + }; + } ), + + // Miscellaneous + "target": function( elem ) { + var hash = window.location && window.location.hash; + return hash && hash.slice( 1 ) === elem.id; + }, + + "root": function( elem ) { + return elem === docElem; + }, + + "focus": function( elem ) { + return elem === document.activeElement && + ( !document.hasFocus || document.hasFocus() ) && + !!( elem.type || elem.href || ~elem.tabIndex ); + }, + + // Boolean properties + "enabled": createDisabledPseudo( false ), + "disabled": createDisabledPseudo( true ), + + "checked": function( elem ) { + + // In CSS3, :checked should return both checked and selected elements + // http://www.w3.org/TR/2011/REC-css3-selectors-20110929/#checked + var nodeName = elem.nodeName.toLowerCase(); + return ( nodeName === "input" && !!elem.checked ) || + ( nodeName === "option" && !!elem.selected ); + }, + + "selected": function( elem ) { + + // Accessing this property makes selected-by-default + // options in Safari work properly + if ( elem.parentNode ) { + // eslint-disable-next-line no-unused-expressions + elem.parentNode.selectedIndex; + } + + return elem.selected === true; + }, + + // Contents + "empty": function( elem ) { + + // http://www.w3.org/TR/selectors/#empty-pseudo + // :empty is negated by element (1) or content nodes (text: 3; cdata: 4; entity ref: 5), + // but not by others (comment: 8; processing instruction: 7; etc.) + // nodeType < 6 works because attributes (2) do not appear as children + for ( elem = elem.firstChild; elem; elem = elem.nextSibling ) { + if ( elem.nodeType < 6 ) { + return false; + } + } + return true; + }, + + "parent": function( elem ) { + return !Expr.pseudos[ "empty" ]( elem ); + }, + + // Element/input types + "header": function( elem ) { + return rheader.test( elem.nodeName ); + }, + + "input": function( elem ) { + return rinputs.test( elem.nodeName ); + }, + + "button": function( elem ) { + var name = elem.nodeName.toLowerCase(); + return name === "input" && elem.type === "button" || name === "button"; + }, + + "text": function( elem ) { + var attr; + return elem.nodeName.toLowerCase() === "input" && + elem.type === "text" && + + // Support: IE<8 + // New HTML5 attribute values (e.g., "search") appear with elem.type === "text" + ( ( attr = elem.getAttribute( "type" ) ) == null || + attr.toLowerCase() === "text" ); + }, + + // Position-in-collection + "first": createPositionalPseudo( function() { + return [ 0 ]; + } ), + + "last": createPositionalPseudo( function( _matchIndexes, length ) { + return [ length - 1 ]; + } ), + + "eq": createPositionalPseudo( function( _matchIndexes, length, argument ) { + return [ argument < 0 ? argument + length : argument ]; + } ), + + "even": createPositionalPseudo( function( matchIndexes, length ) { + var i = 0; + for ( ; i < length; i += 2 ) { + matchIndexes.push( i ); + } + return matchIndexes; + } ), + + "odd": createPositionalPseudo( function( matchIndexes, length ) { + var i = 1; + for ( ; i < length; i += 2 ) { + matchIndexes.push( i ); + } + return matchIndexes; + } ), + + "lt": createPositionalPseudo( function( matchIndexes, length, argument ) { + var i = argument < 0 ? + argument + length : + argument > length ? + length : + argument; + for ( ; --i >= 0; ) { + matchIndexes.push( i ); + } + return matchIndexes; + } ), + + "gt": createPositionalPseudo( function( matchIndexes, length, argument ) { + var i = argument < 0 ? argument + length : argument; + for ( ; ++i < length; ) { + matchIndexes.push( i ); + } + return matchIndexes; + } ) + } +}; + +Expr.pseudos[ "nth" ] = Expr.pseudos[ "eq" ]; + +// Add button/input type pseudos +for ( i in { radio: true, checkbox: true, file: true, password: true, image: true } ) { + Expr.pseudos[ i ] = createInputPseudo( i ); +} +for ( i in { submit: true, reset: true } ) { + Expr.pseudos[ i ] = createButtonPseudo( i ); +} + +// Easy API for creating new setFilters +function setFilters() {} +setFilters.prototype = Expr.filters = Expr.pseudos; +Expr.setFilters = new setFilters(); + +tokenize = Sizzle.tokenize = function( selector, parseOnly ) { + var matched, match, tokens, type, + soFar, groups, preFilters, + cached = tokenCache[ selector + " " ]; + + if ( cached ) { + return parseOnly ? 0 : cached.slice( 0 ); + } + + soFar = selector; + groups = []; + preFilters = Expr.preFilter; + + while ( soFar ) { + + // Comma and first run + if ( !matched || ( match = rcomma.exec( soFar ) ) ) { + if ( match ) { + + // Don't consume trailing commas as valid + soFar = soFar.slice( match[ 0 ].length ) || soFar; + } + groups.push( ( tokens = [] ) ); + } + + matched = false; + + // Combinators + if ( ( match = rcombinators.exec( soFar ) ) ) { + matched = match.shift(); + tokens.push( { + value: matched, + + // Cast descendant combinators to space + type: match[ 0 ].replace( rtrim, " " ) + } ); + soFar = soFar.slice( matched.length ); + } + + // Filters + for ( type in Expr.filter ) { + if ( ( match = matchExpr[ type ].exec( soFar ) ) && ( !preFilters[ type ] || + ( match = preFilters[ type ]( match ) ) ) ) { + matched = match.shift(); + tokens.push( { + value: matched, + type: type, + matches: match + } ); + soFar = soFar.slice( matched.length ); + } + } + + if ( !matched ) { + break; + } + } + + // Return the length of the invalid excess + // if we're just parsing + // Otherwise, throw an error or return tokens + return parseOnly ? + soFar.length : + soFar ? + Sizzle.error( selector ) : + + // Cache the tokens + tokenCache( selector, groups ).slice( 0 ); +}; + +function toSelector( tokens ) { + var i = 0, + len = tokens.length, + selector = ""; + for ( ; i < len; i++ ) { + selector += tokens[ i ].value; + } + return selector; +} + +function addCombinator( matcher, combinator, base ) { + var dir = combinator.dir, + skip = combinator.next, + key = skip || dir, + checkNonElements = base && key === "parentNode", + doneName = done++; + + return combinator.first ? + + // Check against closest ancestor/preceding element + function( elem, context, xml ) { + while ( ( elem = elem[ dir ] ) ) { + if ( elem.nodeType === 1 || checkNonElements ) { + return matcher( elem, context, xml ); + } + } + return false; + } : + + // Check against all ancestor/preceding elements + function( elem, context, xml ) { + var oldCache, uniqueCache, outerCache, + newCache = [ dirruns, doneName ]; + + // We can't set arbitrary data on XML nodes, so they don't benefit from combinator caching + if ( xml ) { + while ( ( elem = elem[ dir ] ) ) { + if ( elem.nodeType === 1 || checkNonElements ) { + if ( matcher( elem, context, xml ) ) { + return true; + } + } + } + } else { + while ( ( elem = elem[ dir ] ) ) { + if ( elem.nodeType === 1 || checkNonElements ) { + outerCache = elem[ expando ] || ( elem[ expando ] = {} ); + + // Support: IE <9 only + // Defend against cloned attroperties (jQuery gh-1709) + uniqueCache = outerCache[ elem.uniqueID ] || + ( outerCache[ elem.uniqueID ] = {} ); + + if ( skip && skip === elem.nodeName.toLowerCase() ) { + elem = elem[ dir ] || elem; + } else if ( ( oldCache = uniqueCache[ key ] ) && + oldCache[ 0 ] === dirruns && oldCache[ 1 ] === doneName ) { + + // Assign to newCache so results back-propagate to previous elements + return ( newCache[ 2 ] = oldCache[ 2 ] ); + } else { + + // Reuse newcache so results back-propagate to previous elements + uniqueCache[ key ] = newCache; + + // A match means we're done; a fail means we have to keep checking + if ( ( newCache[ 2 ] = matcher( elem, context, xml ) ) ) { + return true; + } + } + } + } + } + return false; + }; +} + +function elementMatcher( matchers ) { + return matchers.length > 1 ? + function( elem, context, xml ) { + var i = matchers.length; + while ( i-- ) { + if ( !matchers[ i ]( elem, context, xml ) ) { + return false; + } + } + return true; + } : + matchers[ 0 ]; +} + +function multipleContexts( selector, contexts, results ) { + var i = 0, + len = contexts.length; + for ( ; i < len; i++ ) { + Sizzle( selector, contexts[ i ], results ); + } + return results; +} + +function condense( unmatched, map, filter, context, xml ) { + var elem, + newUnmatched = [], + i = 0, + len = unmatched.length, + mapped = map != null; + + for ( ; i < len; i++ ) { + if ( ( elem = unmatched[ i ] ) ) { + if ( !filter || filter( elem, context, xml ) ) { + newUnmatched.push( elem ); + if ( mapped ) { + map.push( i ); + } + } + } + } + + return newUnmatched; +} + +function setMatcher( preFilter, selector, matcher, postFilter, postFinder, postSelector ) { + if ( postFilter && !postFilter[ expando ] ) { + postFilter = setMatcher( postFilter ); + } + if ( postFinder && !postFinder[ expando ] ) { + postFinder = setMatcher( postFinder, postSelector ); + } + return markFunction( function( seed, results, context, xml ) { + var temp, i, elem, + preMap = [], + postMap = [], + preexisting = results.length, + + // Get initial elements from seed or context + elems = seed || multipleContexts( + selector || "*", + context.nodeType ? [ context ] : context, + [] + ), + + // Prefilter to get matcher input, preserving a map for seed-results synchronization + matcherIn = preFilter && ( seed || !selector ) ? + condense( elems, preMap, preFilter, context, xml ) : + elems, + + matcherOut = matcher ? + + // If we have a postFinder, or filtered seed, or non-seed postFilter or preexisting results, + postFinder || ( seed ? preFilter : preexisting || postFilter ) ? + + // ...intermediate processing is necessary + [] : + + // ...otherwise use results directly + results : + matcherIn; + + // Find primary matches + if ( matcher ) { + matcher( matcherIn, matcherOut, context, xml ); + } + + // Apply postFilter + if ( postFilter ) { + temp = condense( matcherOut, postMap ); + postFilter( temp, [], context, xml ); + + // Un-match failing elements by moving them back to matcherIn + i = temp.length; + while ( i-- ) { + if ( ( elem = temp[ i ] ) ) { + matcherOut[ postMap[ i ] ] = !( matcherIn[ postMap[ i ] ] = elem ); + } + } + } + + if ( seed ) { + if ( postFinder || preFilter ) { + if ( postFinder ) { + + // Get the final matcherOut by condensing this intermediate into postFinder contexts + temp = []; + i = matcherOut.length; + while ( i-- ) { + if ( ( elem = matcherOut[ i ] ) ) { + + // Restore matcherIn since elem is not yet a final match + temp.push( ( matcherIn[ i ] = elem ) ); + } + } + postFinder( null, ( matcherOut = [] ), temp, xml ); + } + + // Move matched elements from seed to results to keep them synchronized + i = matcherOut.length; + while ( i-- ) { + if ( ( elem = matcherOut[ i ] ) && + ( temp = postFinder ? indexOf( seed, elem ) : preMap[ i ] ) > -1 ) { + + seed[ temp ] = !( results[ temp ] = elem ); + } + } + } + + // Add elements to results, through postFinder if defined + } else { + matcherOut = condense( + matcherOut === results ? + matcherOut.splice( preexisting, matcherOut.length ) : + matcherOut + ); + if ( postFinder ) { + postFinder( null, results, matcherOut, xml ); + } else { + push.apply( results, matcherOut ); + } + } + } ); +} + +function matcherFromTokens( tokens ) { + var checkContext, matcher, j, + len = tokens.length, + leadingRelative = Expr.relative[ tokens[ 0 ].type ], + implicitRelative = leadingRelative || Expr.relative[ " " ], + i = leadingRelative ? 1 : 0, + + // The foundational matcher ensures that elements are reachable from top-level context(s) + matchContext = addCombinator( function( elem ) { + return elem === checkContext; + }, implicitRelative, true ), + matchAnyContext = addCombinator( function( elem ) { + return indexOf( checkContext, elem ) > -1; + }, implicitRelative, true ), + matchers = [ function( elem, context, xml ) { + var ret = ( !leadingRelative && ( xml || context !== outermostContext ) ) || ( + ( checkContext = context ).nodeType ? + matchContext( elem, context, xml ) : + matchAnyContext( elem, context, xml ) ); + + // Avoid hanging onto element (issue #299) + checkContext = null; + return ret; + } ]; + + for ( ; i < len; i++ ) { + if ( ( matcher = Expr.relative[ tokens[ i ].type ] ) ) { + matchers = [ addCombinator( elementMatcher( matchers ), matcher ) ]; + } else { + matcher = Expr.filter[ tokens[ i ].type ].apply( null, tokens[ i ].matches ); + + // Return special upon seeing a positional matcher + if ( matcher[ expando ] ) { + + // Find the next relative operator (if any) for proper handling + j = ++i; + for ( ; j < len; j++ ) { + if ( Expr.relative[ tokens[ j ].type ] ) { + break; + } + } + return setMatcher( + i > 1 && elementMatcher( matchers ), + i > 1 && toSelector( + + // If the preceding token was a descendant combinator, insert an implicit any-element `*` + tokens + .slice( 0, i - 1 ) + .concat( { value: tokens[ i - 2 ].type === " " ? "*" : "" } ) + ).replace( rtrim, "$1" ), + matcher, + i < j && matcherFromTokens( tokens.slice( i, j ) ), + j < len && matcherFromTokens( ( tokens = tokens.slice( j ) ) ), + j < len && toSelector( tokens ) + ); + } + matchers.push( matcher ); + } + } + + return elementMatcher( matchers ); +} + +function matcherFromGroupMatchers( elementMatchers, setMatchers ) { + var bySet = setMatchers.length > 0, + byElement = elementMatchers.length > 0, + superMatcher = function( seed, context, xml, results, outermost ) { + var elem, j, matcher, + matchedCount = 0, + i = "0", + unmatched = seed && [], + setMatched = [], + contextBackup = outermostContext, + + // We must always have either seed elements or outermost context + elems = seed || byElement && Expr.find[ "TAG" ]( "*", outermost ), + + // Use integer dirruns iff this is the outermost matcher + dirrunsUnique = ( dirruns += contextBackup == null ? 1 : Math.random() || 0.1 ), + len = elems.length; + + if ( outermost ) { + + // Support: IE 11+, Edge 17 - 18+ + // IE/Edge sometimes throw a "Permission denied" error when strict-comparing + // two documents; shallow comparisons work. + // eslint-disable-next-line eqeqeq + outermostContext = context == document || context || outermost; + } + + // Add elements passing elementMatchers directly to results + // Support: IE<9, Safari + // Tolerate NodeList properties (IE: "length"; Safari: ) matching elements by id + for ( ; i !== len && ( elem = elems[ i ] ) != null; i++ ) { + if ( byElement && elem ) { + j = 0; + + // Support: IE 11+, Edge 17 - 18+ + // IE/Edge sometimes throw a "Permission denied" error when strict-comparing + // two documents; shallow comparisons work. + // eslint-disable-next-line eqeqeq + if ( !context && elem.ownerDocument != document ) { + setDocument( elem ); + xml = !documentIsHTML; + } + while ( ( matcher = elementMatchers[ j++ ] ) ) { + if ( matcher( elem, context || document, xml ) ) { + results.push( elem ); + break; + } + } + if ( outermost ) { + dirruns = dirrunsUnique; + } + } + + // Track unmatched elements for set filters + if ( bySet ) { + + // They will have gone through all possible matchers + if ( ( elem = !matcher && elem ) ) { + matchedCount--; + } + + // Lengthen the array for every element, matched or not + if ( seed ) { + unmatched.push( elem ); + } + } + } + + // `i` is now the count of elements visited above, and adding it to `matchedCount` + // makes the latter nonnegative. + matchedCount += i; + + // Apply set filters to unmatched elements + // NOTE: This can be skipped if there are no unmatched elements (i.e., `matchedCount` + // equals `i`), unless we didn't visit _any_ elements in the above loop because we have + // no element matchers and no seed. + // Incrementing an initially-string "0" `i` allows `i` to remain a string only in that + // case, which will result in a "00" `matchedCount` that differs from `i` but is also + // numerically zero. + if ( bySet && i !== matchedCount ) { + j = 0; + while ( ( matcher = setMatchers[ j++ ] ) ) { + matcher( unmatched, setMatched, context, xml ); + } + + if ( seed ) { + + // Reintegrate element matches to eliminate the need for sorting + if ( matchedCount > 0 ) { + while ( i-- ) { + if ( !( unmatched[ i ] || setMatched[ i ] ) ) { + setMatched[ i ] = pop.call( results ); + } + } + } + + // Discard index placeholder values to get only actual matches + setMatched = condense( setMatched ); + } + + // Add matches to results + push.apply( results, setMatched ); + + // Seedless set matches succeeding multiple successful matchers stipulate sorting + if ( outermost && !seed && setMatched.length > 0 && + ( matchedCount + setMatchers.length ) > 1 ) { + + Sizzle.uniqueSort( results ); + } + } + + // Override manipulation of globals by nested matchers + if ( outermost ) { + dirruns = dirrunsUnique; + outermostContext = contextBackup; + } + + return unmatched; + }; + + return bySet ? + markFunction( superMatcher ) : + superMatcher; +} + +compile = Sizzle.compile = function( selector, match /* Internal Use Only */ ) { + var i, + setMatchers = [], + elementMatchers = [], + cached = compilerCache[ selector + " " ]; + + if ( !cached ) { + + // Generate a function of recursive functions that can be used to check each element + if ( !match ) { + match = tokenize( selector ); + } + i = match.length; + while ( i-- ) { + cached = matcherFromTokens( match[ i ] ); + if ( cached[ expando ] ) { + setMatchers.push( cached ); + } else { + elementMatchers.push( cached ); + } + } + + // Cache the compiled function + cached = compilerCache( + selector, + matcherFromGroupMatchers( elementMatchers, setMatchers ) + ); + + // Save selector and tokenization + cached.selector = selector; + } + return cached; +}; + +/** + * A low-level selection function that works with Sizzle's compiled + * selector functions + * @param {String|Function} selector A selector or a pre-compiled + * selector function built with Sizzle.compile + * @param {Element} context + * @param {Array} [results] + * @param {Array} [seed] A set of elements to match against + */ +select = Sizzle.select = function( selector, context, results, seed ) { + var i, tokens, token, type, find, + compiled = typeof selector === "function" && selector, + match = !seed && tokenize( ( selector = compiled.selector || selector ) ); + + results = results || []; + + // Try to minimize operations if there is only one selector in the list and no seed + // (the latter of which guarantees us context) + if ( match.length === 1 ) { + + // Reduce context if the leading compound selector is an ID + tokens = match[ 0 ] = match[ 0 ].slice( 0 ); + if ( tokens.length > 2 && ( token = tokens[ 0 ] ).type === "ID" && + context.nodeType === 9 && documentIsHTML && Expr.relative[ tokens[ 1 ].type ] ) { + + context = ( Expr.find[ "ID" ]( token.matches[ 0 ] + .replace( runescape, funescape ), context ) || [] )[ 0 ]; + if ( !context ) { + return results; + + // Precompiled matchers will still verify ancestry, so step up a level + } else if ( compiled ) { + context = context.parentNode; + } + + selector = selector.slice( tokens.shift().value.length ); + } + + // Fetch a seed set for right-to-left matching + i = matchExpr[ "needsContext" ].test( selector ) ? 0 : tokens.length; + while ( i-- ) { + token = tokens[ i ]; + + // Abort if we hit a combinator + if ( Expr.relative[ ( type = token.type ) ] ) { + break; + } + if ( ( find = Expr.find[ type ] ) ) { + + // Search, expanding context for leading sibling combinators + if ( ( seed = find( + token.matches[ 0 ].replace( runescape, funescape ), + rsibling.test( tokens[ 0 ].type ) && testContext( context.parentNode ) || + context + ) ) ) { + + // If seed is empty or no tokens remain, we can return early + tokens.splice( i, 1 ); + selector = seed.length && toSelector( tokens ); + if ( !selector ) { + push.apply( results, seed ); + return results; + } + + break; + } + } + } + } + + // Compile and execute a filtering function if one is not provided + // Provide `match` to avoid retokenization if we modified the selector above + ( compiled || compile( selector, match ) )( + seed, + context, + !documentIsHTML, + results, + !context || rsibling.test( selector ) && testContext( context.parentNode ) || context + ); + return results; +}; + +// One-time assignments + +// Sort stability +support.sortStable = expando.split( "" ).sort( sortOrder ).join( "" ) === expando; + +// Support: Chrome 14-35+ +// Always assume duplicates if they aren't passed to the comparison function +support.detectDuplicates = !!hasDuplicate; + +// Initialize against the default document +setDocument(); + +// Support: Webkit<537.32 - Safari 6.0.3/Chrome 25 (fixed in Chrome 27) +// Detached nodes confoundingly follow *each other* +support.sortDetached = assert( function( el ) { + + // Should return 1, but returns 4 (following) + return el.compareDocumentPosition( document.createElement( "fieldset" ) ) & 1; +} ); + +// Support: IE<8 +// Prevent attribute/property "interpolation" +// https://msdn.microsoft.com/en-us/library/ms536429%28VS.85%29.aspx +if ( !assert( function( el ) { + el.innerHTML = ""; + return el.firstChild.getAttribute( "href" ) === "#"; +} ) ) { + addHandle( "type|href|height|width", function( elem, name, isXML ) { + if ( !isXML ) { + return elem.getAttribute( name, name.toLowerCase() === "type" ? 1 : 2 ); + } + } ); +} + +// Support: IE<9 +// Use defaultValue in place of getAttribute("value") +if ( !support.attributes || !assert( function( el ) { + el.innerHTML = ""; + el.firstChild.setAttribute( "value", "" ); + return el.firstChild.getAttribute( "value" ) === ""; +} ) ) { + addHandle( "value", function( elem, _name, isXML ) { + if ( !isXML && elem.nodeName.toLowerCase() === "input" ) { + return elem.defaultValue; + } + } ); +} + +// Support: IE<9 +// Use getAttributeNode to fetch booleans when getAttribute lies +if ( !assert( function( el ) { + return el.getAttribute( "disabled" ) == null; +} ) ) { + addHandle( booleans, function( elem, name, isXML ) { + var val; + if ( !isXML ) { + return elem[ name ] === true ? name.toLowerCase() : + ( val = elem.getAttributeNode( name ) ) && val.specified ? + val.value : + null; + } + } ); +} + +return Sizzle; + +} )( window ); + + + +jQuery.find = Sizzle; +jQuery.expr = Sizzle.selectors; + +// Deprecated +jQuery.expr[ ":" ] = jQuery.expr.pseudos; +jQuery.uniqueSort = jQuery.unique = Sizzle.uniqueSort; +jQuery.text = Sizzle.getText; +jQuery.isXMLDoc = Sizzle.isXML; +jQuery.contains = Sizzle.contains; +jQuery.escapeSelector = Sizzle.escape; + + + + +var dir = function( elem, dir, until ) { + var matched = [], + truncate = until !== undefined; + + while ( ( elem = elem[ dir ] ) && elem.nodeType !== 9 ) { + if ( elem.nodeType === 1 ) { + if ( truncate && jQuery( elem ).is( until ) ) { + break; + } + matched.push( elem ); + } + } + return matched; +}; + + +var siblings = function( n, elem ) { + var matched = []; + + for ( ; n; n = n.nextSibling ) { + if ( n.nodeType === 1 && n !== elem ) { + matched.push( n ); + } + } + + return matched; +}; + + +var rneedsContext = jQuery.expr.match.needsContext; + + + +function nodeName( elem, name ) { + + return elem.nodeName && elem.nodeName.toLowerCase() === name.toLowerCase(); + +}; +var rsingleTag = ( /^<([a-z][^\/\0>:\x20\t\r\n\f]*)[\x20\t\r\n\f]*\/?>(?:<\/\1>|)$/i ); + + + +// Implement the identical functionality for filter and not +function winnow( elements, qualifier, not ) { + if ( isFunction( qualifier ) ) { + return jQuery.grep( elements, function( elem, i ) { + return !!qualifier.call( elem, i, elem ) !== not; + } ); + } + + // Single element + if ( qualifier.nodeType ) { + return jQuery.grep( elements, function( elem ) { + return ( elem === qualifier ) !== not; + } ); + } + + // Arraylike of elements (jQuery, arguments, Array) + if ( typeof qualifier !== "string" ) { + return jQuery.grep( elements, function( elem ) { + return ( indexOf.call( qualifier, elem ) > -1 ) !== not; + } ); + } + + // Filtered directly for both simple and complex selectors + return jQuery.filter( qualifier, elements, not ); +} + +jQuery.filter = function( expr, elems, not ) { + var elem = elems[ 0 ]; + + if ( not ) { + expr = ":not(" + expr + ")"; + } + + if ( elems.length === 1 && elem.nodeType === 1 ) { + return jQuery.find.matchesSelector( elem, expr ) ? [ elem ] : []; + } + + return jQuery.find.matches( expr, jQuery.grep( elems, function( elem ) { + return elem.nodeType === 1; + } ) ); +}; + +jQuery.fn.extend( { + find: function( selector ) { + var i, ret, + len = this.length, + self = this; + + if ( typeof selector !== "string" ) { + return this.pushStack( jQuery( selector ).filter( function() { + for ( i = 0; i < len; i++ ) { + if ( jQuery.contains( self[ i ], this ) ) { + return true; + } + } + } ) ); + } + + ret = this.pushStack( [] ); + + for ( i = 0; i < len; i++ ) { + jQuery.find( selector, self[ i ], ret ); + } + + return len > 1 ? jQuery.uniqueSort( ret ) : ret; + }, + filter: function( selector ) { + return this.pushStack( winnow( this, selector || [], false ) ); + }, + not: function( selector ) { + return this.pushStack( winnow( this, selector || [], true ) ); + }, + is: function( selector ) { + return !!winnow( + this, + + // If this is a positional/relative selector, check membership in the returned set + // so $("p:first").is("p:last") won't return true for a doc with two "p". + typeof selector === "string" && rneedsContext.test( selector ) ? + jQuery( selector ) : + selector || [], + false + ).length; + } +} ); + + +// Initialize a jQuery object + + +// A central reference to the root jQuery(document) +var rootjQuery, + + // A simple way to check for HTML strings + // Prioritize #id over to avoid XSS via location.hash (#9521) + // Strict HTML recognition (#11290: must start with <) + // Shortcut simple #id case for speed + rquickExpr = /^(?:\s*(<[\w\W]+>)[^>]*|#([\w-]+))$/, + + init = jQuery.fn.init = function( selector, context, root ) { + var match, elem; + + // HANDLE: $(""), $(null), $(undefined), $(false) + if ( !selector ) { + return this; + } + + // Method init() accepts an alternate rootjQuery + // so migrate can support jQuery.sub (gh-2101) + root = root || rootjQuery; + + // Handle HTML strings + if ( typeof selector === "string" ) { + if ( selector[ 0 ] === "<" && + selector[ selector.length - 1 ] === ">" && + selector.length >= 3 ) { + + // Assume that strings that start and end with <> are HTML and skip the regex check + match = [ null, selector, null ]; + + } else { + match = rquickExpr.exec( selector ); + } + + // Match html or make sure no context is specified for #id + if ( match && ( match[ 1 ] || !context ) ) { + + // HANDLE: $(html) -> $(array) + if ( match[ 1 ] ) { + context = context instanceof jQuery ? context[ 0 ] : context; + + // Option to run scripts is true for back-compat + // Intentionally let the error be thrown if parseHTML is not present + jQuery.merge( this, jQuery.parseHTML( + match[ 1 ], + context && context.nodeType ? context.ownerDocument || context : document, + true + ) ); + + // HANDLE: $(html, props) + if ( rsingleTag.test( match[ 1 ] ) && jQuery.isPlainObject( context ) ) { + for ( match in context ) { + + // Properties of context are called as methods if possible + if ( isFunction( this[ match ] ) ) { + this[ match ]( context[ match ] ); + + // ...and otherwise set as attributes + } else { + this.attr( match, context[ match ] ); + } + } + } + + return this; + + // HANDLE: $(#id) + } else { + elem = document.getElementById( match[ 2 ] ); + + if ( elem ) { + + // Inject the element directly into the jQuery object + this[ 0 ] = elem; + this.length = 1; + } + return this; + } + + // HANDLE: $(expr, $(...)) + } else if ( !context || context.jquery ) { + return ( context || root ).find( selector ); + + // HANDLE: $(expr, context) + // (which is just equivalent to: $(context).find(expr) + } else { + return this.constructor( context ).find( selector ); + } + + // HANDLE: $(DOMElement) + } else if ( selector.nodeType ) { + this[ 0 ] = selector; + this.length = 1; + return this; + + // HANDLE: $(function) + // Shortcut for document ready + } else if ( isFunction( selector ) ) { + return root.ready !== undefined ? + root.ready( selector ) : + + // Execute immediately if ready is not present + selector( jQuery ); + } + + return jQuery.makeArray( selector, this ); + }; + +// Give the init function the jQuery prototype for later instantiation +init.prototype = jQuery.fn; + +// Initialize central reference +rootjQuery = jQuery( document ); + + +var rparentsprev = /^(?:parents|prev(?:Until|All))/, + + // Methods guaranteed to produce a unique set when starting from a unique set + guaranteedUnique = { + children: true, + contents: true, + next: true, + prev: true + }; + +jQuery.fn.extend( { + has: function( target ) { + var targets = jQuery( target, this ), + l = targets.length; + + return this.filter( function() { + var i = 0; + for ( ; i < l; i++ ) { + if ( jQuery.contains( this, targets[ i ] ) ) { + return true; + } + } + } ); + }, + + closest: function( selectors, context ) { + var cur, + i = 0, + l = this.length, + matched = [], + targets = typeof selectors !== "string" && jQuery( selectors ); + + // Positional selectors never match, since there's no _selection_ context + if ( !rneedsContext.test( selectors ) ) { + for ( ; i < l; i++ ) { + for ( cur = this[ i ]; cur && cur !== context; cur = cur.parentNode ) { + + // Always skip document fragments + if ( cur.nodeType < 11 && ( targets ? + targets.index( cur ) > -1 : + + // Don't pass non-elements to Sizzle + cur.nodeType === 1 && + jQuery.find.matchesSelector( cur, selectors ) ) ) { + + matched.push( cur ); + break; + } + } + } + } + + return this.pushStack( matched.length > 1 ? jQuery.uniqueSort( matched ) : matched ); + }, + + // Determine the position of an element within the set + index: function( elem ) { + + // No argument, return index in parent + if ( !elem ) { + return ( this[ 0 ] && this[ 0 ].parentNode ) ? this.first().prevAll().length : -1; + } + + // Index in selector + if ( typeof elem === "string" ) { + return indexOf.call( jQuery( elem ), this[ 0 ] ); + } + + // Locate the position of the desired element + return indexOf.call( this, + + // If it receives a jQuery object, the first element is used + elem.jquery ? elem[ 0 ] : elem + ); + }, + + add: function( selector, context ) { + return this.pushStack( + jQuery.uniqueSort( + jQuery.merge( this.get(), jQuery( selector, context ) ) + ) + ); + }, + + addBack: function( selector ) { + return this.add( selector == null ? + this.prevObject : this.prevObject.filter( selector ) + ); + } +} ); + +function sibling( cur, dir ) { + while ( ( cur = cur[ dir ] ) && cur.nodeType !== 1 ) {} + return cur; +} + +jQuery.each( { + parent: function( elem ) { + var parent = elem.parentNode; + return parent && parent.nodeType !== 11 ? parent : null; + }, + parents: function( elem ) { + return dir( elem, "parentNode" ); + }, + parentsUntil: function( elem, _i, until ) { + return dir( elem, "parentNode", until ); + }, + next: function( elem ) { + return sibling( elem, "nextSibling" ); + }, + prev: function( elem ) { + return sibling( elem, "previousSibling" ); + }, + nextAll: function( elem ) { + return dir( elem, "nextSibling" ); + }, + prevAll: function( elem ) { + return dir( elem, "previousSibling" ); + }, + nextUntil: function( elem, _i, until ) { + return dir( elem, "nextSibling", until ); + }, + prevUntil: function( elem, _i, until ) { + return dir( elem, "previousSibling", until ); + }, + siblings: function( elem ) { + return siblings( ( elem.parentNode || {} ).firstChild, elem ); + }, + children: function( elem ) { + return siblings( elem.firstChild ); + }, + contents: function( elem ) { + if ( elem.contentDocument != null && + + // Support: IE 11+ + // elements with no `data` attribute has an object + // `contentDocument` with a `null` prototype. + getProto( elem.contentDocument ) ) { + + return elem.contentDocument; + } + + // Support: IE 9 - 11 only, iOS 7 only, Android Browser <=4.3 only + // Treat the template element as a regular one in browsers that + // don't support it. + if ( nodeName( elem, "template" ) ) { + elem = elem.content || elem; + } + + return jQuery.merge( [], elem.childNodes ); + } +}, function( name, fn ) { + jQuery.fn[ name ] = function( until, selector ) { + var matched = jQuery.map( this, fn, until ); + + if ( name.slice( -5 ) !== "Until" ) { + selector = until; + } + + if ( selector && typeof selector === "string" ) { + matched = jQuery.filter( selector, matched ); + } + + if ( this.length > 1 ) { + + // Remove duplicates + if ( !guaranteedUnique[ name ] ) { + jQuery.uniqueSort( matched ); + } + + // Reverse order for parents* and prev-derivatives + if ( rparentsprev.test( name ) ) { + matched.reverse(); + } + } + + return this.pushStack( matched ); + }; +} ); +var rnothtmlwhite = ( /[^\x20\t\r\n\f]+/g ); + + + +// Convert String-formatted options into Object-formatted ones +function createOptions( options ) { + var object = {}; + jQuery.each( options.match( rnothtmlwhite ) || [], function( _, flag ) { + object[ flag ] = true; + } ); + return object; +} + +/* + * Create a callback list using the following parameters: + * + * options: an optional list of space-separated options that will change how + * the callback list behaves or a more traditional option object + * + * By default a callback list will act like an event callback list and can be + * "fired" multiple times. + * + * Possible options: + * + * once: will ensure the callback list can only be fired once (like a Deferred) + * + * memory: will keep track of previous values and will call any callback added + * after the list has been fired right away with the latest "memorized" + * values (like a Deferred) + * + * unique: will ensure a callback can only be added once (no duplicate in the list) + * + * stopOnFalse: interrupt callings when a callback returns false + * + */ +jQuery.Callbacks = function( options ) { + + // Convert options from String-formatted to Object-formatted if needed + // (we check in cache first) + options = typeof options === "string" ? + createOptions( options ) : + jQuery.extend( {}, options ); + + var // Flag to know if list is currently firing + firing, + + // Last fire value for non-forgettable lists + memory, + + // Flag to know if list was already fired + fired, + + // Flag to prevent firing + locked, + + // Actual callback list + list = [], + + // Queue of execution data for repeatable lists + queue = [], + + // Index of currently firing callback (modified by add/remove as needed) + firingIndex = -1, + + // Fire callbacks + fire = function() { + + // Enforce single-firing + locked = locked || options.once; + + // Execute callbacks for all pending executions, + // respecting firingIndex overrides and runtime changes + fired = firing = true; + for ( ; queue.length; firingIndex = -1 ) { + memory = queue.shift(); + while ( ++firingIndex < list.length ) { + + // Run callback and check for early termination + if ( list[ firingIndex ].apply( memory[ 0 ], memory[ 1 ] ) === false && + options.stopOnFalse ) { + + // Jump to end and forget the data so .add doesn't re-fire + firingIndex = list.length; + memory = false; + } + } + } + + // Forget the data if we're done with it + if ( !options.memory ) { + memory = false; + } + + firing = false; + + // Clean up if we're done firing for good + if ( locked ) { + + // Keep an empty list if we have data for future add calls + if ( memory ) { + list = []; + + // Otherwise, this object is spent + } else { + list = ""; + } + } + }, + + // Actual Callbacks object + self = { + + // Add a callback or a collection of callbacks to the list + add: function() { + if ( list ) { + + // If we have memory from a past run, we should fire after adding + if ( memory && !firing ) { + firingIndex = list.length - 1; + queue.push( memory ); + } + + ( function add( args ) { + jQuery.each( args, function( _, arg ) { + if ( isFunction( arg ) ) { + if ( !options.unique || !self.has( arg ) ) { + list.push( arg ); + } + } else if ( arg && arg.length && toType( arg ) !== "string" ) { + + // Inspect recursively + add( arg ); + } + } ); + } )( arguments ); + + if ( memory && !firing ) { + fire(); + } + } + return this; + }, + + // Remove a callback from the list + remove: function() { + jQuery.each( arguments, function( _, arg ) { + var index; + while ( ( index = jQuery.inArray( arg, list, index ) ) > -1 ) { + list.splice( index, 1 ); + + // Handle firing indexes + if ( index <= firingIndex ) { + firingIndex--; + } + } + } ); + return this; + }, + + // Check if a given callback is in the list. + // If no argument is given, return whether or not list has callbacks attached. + has: function( fn ) { + return fn ? + jQuery.inArray( fn, list ) > -1 : + list.length > 0; + }, + + // Remove all callbacks from the list + empty: function() { + if ( list ) { + list = []; + } + return this; + }, + + // Disable .fire and .add + // Abort any current/pending executions + // Clear all callbacks and values + disable: function() { + locked = queue = []; + list = memory = ""; + return this; + }, + disabled: function() { + return !list; + }, + + // Disable .fire + // Also disable .add unless we have memory (since it would have no effect) + // Abort any pending executions + lock: function() { + locked = queue = []; + if ( !memory && !firing ) { + list = memory = ""; + } + return this; + }, + locked: function() { + return !!locked; + }, + + // Call all callbacks with the given context and arguments + fireWith: function( context, args ) { + if ( !locked ) { + args = args || []; + args = [ context, args.slice ? args.slice() : args ]; + queue.push( args ); + if ( !firing ) { + fire(); + } + } + return this; + }, + + // Call all the callbacks with the given arguments + fire: function() { + self.fireWith( this, arguments ); + return this; + }, + + // To know if the callbacks have already been called at least once + fired: function() { + return !!fired; + } + }; + + return self; +}; + + +function Identity( v ) { + return v; +} +function Thrower( ex ) { + throw ex; +} + +function adoptValue( value, resolve, reject, noValue ) { + var method; + + try { + + // Check for promise aspect first to privilege synchronous behavior + if ( value && isFunction( ( method = value.promise ) ) ) { + method.call( value ).done( resolve ).fail( reject ); + + // Other thenables + } else if ( value && isFunction( ( method = value.then ) ) ) { + method.call( value, resolve, reject ); + + // Other non-thenables + } else { + + // Control `resolve` arguments by letting Array#slice cast boolean `noValue` to integer: + // * false: [ value ].slice( 0 ) => resolve( value ) + // * true: [ value ].slice( 1 ) => resolve() + resolve.apply( undefined, [ value ].slice( noValue ) ); + } + + // For Promises/A+, convert exceptions into rejections + // Since jQuery.when doesn't unwrap thenables, we can skip the extra checks appearing in + // Deferred#then to conditionally suppress rejection. + } catch ( value ) { + + // Support: Android 4.0 only + // Strict mode functions invoked without .call/.apply get global-object context + reject.apply( undefined, [ value ] ); + } +} + +jQuery.extend( { + + Deferred: function( func ) { + var tuples = [ + + // action, add listener, callbacks, + // ... .then handlers, argument index, [final state] + [ "notify", "progress", jQuery.Callbacks( "memory" ), + jQuery.Callbacks( "memory" ), 2 ], + [ "resolve", "done", jQuery.Callbacks( "once memory" ), + jQuery.Callbacks( "once memory" ), 0, "resolved" ], + [ "reject", "fail", jQuery.Callbacks( "once memory" ), + jQuery.Callbacks( "once memory" ), 1, "rejected" ] + ], + state = "pending", + promise = { + state: function() { + return state; + }, + always: function() { + deferred.done( arguments ).fail( arguments ); + return this; + }, + "catch": function( fn ) { + return promise.then( null, fn ); + }, + + // Keep pipe for back-compat + pipe: function( /* fnDone, fnFail, fnProgress */ ) { + var fns = arguments; + + return jQuery.Deferred( function( newDefer ) { + jQuery.each( tuples, function( _i, tuple ) { + + // Map tuples (progress, done, fail) to arguments (done, fail, progress) + var fn = isFunction( fns[ tuple[ 4 ] ] ) && fns[ tuple[ 4 ] ]; + + // deferred.progress(function() { bind to newDefer or newDefer.notify }) + // deferred.done(function() { bind to newDefer or newDefer.resolve }) + // deferred.fail(function() { bind to newDefer or newDefer.reject }) + deferred[ tuple[ 1 ] ]( function() { + var returned = fn && fn.apply( this, arguments ); + if ( returned && isFunction( returned.promise ) ) { + returned.promise() + .progress( newDefer.notify ) + .done( newDefer.resolve ) + .fail( newDefer.reject ); + } else { + newDefer[ tuple[ 0 ] + "With" ]( + this, + fn ? [ returned ] : arguments + ); + } + } ); + } ); + fns = null; + } ).promise(); + }, + then: function( onFulfilled, onRejected, onProgress ) { + var maxDepth = 0; + function resolve( depth, deferred, handler, special ) { + return function() { + var that = this, + args = arguments, + mightThrow = function() { + var returned, then; + + // Support: Promises/A+ section 2.3.3.3.3 + // https://promisesaplus.com/#point-59 + // Ignore double-resolution attempts + if ( depth < maxDepth ) { + return; + } + + returned = handler.apply( that, args ); + + // Support: Promises/A+ section 2.3.1 + // https://promisesaplus.com/#point-48 + if ( returned === deferred.promise() ) { + throw new TypeError( "Thenable self-resolution" ); + } + + // Support: Promises/A+ sections 2.3.3.1, 3.5 + // https://promisesaplus.com/#point-54 + // https://promisesaplus.com/#point-75 + // Retrieve `then` only once + then = returned && + + // Support: Promises/A+ section 2.3.4 + // https://promisesaplus.com/#point-64 + // Only check objects and functions for thenability + ( typeof returned === "object" || + typeof returned === "function" ) && + returned.then; + + // Handle a returned thenable + if ( isFunction( then ) ) { + + // Special processors (notify) just wait for resolution + if ( special ) { + then.call( + returned, + resolve( maxDepth, deferred, Identity, special ), + resolve( maxDepth, deferred, Thrower, special ) + ); + + // Normal processors (resolve) also hook into progress + } else { + + // ...and disregard older resolution values + maxDepth++; + + then.call( + returned, + resolve( maxDepth, deferred, Identity, special ), + resolve( maxDepth, deferred, Thrower, special ), + resolve( maxDepth, deferred, Identity, + deferred.notifyWith ) + ); + } + + // Handle all other returned values + } else { + + // Only substitute handlers pass on context + // and multiple values (non-spec behavior) + if ( handler !== Identity ) { + that = undefined; + args = [ returned ]; + } + + // Process the value(s) + // Default process is resolve + ( special || deferred.resolveWith )( that, args ); + } + }, + + // Only normal processors (resolve) catch and reject exceptions + process = special ? + mightThrow : + function() { + try { + mightThrow(); + } catch ( e ) { + + if ( jQuery.Deferred.exceptionHook ) { + jQuery.Deferred.exceptionHook( e, + process.stackTrace ); + } + + // Support: Promises/A+ section 2.3.3.3.4.1 + // https://promisesaplus.com/#point-61 + // Ignore post-resolution exceptions + if ( depth + 1 >= maxDepth ) { + + // Only substitute handlers pass on context + // and multiple values (non-spec behavior) + if ( handler !== Thrower ) { + that = undefined; + args = [ e ]; + } + + deferred.rejectWith( that, args ); + } + } + }; + + // Support: Promises/A+ section 2.3.3.3.1 + // https://promisesaplus.com/#point-57 + // Re-resolve promises immediately to dodge false rejection from + // subsequent errors + if ( depth ) { + process(); + } else { + + // Call an optional hook to record the stack, in case of exception + // since it's otherwise lost when execution goes async + if ( jQuery.Deferred.getStackHook ) { + process.stackTrace = jQuery.Deferred.getStackHook(); + } + window.setTimeout( process ); + } + }; + } + + return jQuery.Deferred( function( newDefer ) { + + // progress_handlers.add( ... ) + tuples[ 0 ][ 3 ].add( + resolve( + 0, + newDefer, + isFunction( onProgress ) ? + onProgress : + Identity, + newDefer.notifyWith + ) + ); + + // fulfilled_handlers.add( ... ) + tuples[ 1 ][ 3 ].add( + resolve( + 0, + newDefer, + isFunction( onFulfilled ) ? + onFulfilled : + Identity + ) + ); + + // rejected_handlers.add( ... ) + tuples[ 2 ][ 3 ].add( + resolve( + 0, + newDefer, + isFunction( onRejected ) ? + onRejected : + Thrower + ) + ); + } ).promise(); + }, + + // Get a promise for this deferred + // If obj is provided, the promise aspect is added to the object + promise: function( obj ) { + return obj != null ? jQuery.extend( obj, promise ) : promise; + } + }, + deferred = {}; + + // Add list-specific methods + jQuery.each( tuples, function( i, tuple ) { + var list = tuple[ 2 ], + stateString = tuple[ 5 ]; + + // promise.progress = list.add + // promise.done = list.add + // promise.fail = list.add + promise[ tuple[ 1 ] ] = list.add; + + // Handle state + if ( stateString ) { + list.add( + function() { + + // state = "resolved" (i.e., fulfilled) + // state = "rejected" + state = stateString; + }, + + // rejected_callbacks.disable + // fulfilled_callbacks.disable + tuples[ 3 - i ][ 2 ].disable, + + // rejected_handlers.disable + // fulfilled_handlers.disable + tuples[ 3 - i ][ 3 ].disable, + + // progress_callbacks.lock + tuples[ 0 ][ 2 ].lock, + + // progress_handlers.lock + tuples[ 0 ][ 3 ].lock + ); + } + + // progress_handlers.fire + // fulfilled_handlers.fire + // rejected_handlers.fire + list.add( tuple[ 3 ].fire ); + + // deferred.notify = function() { deferred.notifyWith(...) } + // deferred.resolve = function() { deferred.resolveWith(...) } + // deferred.reject = function() { deferred.rejectWith(...) } + deferred[ tuple[ 0 ] ] = function() { + deferred[ tuple[ 0 ] + "With" ]( this === deferred ? undefined : this, arguments ); + return this; + }; + + // deferred.notifyWith = list.fireWith + // deferred.resolveWith = list.fireWith + // deferred.rejectWith = list.fireWith + deferred[ tuple[ 0 ] + "With" ] = list.fireWith; + } ); + + // Make the deferred a promise + promise.promise( deferred ); + + // Call given func if any + if ( func ) { + func.call( deferred, deferred ); + } + + // All done! + return deferred; + }, + + // Deferred helper + when: function( singleValue ) { + var + + // count of uncompleted subordinates + remaining = arguments.length, + + // count of unprocessed arguments + i = remaining, + + // subordinate fulfillment data + resolveContexts = Array( i ), + resolveValues = slice.call( arguments ), + + // the master Deferred + master = jQuery.Deferred(), + + // subordinate callback factory + updateFunc = function( i ) { + return function( value ) { + resolveContexts[ i ] = this; + resolveValues[ i ] = arguments.length > 1 ? slice.call( arguments ) : value; + if ( !( --remaining ) ) { + master.resolveWith( resolveContexts, resolveValues ); + } + }; + }; + + // Single- and empty arguments are adopted like Promise.resolve + if ( remaining <= 1 ) { + adoptValue( singleValue, master.done( updateFunc( i ) ).resolve, master.reject, + !remaining ); + + // Use .then() to unwrap secondary thenables (cf. gh-3000) + if ( master.state() === "pending" || + isFunction( resolveValues[ i ] && resolveValues[ i ].then ) ) { + + return master.then(); + } + } + + // Multiple arguments are aggregated like Promise.all array elements + while ( i-- ) { + adoptValue( resolveValues[ i ], updateFunc( i ), master.reject ); + } + + return master.promise(); + } +} ); + + +// These usually indicate a programmer mistake during development, +// warn about them ASAP rather than swallowing them by default. +var rerrorNames = /^(Eval|Internal|Range|Reference|Syntax|Type|URI)Error$/; + +jQuery.Deferred.exceptionHook = function( error, stack ) { + + // Support: IE 8 - 9 only + // Console exists when dev tools are open, which can happen at any time + if ( window.console && window.console.warn && error && rerrorNames.test( error.name ) ) { + window.console.warn( "jQuery.Deferred exception: " + error.message, error.stack, stack ); + } +}; + + + + +jQuery.readyException = function( error ) { + window.setTimeout( function() { + throw error; + } ); +}; + + + + +// The deferred used on DOM ready +var readyList = jQuery.Deferred(); + +jQuery.fn.ready = function( fn ) { + + readyList + .then( fn ) + + // Wrap jQuery.readyException in a function so that the lookup + // happens at the time of error handling instead of callback + // registration. + .catch( function( error ) { + jQuery.readyException( error ); + } ); + + return this; +}; + +jQuery.extend( { + + // Is the DOM ready to be used? Set to true once it occurs. + isReady: false, + + // A counter to track how many items to wait for before + // the ready event fires. See #6781 + readyWait: 1, + + // Handle when the DOM is ready + ready: function( wait ) { + + // Abort if there are pending holds or we're already ready + if ( wait === true ? --jQuery.readyWait : jQuery.isReady ) { + return; + } + + // Remember that the DOM is ready + jQuery.isReady = true; + + // If a normal DOM Ready event fired, decrement, and wait if need be + if ( wait !== true && --jQuery.readyWait > 0 ) { + return; + } + + // If there are functions bound, to execute + readyList.resolveWith( document, [ jQuery ] ); + } +} ); + +jQuery.ready.then = readyList.then; + +// The ready event handler and self cleanup method +function completed() { + document.removeEventListener( "DOMContentLoaded", completed ); + window.removeEventListener( "load", completed ); + jQuery.ready(); +} + +// Catch cases where $(document).ready() is called +// after the browser event has already occurred. +// Support: IE <=9 - 10 only +// Older IE sometimes signals "interactive" too soon +if ( document.readyState === "complete" || + ( document.readyState !== "loading" && !document.documentElement.doScroll ) ) { + + // Handle it asynchronously to allow scripts the opportunity to delay ready + window.setTimeout( jQuery.ready ); + +} else { + + // Use the handy event callback + document.addEventListener( "DOMContentLoaded", completed ); + + // A fallback to window.onload, that will always work + window.addEventListener( "load", completed ); +} + + + + +// Multifunctional method to get and set values of a collection +// The value/s can optionally be executed if it's a function +var access = function( elems, fn, key, value, chainable, emptyGet, raw ) { + var i = 0, + len = elems.length, + bulk = key == null; + + // Sets many values + if ( toType( key ) === "object" ) { + chainable = true; + for ( i in key ) { + access( elems, fn, i, key[ i ], true, emptyGet, raw ); + } + + // Sets one value + } else if ( value !== undefined ) { + chainable = true; + + if ( !isFunction( value ) ) { + raw = true; + } + + if ( bulk ) { + + // Bulk operations run against the entire set + if ( raw ) { + fn.call( elems, value ); + fn = null; + + // ...except when executing function values + } else { + bulk = fn; + fn = function( elem, _key, value ) { + return bulk.call( jQuery( elem ), value ); + }; + } + } + + if ( fn ) { + for ( ; i < len; i++ ) { + fn( + elems[ i ], key, raw ? + value : + value.call( elems[ i ], i, fn( elems[ i ], key ) ) + ); + } + } + } + + if ( chainable ) { + return elems; + } + + // Gets + if ( bulk ) { + return fn.call( elems ); + } + + return len ? fn( elems[ 0 ], key ) : emptyGet; +}; + + +// Matches dashed string for camelizing +var rmsPrefix = /^-ms-/, + rdashAlpha = /-([a-z])/g; + +// Used by camelCase as callback to replace() +function fcamelCase( _all, letter ) { + return letter.toUpperCase(); +} + +// Convert dashed to camelCase; used by the css and data modules +// Support: IE <=9 - 11, Edge 12 - 15 +// Microsoft forgot to hump their vendor prefix (#9572) +function camelCase( string ) { + return string.replace( rmsPrefix, "ms-" ).replace( rdashAlpha, fcamelCase ); +} +var acceptData = function( owner ) { + + // Accepts only: + // - Node + // - Node.ELEMENT_NODE + // - Node.DOCUMENT_NODE + // - Object + // - Any + return owner.nodeType === 1 || owner.nodeType === 9 || !( +owner.nodeType ); +}; + + + + +function Data() { + this.expando = jQuery.expando + Data.uid++; +} + +Data.uid = 1; + +Data.prototype = { + + cache: function( owner ) { + + // Check if the owner object already has a cache + var value = owner[ this.expando ]; + + // If not, create one + if ( !value ) { + value = {}; + + // We can accept data for non-element nodes in modern browsers, + // but we should not, see #8335. + // Always return an empty object. + if ( acceptData( owner ) ) { + + // If it is a node unlikely to be stringify-ed or looped over + // use plain assignment + if ( owner.nodeType ) { + owner[ this.expando ] = value; + + // Otherwise secure it in a non-enumerable property + // configurable must be true to allow the property to be + // deleted when data is removed + } else { + Object.defineProperty( owner, this.expando, { + value: value, + configurable: true + } ); + } + } + } + + return value; + }, + set: function( owner, data, value ) { + var prop, + cache = this.cache( owner ); + + // Handle: [ owner, key, value ] args + // Always use camelCase key (gh-2257) + if ( typeof data === "string" ) { + cache[ camelCase( data ) ] = value; + + // Handle: [ owner, { properties } ] args + } else { + + // Copy the properties one-by-one to the cache object + for ( prop in data ) { + cache[ camelCase( prop ) ] = data[ prop ]; + } + } + return cache; + }, + get: function( owner, key ) { + return key === undefined ? + this.cache( owner ) : + + // Always use camelCase key (gh-2257) + owner[ this.expando ] && owner[ this.expando ][ camelCase( key ) ]; + }, + access: function( owner, key, value ) { + + // In cases where either: + // + // 1. No key was specified + // 2. A string key was specified, but no value provided + // + // Take the "read" path and allow the get method to determine + // which value to return, respectively either: + // + // 1. The entire cache object + // 2. The data stored at the key + // + if ( key === undefined || + ( ( key && typeof key === "string" ) && value === undefined ) ) { + + return this.get( owner, key ); + } + + // When the key is not a string, or both a key and value + // are specified, set or extend (existing objects) with either: + // + // 1. An object of properties + // 2. A key and value + // + this.set( owner, key, value ); + + // Since the "set" path can have two possible entry points + // return the expected data based on which path was taken[*] + return value !== undefined ? value : key; + }, + remove: function( owner, key ) { + var i, + cache = owner[ this.expando ]; + + if ( cache === undefined ) { + return; + } + + if ( key !== undefined ) { + + // Support array or space separated string of keys + if ( Array.isArray( key ) ) { + + // If key is an array of keys... + // We always set camelCase keys, so remove that. + key = key.map( camelCase ); + } else { + key = camelCase( key ); + + // If a key with the spaces exists, use it. + // Otherwise, create an array by matching non-whitespace + key = key in cache ? + [ key ] : + ( key.match( rnothtmlwhite ) || [] ); + } + + i = key.length; + + while ( i-- ) { + delete cache[ key[ i ] ]; + } + } + + // Remove the expando if there's no more data + if ( key === undefined || jQuery.isEmptyObject( cache ) ) { + + // Support: Chrome <=35 - 45 + // Webkit & Blink performance suffers when deleting properties + // from DOM nodes, so set to undefined instead + // https://bugs.chromium.org/p/chromium/issues/detail?id=378607 (bug restricted) + if ( owner.nodeType ) { + owner[ this.expando ] = undefined; + } else { + delete owner[ this.expando ]; + } + } + }, + hasData: function( owner ) { + var cache = owner[ this.expando ]; + return cache !== undefined && !jQuery.isEmptyObject( cache ); + } +}; +var dataPriv = new Data(); + +var dataUser = new Data(); + + + +// Implementation Summary +// +// 1. Enforce API surface and semantic compatibility with 1.9.x branch +// 2. Improve the module's maintainability by reducing the storage +// paths to a single mechanism. +// 3. Use the same single mechanism to support "private" and "user" data. +// 4. _Never_ expose "private" data to user code (TODO: Drop _data, _removeData) +// 5. Avoid exposing implementation details on user objects (eg. expando properties) +// 6. Provide a clear path for implementation upgrade to WeakMap in 2014 + +var rbrace = /^(?:\{[\w\W]*\}|\[[\w\W]*\])$/, + rmultiDash = /[A-Z]/g; + +function getData( data ) { + if ( data === "true" ) { + return true; + } + + if ( data === "false" ) { + return false; + } + + if ( data === "null" ) { + return null; + } + + // Only convert to a number if it doesn't change the string + if ( data === +data + "" ) { + return +data; + } + + if ( rbrace.test( data ) ) { + return JSON.parse( data ); + } + + return data; +} + +function dataAttr( elem, key, data ) { + var name; + + // If nothing was found internally, try to fetch any + // data from the HTML5 data-* attribute + if ( data === undefined && elem.nodeType === 1 ) { + name = "data-" + key.replace( rmultiDash, "-$&" ).toLowerCase(); + data = elem.getAttribute( name ); + + if ( typeof data === "string" ) { + try { + data = getData( data ); + } catch ( e ) {} + + // Make sure we set the data so it isn't changed later + dataUser.set( elem, key, data ); + } else { + data = undefined; + } + } + return data; +} + +jQuery.extend( { + hasData: function( elem ) { + return dataUser.hasData( elem ) || dataPriv.hasData( elem ); + }, + + data: function( elem, name, data ) { + return dataUser.access( elem, name, data ); + }, + + removeData: function( elem, name ) { + dataUser.remove( elem, name ); + }, + + // TODO: Now that all calls to _data and _removeData have been replaced + // with direct calls to dataPriv methods, these can be deprecated. + _data: function( elem, name, data ) { + return dataPriv.access( elem, name, data ); + }, + + _removeData: function( elem, name ) { + dataPriv.remove( elem, name ); + } +} ); + +jQuery.fn.extend( { + data: function( key, value ) { + var i, name, data, + elem = this[ 0 ], + attrs = elem && elem.attributes; + + // Gets all values + if ( key === undefined ) { + if ( this.length ) { + data = dataUser.get( elem ); + + if ( elem.nodeType === 1 && !dataPriv.get( elem, "hasDataAttrs" ) ) { + i = attrs.length; + while ( i-- ) { + + // Support: IE 11 only + // The attrs elements can be null (#14894) + if ( attrs[ i ] ) { + name = attrs[ i ].name; + if ( name.indexOf( "data-" ) === 0 ) { + name = camelCase( name.slice( 5 ) ); + dataAttr( elem, name, data[ name ] ); + } + } + } + dataPriv.set( elem, "hasDataAttrs", true ); + } + } + + return data; + } + + // Sets multiple values + if ( typeof key === "object" ) { + return this.each( function() { + dataUser.set( this, key ); + } ); + } + + return access( this, function( value ) { + var data; + + // The calling jQuery object (element matches) is not empty + // (and therefore has an element appears at this[ 0 ]) and the + // `value` parameter was not undefined. An empty jQuery object + // will result in `undefined` for elem = this[ 0 ] which will + // throw an exception if an attempt to read a data cache is made. + if ( elem && value === undefined ) { + + // Attempt to get data from the cache + // The key will always be camelCased in Data + data = dataUser.get( elem, key ); + if ( data !== undefined ) { + return data; + } + + // Attempt to "discover" the data in + // HTML5 custom data-* attrs + data = dataAttr( elem, key ); + if ( data !== undefined ) { + return data; + } + + // We tried really hard, but the data doesn't exist. + return; + } + + // Set the data... + this.each( function() { + + // We always store the camelCased key + dataUser.set( this, key, value ); + } ); + }, null, value, arguments.length > 1, null, true ); + }, + + removeData: function( key ) { + return this.each( function() { + dataUser.remove( this, key ); + } ); + } +} ); + + +jQuery.extend( { + queue: function( elem, type, data ) { + var queue; + + if ( elem ) { + type = ( type || "fx" ) + "queue"; + queue = dataPriv.get( elem, type ); + + // Speed up dequeue by getting out quickly if this is just a lookup + if ( data ) { + if ( !queue || Array.isArray( data ) ) { + queue = dataPriv.access( elem, type, jQuery.makeArray( data ) ); + } else { + queue.push( data ); + } + } + return queue || []; + } + }, + + dequeue: function( elem, type ) { + type = type || "fx"; + + var queue = jQuery.queue( elem, type ), + startLength = queue.length, + fn = queue.shift(), + hooks = jQuery._queueHooks( elem, type ), + next = function() { + jQuery.dequeue( elem, type ); + }; + + // If the fx queue is dequeued, always remove the progress sentinel + if ( fn === "inprogress" ) { + fn = queue.shift(); + startLength--; + } + + if ( fn ) { + + // Add a progress sentinel to prevent the fx queue from being + // automatically dequeued + if ( type === "fx" ) { + queue.unshift( "inprogress" ); + } + + // Clear up the last queue stop function + delete hooks.stop; + fn.call( elem, next, hooks ); + } + + if ( !startLength && hooks ) { + hooks.empty.fire(); + } + }, + + // Not public - generate a queueHooks object, or return the current one + _queueHooks: function( elem, type ) { + var key = type + "queueHooks"; + return dataPriv.get( elem, key ) || dataPriv.access( elem, key, { + empty: jQuery.Callbacks( "once memory" ).add( function() { + dataPriv.remove( elem, [ type + "queue", key ] ); + } ) + } ); + } +} ); + +jQuery.fn.extend( { + queue: function( type, data ) { + var setter = 2; + + if ( typeof type !== "string" ) { + data = type; + type = "fx"; + setter--; + } + + if ( arguments.length < setter ) { + return jQuery.queue( this[ 0 ], type ); + } + + return data === undefined ? + this : + this.each( function() { + var queue = jQuery.queue( this, type, data ); + + // Ensure a hooks for this queue + jQuery._queueHooks( this, type ); + + if ( type === "fx" && queue[ 0 ] !== "inprogress" ) { + jQuery.dequeue( this, type ); + } + } ); + }, + dequeue: function( type ) { + return this.each( function() { + jQuery.dequeue( this, type ); + } ); + }, + clearQueue: function( type ) { + return this.queue( type || "fx", [] ); + }, + + // Get a promise resolved when queues of a certain type + // are emptied (fx is the type by default) + promise: function( type, obj ) { + var tmp, + count = 1, + defer = jQuery.Deferred(), + elements = this, + i = this.length, + resolve = function() { + if ( !( --count ) ) { + defer.resolveWith( elements, [ elements ] ); + } + }; + + if ( typeof type !== "string" ) { + obj = type; + type = undefined; + } + type = type || "fx"; + + while ( i-- ) { + tmp = dataPriv.get( elements[ i ], type + "queueHooks" ); + if ( tmp && tmp.empty ) { + count++; + tmp.empty.add( resolve ); + } + } + resolve(); + return defer.promise( obj ); + } +} ); +var pnum = ( /[+-]?(?:\d*\.|)\d+(?:[eE][+-]?\d+|)/ ).source; + +var rcssNum = new RegExp( "^(?:([+-])=|)(" + pnum + ")([a-z%]*)$", "i" ); + + +var cssExpand = [ "Top", "Right", "Bottom", "Left" ]; + +var documentElement = document.documentElement; + + + + var isAttached = function( elem ) { + return jQuery.contains( elem.ownerDocument, elem ); + }, + composed = { composed: true }; + + // Support: IE 9 - 11+, Edge 12 - 18+, iOS 10.0 - 10.2 only + // Check attachment across shadow DOM boundaries when possible (gh-3504) + // Support: iOS 10.0-10.2 only + // Early iOS 10 versions support `attachShadow` but not `getRootNode`, + // leading to errors. We need to check for `getRootNode`. + if ( documentElement.getRootNode ) { + isAttached = function( elem ) { + return jQuery.contains( elem.ownerDocument, elem ) || + elem.getRootNode( composed ) === elem.ownerDocument; + }; + } +var isHiddenWithinTree = function( elem, el ) { + + // isHiddenWithinTree might be called from jQuery#filter function; + // in that case, element will be second argument + elem = el || elem; + + // Inline style trumps all + return elem.style.display === "none" || + elem.style.display === "" && + + // Otherwise, check computed style + // Support: Firefox <=43 - 45 + // Disconnected elements can have computed display: none, so first confirm that elem is + // in the document. + isAttached( elem ) && + + jQuery.css( elem, "display" ) === "none"; + }; + + + +function adjustCSS( elem, prop, valueParts, tween ) { + var adjusted, scale, + maxIterations = 20, + currentValue = tween ? + function() { + return tween.cur(); + } : + function() { + return jQuery.css( elem, prop, "" ); + }, + initial = currentValue(), + unit = valueParts && valueParts[ 3 ] || ( jQuery.cssNumber[ prop ] ? "" : "px" ), + + // Starting value computation is required for potential unit mismatches + initialInUnit = elem.nodeType && + ( jQuery.cssNumber[ prop ] || unit !== "px" && +initial ) && + rcssNum.exec( jQuery.css( elem, prop ) ); + + if ( initialInUnit && initialInUnit[ 3 ] !== unit ) { + + // Support: Firefox <=54 + // Halve the iteration target value to prevent interference from CSS upper bounds (gh-2144) + initial = initial / 2; + + // Trust units reported by jQuery.css + unit = unit || initialInUnit[ 3 ]; + + // Iteratively approximate from a nonzero starting point + initialInUnit = +initial || 1; + + while ( maxIterations-- ) { + + // Evaluate and update our best guess (doubling guesses that zero out). + // Finish if the scale equals or crosses 1 (making the old*new product non-positive). + jQuery.style( elem, prop, initialInUnit + unit ); + if ( ( 1 - scale ) * ( 1 - ( scale = currentValue() / initial || 0.5 ) ) <= 0 ) { + maxIterations = 0; + } + initialInUnit = initialInUnit / scale; + + } + + initialInUnit = initialInUnit * 2; + jQuery.style( elem, prop, initialInUnit + unit ); + + // Make sure we update the tween properties later on + valueParts = valueParts || []; + } + + if ( valueParts ) { + initialInUnit = +initialInUnit || +initial || 0; + + // Apply relative offset (+=/-=) if specified + adjusted = valueParts[ 1 ] ? + initialInUnit + ( valueParts[ 1 ] + 1 ) * valueParts[ 2 ] : + +valueParts[ 2 ]; + if ( tween ) { + tween.unit = unit; + tween.start = initialInUnit; + tween.end = adjusted; + } + } + return adjusted; +} + + +var defaultDisplayMap = {}; + +function getDefaultDisplay( elem ) { + var temp, + doc = elem.ownerDocument, + nodeName = elem.nodeName, + display = defaultDisplayMap[ nodeName ]; + + if ( display ) { + return display; + } + + temp = doc.body.appendChild( doc.createElement( nodeName ) ); + display = jQuery.css( temp, "display" ); + + temp.parentNode.removeChild( temp ); + + if ( display === "none" ) { + display = "block"; + } + defaultDisplayMap[ nodeName ] = display; + + return display; +} + +function showHide( elements, show ) { + var display, elem, + values = [], + index = 0, + length = elements.length; + + // Determine new display value for elements that need to change + for ( ; index < length; index++ ) { + elem = elements[ index ]; + if ( !elem.style ) { + continue; + } + + display = elem.style.display; + if ( show ) { + + // Since we force visibility upon cascade-hidden elements, an immediate (and slow) + // check is required in this first loop unless we have a nonempty display value (either + // inline or about-to-be-restored) + if ( display === "none" ) { + values[ index ] = dataPriv.get( elem, "display" ) || null; + if ( !values[ index ] ) { + elem.style.display = ""; + } + } + if ( elem.style.display === "" && isHiddenWithinTree( elem ) ) { + values[ index ] = getDefaultDisplay( elem ); + } + } else { + if ( display !== "none" ) { + values[ index ] = "none"; + + // Remember what we're overwriting + dataPriv.set( elem, "display", display ); + } + } + } + + // Set the display of the elements in a second loop to avoid constant reflow + for ( index = 0; index < length; index++ ) { + if ( values[ index ] != null ) { + elements[ index ].style.display = values[ index ]; + } + } + + return elements; +} + +jQuery.fn.extend( { + show: function() { + return showHide( this, true ); + }, + hide: function() { + return showHide( this ); + }, + toggle: function( state ) { + if ( typeof state === "boolean" ) { + return state ? this.show() : this.hide(); + } + + return this.each( function() { + if ( isHiddenWithinTree( this ) ) { + jQuery( this ).show(); + } else { + jQuery( this ).hide(); + } + } ); + } +} ); +var rcheckableType = ( /^(?:checkbox|radio)$/i ); + +var rtagName = ( /<([a-z][^\/\0>\x20\t\r\n\f]*)/i ); + +var rscriptType = ( /^$|^module$|\/(?:java|ecma)script/i ); + + + +( function() { + var fragment = document.createDocumentFragment(), + div = fragment.appendChild( document.createElement( "div" ) ), + input = document.createElement( "input" ); + + // Support: Android 4.0 - 4.3 only + // Check state lost if the name is set (#11217) + // Support: Windows Web Apps (WWA) + // `name` and `type` must use .setAttribute for WWA (#14901) + input.setAttribute( "type", "radio" ); + input.setAttribute( "checked", "checked" ); + input.setAttribute( "name", "t" ); + + div.appendChild( input ); + + // Support: Android <=4.1 only + // Older WebKit doesn't clone checked state correctly in fragments + support.checkClone = div.cloneNode( true ).cloneNode( true ).lastChild.checked; + + // Support: IE <=11 only + // Make sure textarea (and checkbox) defaultValue is properly cloned + div.innerHTML = ""; + support.noCloneChecked = !!div.cloneNode( true ).lastChild.defaultValue; + + // Support: IE <=9 only + // IE <=9 replaces "; + support.option = !!div.lastChild; +} )(); + + +// We have to close these tags to support XHTML (#13200) +var wrapMap = { + + // XHTML parsers do not magically insert elements in the + // same way that tag soup parsers do. So we cannot shorten + // this by omitting or other required elements. + thead: [ 1, "", "
" ], + col: [ 2, "", "
" ], + tr: [ 2, "", "
" ], + td: [ 3, "", "
" ], + + _default: [ 0, "", "" ] +}; + +wrapMap.tbody = wrapMap.tfoot = wrapMap.colgroup = wrapMap.caption = wrapMap.thead; +wrapMap.th = wrapMap.td; + +// Support: IE <=9 only +if ( !support.option ) { + wrapMap.optgroup = wrapMap.option = [ 1, "" ]; +} + + +function getAll( context, tag ) { + + // Support: IE <=9 - 11 only + // Use typeof to avoid zero-argument method invocation on host objects (#15151) + var ret; + + if ( typeof context.getElementsByTagName !== "undefined" ) { + ret = context.getElementsByTagName( tag || "*" ); + + } else if ( typeof context.querySelectorAll !== "undefined" ) { + ret = context.querySelectorAll( tag || "*" ); + + } else { + ret = []; + } + + if ( tag === undefined || tag && nodeName( context, tag ) ) { + return jQuery.merge( [ context ], ret ); + } + + return ret; +} + + +// Mark scripts as having already been evaluated +function setGlobalEval( elems, refElements ) { + var i = 0, + l = elems.length; + + for ( ; i < l; i++ ) { + dataPriv.set( + elems[ i ], + "globalEval", + !refElements || dataPriv.get( refElements[ i ], "globalEval" ) + ); + } +} + + +var rhtml = /<|&#?\w+;/; + +function buildFragment( elems, context, scripts, selection, ignored ) { + var elem, tmp, tag, wrap, attached, j, + fragment = context.createDocumentFragment(), + nodes = [], + i = 0, + l = elems.length; + + for ( ; i < l; i++ ) { + elem = elems[ i ]; + + if ( elem || elem === 0 ) { + + // Add nodes directly + if ( toType( elem ) === "object" ) { + + // Support: Android <=4.0 only, PhantomJS 1 only + // push.apply(_, arraylike) throws on ancient WebKit + jQuery.merge( nodes, elem.nodeType ? [ elem ] : elem ); + + // Convert non-html into a text node + } else if ( !rhtml.test( elem ) ) { + nodes.push( context.createTextNode( elem ) ); + + // Convert html into DOM nodes + } else { + tmp = tmp || fragment.appendChild( context.createElement( "div" ) ); + + // Deserialize a standard representation + tag = ( rtagName.exec( elem ) || [ "", "" ] )[ 1 ].toLowerCase(); + wrap = wrapMap[ tag ] || wrapMap._default; + tmp.innerHTML = wrap[ 1 ] + jQuery.htmlPrefilter( elem ) + wrap[ 2 ]; + + // Descend through wrappers to the right content + j = wrap[ 0 ]; + while ( j-- ) { + tmp = tmp.lastChild; + } + + // Support: Android <=4.0 only, PhantomJS 1 only + // push.apply(_, arraylike) throws on ancient WebKit + jQuery.merge( nodes, tmp.childNodes ); + + // Remember the top-level container + tmp = fragment.firstChild; + + // Ensure the created nodes are orphaned (#12392) + tmp.textContent = ""; + } + } + } + + // Remove wrapper from fragment + fragment.textContent = ""; + + i = 0; + while ( ( elem = nodes[ i++ ] ) ) { + + // Skip elements already in the context collection (trac-4087) + if ( selection && jQuery.inArray( elem, selection ) > -1 ) { + if ( ignored ) { + ignored.push( elem ); + } + continue; + } + + attached = isAttached( elem ); + + // Append to fragment + tmp = getAll( fragment.appendChild( elem ), "script" ); + + // Preserve script evaluation history + if ( attached ) { + setGlobalEval( tmp ); + } + + // Capture executables + if ( scripts ) { + j = 0; + while ( ( elem = tmp[ j++ ] ) ) { + if ( rscriptType.test( elem.type || "" ) ) { + scripts.push( elem ); + } + } + } + } + + return fragment; +} + + +var + rkeyEvent = /^key/, + rmouseEvent = /^(?:mouse|pointer|contextmenu|drag|drop)|click/, + rtypenamespace = /^([^.]*)(?:\.(.+)|)/; + +function returnTrue() { + return true; +} + +function returnFalse() { + return false; +} + +// Support: IE <=9 - 11+ +// focus() and blur() are asynchronous, except when they are no-op. +// So expect focus to be synchronous when the element is already active, +// and blur to be synchronous when the element is not already active. +// (focus and blur are always synchronous in other supported browsers, +// this just defines when we can count on it). +function expectSync( elem, type ) { + return ( elem === safeActiveElement() ) === ( type === "focus" ); +} + +// Support: IE <=9 only +// Accessing document.activeElement can throw unexpectedly +// https://bugs.jquery.com/ticket/13393 +function safeActiveElement() { + try { + return document.activeElement; + } catch ( err ) { } +} + +function on( elem, types, selector, data, fn, one ) { + var origFn, type; + + // Types can be a map of types/handlers + if ( typeof types === "object" ) { + + // ( types-Object, selector, data ) + if ( typeof selector !== "string" ) { + + // ( types-Object, data ) + data = data || selector; + selector = undefined; + } + for ( type in types ) { + on( elem, type, selector, data, types[ type ], one ); + } + return elem; + } + + if ( data == null && fn == null ) { + + // ( types, fn ) + fn = selector; + data = selector = undefined; + } else if ( fn == null ) { + if ( typeof selector === "string" ) { + + // ( types, selector, fn ) + fn = data; + data = undefined; + } else { + + // ( types, data, fn ) + fn = data; + data = selector; + selector = undefined; + } + } + if ( fn === false ) { + fn = returnFalse; + } else if ( !fn ) { + return elem; + } + + if ( one === 1 ) { + origFn = fn; + fn = function( event ) { + + // Can use an empty set, since event contains the info + jQuery().off( event ); + return origFn.apply( this, arguments ); + }; + + // Use same guid so caller can remove using origFn + fn.guid = origFn.guid || ( origFn.guid = jQuery.guid++ ); + } + return elem.each( function() { + jQuery.event.add( this, types, fn, data, selector ); + } ); +} + +/* + * Helper functions for managing events -- not part of the public interface. + * Props to Dean Edwards' addEvent library for many of the ideas. + */ +jQuery.event = { + + global: {}, + + add: function( elem, types, handler, data, selector ) { + + var handleObjIn, eventHandle, tmp, + events, t, handleObj, + special, handlers, type, namespaces, origType, + elemData = dataPriv.get( elem ); + + // Only attach events to objects that accept data + if ( !acceptData( elem ) ) { + return; + } + + // Caller can pass in an object of custom data in lieu of the handler + if ( handler.handler ) { + handleObjIn = handler; + handler = handleObjIn.handler; + selector = handleObjIn.selector; + } + + // Ensure that invalid selectors throw exceptions at attach time + // Evaluate against documentElement in case elem is a non-element node (e.g., document) + if ( selector ) { + jQuery.find.matchesSelector( documentElement, selector ); + } + + // Make sure that the handler has a unique ID, used to find/remove it later + if ( !handler.guid ) { + handler.guid = jQuery.guid++; + } + + // Init the element's event structure and main handler, if this is the first + if ( !( events = elemData.events ) ) { + events = elemData.events = Object.create( null ); + } + if ( !( eventHandle = elemData.handle ) ) { + eventHandle = elemData.handle = function( e ) { + + // Discard the second event of a jQuery.event.trigger() and + // when an event is called after a page has unloaded + return typeof jQuery !== "undefined" && jQuery.event.triggered !== e.type ? + jQuery.event.dispatch.apply( elem, arguments ) : undefined; + }; + } + + // Handle multiple events separated by a space + types = ( types || "" ).match( rnothtmlwhite ) || [ "" ]; + t = types.length; + while ( t-- ) { + tmp = rtypenamespace.exec( types[ t ] ) || []; + type = origType = tmp[ 1 ]; + namespaces = ( tmp[ 2 ] || "" ).split( "." ).sort(); + + // There *must* be a type, no attaching namespace-only handlers + if ( !type ) { + continue; + } + + // If event changes its type, use the special event handlers for the changed type + special = jQuery.event.special[ type ] || {}; + + // If selector defined, determine special event api type, otherwise given type + type = ( selector ? special.delegateType : special.bindType ) || type; + + // Update special based on newly reset type + special = jQuery.event.special[ type ] || {}; + + // handleObj is passed to all event handlers + handleObj = jQuery.extend( { + type: type, + origType: origType, + data: data, + handler: handler, + guid: handler.guid, + selector: selector, + needsContext: selector && jQuery.expr.match.needsContext.test( selector ), + namespace: namespaces.join( "." ) + }, handleObjIn ); + + // Init the event handler queue if we're the first + if ( !( handlers = events[ type ] ) ) { + handlers = events[ type ] = []; + handlers.delegateCount = 0; + + // Only use addEventListener if the special events handler returns false + if ( !special.setup || + special.setup.call( elem, data, namespaces, eventHandle ) === false ) { + + if ( elem.addEventListener ) { + elem.addEventListener( type, eventHandle ); + } + } + } + + if ( special.add ) { + special.add.call( elem, handleObj ); + + if ( !handleObj.handler.guid ) { + handleObj.handler.guid = handler.guid; + } + } + + // Add to the element's handler list, delegates in front + if ( selector ) { + handlers.splice( handlers.delegateCount++, 0, handleObj ); + } else { + handlers.push( handleObj ); + } + + // Keep track of which events have ever been used, for event optimization + jQuery.event.global[ type ] = true; + } + + }, + + // Detach an event or set of events from an element + remove: function( elem, types, handler, selector, mappedTypes ) { + + var j, origCount, tmp, + events, t, handleObj, + special, handlers, type, namespaces, origType, + elemData = dataPriv.hasData( elem ) && dataPriv.get( elem ); + + if ( !elemData || !( events = elemData.events ) ) { + return; + } + + // Once for each type.namespace in types; type may be omitted + types = ( types || "" ).match( rnothtmlwhite ) || [ "" ]; + t = types.length; + while ( t-- ) { + tmp = rtypenamespace.exec( types[ t ] ) || []; + type = origType = tmp[ 1 ]; + namespaces = ( tmp[ 2 ] || "" ).split( "." ).sort(); + + // Unbind all events (on this namespace, if provided) for the element + if ( !type ) { + for ( type in events ) { + jQuery.event.remove( elem, type + types[ t ], handler, selector, true ); + } + continue; + } + + special = jQuery.event.special[ type ] || {}; + type = ( selector ? special.delegateType : special.bindType ) || type; + handlers = events[ type ] || []; + tmp = tmp[ 2 ] && + new RegExp( "(^|\\.)" + namespaces.join( "\\.(?:.*\\.|)" ) + "(\\.|$)" ); + + // Remove matching events + origCount = j = handlers.length; + while ( j-- ) { + handleObj = handlers[ j ]; + + if ( ( mappedTypes || origType === handleObj.origType ) && + ( !handler || handler.guid === handleObj.guid ) && + ( !tmp || tmp.test( handleObj.namespace ) ) && + ( !selector || selector === handleObj.selector || + selector === "**" && handleObj.selector ) ) { + handlers.splice( j, 1 ); + + if ( handleObj.selector ) { + handlers.delegateCount--; + } + if ( special.remove ) { + special.remove.call( elem, handleObj ); + } + } + } + + // Remove generic event handler if we removed something and no more handlers exist + // (avoids potential for endless recursion during removal of special event handlers) + if ( origCount && !handlers.length ) { + if ( !special.teardown || + special.teardown.call( elem, namespaces, elemData.handle ) === false ) { + + jQuery.removeEvent( elem, type, elemData.handle ); + } + + delete events[ type ]; + } + } + + // Remove data and the expando if it's no longer used + if ( jQuery.isEmptyObject( events ) ) { + dataPriv.remove( elem, "handle events" ); + } + }, + + dispatch: function( nativeEvent ) { + + var i, j, ret, matched, handleObj, handlerQueue, + args = new Array( arguments.length ), + + // Make a writable jQuery.Event from the native event object + event = jQuery.event.fix( nativeEvent ), + + handlers = ( + dataPriv.get( this, "events" ) || Object.create( null ) + )[ event.type ] || [], + special = jQuery.event.special[ event.type ] || {}; + + // Use the fix-ed jQuery.Event rather than the (read-only) native event + args[ 0 ] = event; + + for ( i = 1; i < arguments.length; i++ ) { + args[ i ] = arguments[ i ]; + } + + event.delegateTarget = this; + + // Call the preDispatch hook for the mapped type, and let it bail if desired + if ( special.preDispatch && special.preDispatch.call( this, event ) === false ) { + return; + } + + // Determine handlers + handlerQueue = jQuery.event.handlers.call( this, event, handlers ); + + // Run delegates first; they may want to stop propagation beneath us + i = 0; + while ( ( matched = handlerQueue[ i++ ] ) && !event.isPropagationStopped() ) { + event.currentTarget = matched.elem; + + j = 0; + while ( ( handleObj = matched.handlers[ j++ ] ) && + !event.isImmediatePropagationStopped() ) { + + // If the event is namespaced, then each handler is only invoked if it is + // specially universal or its namespaces are a superset of the event's. + if ( !event.rnamespace || handleObj.namespace === false || + event.rnamespace.test( handleObj.namespace ) ) { + + event.handleObj = handleObj; + event.data = handleObj.data; + + ret = ( ( jQuery.event.special[ handleObj.origType ] || {} ).handle || + handleObj.handler ).apply( matched.elem, args ); + + if ( ret !== undefined ) { + if ( ( event.result = ret ) === false ) { + event.preventDefault(); + event.stopPropagation(); + } + } + } + } + } + + // Call the postDispatch hook for the mapped type + if ( special.postDispatch ) { + special.postDispatch.call( this, event ); + } + + return event.result; + }, + + handlers: function( event, handlers ) { + var i, handleObj, sel, matchedHandlers, matchedSelectors, + handlerQueue = [], + delegateCount = handlers.delegateCount, + cur = event.target; + + // Find delegate handlers + if ( delegateCount && + + // Support: IE <=9 + // Black-hole SVG instance trees (trac-13180) + cur.nodeType && + + // Support: Firefox <=42 + // Suppress spec-violating clicks indicating a non-primary pointer button (trac-3861) + // https://www.w3.org/TR/DOM-Level-3-Events/#event-type-click + // Support: IE 11 only + // ...but not arrow key "clicks" of radio inputs, which can have `button` -1 (gh-2343) + !( event.type === "click" && event.button >= 1 ) ) { + + for ( ; cur !== this; cur = cur.parentNode || this ) { + + // Don't check non-elements (#13208) + // Don't process clicks on disabled elements (#6911, #8165, #11382, #11764) + if ( cur.nodeType === 1 && !( event.type === "click" && cur.disabled === true ) ) { + matchedHandlers = []; + matchedSelectors = {}; + for ( i = 0; i < delegateCount; i++ ) { + handleObj = handlers[ i ]; + + // Don't conflict with Object.prototype properties (#13203) + sel = handleObj.selector + " "; + + if ( matchedSelectors[ sel ] === undefined ) { + matchedSelectors[ sel ] = handleObj.needsContext ? + jQuery( sel, this ).index( cur ) > -1 : + jQuery.find( sel, this, null, [ cur ] ).length; + } + if ( matchedSelectors[ sel ] ) { + matchedHandlers.push( handleObj ); + } + } + if ( matchedHandlers.length ) { + handlerQueue.push( { elem: cur, handlers: matchedHandlers } ); + } + } + } + } + + // Add the remaining (directly-bound) handlers + cur = this; + if ( delegateCount < handlers.length ) { + handlerQueue.push( { elem: cur, handlers: handlers.slice( delegateCount ) } ); + } + + return handlerQueue; + }, + + addProp: function( name, hook ) { + Object.defineProperty( jQuery.Event.prototype, name, { + enumerable: true, + configurable: true, + + get: isFunction( hook ) ? + function() { + if ( this.originalEvent ) { + return hook( this.originalEvent ); + } + } : + function() { + if ( this.originalEvent ) { + return this.originalEvent[ name ]; + } + }, + + set: function( value ) { + Object.defineProperty( this, name, { + enumerable: true, + configurable: true, + writable: true, + value: value + } ); + } + } ); + }, + + fix: function( originalEvent ) { + return originalEvent[ jQuery.expando ] ? + originalEvent : + new jQuery.Event( originalEvent ); + }, + + special: { + load: { + + // Prevent triggered image.load events from bubbling to window.load + noBubble: true + }, + click: { + + // Utilize native event to ensure correct state for checkable inputs + setup: function( data ) { + + // For mutual compressibility with _default, replace `this` access with a local var. + // `|| data` is dead code meant only to preserve the variable through minification. + var el = this || data; + + // Claim the first handler + if ( rcheckableType.test( el.type ) && + el.click && nodeName( el, "input" ) ) { + + // dataPriv.set( el, "click", ... ) + leverageNative( el, "click", returnTrue ); + } + + // Return false to allow normal processing in the caller + return false; + }, + trigger: function( data ) { + + // For mutual compressibility with _default, replace `this` access with a local var. + // `|| data` is dead code meant only to preserve the variable through minification. + var el = this || data; + + // Force setup before triggering a click + if ( rcheckableType.test( el.type ) && + el.click && nodeName( el, "input" ) ) { + + leverageNative( el, "click" ); + } + + // Return non-false to allow normal event-path propagation + return true; + }, + + // For cross-browser consistency, suppress native .click() on links + // Also prevent it if we're currently inside a leveraged native-event stack + _default: function( event ) { + var target = event.target; + return rcheckableType.test( target.type ) && + target.click && nodeName( target, "input" ) && + dataPriv.get( target, "click" ) || + nodeName( target, "a" ); + } + }, + + beforeunload: { + postDispatch: function( event ) { + + // Support: Firefox 20+ + // Firefox doesn't alert if the returnValue field is not set. + if ( event.result !== undefined && event.originalEvent ) { + event.originalEvent.returnValue = event.result; + } + } + } + } +}; + +// Ensure the presence of an event listener that handles manually-triggered +// synthetic events by interrupting progress until reinvoked in response to +// *native* events that it fires directly, ensuring that state changes have +// already occurred before other listeners are invoked. +function leverageNative( el, type, expectSync ) { + + // Missing expectSync indicates a trigger call, which must force setup through jQuery.event.add + if ( !expectSync ) { + if ( dataPriv.get( el, type ) === undefined ) { + jQuery.event.add( el, type, returnTrue ); + } + return; + } + + // Register the controller as a special universal handler for all event namespaces + dataPriv.set( el, type, false ); + jQuery.event.add( el, type, { + namespace: false, + handler: function( event ) { + var notAsync, result, + saved = dataPriv.get( this, type ); + + if ( ( event.isTrigger & 1 ) && this[ type ] ) { + + // Interrupt processing of the outer synthetic .trigger()ed event + // Saved data should be false in such cases, but might be a leftover capture object + // from an async native handler (gh-4350) + if ( !saved.length ) { + + // Store arguments for use when handling the inner native event + // There will always be at least one argument (an event object), so this array + // will not be confused with a leftover capture object. + saved = slice.call( arguments ); + dataPriv.set( this, type, saved ); + + // Trigger the native event and capture its result + // Support: IE <=9 - 11+ + // focus() and blur() are asynchronous + notAsync = expectSync( this, type ); + this[ type ](); + result = dataPriv.get( this, type ); + if ( saved !== result || notAsync ) { + dataPriv.set( this, type, false ); + } else { + result = {}; + } + if ( saved !== result ) { + + // Cancel the outer synthetic event + event.stopImmediatePropagation(); + event.preventDefault(); + return result.value; + } + + // If this is an inner synthetic event for an event with a bubbling surrogate + // (focus or blur), assume that the surrogate already propagated from triggering the + // native event and prevent that from happening again here. + // This technically gets the ordering wrong w.r.t. to `.trigger()` (in which the + // bubbling surrogate propagates *after* the non-bubbling base), but that seems + // less bad than duplication. + } else if ( ( jQuery.event.special[ type ] || {} ).delegateType ) { + event.stopPropagation(); + } + + // If this is a native event triggered above, everything is now in order + // Fire an inner synthetic event with the original arguments + } else if ( saved.length ) { + + // ...and capture the result + dataPriv.set( this, type, { + value: jQuery.event.trigger( + + // Support: IE <=9 - 11+ + // Extend with the prototype to reset the above stopImmediatePropagation() + jQuery.extend( saved[ 0 ], jQuery.Event.prototype ), + saved.slice( 1 ), + this + ) + } ); + + // Abort handling of the native event + event.stopImmediatePropagation(); + } + } + } ); +} + +jQuery.removeEvent = function( elem, type, handle ) { + + // This "if" is needed for plain objects + if ( elem.removeEventListener ) { + elem.removeEventListener( type, handle ); + } +}; + +jQuery.Event = function( src, props ) { + + // Allow instantiation without the 'new' keyword + if ( !( this instanceof jQuery.Event ) ) { + return new jQuery.Event( src, props ); + } + + // Event object + if ( src && src.type ) { + this.originalEvent = src; + this.type = src.type; + + // Events bubbling up the document may have been marked as prevented + // by a handler lower down the tree; reflect the correct value. + this.isDefaultPrevented = src.defaultPrevented || + src.defaultPrevented === undefined && + + // Support: Android <=2.3 only + src.returnValue === false ? + returnTrue : + returnFalse; + + // Create target properties + // Support: Safari <=6 - 7 only + // Target should not be a text node (#504, #13143) + this.target = ( src.target && src.target.nodeType === 3 ) ? + src.target.parentNode : + src.target; + + this.currentTarget = src.currentTarget; + this.relatedTarget = src.relatedTarget; + + // Event type + } else { + this.type = src; + } + + // Put explicitly provided properties onto the event object + if ( props ) { + jQuery.extend( this, props ); + } + + // Create a timestamp if incoming event doesn't have one + this.timeStamp = src && src.timeStamp || Date.now(); + + // Mark it as fixed + this[ jQuery.expando ] = true; +}; + +// jQuery.Event is based on DOM3 Events as specified by the ECMAScript Language Binding +// https://www.w3.org/TR/2003/WD-DOM-Level-3-Events-20030331/ecma-script-binding.html +jQuery.Event.prototype = { + constructor: jQuery.Event, + isDefaultPrevented: returnFalse, + isPropagationStopped: returnFalse, + isImmediatePropagationStopped: returnFalse, + isSimulated: false, + + preventDefault: function() { + var e = this.originalEvent; + + this.isDefaultPrevented = returnTrue; + + if ( e && !this.isSimulated ) { + e.preventDefault(); + } + }, + stopPropagation: function() { + var e = this.originalEvent; + + this.isPropagationStopped = returnTrue; + + if ( e && !this.isSimulated ) { + e.stopPropagation(); + } + }, + stopImmediatePropagation: function() { + var e = this.originalEvent; + + this.isImmediatePropagationStopped = returnTrue; + + if ( e && !this.isSimulated ) { + e.stopImmediatePropagation(); + } + + this.stopPropagation(); + } +}; + +// Includes all common event props including KeyEvent and MouseEvent specific props +jQuery.each( { + altKey: true, + bubbles: true, + cancelable: true, + changedTouches: true, + ctrlKey: true, + detail: true, + eventPhase: true, + metaKey: true, + pageX: true, + pageY: true, + shiftKey: true, + view: true, + "char": true, + code: true, + charCode: true, + key: true, + keyCode: true, + button: true, + buttons: true, + clientX: true, + clientY: true, + offsetX: true, + offsetY: true, + pointerId: true, + pointerType: true, + screenX: true, + screenY: true, + targetTouches: true, + toElement: true, + touches: true, + + which: function( event ) { + var button = event.button; + + // Add which for key events + if ( event.which == null && rkeyEvent.test( event.type ) ) { + return event.charCode != null ? event.charCode : event.keyCode; + } + + // Add which for click: 1 === left; 2 === middle; 3 === right + if ( !event.which && button !== undefined && rmouseEvent.test( event.type ) ) { + if ( button & 1 ) { + return 1; + } + + if ( button & 2 ) { + return 3; + } + + if ( button & 4 ) { + return 2; + } + + return 0; + } + + return event.which; + } +}, jQuery.event.addProp ); + +jQuery.each( { focus: "focusin", blur: "focusout" }, function( type, delegateType ) { + jQuery.event.special[ type ] = { + + // Utilize native event if possible so blur/focus sequence is correct + setup: function() { + + // Claim the first handler + // dataPriv.set( this, "focus", ... ) + // dataPriv.set( this, "blur", ... ) + leverageNative( this, type, expectSync ); + + // Return false to allow normal processing in the caller + return false; + }, + trigger: function() { + + // Force setup before trigger + leverageNative( this, type ); + + // Return non-false to allow normal event-path propagation + return true; + }, + + delegateType: delegateType + }; +} ); + +// Create mouseenter/leave events using mouseover/out and event-time checks +// so that event delegation works in jQuery. +// Do the same for pointerenter/pointerleave and pointerover/pointerout +// +// Support: Safari 7 only +// Safari sends mouseenter too often; see: +// https://bugs.chromium.org/p/chromium/issues/detail?id=470258 +// for the description of the bug (it existed in older Chrome versions as well). +jQuery.each( { + mouseenter: "mouseover", + mouseleave: "mouseout", + pointerenter: "pointerover", + pointerleave: "pointerout" +}, function( orig, fix ) { + jQuery.event.special[ orig ] = { + delegateType: fix, + bindType: fix, + + handle: function( event ) { + var ret, + target = this, + related = event.relatedTarget, + handleObj = event.handleObj; + + // For mouseenter/leave call the handler if related is outside the target. + // NB: No relatedTarget if the mouse left/entered the browser window + if ( !related || ( related !== target && !jQuery.contains( target, related ) ) ) { + event.type = handleObj.origType; + ret = handleObj.handler.apply( this, arguments ); + event.type = fix; + } + return ret; + } + }; +} ); + +jQuery.fn.extend( { + + on: function( types, selector, data, fn ) { + return on( this, types, selector, data, fn ); + }, + one: function( types, selector, data, fn ) { + return on( this, types, selector, data, fn, 1 ); + }, + off: function( types, selector, fn ) { + var handleObj, type; + if ( types && types.preventDefault && types.handleObj ) { + + // ( event ) dispatched jQuery.Event + handleObj = types.handleObj; + jQuery( types.delegateTarget ).off( + handleObj.namespace ? + handleObj.origType + "." + handleObj.namespace : + handleObj.origType, + handleObj.selector, + handleObj.handler + ); + return this; + } + if ( typeof types === "object" ) { + + // ( types-object [, selector] ) + for ( type in types ) { + this.off( type, selector, types[ type ] ); + } + return this; + } + if ( selector === false || typeof selector === "function" ) { + + // ( types [, fn] ) + fn = selector; + selector = undefined; + } + if ( fn === false ) { + fn = returnFalse; + } + return this.each( function() { + jQuery.event.remove( this, types, fn, selector ); + } ); + } +} ); + + +var + + // Support: IE <=10 - 11, Edge 12 - 13 only + // In IE/Edge using regex groups here causes severe slowdowns. + // See https://connect.microsoft.com/IE/feedback/details/1736512/ + rnoInnerhtml = /\s*$/g; + +// Prefer a tbody over its parent table for containing new rows +function manipulationTarget( elem, content ) { + if ( nodeName( elem, "table" ) && + nodeName( content.nodeType !== 11 ? content : content.firstChild, "tr" ) ) { + + return jQuery( elem ).children( "tbody" )[ 0 ] || elem; + } + + return elem; +} + +// Replace/restore the type attribute of script elements for safe DOM manipulation +function disableScript( elem ) { + elem.type = ( elem.getAttribute( "type" ) !== null ) + "/" + elem.type; + return elem; +} +function restoreScript( elem ) { + if ( ( elem.type || "" ).slice( 0, 5 ) === "true/" ) { + elem.type = elem.type.slice( 5 ); + } else { + elem.removeAttribute( "type" ); + } + + return elem; +} + +function cloneCopyEvent( src, dest ) { + var i, l, type, pdataOld, udataOld, udataCur, events; + + if ( dest.nodeType !== 1 ) { + return; + } + + // 1. Copy private data: events, handlers, etc. + if ( dataPriv.hasData( src ) ) { + pdataOld = dataPriv.get( src ); + events = pdataOld.events; + + if ( events ) { + dataPriv.remove( dest, "handle events" ); + + for ( type in events ) { + for ( i = 0, l = events[ type ].length; i < l; i++ ) { + jQuery.event.add( dest, type, events[ type ][ i ] ); + } + } + } + } + + // 2. Copy user data + if ( dataUser.hasData( src ) ) { + udataOld = dataUser.access( src ); + udataCur = jQuery.extend( {}, udataOld ); + + dataUser.set( dest, udataCur ); + } +} + +// Fix IE bugs, see support tests +function fixInput( src, dest ) { + var nodeName = dest.nodeName.toLowerCase(); + + // Fails to persist the checked state of a cloned checkbox or radio button. + if ( nodeName === "input" && rcheckableType.test( src.type ) ) { + dest.checked = src.checked; + + // Fails to return the selected option to the default selected state when cloning options + } else if ( nodeName === "input" || nodeName === "textarea" ) { + dest.defaultValue = src.defaultValue; + } +} + +function domManip( collection, args, callback, ignored ) { + + // Flatten any nested arrays + args = flat( args ); + + var fragment, first, scripts, hasScripts, node, doc, + i = 0, + l = collection.length, + iNoClone = l - 1, + value = args[ 0 ], + valueIsFunction = isFunction( value ); + + // We can't cloneNode fragments that contain checked, in WebKit + if ( valueIsFunction || + ( l > 1 && typeof value === "string" && + !support.checkClone && rchecked.test( value ) ) ) { + return collection.each( function( index ) { + var self = collection.eq( index ); + if ( valueIsFunction ) { + args[ 0 ] = value.call( this, index, self.html() ); + } + domManip( self, args, callback, ignored ); + } ); + } + + if ( l ) { + fragment = buildFragment( args, collection[ 0 ].ownerDocument, false, collection, ignored ); + first = fragment.firstChild; + + if ( fragment.childNodes.length === 1 ) { + fragment = first; + } + + // Require either new content or an interest in ignored elements to invoke the callback + if ( first || ignored ) { + scripts = jQuery.map( getAll( fragment, "script" ), disableScript ); + hasScripts = scripts.length; + + // Use the original fragment for the last item + // instead of the first because it can end up + // being emptied incorrectly in certain situations (#8070). + for ( ; i < l; i++ ) { + node = fragment; + + if ( i !== iNoClone ) { + node = jQuery.clone( node, true, true ); + + // Keep references to cloned scripts for later restoration + if ( hasScripts ) { + + // Support: Android <=4.0 only, PhantomJS 1 only + // push.apply(_, arraylike) throws on ancient WebKit + jQuery.merge( scripts, getAll( node, "script" ) ); + } + } + + callback.call( collection[ i ], node, i ); + } + + if ( hasScripts ) { + doc = scripts[ scripts.length - 1 ].ownerDocument; + + // Reenable scripts + jQuery.map( scripts, restoreScript ); + + // Evaluate executable scripts on first document insertion + for ( i = 0; i < hasScripts; i++ ) { + node = scripts[ i ]; + if ( rscriptType.test( node.type || "" ) && + !dataPriv.access( node, "globalEval" ) && + jQuery.contains( doc, node ) ) { + + if ( node.src && ( node.type || "" ).toLowerCase() !== "module" ) { + + // Optional AJAX dependency, but won't run scripts if not present + if ( jQuery._evalUrl && !node.noModule ) { + jQuery._evalUrl( node.src, { + nonce: node.nonce || node.getAttribute( "nonce" ) + }, doc ); + } + } else { + DOMEval( node.textContent.replace( rcleanScript, "" ), node, doc ); + } + } + } + } + } + } + + return collection; +} + +function remove( elem, selector, keepData ) { + var node, + nodes = selector ? jQuery.filter( selector, elem ) : elem, + i = 0; + + for ( ; ( node = nodes[ i ] ) != null; i++ ) { + if ( !keepData && node.nodeType === 1 ) { + jQuery.cleanData( getAll( node ) ); + } + + if ( node.parentNode ) { + if ( keepData && isAttached( node ) ) { + setGlobalEval( getAll( node, "script" ) ); + } + node.parentNode.removeChild( node ); + } + } + + return elem; +} + +jQuery.extend( { + htmlPrefilter: function( html ) { + return html; + }, + + clone: function( elem, dataAndEvents, deepDataAndEvents ) { + var i, l, srcElements, destElements, + clone = elem.cloneNode( true ), + inPage = isAttached( elem ); + + // Fix IE cloning issues + if ( !support.noCloneChecked && ( elem.nodeType === 1 || elem.nodeType === 11 ) && + !jQuery.isXMLDoc( elem ) ) { + + // We eschew Sizzle here for performance reasons: https://jsperf.com/getall-vs-sizzle/2 + destElements = getAll( clone ); + srcElements = getAll( elem ); + + for ( i = 0, l = srcElements.length; i < l; i++ ) { + fixInput( srcElements[ i ], destElements[ i ] ); + } + } + + // Copy the events from the original to the clone + if ( dataAndEvents ) { + if ( deepDataAndEvents ) { + srcElements = srcElements || getAll( elem ); + destElements = destElements || getAll( clone ); + + for ( i = 0, l = srcElements.length; i < l; i++ ) { + cloneCopyEvent( srcElements[ i ], destElements[ i ] ); + } + } else { + cloneCopyEvent( elem, clone ); + } + } + + // Preserve script evaluation history + destElements = getAll( clone, "script" ); + if ( destElements.length > 0 ) { + setGlobalEval( destElements, !inPage && getAll( elem, "script" ) ); + } + + // Return the cloned set + return clone; + }, + + cleanData: function( elems ) { + var data, elem, type, + special = jQuery.event.special, + i = 0; + + for ( ; ( elem = elems[ i ] ) !== undefined; i++ ) { + if ( acceptData( elem ) ) { + if ( ( data = elem[ dataPriv.expando ] ) ) { + if ( data.events ) { + for ( type in data.events ) { + if ( special[ type ] ) { + jQuery.event.remove( elem, type ); + + // This is a shortcut to avoid jQuery.event.remove's overhead + } else { + jQuery.removeEvent( elem, type, data.handle ); + } + } + } + + // Support: Chrome <=35 - 45+ + // Assign undefined instead of using delete, see Data#remove + elem[ dataPriv.expando ] = undefined; + } + if ( elem[ dataUser.expando ] ) { + + // Support: Chrome <=35 - 45+ + // Assign undefined instead of using delete, see Data#remove + elem[ dataUser.expando ] = undefined; + } + } + } + } +} ); + +jQuery.fn.extend( { + detach: function( selector ) { + return remove( this, selector, true ); + }, + + remove: function( selector ) { + return remove( this, selector ); + }, + + text: function( value ) { + return access( this, function( value ) { + return value === undefined ? + jQuery.text( this ) : + this.empty().each( function() { + if ( this.nodeType === 1 || this.nodeType === 11 || this.nodeType === 9 ) { + this.textContent = value; + } + } ); + }, null, value, arguments.length ); + }, + + append: function() { + return domManip( this, arguments, function( elem ) { + if ( this.nodeType === 1 || this.nodeType === 11 || this.nodeType === 9 ) { + var target = manipulationTarget( this, elem ); + target.appendChild( elem ); + } + } ); + }, + + prepend: function() { + return domManip( this, arguments, function( elem ) { + if ( this.nodeType === 1 || this.nodeType === 11 || this.nodeType === 9 ) { + var target = manipulationTarget( this, elem ); + target.insertBefore( elem, target.firstChild ); + } + } ); + }, + + before: function() { + return domManip( this, arguments, function( elem ) { + if ( this.parentNode ) { + this.parentNode.insertBefore( elem, this ); + } + } ); + }, + + after: function() { + return domManip( this, arguments, function( elem ) { + if ( this.parentNode ) { + this.parentNode.insertBefore( elem, this.nextSibling ); + } + } ); + }, + + empty: function() { + var elem, + i = 0; + + for ( ; ( elem = this[ i ] ) != null; i++ ) { + if ( elem.nodeType === 1 ) { + + // Prevent memory leaks + jQuery.cleanData( getAll( elem, false ) ); + + // Remove any remaining nodes + elem.textContent = ""; + } + } + + return this; + }, + + clone: function( dataAndEvents, deepDataAndEvents ) { + dataAndEvents = dataAndEvents == null ? false : dataAndEvents; + deepDataAndEvents = deepDataAndEvents == null ? dataAndEvents : deepDataAndEvents; + + return this.map( function() { + return jQuery.clone( this, dataAndEvents, deepDataAndEvents ); + } ); + }, + + html: function( value ) { + return access( this, function( value ) { + var elem = this[ 0 ] || {}, + i = 0, + l = this.length; + + if ( value === undefined && elem.nodeType === 1 ) { + return elem.innerHTML; + } + + // See if we can take a shortcut and just use innerHTML + if ( typeof value === "string" && !rnoInnerhtml.test( value ) && + !wrapMap[ ( rtagName.exec( value ) || [ "", "" ] )[ 1 ].toLowerCase() ] ) { + + value = jQuery.htmlPrefilter( value ); + + try { + for ( ; i < l; i++ ) { + elem = this[ i ] || {}; + + // Remove element nodes and prevent memory leaks + if ( elem.nodeType === 1 ) { + jQuery.cleanData( getAll( elem, false ) ); + elem.innerHTML = value; + } + } + + elem = 0; + + // If using innerHTML throws an exception, use the fallback method + } catch ( e ) {} + } + + if ( elem ) { + this.empty().append( value ); + } + }, null, value, arguments.length ); + }, + + replaceWith: function() { + var ignored = []; + + // Make the changes, replacing each non-ignored context element with the new content + return domManip( this, arguments, function( elem ) { + var parent = this.parentNode; + + if ( jQuery.inArray( this, ignored ) < 0 ) { + jQuery.cleanData( getAll( this ) ); + if ( parent ) { + parent.replaceChild( elem, this ); + } + } + + // Force callback invocation + }, ignored ); + } +} ); + +jQuery.each( { + appendTo: "append", + prependTo: "prepend", + insertBefore: "before", + insertAfter: "after", + replaceAll: "replaceWith" +}, function( name, original ) { + jQuery.fn[ name ] = function( selector ) { + var elems, + ret = [], + insert = jQuery( selector ), + last = insert.length - 1, + i = 0; + + for ( ; i <= last; i++ ) { + elems = i === last ? this : this.clone( true ); + jQuery( insert[ i ] )[ original ]( elems ); + + // Support: Android <=4.0 only, PhantomJS 1 only + // .get() because push.apply(_, arraylike) throws on ancient WebKit + push.apply( ret, elems.get() ); + } + + return this.pushStack( ret ); + }; +} ); +var rnumnonpx = new RegExp( "^(" + pnum + ")(?!px)[a-z%]+$", "i" ); + +var getStyles = function( elem ) { + + // Support: IE <=11 only, Firefox <=30 (#15098, #14150) + // IE throws on elements created in popups + // FF meanwhile throws on frame elements through "defaultView.getComputedStyle" + var view = elem.ownerDocument.defaultView; + + if ( !view || !view.opener ) { + view = window; + } + + return view.getComputedStyle( elem ); + }; + +var swap = function( elem, options, callback ) { + var ret, name, + old = {}; + + // Remember the old values, and insert the new ones + for ( name in options ) { + old[ name ] = elem.style[ name ]; + elem.style[ name ] = options[ name ]; + } + + ret = callback.call( elem ); + + // Revert the old values + for ( name in options ) { + elem.style[ name ] = old[ name ]; + } + + return ret; +}; + + +var rboxStyle = new RegExp( cssExpand.join( "|" ), "i" ); + + + +( function() { + + // Executing both pixelPosition & boxSizingReliable tests require only one layout + // so they're executed at the same time to save the second computation. + function computeStyleTests() { + + // This is a singleton, we need to execute it only once + if ( !div ) { + return; + } + + container.style.cssText = "position:absolute;left:-11111px;width:60px;" + + "margin-top:1px;padding:0;border:0"; + div.style.cssText = + "position:relative;display:block;box-sizing:border-box;overflow:scroll;" + + "margin:auto;border:1px;padding:1px;" + + "width:60%;top:1%"; + documentElement.appendChild( container ).appendChild( div ); + + var divStyle = window.getComputedStyle( div ); + pixelPositionVal = divStyle.top !== "1%"; + + // Support: Android 4.0 - 4.3 only, Firefox <=3 - 44 + reliableMarginLeftVal = roundPixelMeasures( divStyle.marginLeft ) === 12; + + // Support: Android 4.0 - 4.3 only, Safari <=9.1 - 10.1, iOS <=7.0 - 9.3 + // Some styles come back with percentage values, even though they shouldn't + div.style.right = "60%"; + pixelBoxStylesVal = roundPixelMeasures( divStyle.right ) === 36; + + // Support: IE 9 - 11 only + // Detect misreporting of content dimensions for box-sizing:border-box elements + boxSizingReliableVal = roundPixelMeasures( divStyle.width ) === 36; + + // Support: IE 9 only + // Detect overflow:scroll screwiness (gh-3699) + // Support: Chrome <=64 + // Don't get tricked when zoom affects offsetWidth (gh-4029) + div.style.position = "absolute"; + scrollboxSizeVal = roundPixelMeasures( div.offsetWidth / 3 ) === 12; + + documentElement.removeChild( container ); + + // Nullify the div so it wouldn't be stored in the memory and + // it will also be a sign that checks already performed + div = null; + } + + function roundPixelMeasures( measure ) { + return Math.round( parseFloat( measure ) ); + } + + var pixelPositionVal, boxSizingReliableVal, scrollboxSizeVal, pixelBoxStylesVal, + reliableTrDimensionsVal, reliableMarginLeftVal, + container = document.createElement( "div" ), + div = document.createElement( "div" ); + + // Finish early in limited (non-browser) environments + if ( !div.style ) { + return; + } + + // Support: IE <=9 - 11 only + // Style of cloned element affects source element cloned (#8908) + div.style.backgroundClip = "content-box"; + div.cloneNode( true ).style.backgroundClip = ""; + support.clearCloneStyle = div.style.backgroundClip === "content-box"; + + jQuery.extend( support, { + boxSizingReliable: function() { + computeStyleTests(); + return boxSizingReliableVal; + }, + pixelBoxStyles: function() { + computeStyleTests(); + return pixelBoxStylesVal; + }, + pixelPosition: function() { + computeStyleTests(); + return pixelPositionVal; + }, + reliableMarginLeft: function() { + computeStyleTests(); + return reliableMarginLeftVal; + }, + scrollboxSize: function() { + computeStyleTests(); + return scrollboxSizeVal; + }, + + // Support: IE 9 - 11+, Edge 15 - 18+ + // IE/Edge misreport `getComputedStyle` of table rows with width/height + // set in CSS while `offset*` properties report correct values. + // Behavior in IE 9 is more subtle than in newer versions & it passes + // some versions of this test; make sure not to make it pass there! + reliableTrDimensions: function() { + var table, tr, trChild, trStyle; + if ( reliableTrDimensionsVal == null ) { + table = document.createElement( "table" ); + tr = document.createElement( "tr" ); + trChild = document.createElement( "div" ); + + table.style.cssText = "position:absolute;left:-11111px"; + tr.style.height = "1px"; + trChild.style.height = "9px"; + + documentElement + .appendChild( table ) + .appendChild( tr ) + .appendChild( trChild ); + + trStyle = window.getComputedStyle( tr ); + reliableTrDimensionsVal = parseInt( trStyle.height ) > 3; + + documentElement.removeChild( table ); + } + return reliableTrDimensionsVal; + } + } ); +} )(); + + +function curCSS( elem, name, computed ) { + var width, minWidth, maxWidth, ret, + + // Support: Firefox 51+ + // Retrieving style before computed somehow + // fixes an issue with getting wrong values + // on detached elements + style = elem.style; + + computed = computed || getStyles( elem ); + + // getPropertyValue is needed for: + // .css('filter') (IE 9 only, #12537) + // .css('--customProperty) (#3144) + if ( computed ) { + ret = computed.getPropertyValue( name ) || computed[ name ]; + + if ( ret === "" && !isAttached( elem ) ) { + ret = jQuery.style( elem, name ); + } + + // A tribute to the "awesome hack by Dean Edwards" + // Android Browser returns percentage for some values, + // but width seems to be reliably pixels. + // This is against the CSSOM draft spec: + // https://drafts.csswg.org/cssom/#resolved-values + if ( !support.pixelBoxStyles() && rnumnonpx.test( ret ) && rboxStyle.test( name ) ) { + + // Remember the original values + width = style.width; + minWidth = style.minWidth; + maxWidth = style.maxWidth; + + // Put in the new values to get a computed value out + style.minWidth = style.maxWidth = style.width = ret; + ret = computed.width; + + // Revert the changed values + style.width = width; + style.minWidth = minWidth; + style.maxWidth = maxWidth; + } + } + + return ret !== undefined ? + + // Support: IE <=9 - 11 only + // IE returns zIndex value as an integer. + ret + "" : + ret; +} + + +function addGetHookIf( conditionFn, hookFn ) { + + // Define the hook, we'll check on the first run if it's really needed. + return { + get: function() { + if ( conditionFn() ) { + + // Hook not needed (or it's not possible to use it due + // to missing dependency), remove it. + delete this.get; + return; + } + + // Hook needed; redefine it so that the support test is not executed again. + return ( this.get = hookFn ).apply( this, arguments ); + } + }; +} + + +var cssPrefixes = [ "Webkit", "Moz", "ms" ], + emptyStyle = document.createElement( "div" ).style, + vendorProps = {}; + +// Return a vendor-prefixed property or undefined +function vendorPropName( name ) { + + // Check for vendor prefixed names + var capName = name[ 0 ].toUpperCase() + name.slice( 1 ), + i = cssPrefixes.length; + + while ( i-- ) { + name = cssPrefixes[ i ] + capName; + if ( name in emptyStyle ) { + return name; + } + } +} + +// Return a potentially-mapped jQuery.cssProps or vendor prefixed property +function finalPropName( name ) { + var final = jQuery.cssProps[ name ] || vendorProps[ name ]; + + if ( final ) { + return final; + } + if ( name in emptyStyle ) { + return name; + } + return vendorProps[ name ] = vendorPropName( name ) || name; +} + + +var + + // Swappable if display is none or starts with table + // except "table", "table-cell", or "table-caption" + // See here for display values: https://developer.mozilla.org/en-US/docs/CSS/display + rdisplayswap = /^(none|table(?!-c[ea]).+)/, + rcustomProp = /^--/, + cssShow = { position: "absolute", visibility: "hidden", display: "block" }, + cssNormalTransform = { + letterSpacing: "0", + fontWeight: "400" + }; + +function setPositiveNumber( _elem, value, subtract ) { + + // Any relative (+/-) values have already been + // normalized at this point + var matches = rcssNum.exec( value ); + return matches ? + + // Guard against undefined "subtract", e.g., when used as in cssHooks + Math.max( 0, matches[ 2 ] - ( subtract || 0 ) ) + ( matches[ 3 ] || "px" ) : + value; +} + +function boxModelAdjustment( elem, dimension, box, isBorderBox, styles, computedVal ) { + var i = dimension === "width" ? 1 : 0, + extra = 0, + delta = 0; + + // Adjustment may not be necessary + if ( box === ( isBorderBox ? "border" : "content" ) ) { + return 0; + } + + for ( ; i < 4; i += 2 ) { + + // Both box models exclude margin + if ( box === "margin" ) { + delta += jQuery.css( elem, box + cssExpand[ i ], true, styles ); + } + + // If we get here with a content-box, we're seeking "padding" or "border" or "margin" + if ( !isBorderBox ) { + + // Add padding + delta += jQuery.css( elem, "padding" + cssExpand[ i ], true, styles ); + + // For "border" or "margin", add border + if ( box !== "padding" ) { + delta += jQuery.css( elem, "border" + cssExpand[ i ] + "Width", true, styles ); + + // But still keep track of it otherwise + } else { + extra += jQuery.css( elem, "border" + cssExpand[ i ] + "Width", true, styles ); + } + + // If we get here with a border-box (content + padding + border), we're seeking "content" or + // "padding" or "margin" + } else { + + // For "content", subtract padding + if ( box === "content" ) { + delta -= jQuery.css( elem, "padding" + cssExpand[ i ], true, styles ); + } + + // For "content" or "padding", subtract border + if ( box !== "margin" ) { + delta -= jQuery.css( elem, "border" + cssExpand[ i ] + "Width", true, styles ); + } + } + } + + // Account for positive content-box scroll gutter when requested by providing computedVal + if ( !isBorderBox && computedVal >= 0 ) { + + // offsetWidth/offsetHeight is a rounded sum of content, padding, scroll gutter, and border + // Assuming integer scroll gutter, subtract the rest and round down + delta += Math.max( 0, Math.ceil( + elem[ "offset" + dimension[ 0 ].toUpperCase() + dimension.slice( 1 ) ] - + computedVal - + delta - + extra - + 0.5 + + // If offsetWidth/offsetHeight is unknown, then we can't determine content-box scroll gutter + // Use an explicit zero to avoid NaN (gh-3964) + ) ) || 0; + } + + return delta; +} + +function getWidthOrHeight( elem, dimension, extra ) { + + // Start with computed style + var styles = getStyles( elem ), + + // To avoid forcing a reflow, only fetch boxSizing if we need it (gh-4322). + // Fake content-box until we know it's needed to know the true value. + boxSizingNeeded = !support.boxSizingReliable() || extra, + isBorderBox = boxSizingNeeded && + jQuery.css( elem, "boxSizing", false, styles ) === "border-box", + valueIsBorderBox = isBorderBox, + + val = curCSS( elem, dimension, styles ), + offsetProp = "offset" + dimension[ 0 ].toUpperCase() + dimension.slice( 1 ); + + // Support: Firefox <=54 + // Return a confounding non-pixel value or feign ignorance, as appropriate. + if ( rnumnonpx.test( val ) ) { + if ( !extra ) { + return val; + } + val = "auto"; + } + + + // Support: IE 9 - 11 only + // Use offsetWidth/offsetHeight for when box sizing is unreliable. + // In those cases, the computed value can be trusted to be border-box. + if ( ( !support.boxSizingReliable() && isBorderBox || + + // Support: IE 10 - 11+, Edge 15 - 18+ + // IE/Edge misreport `getComputedStyle` of table rows with width/height + // set in CSS while `offset*` properties report correct values. + // Interestingly, in some cases IE 9 doesn't suffer from this issue. + !support.reliableTrDimensions() && nodeName( elem, "tr" ) || + + // Fall back to offsetWidth/offsetHeight when value is "auto" + // This happens for inline elements with no explicit setting (gh-3571) + val === "auto" || + + // Support: Android <=4.1 - 4.3 only + // Also use offsetWidth/offsetHeight for misreported inline dimensions (gh-3602) + !parseFloat( val ) && jQuery.css( elem, "display", false, styles ) === "inline" ) && + + // Make sure the element is visible & connected + elem.getClientRects().length ) { + + isBorderBox = jQuery.css( elem, "boxSizing", false, styles ) === "border-box"; + + // Where available, offsetWidth/offsetHeight approximate border box dimensions. + // Where not available (e.g., SVG), assume unreliable box-sizing and interpret the + // retrieved value as a content box dimension. + valueIsBorderBox = offsetProp in elem; + if ( valueIsBorderBox ) { + val = elem[ offsetProp ]; + } + } + + // Normalize "" and auto + val = parseFloat( val ) || 0; + + // Adjust for the element's box model + return ( val + + boxModelAdjustment( + elem, + dimension, + extra || ( isBorderBox ? "border" : "content" ), + valueIsBorderBox, + styles, + + // Provide the current computed size to request scroll gutter calculation (gh-3589) + val + ) + ) + "px"; +} + +jQuery.extend( { + + // Add in style property hooks for overriding the default + // behavior of getting and setting a style property + cssHooks: { + opacity: { + get: function( elem, computed ) { + if ( computed ) { + + // We should always get a number back from opacity + var ret = curCSS( elem, "opacity" ); + return ret === "" ? "1" : ret; + } + } + } + }, + + // Don't automatically add "px" to these possibly-unitless properties + cssNumber: { + "animationIterationCount": true, + "columnCount": true, + "fillOpacity": true, + "flexGrow": true, + "flexShrink": true, + "fontWeight": true, + "gridArea": true, + "gridColumn": true, + "gridColumnEnd": true, + "gridColumnStart": true, + "gridRow": true, + "gridRowEnd": true, + "gridRowStart": true, + "lineHeight": true, + "opacity": true, + "order": true, + "orphans": true, + "widows": true, + "zIndex": true, + "zoom": true + }, + + // Add in properties whose names you wish to fix before + // setting or getting the value + cssProps: {}, + + // Get and set the style property on a DOM Node + style: function( elem, name, value, extra ) { + + // Don't set styles on text and comment nodes + if ( !elem || elem.nodeType === 3 || elem.nodeType === 8 || !elem.style ) { + return; + } + + // Make sure that we're working with the right name + var ret, type, hooks, + origName = camelCase( name ), + isCustomProp = rcustomProp.test( name ), + style = elem.style; + + // Make sure that we're working with the right name. We don't + // want to query the value if it is a CSS custom property + // since they are user-defined. + if ( !isCustomProp ) { + name = finalPropName( origName ); + } + + // Gets hook for the prefixed version, then unprefixed version + hooks = jQuery.cssHooks[ name ] || jQuery.cssHooks[ origName ]; + + // Check if we're setting a value + if ( value !== undefined ) { + type = typeof value; + + // Convert "+=" or "-=" to relative numbers (#7345) + if ( type === "string" && ( ret = rcssNum.exec( value ) ) && ret[ 1 ] ) { + value = adjustCSS( elem, name, ret ); + + // Fixes bug #9237 + type = "number"; + } + + // Make sure that null and NaN values aren't set (#7116) + if ( value == null || value !== value ) { + return; + } + + // If a number was passed in, add the unit (except for certain CSS properties) + // The isCustomProp check can be removed in jQuery 4.0 when we only auto-append + // "px" to a few hardcoded values. + if ( type === "number" && !isCustomProp ) { + value += ret && ret[ 3 ] || ( jQuery.cssNumber[ origName ] ? "" : "px" ); + } + + // background-* props affect original clone's values + if ( !support.clearCloneStyle && value === "" && name.indexOf( "background" ) === 0 ) { + style[ name ] = "inherit"; + } + + // If a hook was provided, use that value, otherwise just set the specified value + if ( !hooks || !( "set" in hooks ) || + ( value = hooks.set( elem, value, extra ) ) !== undefined ) { + + if ( isCustomProp ) { + style.setProperty( name, value ); + } else { + style[ name ] = value; + } + } + + } else { + + // If a hook was provided get the non-computed value from there + if ( hooks && "get" in hooks && + ( ret = hooks.get( elem, false, extra ) ) !== undefined ) { + + return ret; + } + + // Otherwise just get the value from the style object + return style[ name ]; + } + }, + + css: function( elem, name, extra, styles ) { + var val, num, hooks, + origName = camelCase( name ), + isCustomProp = rcustomProp.test( name ); + + // Make sure that we're working with the right name. We don't + // want to modify the value if it is a CSS custom property + // since they are user-defined. + if ( !isCustomProp ) { + name = finalPropName( origName ); + } + + // Try prefixed name followed by the unprefixed name + hooks = jQuery.cssHooks[ name ] || jQuery.cssHooks[ origName ]; + + // If a hook was provided get the computed value from there + if ( hooks && "get" in hooks ) { + val = hooks.get( elem, true, extra ); + } + + // Otherwise, if a way to get the computed value exists, use that + if ( val === undefined ) { + val = curCSS( elem, name, styles ); + } + + // Convert "normal" to computed value + if ( val === "normal" && name in cssNormalTransform ) { + val = cssNormalTransform[ name ]; + } + + // Make numeric if forced or a qualifier was provided and val looks numeric + if ( extra === "" || extra ) { + num = parseFloat( val ); + return extra === true || isFinite( num ) ? num || 0 : val; + } + + return val; + } +} ); + +jQuery.each( [ "height", "width" ], function( _i, dimension ) { + jQuery.cssHooks[ dimension ] = { + get: function( elem, computed, extra ) { + if ( computed ) { + + // Certain elements can have dimension info if we invisibly show them + // but it must have a current display style that would benefit + return rdisplayswap.test( jQuery.css( elem, "display" ) ) && + + // Support: Safari 8+ + // Table columns in Safari have non-zero offsetWidth & zero + // getBoundingClientRect().width unless display is changed. + // Support: IE <=11 only + // Running getBoundingClientRect on a disconnected node + // in IE throws an error. + ( !elem.getClientRects().length || !elem.getBoundingClientRect().width ) ? + swap( elem, cssShow, function() { + return getWidthOrHeight( elem, dimension, extra ); + } ) : + getWidthOrHeight( elem, dimension, extra ); + } + }, + + set: function( elem, value, extra ) { + var matches, + styles = getStyles( elem ), + + // Only read styles.position if the test has a chance to fail + // to avoid forcing a reflow. + scrollboxSizeBuggy = !support.scrollboxSize() && + styles.position === "absolute", + + // To avoid forcing a reflow, only fetch boxSizing if we need it (gh-3991) + boxSizingNeeded = scrollboxSizeBuggy || extra, + isBorderBox = boxSizingNeeded && + jQuery.css( elem, "boxSizing", false, styles ) === "border-box", + subtract = extra ? + boxModelAdjustment( + elem, + dimension, + extra, + isBorderBox, + styles + ) : + 0; + + // Account for unreliable border-box dimensions by comparing offset* to computed and + // faking a content-box to get border and padding (gh-3699) + if ( isBorderBox && scrollboxSizeBuggy ) { + subtract -= Math.ceil( + elem[ "offset" + dimension[ 0 ].toUpperCase() + dimension.slice( 1 ) ] - + parseFloat( styles[ dimension ] ) - + boxModelAdjustment( elem, dimension, "border", false, styles ) - + 0.5 + ); + } + + // Convert to pixels if value adjustment is needed + if ( subtract && ( matches = rcssNum.exec( value ) ) && + ( matches[ 3 ] || "px" ) !== "px" ) { + + elem.style[ dimension ] = value; + value = jQuery.css( elem, dimension ); + } + + return setPositiveNumber( elem, value, subtract ); + } + }; +} ); + +jQuery.cssHooks.marginLeft = addGetHookIf( support.reliableMarginLeft, + function( elem, computed ) { + if ( computed ) { + return ( parseFloat( curCSS( elem, "marginLeft" ) ) || + elem.getBoundingClientRect().left - + swap( elem, { marginLeft: 0 }, function() { + return elem.getBoundingClientRect().left; + } ) + ) + "px"; + } + } +); + +// These hooks are used by animate to expand properties +jQuery.each( { + margin: "", + padding: "", + border: "Width" +}, function( prefix, suffix ) { + jQuery.cssHooks[ prefix + suffix ] = { + expand: function( value ) { + var i = 0, + expanded = {}, + + // Assumes a single number if not a string + parts = typeof value === "string" ? value.split( " " ) : [ value ]; + + for ( ; i < 4; i++ ) { + expanded[ prefix + cssExpand[ i ] + suffix ] = + parts[ i ] || parts[ i - 2 ] || parts[ 0 ]; + } + + return expanded; + } + }; + + if ( prefix !== "margin" ) { + jQuery.cssHooks[ prefix + suffix ].set = setPositiveNumber; + } +} ); + +jQuery.fn.extend( { + css: function( name, value ) { + return access( this, function( elem, name, value ) { + var styles, len, + map = {}, + i = 0; + + if ( Array.isArray( name ) ) { + styles = getStyles( elem ); + len = name.length; + + for ( ; i < len; i++ ) { + map[ name[ i ] ] = jQuery.css( elem, name[ i ], false, styles ); + } + + return map; + } + + return value !== undefined ? + jQuery.style( elem, name, value ) : + jQuery.css( elem, name ); + }, name, value, arguments.length > 1 ); + } +} ); + + +function Tween( elem, options, prop, end, easing ) { + return new Tween.prototype.init( elem, options, prop, end, easing ); +} +jQuery.Tween = Tween; + +Tween.prototype = { + constructor: Tween, + init: function( elem, options, prop, end, easing, unit ) { + this.elem = elem; + this.prop = prop; + this.easing = easing || jQuery.easing._default; + this.options = options; + this.start = this.now = this.cur(); + this.end = end; + this.unit = unit || ( jQuery.cssNumber[ prop ] ? "" : "px" ); + }, + cur: function() { + var hooks = Tween.propHooks[ this.prop ]; + + return hooks && hooks.get ? + hooks.get( this ) : + Tween.propHooks._default.get( this ); + }, + run: function( percent ) { + var eased, + hooks = Tween.propHooks[ this.prop ]; + + if ( this.options.duration ) { + this.pos = eased = jQuery.easing[ this.easing ]( + percent, this.options.duration * percent, 0, 1, this.options.duration + ); + } else { + this.pos = eased = percent; + } + this.now = ( this.end - this.start ) * eased + this.start; + + if ( this.options.step ) { + this.options.step.call( this.elem, this.now, this ); + } + + if ( hooks && hooks.set ) { + hooks.set( this ); + } else { + Tween.propHooks._default.set( this ); + } + return this; + } +}; + +Tween.prototype.init.prototype = Tween.prototype; + +Tween.propHooks = { + _default: { + get: function( tween ) { + var result; + + // Use a property on the element directly when it is not a DOM element, + // or when there is no matching style property that exists. + if ( tween.elem.nodeType !== 1 || + tween.elem[ tween.prop ] != null && tween.elem.style[ tween.prop ] == null ) { + return tween.elem[ tween.prop ]; + } + + // Passing an empty string as a 3rd parameter to .css will automatically + // attempt a parseFloat and fallback to a string if the parse fails. + // Simple values such as "10px" are parsed to Float; + // complex values such as "rotate(1rad)" are returned as-is. + result = jQuery.css( tween.elem, tween.prop, "" ); + + // Empty strings, null, undefined and "auto" are converted to 0. + return !result || result === "auto" ? 0 : result; + }, + set: function( tween ) { + + // Use step hook for back compat. + // Use cssHook if its there. + // Use .style if available and use plain properties where available. + if ( jQuery.fx.step[ tween.prop ] ) { + jQuery.fx.step[ tween.prop ]( tween ); + } else if ( tween.elem.nodeType === 1 && ( + jQuery.cssHooks[ tween.prop ] || + tween.elem.style[ finalPropName( tween.prop ) ] != null ) ) { + jQuery.style( tween.elem, tween.prop, tween.now + tween.unit ); + } else { + tween.elem[ tween.prop ] = tween.now; + } + } + } +}; + +// Support: IE <=9 only +// Panic based approach to setting things on disconnected nodes +Tween.propHooks.scrollTop = Tween.propHooks.scrollLeft = { + set: function( tween ) { + if ( tween.elem.nodeType && tween.elem.parentNode ) { + tween.elem[ tween.prop ] = tween.now; + } + } +}; + +jQuery.easing = { + linear: function( p ) { + return p; + }, + swing: function( p ) { + return 0.5 - Math.cos( p * Math.PI ) / 2; + }, + _default: "swing" +}; + +jQuery.fx = Tween.prototype.init; + +// Back compat <1.8 extension point +jQuery.fx.step = {}; + + + + +var + fxNow, inProgress, + rfxtypes = /^(?:toggle|show|hide)$/, + rrun = /queueHooks$/; + +function schedule() { + if ( inProgress ) { + if ( document.hidden === false && window.requestAnimationFrame ) { + window.requestAnimationFrame( schedule ); + } else { + window.setTimeout( schedule, jQuery.fx.interval ); + } + + jQuery.fx.tick(); + } +} + +// Animations created synchronously will run synchronously +function createFxNow() { + window.setTimeout( function() { + fxNow = undefined; + } ); + return ( fxNow = Date.now() ); +} + +// Generate parameters to create a standard animation +function genFx( type, includeWidth ) { + var which, + i = 0, + attrs = { height: type }; + + // If we include width, step value is 1 to do all cssExpand values, + // otherwise step value is 2 to skip over Left and Right + includeWidth = includeWidth ? 1 : 0; + for ( ; i < 4; i += 2 - includeWidth ) { + which = cssExpand[ i ]; + attrs[ "margin" + which ] = attrs[ "padding" + which ] = type; + } + + if ( includeWidth ) { + attrs.opacity = attrs.width = type; + } + + return attrs; +} + +function createTween( value, prop, animation ) { + var tween, + collection = ( Animation.tweeners[ prop ] || [] ).concat( Animation.tweeners[ "*" ] ), + index = 0, + length = collection.length; + for ( ; index < length; index++ ) { + if ( ( tween = collection[ index ].call( animation, prop, value ) ) ) { + + // We're done with this property + return tween; + } + } +} + +function defaultPrefilter( elem, props, opts ) { + var prop, value, toggle, hooks, oldfire, propTween, restoreDisplay, display, + isBox = "width" in props || "height" in props, + anim = this, + orig = {}, + style = elem.style, + hidden = elem.nodeType && isHiddenWithinTree( elem ), + dataShow = dataPriv.get( elem, "fxshow" ); + + // Queue-skipping animations hijack the fx hooks + if ( !opts.queue ) { + hooks = jQuery._queueHooks( elem, "fx" ); + if ( hooks.unqueued == null ) { + hooks.unqueued = 0; + oldfire = hooks.empty.fire; + hooks.empty.fire = function() { + if ( !hooks.unqueued ) { + oldfire(); + } + }; + } + hooks.unqueued++; + + anim.always( function() { + + // Ensure the complete handler is called before this completes + anim.always( function() { + hooks.unqueued--; + if ( !jQuery.queue( elem, "fx" ).length ) { + hooks.empty.fire(); + } + } ); + } ); + } + + // Detect show/hide animations + for ( prop in props ) { + value = props[ prop ]; + if ( rfxtypes.test( value ) ) { + delete props[ prop ]; + toggle = toggle || value === "toggle"; + if ( value === ( hidden ? "hide" : "show" ) ) { + + // Pretend to be hidden if this is a "show" and + // there is still data from a stopped show/hide + if ( value === "show" && dataShow && dataShow[ prop ] !== undefined ) { + hidden = true; + + // Ignore all other no-op show/hide data + } else { + continue; + } + } + orig[ prop ] = dataShow && dataShow[ prop ] || jQuery.style( elem, prop ); + } + } + + // Bail out if this is a no-op like .hide().hide() + propTween = !jQuery.isEmptyObject( props ); + if ( !propTween && jQuery.isEmptyObject( orig ) ) { + return; + } + + // Restrict "overflow" and "display" styles during box animations + if ( isBox && elem.nodeType === 1 ) { + + // Support: IE <=9 - 11, Edge 12 - 15 + // Record all 3 overflow attributes because IE does not infer the shorthand + // from identically-valued overflowX and overflowY and Edge just mirrors + // the overflowX value there. + opts.overflow = [ style.overflow, style.overflowX, style.overflowY ]; + + // Identify a display type, preferring old show/hide data over the CSS cascade + restoreDisplay = dataShow && dataShow.display; + if ( restoreDisplay == null ) { + restoreDisplay = dataPriv.get( elem, "display" ); + } + display = jQuery.css( elem, "display" ); + if ( display === "none" ) { + if ( restoreDisplay ) { + display = restoreDisplay; + } else { + + // Get nonempty value(s) by temporarily forcing visibility + showHide( [ elem ], true ); + restoreDisplay = elem.style.display || restoreDisplay; + display = jQuery.css( elem, "display" ); + showHide( [ elem ] ); + } + } + + // Animate inline elements as inline-block + if ( display === "inline" || display === "inline-block" && restoreDisplay != null ) { + if ( jQuery.css( elem, "float" ) === "none" ) { + + // Restore the original display value at the end of pure show/hide animations + if ( !propTween ) { + anim.done( function() { + style.display = restoreDisplay; + } ); + if ( restoreDisplay == null ) { + display = style.display; + restoreDisplay = display === "none" ? "" : display; + } + } + style.display = "inline-block"; + } + } + } + + if ( opts.overflow ) { + style.overflow = "hidden"; + anim.always( function() { + style.overflow = opts.overflow[ 0 ]; + style.overflowX = opts.overflow[ 1 ]; + style.overflowY = opts.overflow[ 2 ]; + } ); + } + + // Implement show/hide animations + propTween = false; + for ( prop in orig ) { + + // General show/hide setup for this element animation + if ( !propTween ) { + if ( dataShow ) { + if ( "hidden" in dataShow ) { + hidden = dataShow.hidden; + } + } else { + dataShow = dataPriv.access( elem, "fxshow", { display: restoreDisplay } ); + } + + // Store hidden/visible for toggle so `.stop().toggle()` "reverses" + if ( toggle ) { + dataShow.hidden = !hidden; + } + + // Show elements before animating them + if ( hidden ) { + showHide( [ elem ], true ); + } + + /* eslint-disable no-loop-func */ + + anim.done( function() { + + /* eslint-enable no-loop-func */ + + // The final step of a "hide" animation is actually hiding the element + if ( !hidden ) { + showHide( [ elem ] ); + } + dataPriv.remove( elem, "fxshow" ); + for ( prop in orig ) { + jQuery.style( elem, prop, orig[ prop ] ); + } + } ); + } + + // Per-property setup + propTween = createTween( hidden ? dataShow[ prop ] : 0, prop, anim ); + if ( !( prop in dataShow ) ) { + dataShow[ prop ] = propTween.start; + if ( hidden ) { + propTween.end = propTween.start; + propTween.start = 0; + } + } + } +} + +function propFilter( props, specialEasing ) { + var index, name, easing, value, hooks; + + // camelCase, specialEasing and expand cssHook pass + for ( index in props ) { + name = camelCase( index ); + easing = specialEasing[ name ]; + value = props[ index ]; + if ( Array.isArray( value ) ) { + easing = value[ 1 ]; + value = props[ index ] = value[ 0 ]; + } + + if ( index !== name ) { + props[ name ] = value; + delete props[ index ]; + } + + hooks = jQuery.cssHooks[ name ]; + if ( hooks && "expand" in hooks ) { + value = hooks.expand( value ); + delete props[ name ]; + + // Not quite $.extend, this won't overwrite existing keys. + // Reusing 'index' because we have the correct "name" + for ( index in value ) { + if ( !( index in props ) ) { + props[ index ] = value[ index ]; + specialEasing[ index ] = easing; + } + } + } else { + specialEasing[ name ] = easing; + } + } +} + +function Animation( elem, properties, options ) { + var result, + stopped, + index = 0, + length = Animation.prefilters.length, + deferred = jQuery.Deferred().always( function() { + + // Don't match elem in the :animated selector + delete tick.elem; + } ), + tick = function() { + if ( stopped ) { + return false; + } + var currentTime = fxNow || createFxNow(), + remaining = Math.max( 0, animation.startTime + animation.duration - currentTime ), + + // Support: Android 2.3 only + // Archaic crash bug won't allow us to use `1 - ( 0.5 || 0 )` (#12497) + temp = remaining / animation.duration || 0, + percent = 1 - temp, + index = 0, + length = animation.tweens.length; + + for ( ; index < length; index++ ) { + animation.tweens[ index ].run( percent ); + } + + deferred.notifyWith( elem, [ animation, percent, remaining ] ); + + // If there's more to do, yield + if ( percent < 1 && length ) { + return remaining; + } + + // If this was an empty animation, synthesize a final progress notification + if ( !length ) { + deferred.notifyWith( elem, [ animation, 1, 0 ] ); + } + + // Resolve the animation and report its conclusion + deferred.resolveWith( elem, [ animation ] ); + return false; + }, + animation = deferred.promise( { + elem: elem, + props: jQuery.extend( {}, properties ), + opts: jQuery.extend( true, { + specialEasing: {}, + easing: jQuery.easing._default + }, options ), + originalProperties: properties, + originalOptions: options, + startTime: fxNow || createFxNow(), + duration: options.duration, + tweens: [], + createTween: function( prop, end ) { + var tween = jQuery.Tween( elem, animation.opts, prop, end, + animation.opts.specialEasing[ prop ] || animation.opts.easing ); + animation.tweens.push( tween ); + return tween; + }, + stop: function( gotoEnd ) { + var index = 0, + + // If we are going to the end, we want to run all the tweens + // otherwise we skip this part + length = gotoEnd ? animation.tweens.length : 0; + if ( stopped ) { + return this; + } + stopped = true; + for ( ; index < length; index++ ) { + animation.tweens[ index ].run( 1 ); + } + + // Resolve when we played the last frame; otherwise, reject + if ( gotoEnd ) { + deferred.notifyWith( elem, [ animation, 1, 0 ] ); + deferred.resolveWith( elem, [ animation, gotoEnd ] ); + } else { + deferred.rejectWith( elem, [ animation, gotoEnd ] ); + } + return this; + } + } ), + props = animation.props; + + propFilter( props, animation.opts.specialEasing ); + + for ( ; index < length; index++ ) { + result = Animation.prefilters[ index ].call( animation, elem, props, animation.opts ); + if ( result ) { + if ( isFunction( result.stop ) ) { + jQuery._queueHooks( animation.elem, animation.opts.queue ).stop = + result.stop.bind( result ); + } + return result; + } + } + + jQuery.map( props, createTween, animation ); + + if ( isFunction( animation.opts.start ) ) { + animation.opts.start.call( elem, animation ); + } + + // Attach callbacks from options + animation + .progress( animation.opts.progress ) + .done( animation.opts.done, animation.opts.complete ) + .fail( animation.opts.fail ) + .always( animation.opts.always ); + + jQuery.fx.timer( + jQuery.extend( tick, { + elem: elem, + anim: animation, + queue: animation.opts.queue + } ) + ); + + return animation; +} + +jQuery.Animation = jQuery.extend( Animation, { + + tweeners: { + "*": [ function( prop, value ) { + var tween = this.createTween( prop, value ); + adjustCSS( tween.elem, prop, rcssNum.exec( value ), tween ); + return tween; + } ] + }, + + tweener: function( props, callback ) { + if ( isFunction( props ) ) { + callback = props; + props = [ "*" ]; + } else { + props = props.match( rnothtmlwhite ); + } + + var prop, + index = 0, + length = props.length; + + for ( ; index < length; index++ ) { + prop = props[ index ]; + Animation.tweeners[ prop ] = Animation.tweeners[ prop ] || []; + Animation.tweeners[ prop ].unshift( callback ); + } + }, + + prefilters: [ defaultPrefilter ], + + prefilter: function( callback, prepend ) { + if ( prepend ) { + Animation.prefilters.unshift( callback ); + } else { + Animation.prefilters.push( callback ); + } + } +} ); + +jQuery.speed = function( speed, easing, fn ) { + var opt = speed && typeof speed === "object" ? jQuery.extend( {}, speed ) : { + complete: fn || !fn && easing || + isFunction( speed ) && speed, + duration: speed, + easing: fn && easing || easing && !isFunction( easing ) && easing + }; + + // Go to the end state if fx are off + if ( jQuery.fx.off ) { + opt.duration = 0; + + } else { + if ( typeof opt.duration !== "number" ) { + if ( opt.duration in jQuery.fx.speeds ) { + opt.duration = jQuery.fx.speeds[ opt.duration ]; + + } else { + opt.duration = jQuery.fx.speeds._default; + } + } + } + + // Normalize opt.queue - true/undefined/null -> "fx" + if ( opt.queue == null || opt.queue === true ) { + opt.queue = "fx"; + } + + // Queueing + opt.old = opt.complete; + + opt.complete = function() { + if ( isFunction( opt.old ) ) { + opt.old.call( this ); + } + + if ( opt.queue ) { + jQuery.dequeue( this, opt.queue ); + } + }; + + return opt; +}; + +jQuery.fn.extend( { + fadeTo: function( speed, to, easing, callback ) { + + // Show any hidden elements after setting opacity to 0 + return this.filter( isHiddenWithinTree ).css( "opacity", 0 ).show() + + // Animate to the value specified + .end().animate( { opacity: to }, speed, easing, callback ); + }, + animate: function( prop, speed, easing, callback ) { + var empty = jQuery.isEmptyObject( prop ), + optall = jQuery.speed( speed, easing, callback ), + doAnimation = function() { + + // Operate on a copy of prop so per-property easing won't be lost + var anim = Animation( this, jQuery.extend( {}, prop ), optall ); + + // Empty animations, or finishing resolves immediately + if ( empty || dataPriv.get( this, "finish" ) ) { + anim.stop( true ); + } + }; + doAnimation.finish = doAnimation; + + return empty || optall.queue === false ? + this.each( doAnimation ) : + this.queue( optall.queue, doAnimation ); + }, + stop: function( type, clearQueue, gotoEnd ) { + var stopQueue = function( hooks ) { + var stop = hooks.stop; + delete hooks.stop; + stop( gotoEnd ); + }; + + if ( typeof type !== "string" ) { + gotoEnd = clearQueue; + clearQueue = type; + type = undefined; + } + if ( clearQueue ) { + this.queue( type || "fx", [] ); + } + + return this.each( function() { + var dequeue = true, + index = type != null && type + "queueHooks", + timers = jQuery.timers, + data = dataPriv.get( this ); + + if ( index ) { + if ( data[ index ] && data[ index ].stop ) { + stopQueue( data[ index ] ); + } + } else { + for ( index in data ) { + if ( data[ index ] && data[ index ].stop && rrun.test( index ) ) { + stopQueue( data[ index ] ); + } + } + } + + for ( index = timers.length; index--; ) { + if ( timers[ index ].elem === this && + ( type == null || timers[ index ].queue === type ) ) { + + timers[ index ].anim.stop( gotoEnd ); + dequeue = false; + timers.splice( index, 1 ); + } + } + + // Start the next in the queue if the last step wasn't forced. + // Timers currently will call their complete callbacks, which + // will dequeue but only if they were gotoEnd. + if ( dequeue || !gotoEnd ) { + jQuery.dequeue( this, type ); + } + } ); + }, + finish: function( type ) { + if ( type !== false ) { + type = type || "fx"; + } + return this.each( function() { + var index, + data = dataPriv.get( this ), + queue = data[ type + "queue" ], + hooks = data[ type + "queueHooks" ], + timers = jQuery.timers, + length = queue ? queue.length : 0; + + // Enable finishing flag on private data + data.finish = true; + + // Empty the queue first + jQuery.queue( this, type, [] ); + + if ( hooks && hooks.stop ) { + hooks.stop.call( this, true ); + } + + // Look for any active animations, and finish them + for ( index = timers.length; index--; ) { + if ( timers[ index ].elem === this && timers[ index ].queue === type ) { + timers[ index ].anim.stop( true ); + timers.splice( index, 1 ); + } + } + + // Look for any animations in the old queue and finish them + for ( index = 0; index < length; index++ ) { + if ( queue[ index ] && queue[ index ].finish ) { + queue[ index ].finish.call( this ); + } + } + + // Turn off finishing flag + delete data.finish; + } ); + } +} ); + +jQuery.each( [ "toggle", "show", "hide" ], function( _i, name ) { + var cssFn = jQuery.fn[ name ]; + jQuery.fn[ name ] = function( speed, easing, callback ) { + return speed == null || typeof speed === "boolean" ? + cssFn.apply( this, arguments ) : + this.animate( genFx( name, true ), speed, easing, callback ); + }; +} ); + +// Generate shortcuts for custom animations +jQuery.each( { + slideDown: genFx( "show" ), + slideUp: genFx( "hide" ), + slideToggle: genFx( "toggle" ), + fadeIn: { opacity: "show" }, + fadeOut: { opacity: "hide" }, + fadeToggle: { opacity: "toggle" } +}, function( name, props ) { + jQuery.fn[ name ] = function( speed, easing, callback ) { + return this.animate( props, speed, easing, callback ); + }; +} ); + +jQuery.timers = []; +jQuery.fx.tick = function() { + var timer, + i = 0, + timers = jQuery.timers; + + fxNow = Date.now(); + + for ( ; i < timers.length; i++ ) { + timer = timers[ i ]; + + // Run the timer and safely remove it when done (allowing for external removal) + if ( !timer() && timers[ i ] === timer ) { + timers.splice( i--, 1 ); + } + } + + if ( !timers.length ) { + jQuery.fx.stop(); + } + fxNow = undefined; +}; + +jQuery.fx.timer = function( timer ) { + jQuery.timers.push( timer ); + jQuery.fx.start(); +}; + +jQuery.fx.interval = 13; +jQuery.fx.start = function() { + if ( inProgress ) { + return; + } + + inProgress = true; + schedule(); +}; + +jQuery.fx.stop = function() { + inProgress = null; +}; + +jQuery.fx.speeds = { + slow: 600, + fast: 200, + + // Default speed + _default: 400 +}; + + +// Based off of the plugin by Clint Helfers, with permission. +// https://web.archive.org/web/20100324014747/http://blindsignals.com/index.php/2009/07/jquery-delay/ +jQuery.fn.delay = function( time, type ) { + time = jQuery.fx ? jQuery.fx.speeds[ time ] || time : time; + type = type || "fx"; + + return this.queue( type, function( next, hooks ) { + var timeout = window.setTimeout( next, time ); + hooks.stop = function() { + window.clearTimeout( timeout ); + }; + } ); +}; + + +( function() { + var input = document.createElement( "input" ), + select = document.createElement( "select" ), + opt = select.appendChild( document.createElement( "option" ) ); + + input.type = "checkbox"; + + // Support: Android <=4.3 only + // Default value for a checkbox should be "on" + support.checkOn = input.value !== ""; + + // Support: IE <=11 only + // Must access selectedIndex to make default options select + support.optSelected = opt.selected; + + // Support: IE <=11 only + // An input loses its value after becoming a radio + input = document.createElement( "input" ); + input.value = "t"; + input.type = "radio"; + support.radioValue = input.value === "t"; +} )(); + + +var boolHook, + attrHandle = jQuery.expr.attrHandle; + +jQuery.fn.extend( { + attr: function( name, value ) { + return access( this, jQuery.attr, name, value, arguments.length > 1 ); + }, + + removeAttr: function( name ) { + return this.each( function() { + jQuery.removeAttr( this, name ); + } ); + } +} ); + +jQuery.extend( { + attr: function( elem, name, value ) { + var ret, hooks, + nType = elem.nodeType; + + // Don't get/set attributes on text, comment and attribute nodes + if ( nType === 3 || nType === 8 || nType === 2 ) { + return; + } + + // Fallback to prop when attributes are not supported + if ( typeof elem.getAttribute === "undefined" ) { + return jQuery.prop( elem, name, value ); + } + + // Attribute hooks are determined by the lowercase version + // Grab necessary hook if one is defined + if ( nType !== 1 || !jQuery.isXMLDoc( elem ) ) { + hooks = jQuery.attrHooks[ name.toLowerCase() ] || + ( jQuery.expr.match.bool.test( name ) ? boolHook : undefined ); + } + + if ( value !== undefined ) { + if ( value === null ) { + jQuery.removeAttr( elem, name ); + return; + } + + if ( hooks && "set" in hooks && + ( ret = hooks.set( elem, value, name ) ) !== undefined ) { + return ret; + } + + elem.setAttribute( name, value + "" ); + return value; + } + + if ( hooks && "get" in hooks && ( ret = hooks.get( elem, name ) ) !== null ) { + return ret; + } + + ret = jQuery.find.attr( elem, name ); + + // Non-existent attributes return null, we normalize to undefined + return ret == null ? undefined : ret; + }, + + attrHooks: { + type: { + set: function( elem, value ) { + if ( !support.radioValue && value === "radio" && + nodeName( elem, "input" ) ) { + var val = elem.value; + elem.setAttribute( "type", value ); + if ( val ) { + elem.value = val; + } + return value; + } + } + } + }, + + removeAttr: function( elem, value ) { + var name, + i = 0, + + // Attribute names can contain non-HTML whitespace characters + // https://html.spec.whatwg.org/multipage/syntax.html#attributes-2 + attrNames = value && value.match( rnothtmlwhite ); + + if ( attrNames && elem.nodeType === 1 ) { + while ( ( name = attrNames[ i++ ] ) ) { + elem.removeAttribute( name ); + } + } + } +} ); + +// Hooks for boolean attributes +boolHook = { + set: function( elem, value, name ) { + if ( value === false ) { + + // Remove boolean attributes when set to false + jQuery.removeAttr( elem, name ); + } else { + elem.setAttribute( name, name ); + } + return name; + } +}; + +jQuery.each( jQuery.expr.match.bool.source.match( /\w+/g ), function( _i, name ) { + var getter = attrHandle[ name ] || jQuery.find.attr; + + attrHandle[ name ] = function( elem, name, isXML ) { + var ret, handle, + lowercaseName = name.toLowerCase(); + + if ( !isXML ) { + + // Avoid an infinite loop by temporarily removing this function from the getter + handle = attrHandle[ lowercaseName ]; + attrHandle[ lowercaseName ] = ret; + ret = getter( elem, name, isXML ) != null ? + lowercaseName : + null; + attrHandle[ lowercaseName ] = handle; + } + return ret; + }; +} ); + + + + +var rfocusable = /^(?:input|select|textarea|button)$/i, + rclickable = /^(?:a|area)$/i; + +jQuery.fn.extend( { + prop: function( name, value ) { + return access( this, jQuery.prop, name, value, arguments.length > 1 ); + }, + + removeProp: function( name ) { + return this.each( function() { + delete this[ jQuery.propFix[ name ] || name ]; + } ); + } +} ); + +jQuery.extend( { + prop: function( elem, name, value ) { + var ret, hooks, + nType = elem.nodeType; + + // Don't get/set properties on text, comment and attribute nodes + if ( nType === 3 || nType === 8 || nType === 2 ) { + return; + } + + if ( nType !== 1 || !jQuery.isXMLDoc( elem ) ) { + + // Fix name and attach hooks + name = jQuery.propFix[ name ] || name; + hooks = jQuery.propHooks[ name ]; + } + + if ( value !== undefined ) { + if ( hooks && "set" in hooks && + ( ret = hooks.set( elem, value, name ) ) !== undefined ) { + return ret; + } + + return ( elem[ name ] = value ); + } + + if ( hooks && "get" in hooks && ( ret = hooks.get( elem, name ) ) !== null ) { + return ret; + } + + return elem[ name ]; + }, + + propHooks: { + tabIndex: { + get: function( elem ) { + + // Support: IE <=9 - 11 only + // elem.tabIndex doesn't always return the + // correct value when it hasn't been explicitly set + // https://web.archive.org/web/20141116233347/http://fluidproject.org/blog/2008/01/09/getting-setting-and-removing-tabindex-values-with-javascript/ + // Use proper attribute retrieval(#12072) + var tabindex = jQuery.find.attr( elem, "tabindex" ); + + if ( tabindex ) { + return parseInt( tabindex, 10 ); + } + + if ( + rfocusable.test( elem.nodeName ) || + rclickable.test( elem.nodeName ) && + elem.href + ) { + return 0; + } + + return -1; + } + } + }, + + propFix: { + "for": "htmlFor", + "class": "className" + } +} ); + +// Support: IE <=11 only +// Accessing the selectedIndex property +// forces the browser to respect setting selected +// on the option +// The getter ensures a default option is selected +// when in an optgroup +// eslint rule "no-unused-expressions" is disabled for this code +// since it considers such accessions noop +if ( !support.optSelected ) { + jQuery.propHooks.selected = { + get: function( elem ) { + + /* eslint no-unused-expressions: "off" */ + + var parent = elem.parentNode; + if ( parent && parent.parentNode ) { + parent.parentNode.selectedIndex; + } + return null; + }, + set: function( elem ) { + + /* eslint no-unused-expressions: "off" */ + + var parent = elem.parentNode; + if ( parent ) { + parent.selectedIndex; + + if ( parent.parentNode ) { + parent.parentNode.selectedIndex; + } + } + } + }; +} + +jQuery.each( [ + "tabIndex", + "readOnly", + "maxLength", + "cellSpacing", + "cellPadding", + "rowSpan", + "colSpan", + "useMap", + "frameBorder", + "contentEditable" +], function() { + jQuery.propFix[ this.toLowerCase() ] = this; +} ); + + + + + // Strip and collapse whitespace according to HTML spec + // https://infra.spec.whatwg.org/#strip-and-collapse-ascii-whitespace + function stripAndCollapse( value ) { + var tokens = value.match( rnothtmlwhite ) || []; + return tokens.join( " " ); + } + + +function getClass( elem ) { + return elem.getAttribute && elem.getAttribute( "class" ) || ""; +} + +function classesToArray( value ) { + if ( Array.isArray( value ) ) { + return value; + } + if ( typeof value === "string" ) { + return value.match( rnothtmlwhite ) || []; + } + return []; +} + +jQuery.fn.extend( { + addClass: function( value ) { + var classes, elem, cur, curValue, clazz, j, finalValue, + i = 0; + + if ( isFunction( value ) ) { + return this.each( function( j ) { + jQuery( this ).addClass( value.call( this, j, getClass( this ) ) ); + } ); + } + + classes = classesToArray( value ); + + if ( classes.length ) { + while ( ( elem = this[ i++ ] ) ) { + curValue = getClass( elem ); + cur = elem.nodeType === 1 && ( " " + stripAndCollapse( curValue ) + " " ); + + if ( cur ) { + j = 0; + while ( ( clazz = classes[ j++ ] ) ) { + if ( cur.indexOf( " " + clazz + " " ) < 0 ) { + cur += clazz + " "; + } + } + + // Only assign if different to avoid unneeded rendering. + finalValue = stripAndCollapse( cur ); + if ( curValue !== finalValue ) { + elem.setAttribute( "class", finalValue ); + } + } + } + } + + return this; + }, + + removeClass: function( value ) { + var classes, elem, cur, curValue, clazz, j, finalValue, + i = 0; + + if ( isFunction( value ) ) { + return this.each( function( j ) { + jQuery( this ).removeClass( value.call( this, j, getClass( this ) ) ); + } ); + } + + if ( !arguments.length ) { + return this.attr( "class", "" ); + } + + classes = classesToArray( value ); + + if ( classes.length ) { + while ( ( elem = this[ i++ ] ) ) { + curValue = getClass( elem ); + + // This expression is here for better compressibility (see addClass) + cur = elem.nodeType === 1 && ( " " + stripAndCollapse( curValue ) + " " ); + + if ( cur ) { + j = 0; + while ( ( clazz = classes[ j++ ] ) ) { + + // Remove *all* instances + while ( cur.indexOf( " " + clazz + " " ) > -1 ) { + cur = cur.replace( " " + clazz + " ", " " ); + } + } + + // Only assign if different to avoid unneeded rendering. + finalValue = stripAndCollapse( cur ); + if ( curValue !== finalValue ) { + elem.setAttribute( "class", finalValue ); + } + } + } + } + + return this; + }, + + toggleClass: function( value, stateVal ) { + var type = typeof value, + isValidValue = type === "string" || Array.isArray( value ); + + if ( typeof stateVal === "boolean" && isValidValue ) { + return stateVal ? this.addClass( value ) : this.removeClass( value ); + } + + if ( isFunction( value ) ) { + return this.each( function( i ) { + jQuery( this ).toggleClass( + value.call( this, i, getClass( this ), stateVal ), + stateVal + ); + } ); + } + + return this.each( function() { + var className, i, self, classNames; + + if ( isValidValue ) { + + // Toggle individual class names + i = 0; + self = jQuery( this ); + classNames = classesToArray( value ); + + while ( ( className = classNames[ i++ ] ) ) { + + // Check each className given, space separated list + if ( self.hasClass( className ) ) { + self.removeClass( className ); + } else { + self.addClass( className ); + } + } + + // Toggle whole class name + } else if ( value === undefined || type === "boolean" ) { + className = getClass( this ); + if ( className ) { + + // Store className if set + dataPriv.set( this, "__className__", className ); + } + + // If the element has a class name or if we're passed `false`, + // then remove the whole classname (if there was one, the above saved it). + // Otherwise bring back whatever was previously saved (if anything), + // falling back to the empty string if nothing was stored. + if ( this.setAttribute ) { + this.setAttribute( "class", + className || value === false ? + "" : + dataPriv.get( this, "__className__" ) || "" + ); + } + } + } ); + }, + + hasClass: function( selector ) { + var className, elem, + i = 0; + + className = " " + selector + " "; + while ( ( elem = this[ i++ ] ) ) { + if ( elem.nodeType === 1 && + ( " " + stripAndCollapse( getClass( elem ) ) + " " ).indexOf( className ) > -1 ) { + return true; + } + } + + return false; + } +} ); + + + + +var rreturn = /\r/g; + +jQuery.fn.extend( { + val: function( value ) { + var hooks, ret, valueIsFunction, + elem = this[ 0 ]; + + if ( !arguments.length ) { + if ( elem ) { + hooks = jQuery.valHooks[ elem.type ] || + jQuery.valHooks[ elem.nodeName.toLowerCase() ]; + + if ( hooks && + "get" in hooks && + ( ret = hooks.get( elem, "value" ) ) !== undefined + ) { + return ret; + } + + ret = elem.value; + + // Handle most common string cases + if ( typeof ret === "string" ) { + return ret.replace( rreturn, "" ); + } + + // Handle cases where value is null/undef or number + return ret == null ? "" : ret; + } + + return; + } + + valueIsFunction = isFunction( value ); + + return this.each( function( i ) { + var val; + + if ( this.nodeType !== 1 ) { + return; + } + + if ( valueIsFunction ) { + val = value.call( this, i, jQuery( this ).val() ); + } else { + val = value; + } + + // Treat null/undefined as ""; convert numbers to string + if ( val == null ) { + val = ""; + + } else if ( typeof val === "number" ) { + val += ""; + + } else if ( Array.isArray( val ) ) { + val = jQuery.map( val, function( value ) { + return value == null ? "" : value + ""; + } ); + } + + hooks = jQuery.valHooks[ this.type ] || jQuery.valHooks[ this.nodeName.toLowerCase() ]; + + // If set returns undefined, fall back to normal setting + if ( !hooks || !( "set" in hooks ) || hooks.set( this, val, "value" ) === undefined ) { + this.value = val; + } + } ); + } +} ); + +jQuery.extend( { + valHooks: { + option: { + get: function( elem ) { + + var val = jQuery.find.attr( elem, "value" ); + return val != null ? + val : + + // Support: IE <=10 - 11 only + // option.text throws exceptions (#14686, #14858) + // Strip and collapse whitespace + // https://html.spec.whatwg.org/#strip-and-collapse-whitespace + stripAndCollapse( jQuery.text( elem ) ); + } + }, + select: { + get: function( elem ) { + var value, option, i, + options = elem.options, + index = elem.selectedIndex, + one = elem.type === "select-one", + values = one ? null : [], + max = one ? index + 1 : options.length; + + if ( index < 0 ) { + i = max; + + } else { + i = one ? index : 0; + } + + // Loop through all the selected options + for ( ; i < max; i++ ) { + option = options[ i ]; + + // Support: IE <=9 only + // IE8-9 doesn't update selected after form reset (#2551) + if ( ( option.selected || i === index ) && + + // Don't return options that are disabled or in a disabled optgroup + !option.disabled && + ( !option.parentNode.disabled || + !nodeName( option.parentNode, "optgroup" ) ) ) { + + // Get the specific value for the option + value = jQuery( option ).val(); + + // We don't need an array for one selects + if ( one ) { + return value; + } + + // Multi-Selects return an array + values.push( value ); + } + } + + return values; + }, + + set: function( elem, value ) { + var optionSet, option, + options = elem.options, + values = jQuery.makeArray( value ), + i = options.length; + + while ( i-- ) { + option = options[ i ]; + + /* eslint-disable no-cond-assign */ + + if ( option.selected = + jQuery.inArray( jQuery.valHooks.option.get( option ), values ) > -1 + ) { + optionSet = true; + } + + /* eslint-enable no-cond-assign */ + } + + // Force browsers to behave consistently when non-matching value is set + if ( !optionSet ) { + elem.selectedIndex = -1; + } + return values; + } + } + } +} ); + +// Radios and checkboxes getter/setter +jQuery.each( [ "radio", "checkbox" ], function() { + jQuery.valHooks[ this ] = { + set: function( elem, value ) { + if ( Array.isArray( value ) ) { + return ( elem.checked = jQuery.inArray( jQuery( elem ).val(), value ) > -1 ); + } + } + }; + if ( !support.checkOn ) { + jQuery.valHooks[ this ].get = function( elem ) { + return elem.getAttribute( "value" ) === null ? "on" : elem.value; + }; + } +} ); + + + + +// Return jQuery for attributes-only inclusion + + +support.focusin = "onfocusin" in window; + + +var rfocusMorph = /^(?:focusinfocus|focusoutblur)$/, + stopPropagationCallback = function( e ) { + e.stopPropagation(); + }; + +jQuery.extend( jQuery.event, { + + trigger: function( event, data, elem, onlyHandlers ) { + + var i, cur, tmp, bubbleType, ontype, handle, special, lastElement, + eventPath = [ elem || document ], + type = hasOwn.call( event, "type" ) ? event.type : event, + namespaces = hasOwn.call( event, "namespace" ) ? event.namespace.split( "." ) : []; + + cur = lastElement = tmp = elem = elem || document; + + // Don't do events on text and comment nodes + if ( elem.nodeType === 3 || elem.nodeType === 8 ) { + return; + } + + // focus/blur morphs to focusin/out; ensure we're not firing them right now + if ( rfocusMorph.test( type + jQuery.event.triggered ) ) { + return; + } + + if ( type.indexOf( "." ) > -1 ) { + + // Namespaced trigger; create a regexp to match event type in handle() + namespaces = type.split( "." ); + type = namespaces.shift(); + namespaces.sort(); + } + ontype = type.indexOf( ":" ) < 0 && "on" + type; + + // Caller can pass in a jQuery.Event object, Object, or just an event type string + event = event[ jQuery.expando ] ? + event : + new jQuery.Event( type, typeof event === "object" && event ); + + // Trigger bitmask: & 1 for native handlers; & 2 for jQuery (always true) + event.isTrigger = onlyHandlers ? 2 : 3; + event.namespace = namespaces.join( "." ); + event.rnamespace = event.namespace ? + new RegExp( "(^|\\.)" + namespaces.join( "\\.(?:.*\\.|)" ) + "(\\.|$)" ) : + null; + + // Clean up the event in case it is being reused + event.result = undefined; + if ( !event.target ) { + event.target = elem; + } + + // Clone any incoming data and prepend the event, creating the handler arg list + data = data == null ? + [ event ] : + jQuery.makeArray( data, [ event ] ); + + // Allow special events to draw outside the lines + special = jQuery.event.special[ type ] || {}; + if ( !onlyHandlers && special.trigger && special.trigger.apply( elem, data ) === false ) { + return; + } + + // Determine event propagation path in advance, per W3C events spec (#9951) + // Bubble up to document, then to window; watch for a global ownerDocument var (#9724) + if ( !onlyHandlers && !special.noBubble && !isWindow( elem ) ) { + + bubbleType = special.delegateType || type; + if ( !rfocusMorph.test( bubbleType + type ) ) { + cur = cur.parentNode; + } + for ( ; cur; cur = cur.parentNode ) { + eventPath.push( cur ); + tmp = cur; + } + + // Only add window if we got to document (e.g., not plain obj or detached DOM) + if ( tmp === ( elem.ownerDocument || document ) ) { + eventPath.push( tmp.defaultView || tmp.parentWindow || window ); + } + } + + // Fire handlers on the event path + i = 0; + while ( ( cur = eventPath[ i++ ] ) && !event.isPropagationStopped() ) { + lastElement = cur; + event.type = i > 1 ? + bubbleType : + special.bindType || type; + + // jQuery handler + handle = ( + dataPriv.get( cur, "events" ) || Object.create( null ) + )[ event.type ] && + dataPriv.get( cur, "handle" ); + if ( handle ) { + handle.apply( cur, data ); + } + + // Native handler + handle = ontype && cur[ ontype ]; + if ( handle && handle.apply && acceptData( cur ) ) { + event.result = handle.apply( cur, data ); + if ( event.result === false ) { + event.preventDefault(); + } + } + } + event.type = type; + + // If nobody prevented the default action, do it now + if ( !onlyHandlers && !event.isDefaultPrevented() ) { + + if ( ( !special._default || + special._default.apply( eventPath.pop(), data ) === false ) && + acceptData( elem ) ) { + + // Call a native DOM method on the target with the same name as the event. + // Don't do default actions on window, that's where global variables be (#6170) + if ( ontype && isFunction( elem[ type ] ) && !isWindow( elem ) ) { + + // Don't re-trigger an onFOO event when we call its FOO() method + tmp = elem[ ontype ]; + + if ( tmp ) { + elem[ ontype ] = null; + } + + // Prevent re-triggering of the same event, since we already bubbled it above + jQuery.event.triggered = type; + + if ( event.isPropagationStopped() ) { + lastElement.addEventListener( type, stopPropagationCallback ); + } + + elem[ type ](); + + if ( event.isPropagationStopped() ) { + lastElement.removeEventListener( type, stopPropagationCallback ); + } + + jQuery.event.triggered = undefined; + + if ( tmp ) { + elem[ ontype ] = tmp; + } + } + } + } + + return event.result; + }, + + // Piggyback on a donor event to simulate a different one + // Used only for `focus(in | out)` events + simulate: function( type, elem, event ) { + var e = jQuery.extend( + new jQuery.Event(), + event, + { + type: type, + isSimulated: true + } + ); + + jQuery.event.trigger( e, null, elem ); + } + +} ); + +jQuery.fn.extend( { + + trigger: function( type, data ) { + return this.each( function() { + jQuery.event.trigger( type, data, this ); + } ); + }, + triggerHandler: function( type, data ) { + var elem = this[ 0 ]; + if ( elem ) { + return jQuery.event.trigger( type, data, elem, true ); + } + } +} ); + + +// Support: Firefox <=44 +// Firefox doesn't have focus(in | out) events +// Related ticket - https://bugzilla.mozilla.org/show_bug.cgi?id=687787 +// +// Support: Chrome <=48 - 49, Safari <=9.0 - 9.1 +// focus(in | out) events fire after focus & blur events, +// which is spec violation - http://www.w3.org/TR/DOM-Level-3-Events/#events-focusevent-event-order +// Related ticket - https://bugs.chromium.org/p/chromium/issues/detail?id=449857 +if ( !support.focusin ) { + jQuery.each( { focus: "focusin", blur: "focusout" }, function( orig, fix ) { + + // Attach a single capturing handler on the document while someone wants focusin/focusout + var handler = function( event ) { + jQuery.event.simulate( fix, event.target, jQuery.event.fix( event ) ); + }; + + jQuery.event.special[ fix ] = { + setup: function() { + + // Handle: regular nodes (via `this.ownerDocument`), window + // (via `this.document`) & document (via `this`). + var doc = this.ownerDocument || this.document || this, + attaches = dataPriv.access( doc, fix ); + + if ( !attaches ) { + doc.addEventListener( orig, handler, true ); + } + dataPriv.access( doc, fix, ( attaches || 0 ) + 1 ); + }, + teardown: function() { + var doc = this.ownerDocument || this.document || this, + attaches = dataPriv.access( doc, fix ) - 1; + + if ( !attaches ) { + doc.removeEventListener( orig, handler, true ); + dataPriv.remove( doc, fix ); + + } else { + dataPriv.access( doc, fix, attaches ); + } + } + }; + } ); +} +var location = window.location; + +var nonce = { guid: Date.now() }; + +var rquery = ( /\?/ ); + + + +// Cross-browser xml parsing +jQuery.parseXML = function( data ) { + var xml; + if ( !data || typeof data !== "string" ) { + return null; + } + + // Support: IE 9 - 11 only + // IE throws on parseFromString with invalid input. + try { + xml = ( new window.DOMParser() ).parseFromString( data, "text/xml" ); + } catch ( e ) { + xml = undefined; + } + + if ( !xml || xml.getElementsByTagName( "parsererror" ).length ) { + jQuery.error( "Invalid XML: " + data ); + } + return xml; +}; + + +var + rbracket = /\[\]$/, + rCRLF = /\r?\n/g, + rsubmitterTypes = /^(?:submit|button|image|reset|file)$/i, + rsubmittable = /^(?:input|select|textarea|keygen)/i; + +function buildParams( prefix, obj, traditional, add ) { + var name; + + if ( Array.isArray( obj ) ) { + + // Serialize array item. + jQuery.each( obj, function( i, v ) { + if ( traditional || rbracket.test( prefix ) ) { + + // Treat each array item as a scalar. + add( prefix, v ); + + } else { + + // Item is non-scalar (array or object), encode its numeric index. + buildParams( + prefix + "[" + ( typeof v === "object" && v != null ? i : "" ) + "]", + v, + traditional, + add + ); + } + } ); + + } else if ( !traditional && toType( obj ) === "object" ) { + + // Serialize object item. + for ( name in obj ) { + buildParams( prefix + "[" + name + "]", obj[ name ], traditional, add ); + } + + } else { + + // Serialize scalar item. + add( prefix, obj ); + } +} + +// Serialize an array of form elements or a set of +// key/values into a query string +jQuery.param = function( a, traditional ) { + var prefix, + s = [], + add = function( key, valueOrFunction ) { + + // If value is a function, invoke it and use its return value + var value = isFunction( valueOrFunction ) ? + valueOrFunction() : + valueOrFunction; + + s[ s.length ] = encodeURIComponent( key ) + "=" + + encodeURIComponent( value == null ? "" : value ); + }; + + if ( a == null ) { + return ""; + } + + // If an array was passed in, assume that it is an array of form elements. + if ( Array.isArray( a ) || ( a.jquery && !jQuery.isPlainObject( a ) ) ) { + + // Serialize the form elements + jQuery.each( a, function() { + add( this.name, this.value ); + } ); + + } else { + + // If traditional, encode the "old" way (the way 1.3.2 or older + // did it), otherwise encode params recursively. + for ( prefix in a ) { + buildParams( prefix, a[ prefix ], traditional, add ); + } + } + + // Return the resulting serialization + return s.join( "&" ); +}; + +jQuery.fn.extend( { + serialize: function() { + return jQuery.param( this.serializeArray() ); + }, + serializeArray: function() { + return this.map( function() { + + // Can add propHook for "elements" to filter or add form elements + var elements = jQuery.prop( this, "elements" ); + return elements ? jQuery.makeArray( elements ) : this; + } ) + .filter( function() { + var type = this.type; + + // Use .is( ":disabled" ) so that fieldset[disabled] works + return this.name && !jQuery( this ).is( ":disabled" ) && + rsubmittable.test( this.nodeName ) && !rsubmitterTypes.test( type ) && + ( this.checked || !rcheckableType.test( type ) ); + } ) + .map( function( _i, elem ) { + var val = jQuery( this ).val(); + + if ( val == null ) { + return null; + } + + if ( Array.isArray( val ) ) { + return jQuery.map( val, function( val ) { + return { name: elem.name, value: val.replace( rCRLF, "\r\n" ) }; + } ); + } + + return { name: elem.name, value: val.replace( rCRLF, "\r\n" ) }; + } ).get(); + } +} ); + + +var + r20 = /%20/g, + rhash = /#.*$/, + rantiCache = /([?&])_=[^&]*/, + rheaders = /^(.*?):[ \t]*([^\r\n]*)$/mg, + + // #7653, #8125, #8152: local protocol detection + rlocalProtocol = /^(?:about|app|app-storage|.+-extension|file|res|widget):$/, + rnoContent = /^(?:GET|HEAD)$/, + rprotocol = /^\/\//, + + /* Prefilters + * 1) They are useful to introduce custom dataTypes (see ajax/jsonp.js for an example) + * 2) These are called: + * - BEFORE asking for a transport + * - AFTER param serialization (s.data is a string if s.processData is true) + * 3) key is the dataType + * 4) the catchall symbol "*" can be used + * 5) execution will start with transport dataType and THEN continue down to "*" if needed + */ + prefilters = {}, + + /* Transports bindings + * 1) key is the dataType + * 2) the catchall symbol "*" can be used + * 3) selection will start with transport dataType and THEN go to "*" if needed + */ + transports = {}, + + // Avoid comment-prolog char sequence (#10098); must appease lint and evade compression + allTypes = "*/".concat( "*" ), + + // Anchor tag for parsing the document origin + originAnchor = document.createElement( "a" ); + originAnchor.href = location.href; + +// Base "constructor" for jQuery.ajaxPrefilter and jQuery.ajaxTransport +function addToPrefiltersOrTransports( structure ) { + + // dataTypeExpression is optional and defaults to "*" + return function( dataTypeExpression, func ) { + + if ( typeof dataTypeExpression !== "string" ) { + func = dataTypeExpression; + dataTypeExpression = "*"; + } + + var dataType, + i = 0, + dataTypes = dataTypeExpression.toLowerCase().match( rnothtmlwhite ) || []; + + if ( isFunction( func ) ) { + + // For each dataType in the dataTypeExpression + while ( ( dataType = dataTypes[ i++ ] ) ) { + + // Prepend if requested + if ( dataType[ 0 ] === "+" ) { + dataType = dataType.slice( 1 ) || "*"; + ( structure[ dataType ] = structure[ dataType ] || [] ).unshift( func ); + + // Otherwise append + } else { + ( structure[ dataType ] = structure[ dataType ] || [] ).push( func ); + } + } + } + }; +} + +// Base inspection function for prefilters and transports +function inspectPrefiltersOrTransports( structure, options, originalOptions, jqXHR ) { + + var inspected = {}, + seekingTransport = ( structure === transports ); + + function inspect( dataType ) { + var selected; + inspected[ dataType ] = true; + jQuery.each( structure[ dataType ] || [], function( _, prefilterOrFactory ) { + var dataTypeOrTransport = prefilterOrFactory( options, originalOptions, jqXHR ); + if ( typeof dataTypeOrTransport === "string" && + !seekingTransport && !inspected[ dataTypeOrTransport ] ) { + + options.dataTypes.unshift( dataTypeOrTransport ); + inspect( dataTypeOrTransport ); + return false; + } else if ( seekingTransport ) { + return !( selected = dataTypeOrTransport ); + } + } ); + return selected; + } + + return inspect( options.dataTypes[ 0 ] ) || !inspected[ "*" ] && inspect( "*" ); +} + +// A special extend for ajax options +// that takes "flat" options (not to be deep extended) +// Fixes #9887 +function ajaxExtend( target, src ) { + var key, deep, + flatOptions = jQuery.ajaxSettings.flatOptions || {}; + + for ( key in src ) { + if ( src[ key ] !== undefined ) { + ( flatOptions[ key ] ? target : ( deep || ( deep = {} ) ) )[ key ] = src[ key ]; + } + } + if ( deep ) { + jQuery.extend( true, target, deep ); + } + + return target; +} + +/* Handles responses to an ajax request: + * - finds the right dataType (mediates between content-type and expected dataType) + * - returns the corresponding response + */ +function ajaxHandleResponses( s, jqXHR, responses ) { + + var ct, type, finalDataType, firstDataType, + contents = s.contents, + dataTypes = s.dataTypes; + + // Remove auto dataType and get content-type in the process + while ( dataTypes[ 0 ] === "*" ) { + dataTypes.shift(); + if ( ct === undefined ) { + ct = s.mimeType || jqXHR.getResponseHeader( "Content-Type" ); + } + } + + // Check if we're dealing with a known content-type + if ( ct ) { + for ( type in contents ) { + if ( contents[ type ] && contents[ type ].test( ct ) ) { + dataTypes.unshift( type ); + break; + } + } + } + + // Check to see if we have a response for the expected dataType + if ( dataTypes[ 0 ] in responses ) { + finalDataType = dataTypes[ 0 ]; + } else { + + // Try convertible dataTypes + for ( type in responses ) { + if ( !dataTypes[ 0 ] || s.converters[ type + " " + dataTypes[ 0 ] ] ) { + finalDataType = type; + break; + } + if ( !firstDataType ) { + firstDataType = type; + } + } + + // Or just use first one + finalDataType = finalDataType || firstDataType; + } + + // If we found a dataType + // We add the dataType to the list if needed + // and return the corresponding response + if ( finalDataType ) { + if ( finalDataType !== dataTypes[ 0 ] ) { + dataTypes.unshift( finalDataType ); + } + return responses[ finalDataType ]; + } +} + +/* Chain conversions given the request and the original response + * Also sets the responseXXX fields on the jqXHR instance + */ +function ajaxConvert( s, response, jqXHR, isSuccess ) { + var conv2, current, conv, tmp, prev, + converters = {}, + + // Work with a copy of dataTypes in case we need to modify it for conversion + dataTypes = s.dataTypes.slice(); + + // Create converters map with lowercased keys + if ( dataTypes[ 1 ] ) { + for ( conv in s.converters ) { + converters[ conv.toLowerCase() ] = s.converters[ conv ]; + } + } + + current = dataTypes.shift(); + + // Convert to each sequential dataType + while ( current ) { + + if ( s.responseFields[ current ] ) { + jqXHR[ s.responseFields[ current ] ] = response; + } + + // Apply the dataFilter if provided + if ( !prev && isSuccess && s.dataFilter ) { + response = s.dataFilter( response, s.dataType ); + } + + prev = current; + current = dataTypes.shift(); + + if ( current ) { + + // There's only work to do if current dataType is non-auto + if ( current === "*" ) { + + current = prev; + + // Convert response if prev dataType is non-auto and differs from current + } else if ( prev !== "*" && prev !== current ) { + + // Seek a direct converter + conv = converters[ prev + " " + current ] || converters[ "* " + current ]; + + // If none found, seek a pair + if ( !conv ) { + for ( conv2 in converters ) { + + // If conv2 outputs current + tmp = conv2.split( " " ); + if ( tmp[ 1 ] === current ) { + + // If prev can be converted to accepted input + conv = converters[ prev + " " + tmp[ 0 ] ] || + converters[ "* " + tmp[ 0 ] ]; + if ( conv ) { + + // Condense equivalence converters + if ( conv === true ) { + conv = converters[ conv2 ]; + + // Otherwise, insert the intermediate dataType + } else if ( converters[ conv2 ] !== true ) { + current = tmp[ 0 ]; + dataTypes.unshift( tmp[ 1 ] ); + } + break; + } + } + } + } + + // Apply converter (if not an equivalence) + if ( conv !== true ) { + + // Unless errors are allowed to bubble, catch and return them + if ( conv && s.throws ) { + response = conv( response ); + } else { + try { + response = conv( response ); + } catch ( e ) { + return { + state: "parsererror", + error: conv ? e : "No conversion from " + prev + " to " + current + }; + } + } + } + } + } + } + + return { state: "success", data: response }; +} + +jQuery.extend( { + + // Counter for holding the number of active queries + active: 0, + + // Last-Modified header cache for next request + lastModified: {}, + etag: {}, + + ajaxSettings: { + url: location.href, + type: "GET", + isLocal: rlocalProtocol.test( location.protocol ), + global: true, + processData: true, + async: true, + contentType: "application/x-www-form-urlencoded; charset=UTF-8", + + /* + timeout: 0, + data: null, + dataType: null, + username: null, + password: null, + cache: null, + throws: false, + traditional: false, + headers: {}, + */ + + accepts: { + "*": allTypes, + text: "text/plain", + html: "text/html", + xml: "application/xml, text/xml", + json: "application/json, text/javascript" + }, + + contents: { + xml: /\bxml\b/, + html: /\bhtml/, + json: /\bjson\b/ + }, + + responseFields: { + xml: "responseXML", + text: "responseText", + json: "responseJSON" + }, + + // Data converters + // Keys separate source (or catchall "*") and destination types with a single space + converters: { + + // Convert anything to text + "* text": String, + + // Text to html (true = no transformation) + "text html": true, + + // Evaluate text as a json expression + "text json": JSON.parse, + + // Parse text as xml + "text xml": jQuery.parseXML + }, + + // For options that shouldn't be deep extended: + // you can add your own custom options here if + // and when you create one that shouldn't be + // deep extended (see ajaxExtend) + flatOptions: { + url: true, + context: true + } + }, + + // Creates a full fledged settings object into target + // with both ajaxSettings and settings fields. + // If target is omitted, writes into ajaxSettings. + ajaxSetup: function( target, settings ) { + return settings ? + + // Building a settings object + ajaxExtend( ajaxExtend( target, jQuery.ajaxSettings ), settings ) : + + // Extending ajaxSettings + ajaxExtend( jQuery.ajaxSettings, target ); + }, + + ajaxPrefilter: addToPrefiltersOrTransports( prefilters ), + ajaxTransport: addToPrefiltersOrTransports( transports ), + + // Main method + ajax: function( url, options ) { + + // If url is an object, simulate pre-1.5 signature + if ( typeof url === "object" ) { + options = url; + url = undefined; + } + + // Force options to be an object + options = options || {}; + + var transport, + + // URL without anti-cache param + cacheURL, + + // Response headers + responseHeadersString, + responseHeaders, + + // timeout handle + timeoutTimer, + + // Url cleanup var + urlAnchor, + + // Request state (becomes false upon send and true upon completion) + completed, + + // To know if global events are to be dispatched + fireGlobals, + + // Loop variable + i, + + // uncached part of the url + uncached, + + // Create the final options object + s = jQuery.ajaxSetup( {}, options ), + + // Callbacks context + callbackContext = s.context || s, + + // Context for global events is callbackContext if it is a DOM node or jQuery collection + globalEventContext = s.context && + ( callbackContext.nodeType || callbackContext.jquery ) ? + jQuery( callbackContext ) : + jQuery.event, + + // Deferreds + deferred = jQuery.Deferred(), + completeDeferred = jQuery.Callbacks( "once memory" ), + + // Status-dependent callbacks + statusCode = s.statusCode || {}, + + // Headers (they are sent all at once) + requestHeaders = {}, + requestHeadersNames = {}, + + // Default abort message + strAbort = "canceled", + + // Fake xhr + jqXHR = { + readyState: 0, + + // Builds headers hashtable if needed + getResponseHeader: function( key ) { + var match; + if ( completed ) { + if ( !responseHeaders ) { + responseHeaders = {}; + while ( ( match = rheaders.exec( responseHeadersString ) ) ) { + responseHeaders[ match[ 1 ].toLowerCase() + " " ] = + ( responseHeaders[ match[ 1 ].toLowerCase() + " " ] || [] ) + .concat( match[ 2 ] ); + } + } + match = responseHeaders[ key.toLowerCase() + " " ]; + } + return match == null ? null : match.join( ", " ); + }, + + // Raw string + getAllResponseHeaders: function() { + return completed ? responseHeadersString : null; + }, + + // Caches the header + setRequestHeader: function( name, value ) { + if ( completed == null ) { + name = requestHeadersNames[ name.toLowerCase() ] = + requestHeadersNames[ name.toLowerCase() ] || name; + requestHeaders[ name ] = value; + } + return this; + }, + + // Overrides response content-type header + overrideMimeType: function( type ) { + if ( completed == null ) { + s.mimeType = type; + } + return this; + }, + + // Status-dependent callbacks + statusCode: function( map ) { + var code; + if ( map ) { + if ( completed ) { + + // Execute the appropriate callbacks + jqXHR.always( map[ jqXHR.status ] ); + } else { + + // Lazy-add the new callbacks in a way that preserves old ones + for ( code in map ) { + statusCode[ code ] = [ statusCode[ code ], map[ code ] ]; + } + } + } + return this; + }, + + // Cancel the request + abort: function( statusText ) { + var finalText = statusText || strAbort; + if ( transport ) { + transport.abort( finalText ); + } + done( 0, finalText ); + return this; + } + }; + + // Attach deferreds + deferred.promise( jqXHR ); + + // Add protocol if not provided (prefilters might expect it) + // Handle falsy url in the settings object (#10093: consistency with old signature) + // We also use the url parameter if available + s.url = ( ( url || s.url || location.href ) + "" ) + .replace( rprotocol, location.protocol + "//" ); + + // Alias method option to type as per ticket #12004 + s.type = options.method || options.type || s.method || s.type; + + // Extract dataTypes list + s.dataTypes = ( s.dataType || "*" ).toLowerCase().match( rnothtmlwhite ) || [ "" ]; + + // A cross-domain request is in order when the origin doesn't match the current origin. + if ( s.crossDomain == null ) { + urlAnchor = document.createElement( "a" ); + + // Support: IE <=8 - 11, Edge 12 - 15 + // IE throws exception on accessing the href property if url is malformed, + // e.g. http://example.com:80x/ + try { + urlAnchor.href = s.url; + + // Support: IE <=8 - 11 only + // Anchor's host property isn't correctly set when s.url is relative + urlAnchor.href = urlAnchor.href; + s.crossDomain = originAnchor.protocol + "//" + originAnchor.host !== + urlAnchor.protocol + "//" + urlAnchor.host; + } catch ( e ) { + + // If there is an error parsing the URL, assume it is crossDomain, + // it can be rejected by the transport if it is invalid + s.crossDomain = true; + } + } + + // Convert data if not already a string + if ( s.data && s.processData && typeof s.data !== "string" ) { + s.data = jQuery.param( s.data, s.traditional ); + } + + // Apply prefilters + inspectPrefiltersOrTransports( prefilters, s, options, jqXHR ); + + // If request was aborted inside a prefilter, stop there + if ( completed ) { + return jqXHR; + } + + // We can fire global events as of now if asked to + // Don't fire events if jQuery.event is undefined in an AMD-usage scenario (#15118) + fireGlobals = jQuery.event && s.global; + + // Watch for a new set of requests + if ( fireGlobals && jQuery.active++ === 0 ) { + jQuery.event.trigger( "ajaxStart" ); + } + + // Uppercase the type + s.type = s.type.toUpperCase(); + + // Determine if request has content + s.hasContent = !rnoContent.test( s.type ); + + // Save the URL in case we're toying with the If-Modified-Since + // and/or If-None-Match header later on + // Remove hash to simplify url manipulation + cacheURL = s.url.replace( rhash, "" ); + + // More options handling for requests with no content + if ( !s.hasContent ) { + + // Remember the hash so we can put it back + uncached = s.url.slice( cacheURL.length ); + + // If data is available and should be processed, append data to url + if ( s.data && ( s.processData || typeof s.data === "string" ) ) { + cacheURL += ( rquery.test( cacheURL ) ? "&" : "?" ) + s.data; + + // #9682: remove data so that it's not used in an eventual retry + delete s.data; + } + + // Add or update anti-cache param if needed + if ( s.cache === false ) { + cacheURL = cacheURL.replace( rantiCache, "$1" ); + uncached = ( rquery.test( cacheURL ) ? "&" : "?" ) + "_=" + ( nonce.guid++ ) + + uncached; + } + + // Put hash and anti-cache on the URL that will be requested (gh-1732) + s.url = cacheURL + uncached; + + // Change '%20' to '+' if this is encoded form body content (gh-2658) + } else if ( s.data && s.processData && + ( s.contentType || "" ).indexOf( "application/x-www-form-urlencoded" ) === 0 ) { + s.data = s.data.replace( r20, "+" ); + } + + // Set the If-Modified-Since and/or If-None-Match header, if in ifModified mode. + if ( s.ifModified ) { + if ( jQuery.lastModified[ cacheURL ] ) { + jqXHR.setRequestHeader( "If-Modified-Since", jQuery.lastModified[ cacheURL ] ); + } + if ( jQuery.etag[ cacheURL ] ) { + jqXHR.setRequestHeader( "If-None-Match", jQuery.etag[ cacheURL ] ); + } + } + + // Set the correct header, if data is being sent + if ( s.data && s.hasContent && s.contentType !== false || options.contentType ) { + jqXHR.setRequestHeader( "Content-Type", s.contentType ); + } + + // Set the Accepts header for the server, depending on the dataType + jqXHR.setRequestHeader( + "Accept", + s.dataTypes[ 0 ] && s.accepts[ s.dataTypes[ 0 ] ] ? + s.accepts[ s.dataTypes[ 0 ] ] + + ( s.dataTypes[ 0 ] !== "*" ? ", " + allTypes + "; q=0.01" : "" ) : + s.accepts[ "*" ] + ); + + // Check for headers option + for ( i in s.headers ) { + jqXHR.setRequestHeader( i, s.headers[ i ] ); + } + + // Allow custom headers/mimetypes and early abort + if ( s.beforeSend && + ( s.beforeSend.call( callbackContext, jqXHR, s ) === false || completed ) ) { + + // Abort if not done already and return + return jqXHR.abort(); + } + + // Aborting is no longer a cancellation + strAbort = "abort"; + + // Install callbacks on deferreds + completeDeferred.add( s.complete ); + jqXHR.done( s.success ); + jqXHR.fail( s.error ); + + // Get transport + transport = inspectPrefiltersOrTransports( transports, s, options, jqXHR ); + + // If no transport, we auto-abort + if ( !transport ) { + done( -1, "No Transport" ); + } else { + jqXHR.readyState = 1; + + // Send global event + if ( fireGlobals ) { + globalEventContext.trigger( "ajaxSend", [ jqXHR, s ] ); + } + + // If request was aborted inside ajaxSend, stop there + if ( completed ) { + return jqXHR; + } + + // Timeout + if ( s.async && s.timeout > 0 ) { + timeoutTimer = window.setTimeout( function() { + jqXHR.abort( "timeout" ); + }, s.timeout ); + } + + try { + completed = false; + transport.send( requestHeaders, done ); + } catch ( e ) { + + // Rethrow post-completion exceptions + if ( completed ) { + throw e; + } + + // Propagate others as results + done( -1, e ); + } + } + + // Callback for when everything is done + function done( status, nativeStatusText, responses, headers ) { + var isSuccess, success, error, response, modified, + statusText = nativeStatusText; + + // Ignore repeat invocations + if ( completed ) { + return; + } + + completed = true; + + // Clear timeout if it exists + if ( timeoutTimer ) { + window.clearTimeout( timeoutTimer ); + } + + // Dereference transport for early garbage collection + // (no matter how long the jqXHR object will be used) + transport = undefined; + + // Cache response headers + responseHeadersString = headers || ""; + + // Set readyState + jqXHR.readyState = status > 0 ? 4 : 0; + + // Determine if successful + isSuccess = status >= 200 && status < 300 || status === 304; + + // Get response data + if ( responses ) { + response = ajaxHandleResponses( s, jqXHR, responses ); + } + + // Use a noop converter for missing script + if ( !isSuccess && jQuery.inArray( "script", s.dataTypes ) > -1 ) { + s.converters[ "text script" ] = function() {}; + } + + // Convert no matter what (that way responseXXX fields are always set) + response = ajaxConvert( s, response, jqXHR, isSuccess ); + + // If successful, handle type chaining + if ( isSuccess ) { + + // Set the If-Modified-Since and/or If-None-Match header, if in ifModified mode. + if ( s.ifModified ) { + modified = jqXHR.getResponseHeader( "Last-Modified" ); + if ( modified ) { + jQuery.lastModified[ cacheURL ] = modified; + } + modified = jqXHR.getResponseHeader( "etag" ); + if ( modified ) { + jQuery.etag[ cacheURL ] = modified; + } + } + + // if no content + if ( status === 204 || s.type === "HEAD" ) { + statusText = "nocontent"; + + // if not modified + } else if ( status === 304 ) { + statusText = "notmodified"; + + // If we have data, let's convert it + } else { + statusText = response.state; + success = response.data; + error = response.error; + isSuccess = !error; + } + } else { + + // Extract error from statusText and normalize for non-aborts + error = statusText; + if ( status || !statusText ) { + statusText = "error"; + if ( status < 0 ) { + status = 0; + } + } + } + + // Set data for the fake xhr object + jqXHR.status = status; + jqXHR.statusText = ( nativeStatusText || statusText ) + ""; + + // Success/Error + if ( isSuccess ) { + deferred.resolveWith( callbackContext, [ success, statusText, jqXHR ] ); + } else { + deferred.rejectWith( callbackContext, [ jqXHR, statusText, error ] ); + } + + // Status-dependent callbacks + jqXHR.statusCode( statusCode ); + statusCode = undefined; + + if ( fireGlobals ) { + globalEventContext.trigger( isSuccess ? "ajaxSuccess" : "ajaxError", + [ jqXHR, s, isSuccess ? success : error ] ); + } + + // Complete + completeDeferred.fireWith( callbackContext, [ jqXHR, statusText ] ); + + if ( fireGlobals ) { + globalEventContext.trigger( "ajaxComplete", [ jqXHR, s ] ); + + // Handle the global AJAX counter + if ( !( --jQuery.active ) ) { + jQuery.event.trigger( "ajaxStop" ); + } + } + } + + return jqXHR; + }, + + getJSON: function( url, data, callback ) { + return jQuery.get( url, data, callback, "json" ); + }, + + getScript: function( url, callback ) { + return jQuery.get( url, undefined, callback, "script" ); + } +} ); + +jQuery.each( [ "get", "post" ], function( _i, method ) { + jQuery[ method ] = function( url, data, callback, type ) { + + // Shift arguments if data argument was omitted + if ( isFunction( data ) ) { + type = type || callback; + callback = data; + data = undefined; + } + + // The url can be an options object (which then must have .url) + return jQuery.ajax( jQuery.extend( { + url: url, + type: method, + dataType: type, + data: data, + success: callback + }, jQuery.isPlainObject( url ) && url ) ); + }; +} ); + +jQuery.ajaxPrefilter( function( s ) { + var i; + for ( i in s.headers ) { + if ( i.toLowerCase() === "content-type" ) { + s.contentType = s.headers[ i ] || ""; + } + } +} ); + + +jQuery._evalUrl = function( url, options, doc ) { + return jQuery.ajax( { + url: url, + + // Make this explicit, since user can override this through ajaxSetup (#11264) + type: "GET", + dataType: "script", + cache: true, + async: false, + global: false, + + // Only evaluate the response if it is successful (gh-4126) + // dataFilter is not invoked for failure responses, so using it instead + // of the default converter is kludgy but it works. + converters: { + "text script": function() {} + }, + dataFilter: function( response ) { + jQuery.globalEval( response, options, doc ); + } + } ); +}; + + +jQuery.fn.extend( { + wrapAll: function( html ) { + var wrap; + + if ( this[ 0 ] ) { + if ( isFunction( html ) ) { + html = html.call( this[ 0 ] ); + } + + // The elements to wrap the target around + wrap = jQuery( html, this[ 0 ].ownerDocument ).eq( 0 ).clone( true ); + + if ( this[ 0 ].parentNode ) { + wrap.insertBefore( this[ 0 ] ); + } + + wrap.map( function() { + var elem = this; + + while ( elem.firstElementChild ) { + elem = elem.firstElementChild; + } + + return elem; + } ).append( this ); + } + + return this; + }, + + wrapInner: function( html ) { + if ( isFunction( html ) ) { + return this.each( function( i ) { + jQuery( this ).wrapInner( html.call( this, i ) ); + } ); + } + + return this.each( function() { + var self = jQuery( this ), + contents = self.contents(); + + if ( contents.length ) { + contents.wrapAll( html ); + + } else { + self.append( html ); + } + } ); + }, + + wrap: function( html ) { + var htmlIsFunction = isFunction( html ); + + return this.each( function( i ) { + jQuery( this ).wrapAll( htmlIsFunction ? html.call( this, i ) : html ); + } ); + }, + + unwrap: function( selector ) { + this.parent( selector ).not( "body" ).each( function() { + jQuery( this ).replaceWith( this.childNodes ); + } ); + return this; + } +} ); + + +jQuery.expr.pseudos.hidden = function( elem ) { + return !jQuery.expr.pseudos.visible( elem ); +}; +jQuery.expr.pseudos.visible = function( elem ) { + return !!( elem.offsetWidth || elem.offsetHeight || elem.getClientRects().length ); +}; + + + + +jQuery.ajaxSettings.xhr = function() { + try { + return new window.XMLHttpRequest(); + } catch ( e ) {} +}; + +var xhrSuccessStatus = { + + // File protocol always yields status code 0, assume 200 + 0: 200, + + // Support: IE <=9 only + // #1450: sometimes IE returns 1223 when it should be 204 + 1223: 204 + }, + xhrSupported = jQuery.ajaxSettings.xhr(); + +support.cors = !!xhrSupported && ( "withCredentials" in xhrSupported ); +support.ajax = xhrSupported = !!xhrSupported; + +jQuery.ajaxTransport( function( options ) { + var callback, errorCallback; + + // Cross domain only allowed if supported through XMLHttpRequest + if ( support.cors || xhrSupported && !options.crossDomain ) { + return { + send: function( headers, complete ) { + var i, + xhr = options.xhr(); + + xhr.open( + options.type, + options.url, + options.async, + options.username, + options.password + ); + + // Apply custom fields if provided + if ( options.xhrFields ) { + for ( i in options.xhrFields ) { + xhr[ i ] = options.xhrFields[ i ]; + } + } + + // Override mime type if needed + if ( options.mimeType && xhr.overrideMimeType ) { + xhr.overrideMimeType( options.mimeType ); + } + + // X-Requested-With header + // For cross-domain requests, seeing as conditions for a preflight are + // akin to a jigsaw puzzle, we simply never set it to be sure. + // (it can always be set on a per-request basis or even using ajaxSetup) + // For same-domain requests, won't change header if already provided. + if ( !options.crossDomain && !headers[ "X-Requested-With" ] ) { + headers[ "X-Requested-With" ] = "XMLHttpRequest"; + } + + // Set headers + for ( i in headers ) { + xhr.setRequestHeader( i, headers[ i ] ); + } + + // Callback + callback = function( type ) { + return function() { + if ( callback ) { + callback = errorCallback = xhr.onload = + xhr.onerror = xhr.onabort = xhr.ontimeout = + xhr.onreadystatechange = null; + + if ( type === "abort" ) { + xhr.abort(); + } else if ( type === "error" ) { + + // Support: IE <=9 only + // On a manual native abort, IE9 throws + // errors on any property access that is not readyState + if ( typeof xhr.status !== "number" ) { + complete( 0, "error" ); + } else { + complete( + + // File: protocol always yields status 0; see #8605, #14207 + xhr.status, + xhr.statusText + ); + } + } else { + complete( + xhrSuccessStatus[ xhr.status ] || xhr.status, + xhr.statusText, + + // Support: IE <=9 only + // IE9 has no XHR2 but throws on binary (trac-11426) + // For XHR2 non-text, let the caller handle it (gh-2498) + ( xhr.responseType || "text" ) !== "text" || + typeof xhr.responseText !== "string" ? + { binary: xhr.response } : + { text: xhr.responseText }, + xhr.getAllResponseHeaders() + ); + } + } + }; + }; + + // Listen to events + xhr.onload = callback(); + errorCallback = xhr.onerror = xhr.ontimeout = callback( "error" ); + + // Support: IE 9 only + // Use onreadystatechange to replace onabort + // to handle uncaught aborts + if ( xhr.onabort !== undefined ) { + xhr.onabort = errorCallback; + } else { + xhr.onreadystatechange = function() { + + // Check readyState before timeout as it changes + if ( xhr.readyState === 4 ) { + + // Allow onerror to be called first, + // but that will not handle a native abort + // Also, save errorCallback to a variable + // as xhr.onerror cannot be accessed + window.setTimeout( function() { + if ( callback ) { + errorCallback(); + } + } ); + } + }; + } + + // Create the abort callback + callback = callback( "abort" ); + + try { + + // Do send the request (this may raise an exception) + xhr.send( options.hasContent && options.data || null ); + } catch ( e ) { + + // #14683: Only rethrow if this hasn't been notified as an error yet + if ( callback ) { + throw e; + } + } + }, + + abort: function() { + if ( callback ) { + callback(); + } + } + }; + } +} ); + + + + +// Prevent auto-execution of scripts when no explicit dataType was provided (See gh-2432) +jQuery.ajaxPrefilter( function( s ) { + if ( s.crossDomain ) { + s.contents.script = false; + } +} ); + +// Install script dataType +jQuery.ajaxSetup( { + accepts: { + script: "text/javascript, application/javascript, " + + "application/ecmascript, application/x-ecmascript" + }, + contents: { + script: /\b(?:java|ecma)script\b/ + }, + converters: { + "text script": function( text ) { + jQuery.globalEval( text ); + return text; + } + } +} ); + +// Handle cache's special case and crossDomain +jQuery.ajaxPrefilter( "script", function( s ) { + if ( s.cache === undefined ) { + s.cache = false; + } + if ( s.crossDomain ) { + s.type = "GET"; + } +} ); + +// Bind script tag hack transport +jQuery.ajaxTransport( "script", function( s ) { + + // This transport only deals with cross domain or forced-by-attrs requests + if ( s.crossDomain || s.scriptAttrs ) { + var script, callback; + return { + send: function( _, complete ) { + script = jQuery( " +{% endmacro %} \ No newline at end of file diff --git a/0.3/api/collectors/index.html b/0.3/api/collectors/index.html new file mode 100644 index 0000000..bf0ce05 --- /dev/null +++ b/0.3/api/collectors/index.html @@ -0,0 +1,337 @@ + + + + + + + + 7. Collectors & Extractors — MIPLearn 0.3 + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
+
+ + + + + + + + +
+ +
+
+
+
+ + + + +
+ + +
+ + + + + + +
+
+ + + + + + + + + +
+ + +
+ +
+ Contents +
+ +
+
+
+
+
+ +
+ +
+

7. Collectors & Extractors

+
+

7.1. miplearn.classifiers.minprob

+
+
+class miplearn.classifiers.minprob.MinProbabilityClassifier(base_clf: Any, thresholds: List[float], clone_fn: Callable[[Any], Any] = <function clone>)
+

Bases: sklearn.base.BaseEstimator

+

Meta-classifier that returns NaN for predictions made by a base classifier that +have probability below a given threshold. More specifically, this meta-classifier +calls base_clf.predict_proba and compares the result against the provided +thresholds. If the probability for one of the classes is above its threshold, +the meta-classifier returns that prediction. Otherwise, it returns NaN.

+
+
+fit(x: numpy.ndarray, y: numpy.ndarray) → None
+
+ +
+
+predict(x: numpy.ndarray) → numpy.ndarray
+
+ +
+ +
+
+

7.2. miplearn.classifiers.singleclass

+
+
+class miplearn.classifiers.singleclass.SingleClassFix(base_clf: sklearn.base.BaseEstimator, clone_fn: Callable = <function clone>)
+

Bases: sklearn.base.BaseEstimator

+

Some sklearn classifiers, such as logistic regression, have issues with datasets +that contain a single class. This meta-classifier fixes the issue. If the +training data contains a single class, this meta-classifier always returns that +class as a prediction. Otherwise, it fits the provided base classifier, +and returns its predictions instead.

+
+
+fit(x: numpy.ndarray, y: numpy.ndarray) → None
+
+ +
+
+predict(x: numpy.ndarray) → numpy.ndarray
+
+ +
+ +
+
+

7.3. miplearn.collectors.basic

+
+
+class miplearn.collectors.basic.BasicCollector(*, time_limit_sec: float = inf)
+

Bases: object

+
+
+collect(filenames: List[str], build_model: Callable, n_jobs: int = 1, progress: bool = False) → None
+
+ +
+ +
+
+

7.4. miplearn.features.fields

+
+
+

7.5. miplearn.features.AlvLouWeh2017

+
+
+ + +
+ + +
+ + 6. Benchmark Problems + 8. Components + +
+ +
+
+
+
+

+ + © Copyright 2020-2022, UChicago Argonne, LLC.
+

+
+
+
+ + +
+
+ + + + + + \ No newline at end of file diff --git a/0.3/api/components/index.html b/0.3/api/components/index.html new file mode 100644 index 0000000..4408501 --- /dev/null +++ b/0.3/api/components/index.html @@ -0,0 +1,436 @@ + + + + + + + + 8. Components — MIPLearn 0.3 + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
+
+ + + + + + + + +
+ +
+
+
+
+ + + + +
+ + +
+ + + + + + +
+
+ + + + + + + + + +
+ + +
+ +
+ Contents +
+ +
+
+
+
+
+ +
+ +
+

8. Components

+
+

8.1. miplearn.components.primal.actions

+
+
+class miplearn.components.primal.actions.EnforceProximity(tol: float)
+

Bases: miplearn.components.primal.actions.PrimalComponentAction

+
+
+perform(model: miplearn.solvers.abstract.AbstractModel, var_names: numpy.ndarray, var_values: numpy.ndarray, stats: Optional[Dict]) → None
+
+ +
+ +
+
+class miplearn.components.primal.actions.FixVariables
+

Bases: miplearn.components.primal.actions.PrimalComponentAction

+
+
+perform(model: miplearn.solvers.abstract.AbstractModel, var_names: numpy.ndarray, var_values: numpy.ndarray, stats: Optional[Dict]) → None
+
+ +
+ +
+
+class miplearn.components.primal.actions.PrimalComponentAction
+

Bases: abc.ABC

+
+
+abstract perform(model: miplearn.solvers.abstract.AbstractModel, var_names: numpy.ndarray, var_values: numpy.ndarray, stats: Optional[Dict]) → None
+
+ +
+ +
+
+class miplearn.components.primal.actions.SetWarmStart
+

Bases: miplearn.components.primal.actions.PrimalComponentAction

+
+
+perform(model: miplearn.solvers.abstract.AbstractModel, var_names: numpy.ndarray, var_values: numpy.ndarray, stats: Optional[Dict]) → None
+
+ +
+ +
+
+

8.2. miplearn.components.primal.expert

+
+
+class miplearn.components.primal.expert.ExpertPrimalComponent(action: miplearn.components.primal.actions.PrimalComponentAction)
+

Bases: object

+
+
+before_mip(test_h5: str, model: miplearn.solvers.abstract.AbstractModel, stats: Dict[str, Any]) → None
+
+ +
+
+fit(train_h5: List[str]) → None
+
+ +
+ +
+
+

8.3. miplearn.components.primal.indep

+
+
+class miplearn.components.primal.indep.IndependentVarsPrimalComponent(base_clf: Any, extractor: miplearn.extractors.abstract.FeaturesExtractor, action: miplearn.components.primal.actions.PrimalComponentAction, clone_fn: Callable[[Any], Any] = <function clone>)
+

Bases: object

+
+
+before_mip(test_h5: str, model: miplearn.solvers.abstract.AbstractModel, stats: Dict[str, Any]) → None
+
+ +
+
+fit(train_h5: List[str]) → None
+
+ +
+ +
+
+

8.4. miplearn.components.primal.joint

+
+
+class miplearn.components.primal.joint.JointVarsPrimalComponent(clf: Any, extractor: miplearn.extractors.abstract.FeaturesExtractor, action: miplearn.components.primal.actions.PrimalComponentAction)
+

Bases: object

+
+
+before_mip(test_h5: str, model: miplearn.solvers.abstract.AbstractModel, stats: Dict[str, Any]) → None
+
+ +
+
+fit(train_h5: List[str]) → None
+
+ +
+ +
+
+

8.5. miplearn.components.primal.mem

+
+
+class miplearn.components.primal.mem.MemorizingPrimalComponent(clf: Any, extractor: miplearn.extractors.abstract.FeaturesExtractor, constructor: miplearn.components.primal.mem.SolutionConstructor, action: miplearn.components.primal.actions.PrimalComponentAction)
+

Bases: object

+

Component that memorizes all solutions seen during training, then fits a +single classifier to predict which of the memorized solutions should be +provided to the solver. Optionally combines multiple memorized solutions +into a single, partial one.

+
+
+before_mip(test_h5: str, model: miplearn.solvers.abstract.AbstractModel, stats: Dict[str, Any]) → None
+
+ +
+
+fit(train_h5: List[str]) → None
+
+ +
+ +
+
+class miplearn.components.primal.mem.MergeTopSolutions(k: int, thresholds: List[float])
+

Bases: miplearn.components.primal.mem.SolutionConstructor

+

Warm start construction strategy that first selects the top k solutions, +then merges them into a single solution.

+

To merge the solutions, the strategy first computes the mean optimal value of each +decision variable, then: (i) sets the variable to zero if the mean is below +thresholds[0]; (ii) sets the variable to one if the mean is above thresholds[1]; +(iii) leaves the variable free otherwise.

+
+
+construct(y_proba: numpy.ndarray, solutions: numpy.ndarray) → numpy.ndarray
+
+ +
+ +
+
+class miplearn.components.primal.mem.SelectTopSolutions(k: int)
+

Bases: miplearn.components.primal.mem.SolutionConstructor

+

Warm start construction strategy that selects and returns the top k solutions.

+
+
+construct(y_proba: numpy.ndarray, solutions: numpy.ndarray) → numpy.ndarray
+
+ +
+ +
+
+class miplearn.components.primal.mem.SolutionConstructor
+

Bases: abc.ABC

+
+
+abstract construct(y_proba: numpy.ndarray, solutions: numpy.ndarray) → numpy.ndarray
+
+ +
+ +
+
+ + +
+ + +
+ + 7. Collectors & Extractors + 9. Solvers + +
+ +
+
+
+
+

+ + © Copyright 2020-2022, UChicago Argonne, LLC.
+

+
+
+
+ + +
+
+ + + + + + \ No newline at end of file diff --git a/0.3/api/helpers/index.html b/0.3/api/helpers/index.html new file mode 100644 index 0000000..c044039 --- /dev/null +++ b/0.3/api/helpers/index.html @@ -0,0 +1,314 @@ + + + + + + + + 10. Helpers — MIPLearn 0.3 + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
+
+ + + + + + + + +
+ +
+
+
+
+ + + + +
+ + +
+ + + + + + +
+
+ + + + + + + + + +
+ + +
+ +
+ Contents +
+ +
+
+
+
+
+ +
+ +
+

10. Helpers

+
+

10.1. miplearn.io

+
+
+miplearn.io.load(filename: str, build_model: Callable) → Any
+
+ +
+
+miplearn.io.save(objs: List[Any], dirname: str, prefix: str = '', n_jobs: int = 1, progress: bool = False) → List[str]
+
+ +
+
+

10.2. miplearn.h5

+
+
+class miplearn.h5.H5File(filename: str, mode: str = 'r+')
+

Bases: object

+
+
+get_array(key: str) → Optional[numpy.ndarray]
+
+ +
+
+get_bytes(key: str) → Optional[Union[bytes, bytearray]]
+
+ +
+
+get_scalar(key: str) → Optional[Any]
+
+ +
+
+get_sparse(key: str) → Optional[scipy.sparse._coo.coo_matrix]
+
+ +
+
+put_array(key: str, value: Optional[numpy.ndarray]) → None
+
+ +
+
+put_bytes(key: str, value: Union[bytes, bytearray]) → None
+
+ +
+
+put_scalar(key: str, value: Any) → None
+
+ +
+
+put_sparse(key: str, value: scipy.sparse._coo.coo_matrix) → None
+
+ +
+ +
+
+ + +
+ + +
+ + 9. Solvers + +
+ +
+
+
+
+

+ + © Copyright 2020-2022, UChicago Argonne, LLC.
+

+
+
+
+ + +
+
+ + + + + + \ No newline at end of file diff --git a/0.3/api/problems/index.html b/0.3/api/problems/index.html new file mode 100644 index 0000000..2af66c0 --- /dev/null +++ b/0.3/api/problems/index.html @@ -0,0 +1,566 @@ + + + + + + + + 6. Benchmark Problems — MIPLearn 0.3 + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
+
+ + + + + + + + +
+ +
+
+
+
+ + + + +
+ + +
+ + + + + + +
+
+ + + + + + + + + +
+ + +
+ +
+ Contents +
+ +
+
+
+
+
+ +
+ +
+

6. Benchmark Problems

+
+

6.1. miplearn.problems.binpack

+
+
+class miplearn.problems.binpack.BinPackData(sizes: numpy.ndarray, capacity: int)
+

Data for the bin packing problem.

+
+
Parameters
+
    +

  • sizes (numpy.ndarray) – Sizes of the items

    • +

  • capacity (int) – Capacity of the bin

    • +
+
+
+
+ +
+
+class miplearn.problems.binpack.BinPackGenerator(n: scipy.stats._distn_infrastructure.rv_frozen, sizes: scipy.stats._distn_infrastructure.rv_frozen, capacity: scipy.stats._distn_infrastructure.rv_frozen, sizes_jitter: scipy.stats._distn_infrastructure.rv_frozen, capacity_jitter: scipy.stats._distn_infrastructure.rv_frozen, fix_items: bool)
+

Random instance generator for the bin packing problem.

+

If fix_items=False, the class samples the user-provided probability distributions +n, sizes and capacity to decide, respectively, the number of items, the sizes of +the items and capacity of the bin. All values are sampled independently.

+

If fix_items=True, the class creates a reference instance, using the method +previously described, then generates additional instances by perturbing its item +sizes and bin capacity. More specifically, the sizes of the items are set to s_i +* gamma_i where s_i is the size of the i-th item in the reference instance and +gamma_i is sampled from sizes_jitter. Similarly, the bin capacity is set to B * +beta, where B is the reference bin capacity and beta is sampled from +capacity_jitter. The number of items remains the same across all generated +instances.

+
+
Parameters
+
    +

  • n – Probability distribution for the number of items.

    • +

  • sizes – Probability distribution for the item sizes.

    • +

  • capacity – Probability distribution for the bin capacity.

    • +

  • sizes_jitter – Probability distribution for the item size randomization.

    • +

  • capacity_jitter – Probability distribution for the bin capacity.

    • +

  • fix_items – If True, generates a reference instance, then applies some perturbation to it. +If False, generates completely different instances.

    • +
+
+
+
+
+generate(n_samples: int) → List[miplearn.problems.binpack.BinPackData]
+

Generates random instances.

+
+
Parameters
+

n_samples – Number of samples to generate.

+
+
+
+ +
+ +
+
+miplearn.problems.binpack.build_binpack_model(data: miplearn.problems.binpack.BinPackData) → miplearn.solvers.gurobi.GurobiModel
+

Converts bin packing problem data into a concrete Gurobipy model.

+
+ +
+
+

6.2. miplearn.problems.multiknapsack

+
+
+class miplearn.problems.multiknapsack.MultiKnapsackData(prices: numpy.ndarray, capacities: numpy.ndarray, weights: numpy.ndarray)
+

Data for the multi-dimensional knapsack problem

+
+
Parameters
+
    +

  • prices (numpy.ndarray) – Item prices.

    • +

  • capacities (numpy.ndarray) – Knapsack capacities.

    • +

  • weights (numpy.ndarray) – Matrix of item weights.

    • +
+
+
+
+ +
+
+class miplearn.problems.multiknapsack.MultiKnapsackGenerator(n: scipy.stats._distn_infrastructure.rv_frozen = <scipy.stats._distn_infrastructure.rv_frozen object>, m: scipy.stats._distn_infrastructure.rv_frozen = <scipy.stats._distn_infrastructure.rv_frozen object>, w: scipy.stats._distn_infrastructure.rv_frozen = <scipy.stats._distn_infrastructure.rv_frozen object>, K: scipy.stats._distn_infrastructure.rv_frozen = <scipy.stats._distn_infrastructure.rv_frozen object>, u: scipy.stats._distn_infrastructure.rv_frozen = <scipy.stats._distn_infrastructure.rv_frozen object>, alpha: scipy.stats._distn_infrastructure.rv_frozen = <scipy.stats._distn_infrastructure.rv_frozen object>, fix_w: bool = False, w_jitter: scipy.stats._distn_infrastructure.rv_frozen = <scipy.stats._distn_infrastructure.rv_frozen object>, p_jitter: scipy.stats._distn_infrastructure.rv_frozen = <scipy.stats._distn_infrastructure.rv_frozen object>, round: bool = True)
+

Random instance generator for the multi-dimensional knapsack problem.

+

Instances have a random number of items (or variables) and a random number of +knapsacks (or constraints), as specified by the provided probability +distributions n and m, respectively. The weight of each item i on knapsack +j is sampled independently from the provided distribution w. The capacity of +knapsack j is set to alpha_j * sum(w[i,j] for i in range(n)), +where alpha_j, the tightness ratio, is sampled from the provided probability +distribution alpha.

+

To make the instances more challenging, the costs of the items are linearly +correlated to their average weights. More specifically, the weight of each item +i is set to sum(w[i,j]/m for j in range(m)) + K * u_i, where K, +the correlation coefficient, and u_i, the correlation multiplier, are sampled +from the provided probability distributions. Note that K is only sample once +for the entire instance.

+

If fix_w=True, then weights[i,j] are kept the same in all generated +instances. This also implies that n and m are kept fixed. Although the prices and +capacities are derived from weights[i,j], as long as u and K are not +constants, the generated instances will still not be completely identical.

+

If a probability distribution w_jitter is provided, then item weights will be +set to w[i,j] * gamma[i,j] where gamma[i,j] is sampled from w_jitter. +When combined with fix_w=True, this argument may be used to generate instances +where the weight of each item is roughly the same, but not exactly identical, +across all instances. The prices of the items and the capacities of the knapsacks +will be calculated as above, but using these perturbed weights instead.

+

By default, all generated prices, weights and capacities are rounded to the +nearest integer number. If round=False is provided, this rounding will be +disabled.

+
+
Parameters
+
    +

  • n (rv_discrete) – Probability distribution for the number of items (or variables).

    • +

  • m (rv_discrete) – Probability distribution for the number of knapsacks (or constraints).

    • +

  • w (rv_continuous) – Probability distribution for the item weights.

    • +

  • K (rv_continuous) – Probability distribution for the profit correlation coefficient.

    • +

  • u (rv_continuous) – Probability distribution for the profit multiplier.

    • +

  • alpha (rv_continuous) – Probability distribution for the tightness ratio.

    • +

  • fix_w (boolean) – If true, weights are kept the same (minus the noise from w_jitter) in all +instances.

    • +

  • w_jitter (rv_continuous) – Probability distribution for random noise added to the weights.

    • +

  • round (boolean) – If true, all prices, weights and capacities are rounded to the nearest +integer.

    • +
+
+
+
+ +
+
+miplearn.problems.multiknapsack.build_multiknapsack_model(data: miplearn.problems.multiknapsack.MultiKnapsackData) → miplearn.solvers.gurobi.GurobiModel
+

Converts multi-knapsack problem data into a concrete Gurobipy model.

+
+ +
+
+

6.3. miplearn.problems.pmedian

+
+
+class miplearn.problems.pmedian.PMedianData(distances: numpy.ndarray, demands: numpy.ndarray, p: int, capacities: numpy.ndarray)
+

Data for the capacitated p-median problem

+
+
Parameters
+
    +

  • distances (numpy.ndarray) – Matrix of distances between customer i and facility j.

    • +

  • demands (numpy.ndarray) – Customer demands.

    • +

  • p (int) – Number of medians that need to be chosen.

    • +

  • capacities (numpy.ndarray) – Facility capacities.

    • +
+
+
+
+ +
+
+class miplearn.problems.pmedian.PMedianGenerator(x: scipy.stats._distn_infrastructure.rv_frozen = <scipy.stats._distn_infrastructure.rv_frozen object>, y: scipy.stats._distn_infrastructure.rv_frozen = <scipy.stats._distn_infrastructure.rv_frozen object>, n: scipy.stats._distn_infrastructure.rv_frozen = <scipy.stats._distn_infrastructure.rv_frozen object>, p: scipy.stats._distn_infrastructure.rv_frozen = <scipy.stats._distn_infrastructure.rv_frozen object>, demands: scipy.stats._distn_infrastructure.rv_frozen = <scipy.stats._distn_infrastructure.rv_frozen object>, capacities: scipy.stats._distn_infrastructure.rv_frozen = <scipy.stats._distn_infrastructure.rv_frozen object>, distances_jitter: scipy.stats._distn_infrastructure.rv_frozen = <scipy.stats._distn_infrastructure.rv_frozen object>, demands_jitter: scipy.stats._distn_infrastructure.rv_frozen = <scipy.stats._distn_infrastructure.rv_frozen object>, capacities_jitter: scipy.stats._distn_infrastructure.rv_frozen = <scipy.stats._distn_infrastructure.rv_frozen object>, fixed: bool = True)
+

Random generator for the capacitated p-median problem.

+

This class first decides the number of customers and the parameter p by +sampling the provided n and p distributions, respectively. Then, for each +customer i, the class builds its geographical location (xi, yi) by sampling +the provided x and y distributions. For each i, the demand for customer i +and the capacity of facility i are decided by sampling the distributions +demands and capacities, respectively. Finally, the costs w[i,j] are set to +the Euclidean distance between the locations of customers i and j.

+

If fixed=True, then the number of customers, their locations, the parameter +p, the demands and the capacities are only sampled from their respective +distributions exactly once, to build a reference instance which is then +perturbed. Specifically, for each perturbation, the distances, demands and +capacities are multiplied by factors sampled from the distributions +distances_jitter, demands_jitter and capacities_jitter, respectively. The +result is a list of instances that have the same set of customers, but slightly +different demands, capacities and distances.

+
+
Parameters
+
    +

  • x – Probability distribution for the x-coordinate of the points.

    • +

  • y – Probability distribution for the y-coordinate of the points.

    • +

  • n – Probability distribution for the number of customer.

    • +

  • p – Probability distribution for the number of medians.

    • +

  • demands – Probability distribution for the customer demands.

    • +

  • capacities – Probability distribution for the facility capacities.

    • +

  • distances_jitter – Probability distribution for the random scaling factor applied to distances.

    • +

  • demands_jitter – Probability distribution for the random scaling factor applied to demands.

    • +

  • capacities_jitter – Probability distribution for the random scaling factor applied to capacities.

    • +

  • fixed – If True, then customer are kept the same across instances.

    • +
+
+
+
+ +
+
+miplearn.problems.pmedian.build_pmedian_model(data: miplearn.problems.pmedian.PMedianData) → miplearn.solvers.gurobi.GurobiModel
+

Converts capacitated p-median data into a concrete Gurobipy model.

+
+ +
+
+

6.4. miplearn.problems.setcover

+
+
+class miplearn.problems.setcover.SetCoverData(costs: numpy.ndarray, incidence_matrix: numpy.ndarray)
+
+ +
+
+

6.5. miplearn.problems.setpack

+
+
+class miplearn.problems.setpack.SetPackData(costs: numpy.ndarray, incidence_matrix: numpy.ndarray)
+
+ +
+
+

6.6. miplearn.problems.stab

+
+
+class miplearn.problems.stab.MaxWeightStableSetData(graph: networkx.classes.graph.Graph, weights: numpy.ndarray)
+
+ +
+
+class miplearn.problems.stab.MaxWeightStableSetGenerator(w: scipy.stats._distn_infrastructure.rv_frozen = <scipy.stats._distn_infrastructure.rv_frozen object>, n: scipy.stats._distn_infrastructure.rv_frozen = <scipy.stats._distn_infrastructure.rv_frozen object>, p: scipy.stats._distn_infrastructure.rv_frozen = <scipy.stats._distn_infrastructure.rv_frozen object>, fix_graph: bool = True)
+

Random instance generator for the Maximum-Weight Stable Set Problem.

+

The generator has two modes of operation. When fix_graph=True is provided, +one random Erdős-Rényi graph $G_{n,p}$ is generated in the constructor, where $n$ +and $p$ are sampled from user-provided probability distributions n and p. To +generate each instance, the generator independently samples each $w_v$ from the +user-provided probability distribution w.

+

When fix_graph=False, a new random graph is generated for each instance; the +remaining parameters are sampled in the same way.

+
+ +
+
+

6.7. miplearn.problems.tsp

+
+
+class miplearn.problems.tsp.TravelingSalesmanData(n_cities: int, distances: numpy.ndarray)
+
+ +
+
+class miplearn.problems.tsp.TravelingSalesmanGenerator(x: scipy.stats._distn_infrastructure.rv_frozen = <scipy.stats._distn_infrastructure.rv_frozen object>, y: scipy.stats._distn_infrastructure.rv_frozen = <scipy.stats._distn_infrastructure.rv_frozen object>, n: scipy.stats._distn_infrastructure.rv_frozen = <scipy.stats._distn_infrastructure.rv_frozen object>, gamma: scipy.stats._distn_infrastructure.rv_frozen = <scipy.stats._distn_infrastructure.rv_frozen object>, fix_cities: bool = True, round: bool = True)
+

Random generator for the Traveling Salesman Problem.

+
+ +
+
+

6.8. miplearn.problems.uc

+
+
+class miplearn.problems.uc.UnitCommitmentData(demand: numpy.ndarray, min_power: numpy.ndarray, max_power: numpy.ndarray, min_uptime: numpy.ndarray, min_downtime: numpy.ndarray, cost_startup: numpy.ndarray, cost_prod: numpy.ndarray, cost_fixed: numpy.ndarray)
+
+ +
+
+miplearn.problems.uc.build_uc_model(data: miplearn.problems.uc.UnitCommitmentData) → miplearn.solvers.gurobi.GurobiModel
+

Models the unit commitment problem according to equations (1)-(5) of:

+
+

Bendotti, P., Fouilhoux, P. & Rottner, C. The min-up/min-down unit +commitment polytope. J Comb Optim 36, 1024-1058 (2018). +https://doi.org/10.1007/s10878-018-0273-y

+
+
+ +
+
+

6.9. miplearn.problems.vertexcover

+
+
+class miplearn.problems.vertexcover.MinWeightVertexCoverData(graph: networkx.classes.graph.Graph, weights: numpy.ndarray)
+
+ +
+
+ + +
+ + +
+ + 5. Solvers + 7. Collectors & Extractors + +
+ +
+
+
+
+

+ + © Copyright 2020-2022, UChicago Argonne, LLC.
+

+
+
+
+ + +
+
+ + + + + + \ No newline at end of file diff --git a/0.3/api/solvers/index.html b/0.3/api/solvers/index.html new file mode 100644 index 0000000..5542fec --- /dev/null +++ b/0.3/api/solvers/index.html @@ -0,0 +1,403 @@ + + + + + + + + 9. Solvers — MIPLearn 0.3 + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
+
+ + + + + + + + +
+ +
+
+
+
+ + + + +
+ + +
+ + + + + + +
+
+ + + + + + + + + +
+ + +
+ +
+ Contents +
+ +
+
+
+
+
+ +
+ +
+

9. Solvers

+
+

9.1. miplearn.solvers.abstract

+
+
+class miplearn.solvers.abstract.AbstractModel
+

Bases: abc.ABC

+
+
+abstract add_constrs(var_names: numpy.ndarray, constrs_lhs: numpy.ndarray, constrs_sense: numpy.ndarray, constrs_rhs: numpy.ndarray, stats: Optional[Dict] = None) → None
+
+ +
+
+abstract extract_after_load(h5: miplearn.h5.H5File) → None
+
+ +
+
+abstract extract_after_lp(h5: miplearn.h5.H5File) → None
+
+ +
+
+abstract extract_after_mip(h5: miplearn.h5.H5File) → None
+
+ +
+
+abstract fix_variables(var_names: numpy.ndarray, var_values: numpy.ndarray, stats: Optional[Dict] = None) → None
+
+ +
+
+abstract optimize() → None
+
+ +
+
+abstract relax() → miplearn.solvers.abstract.AbstractModel
+
+ +
+
+abstract set_time_limit(time_limit_sec: float) → None
+
+ +
+
+abstract set_warm_starts(var_names: numpy.ndarray, var_values: numpy.ndarray, stats: Optional[Dict] = None) → None
+
+ +
+
+abstract write(filename: str) → None
+
+ +
+ +
+
+

9.2. miplearn.solvers.gurobi

+
+
+class miplearn.solvers.gurobi.GurobiModel(inner: gurobipy.Model, find_violations: Optional[Callable] = None, fix_violations: Optional[Callable] = None)
+

Bases: object

+
+
+add_constrs(var_names: numpy.ndarray, constrs_lhs: numpy.ndarray, constrs_sense: numpy.ndarray, constrs_rhs: numpy.ndarray, stats: Optional[Dict] = None) → None
+
+ +
+
+extract_after_load(h5: miplearn.h5.H5File) → None
+

Given a model that has just been loaded, extracts static problem +features, such as variable names and types, objective coefficients, etc.

+
+ +
+
+extract_after_lp(h5: miplearn.h5.H5File) → None
+

Given a linear programming model that has just been solved, extracts +dynamic problem features, such as optimal LP solution, basis status, +etc.

+
+ +
+
+extract_after_mip(h5: miplearn.h5.H5File) → None
+

Given a mixed-integer linear programming model that has just been +solved, extracts dynamic problem features, such as optimal MIP solution.

+
+ +
+
+fix_variables(var_names: numpy.ndarray, var_values: numpy.ndarray, stats: Optional[Dict] = None) → None
+
+ +
+
+optimize() → None
+
+ +
+
+relax() → miplearn.solvers.gurobi.GurobiModel
+
+ +
+
+set_time_limit(time_limit_sec: float) → None
+
+ +
+
+set_warm_starts(var_names: numpy.ndarray, var_values: numpy.ndarray, stats: Optional[Dict] = None) → None
+
+ +
+
+write(filename: str) → None
+
+ +
+ +
+
+

9.3. miplearn.solvers.learning

+
+
+class miplearn.solvers.learning.LearningSolver(components: List[Any], skip_lp=False)
+

Bases: object

+
+
+fit(train_filenames)
+
+ +
+
+optimize(data_filename, build_model)
+
+ +
+ +
+
+ + +
+ + +
+ + 8. Components + 10. Helpers + +
+ +
+
+
+
+

+ + © Copyright 2020-2022, UChicago Argonne, LLC.
+

+
+
+
+ + +
+
+ + + + + + \ No newline at end of file diff --git a/0.3/genindex/index.html b/0.3/genindex/index.html new file mode 100644 index 0000000..1c0ae2b --- /dev/null +++ b/0.3/genindex/index.html @@ -0,0 +1,775 @@ + + + + + + + + Index — MIPLearn 0.3 + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
+
+ + + + + + + + +
+ +
+
+
+
+ + + + + + + + + + + + +
+ + +
+ +
+
+
+
+
+ +
+ + +

Index

+ +
+ A + | B + | C + | E + | F + | G + | H + | I + | J + | L + | M + | O + | P + | R + | S + | T + | U + | W + +
+

A

+ + + +
+ +

B

+ + + +
+ +

C

+ + +
+ +

E

+ + + +
+ +

F

+ + + +
+ +

G

+ + + +
+ +

H

+ + +
+ +

I

+ + +
+ +

J

+ + +
+ +

L

+ + + +
+ +

M

+ + + +
+ +

O

+ + +
+ +

P

+ + + +
+ +

R

+ + +
+ +

S

+ + + +
+ +

T

+ + + +
+ +

U

+ + +
+ +

W

+ + +
+ + + +
+ + +
+ + +
+ +
+
+
+
+

+ + © Copyright 2020-2022, UChicago Argonne, LLC.
+

+
+
+
+ + +
+
+ + + + + + \ No newline at end of file diff --git a/0.3/guide/collectors.ipynb b/0.3/guide/collectors.ipynb new file mode 100644 index 0000000..4085808 --- /dev/null +++ b/0.3/guide/collectors.ipynb @@ -0,0 +1,285 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "id": "505cea0b-5f5d-478a-9107-42bb5515937d", + "metadata": {}, + "source": [ + "# Training Data Collectors\n", + "The first step in solving mixed-integer optimization problems with the assistance of supervised machine learning methods is solving a large set of training instances and collecting the raw training data. In this section, we describe the various training data collectors included in MIPLearn. Additionally, the framework follows the convention of storing all training data in files with a specific data format (namely, HDF5). In this section, we briefly describe this format and the rationale for choosing it.\n", + "\n", + "## Overview\n", + "\n", + "In MIPLearn, a **collector** is a class that solves or analyzes the problem and collects raw data which may be later useful for machine learning methods. Collectors, by convention, take as input: (i) a list of problem data filenames, in gzipped pickle format, ending with `.pkl.gz`; (ii) a function that builds the optimization model, such as `build_tsp_model`. After processing is done, collectors store the training data in a HDF5 file located alongside with the problem data. For example, if the problem data is stored in file `problem.pkl.gz`, then the collector writes to `problem.h5`. Collectors are, in general, very time consuming, as they may need to solve the problem to optimality, potentially multiple times.\n", + "\n", + "## HDF5 Format\n", + "\n", + "MIPLearn stores all training data in [HDF5](HDF5) (Hierarchical Data Format, Version 5) files. The HDF format was originally developed by the [National Center for Supercomputing Applications][NCSA] (NCSA) for storing and organizing large amounts of data, and supports a variety of data types, including integers, floating-point numbers, strings, and arrays. Compared to other formats, such as CSV, JSON or SQLite, the HDF5 format provides several advantages for MIPLearn, including:\n", + "\n", + "- *Storage of multiple scalars, vectors and matrices in a single file* --- This allows MIPLearn to store all training data related to a given problem instance in a single file, which makes training data easier to store, organize and transfer.\n", + "- *High-performance partial I/O* --- Partial I/O allows MIPLearn to read a single element from the training data (e.g. value of the optimal solution) without loading the entire file to memory or reading it from beginning to end, which dramatically improves performance and reduces memory requirements. This is especially important when processing a large number of training data files.\n", + "- *On-the-fly compression* --- HDF5 files can be transparently compressed, using the gzip method, which reduces storage requirements and accelerates network transfers.\n", + "- *Stable, portable and well-supported data format* --- Training data files are typically expensive to generate. Having a stable and well supported data format ensures that these files remain usable in the future, potentially even by other non-Python MIP/ML frameworks.\n", + "\n", + "MIPLearn currently uses HDF5 as simple key-value storage for numerical data; more advanced features of the format, such as metadata, are not currently used. Although files generated by MIPLearn can be read with any HDF5 library, such as [h5py][h5py], some convenience functions are provided to make the access more simple and less error-prone. Specifically, the class [H5File][H5File], which is built on top of h5py, provides the methods [put_scalar][put_scalar], [put_array][put_array], [put_sparse][put_sparse], [put_bytes][put_bytes] to store, respectively, scalar values, dense multi-dimensional arrays, sparse multi-dimensional arrays and arbitrary binary data. The corresponding *get* methods are also provided. Compared to pure h5py methods, these methods automatically perform type-checking and gzip compression. The example below shows their usage.\n", + "\n", + "[HDF5]: https://en.wikipedia.org/wiki/Hierarchical_Data_Format\n", + "[NCSA]: https://en.wikipedia.org/wiki/National_Center_for_Supercomputing_Applications\n", + "[h5py]: https://www.h5py.org/\n", + "[H5File]: ../../api/helpers/#miplearn.h5.H5File\n", + "[put_scalar]: ../../api/helpers/#miplearn.h5.H5File.put_scalar\n", + "[put_array]: ../../api/helpers/#miplearn.h5.H5File.put_scalar\n", + "[put_sparse]: ../../api/helpers/#miplearn.h5.H5File.put_scalar\n", + "[put_bytes]: ../../api/helpers/#miplearn.h5.H5File.put_scalar\n", + "\n", + "\n", + "### Example" + ] + }, + { + "cell_type": "code", + "execution_count": 1, + "id": "3d9cc182", + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "x1 = 1\n", + "x2 = hello world\n", + "x3 = [1 2 3]\n", + "x4 = [[0.37454012 0.9507143 0.7319939 ]\n", + " [0.5986585 0.15601864 0.15599452]\n", + " [0.05808361 0.8661761 0.601115 ]]\n", + "x5 = (2, 3)\t0.68030757\n", + " (3, 2)\t0.45049927\n", + " (4, 0)\t0.013264962\n", + " (0, 2)\t0.94220173\n", + " (4, 2)\t0.5632882\n", + " (2, 1)\t0.3854165\n", + " (1, 1)\t0.015966251\n", + " (3, 0)\t0.23089382\n", + " (4, 4)\t0.24102546\n", + " (1, 3)\t0.68326354\n", + " (3, 1)\t0.6099967\n", + " (0, 3)\t0.8331949\n" + ] + } + ], + "source": [ + "import numpy as np\n", + "import scipy.sparse\n", + "\n", + "from miplearn.h5 import H5File\n", + "\n", + "# Set random seed to make example reproducible\n", + "np.random.seed(42)\n", + "\n", + "# Create a new empty HDF5 file\n", + "with H5File(\"test.h5\", \"w\") as h5:\n", + " # Store a scalar\n", + " h5.put_scalar(\"x1\", 1)\n", + " h5.put_scalar(\"x2\", \"hello world\")\n", + "\n", + " # Store a dense array and a dense matrix\n", + " h5.put_array(\"x3\", np.array([1, 2, 3]))\n", + " h5.put_array(\"x4\", np.random.rand(3, 3))\n", + "\n", + " # Store a sparse matrix\n", + " h5.put_sparse(\"x5\", scipy.sparse.random(5, 5, 0.5))\n", + "\n", + "# Re-open the file we just created and print\n", + "# previously-stored data\n", + "with H5File(\"test.h5\", \"r\") as h5:\n", + " print(\"x1 =\", h5.get_scalar(\"x1\"))\n", + " print(\"x2 =\", h5.get_scalar(\"x2\"))\n", + " print(\"x3 =\", h5.get_array(\"x3\"))\n", + " print(\"x4 =\", h5.get_array(\"x4\"))\n", + " print(\"x5 =\", h5.get_sparse(\"x5\"))" + ] + }, + { + "cell_type": "markdown", + "id": "e7175752", + "metadata": { + "collapsed": false + }, + "source": [] + }, + { + "cell_type": "markdown", + "id": "e993aa6f", + "metadata": { + "collapsed": false + }, + "source": [ + "## Basic collector\n", + "\n", + "[BasicCollector][BasicCollector] is the most fundamental collector, and performs the following steps:\n", + "\n", + "1. Extracts all model data, such as objective function and constraint right-hand sides into numpy arrays, which can later be easily and efficiently accessed without rebuilding the model or invoking the solver;\n", + "2. Solves the linear relaxation of the problem and stores its optimal solution, basis status and sensitivity information, among other information;\n", + "3. Solves the original mixed-integer optimization problem to optimality and stores its optimal solution, along with solve statistics, such as number of explored nodes and wallclock time.\n", + "\n", + "Data extracted in Phases 1, 2 and 3 above are prefixed, respectively as `static_`, `lp_` and `mip_`. The entire set of fields is shown in the table below.\n", + "\n", + "[BasicCollector]: ../../api/collectors/#miplearn.collectors.basic.BasicCollector\n" + ] + }, + { + "cell_type": "markdown", + "id": "711639bd", + "metadata": { + "collapsed": false + }, + "source": [ + "### Data fields\n", + "\n", + "| Field | Type | Description |\n", + "|-----------------------------------|---------------------|---------------------------------------------------------------------------------------------------------------------------------------------|\n", + "| `static_constr_lhs` | `(nconstrs, nvars)` | Constraint left-hand sides, in sparse matrix format |\n", + "| `static_constr_names` | `(nconstrs,)` | Constraint names |\n", + "| `static_constr_rhs` | `(nconstrs,)` | Constraint right-hand sides |\n", + "| `static_constr_sense` | `(nconstrs,)` | Constraint senses (`\"<\"`, `\">\"` or `\"=\"`) |\n", + "| `static_obj_offset` | `float` | Constant value added to the objective function |\n", + "| `static_sense` | `str` | `\"min\"` if minimization problem or `\"max\"` otherwise |\n", + "| `static_var_lower_bounds` | `(nvars,)` | Variable lower bounds |\n", + "| `static_var_names` | `(nvars,)` | Variable names |\n", + "| `static_var_obj_coeffs` | `(nvars,)` | Objective coefficients |\n", + "| `static_var_types` | `(nvars,)` | Types of the decision variables (`\"C\"`, `\"B\"` and `\"I\"` for continuous, binary and integer, respectively) |\n", + "| `static_var_upper_bounds` | `(nvars,)` | Variable upper bounds |\n", + "| `lp_constr_basis_status` | `(nconstr,)` | Constraint basis status (`0` for basic, `-1` for non-basic) |\n", + "| `lp_constr_dual_values` | `(nconstr,)` | Constraint dual value (or shadow price) |\n", + "| `lp_constr_sa_rhs_{up,down}` | `(nconstr,)` | Sensitivity information for the constraint RHS |\n", + "| `lp_constr_slacks` | `(nconstr,)` | Constraint slack in the solution to the LP relaxation |\n", + "| `lp_obj_value` | `float` | Optimal value of the LP relaxation |\n", + "| `lp_var_basis_status` | `(nvars,)` | Variable basis status (`0`, `-1`, `-2` or `-3` for basic, non-basic at lower bound, non-basic at upper bound, and superbasic, respectively) |\n", + "| `lp_var_reduced_costs` | `(nvars,)` | Variable reduced costs |\n", + "| `lp_var_sa_{obj,ub,lb}_{up,down}` | `(nvars,)` | Sensitivity information for the variable objective coefficient, lower and upper bound. |\n", + "| `lp_var_values` | `(nvars,)` | Optimal solution to the LP relaxation |\n", + "| `lp_wallclock_time` | `float` | Time taken to solve the LP relaxation (in seconds) |\n", + "| `mip_constr_slacks` | `(nconstrs,)` | Constraint slacks in the best MIP solution |\n", + "| `mip_gap` | `float` | Relative MIP optimality gap |\n", + "| `mip_node_count` | `float` | Number of explored branch-and-bound nodes |\n", + "| `mip_obj_bound` | `float` | Dual bound |\n", + "| `mip_obj_value` | `float` | Value of the best MIP solution |\n", + "| `mip_var_values` | `(nvars,)` | Best MIP solution |\n", + "| `mip_wallclock_time` | `float` | Time taken to solve the MIP (in seconds) |" + ] + }, + { + "cell_type": "markdown", + "id": "9b35d7f7", + "metadata": { + "collapsed": false + }, + "source": [ + "### Example\n", + "\n", + "The example below shows how to generate a few random instances of the traveling salesman problem, store its problem data, run the collector and print some of the training data to screen." + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "id": "7ea6b715", + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stderr", + "output_type": "stream", + "text": [ + "/home/axavier/Software/anaconda3/envs/miplearn/lib/python3.8/site-packages/tqdm/auto.py:22: TqdmWarning: IProgress not found. Please update jupyter and ipywidgets. See https://ipywidgets.readthedocs.io/en/stable/user_install.html\n", + " from .autonotebook import tqdm as notebook_tqdm\n" + ] + }, + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Removing empty/corrupted h5 file: data/tsp/00000.h5\n", + "lp_obj_value = 2909.0\n", + "mip_obj_value = 2921.0\n" + ] + } + ], + "source": [ + "import random\n", + "import numpy as np\n", + "from scipy.stats import uniform, randint\n", + "from glob import glob\n", + "\n", + "from miplearn.problems.tsp import (\n", + " TravelingSalesmanGenerator,\n", + " build_tsp_model,\n", + ")\n", + "from miplearn.io import save\n", + "from miplearn.h5 import H5File\n", + "from miplearn.collectors.basic import BasicCollector\n", + "\n", + "# Set random seed to make example reproducible.\n", + "random.seed(42)\n", + "np.random.seed(42)\n", + "\n", + "# Generate a few instances of the traveling salesman problem.\n", + "data = TravelingSalesmanGenerator(\n", + " n=randint(low=10, high=11),\n", + " x=uniform(loc=0.0, scale=1000.0),\n", + " y=uniform(loc=0.0, scale=1000.0),\n", + " gamma=uniform(loc=0.90, scale=0.20),\n", + " fix_cities=True,\n", + " round=True,\n", + ").generate(10)\n", + "\n", + "# Save instance data to data/tsp/00000.pkl.gz, data/tsp/00001.pkl.gz, ...\n", + "save(data, \"data/tsp\")\n", + "\n", + "# Solve all instances and collect basic solution information. Process at most four\n", + "# instances in parallel, with a per-instance time limit of one hour.\n", + "bc = BasicCollector(time_limit_sec=3600)\n", + "bc.collect(glob(\"data/tsp/*.pkl.gz\"), build_tsp_model, n_jobs=4)\n", + "\n", + "# Read and print some training data for the first instance.\n", + "with H5File(\"data/tsp/00000.h5\", \"r\") as h5:\n", + " print(\"lp_obj_value = \", h5.get_scalar(\"lp_obj_value\"))\n", + " print(\"mip_obj_value = \", h5.get_scalar(\"mip_obj_value\"))" + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "id": "97ac9136", + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [] + } + ], + "metadata": { + "kernelspec": { + "display_name": "Python 3", + "language": "python", + "name": "python3" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.8.13" + } + }, + "nbformat": 4, + "nbformat_minor": 5 +} diff --git a/0.3/guide/collectors/index.html b/0.3/guide/collectors/index.html new file mode 100644 index 0000000..d0df632 --- /dev/null +++ b/0.3/guide/collectors/index.html @@ -0,0 +1,839 @@ + + + + + + + + 2. Training Data Collectors — MIPLearn 0.3 + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
+
+ + + + + + + + +
+ +
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+ + + + +
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+ + + + + + +
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+ + + + + + + + + +
+ + +
+ +
+ Contents +
+ +
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+ +
+ + + +
+

2. Training Data Collectors

+

The first step in solving mixed-integer optimization problems with the assistance of supervised machine learning methods is solving a large set of training instances and collecting the raw training data. In this section, we describe the various training data collectors included in MIPLearn. Additionally, the framework follows the convention of storing all training data in files with a specific data format (namely, HDF5). In this section, we briefly describe this format and the rationale for +choosing it.

+
+

2.1. Overview

+

In MIPLearn, a collector is a class that solves or analyzes the problem and collects raw data which may be later useful for machine learning methods. Collectors, by convention, take as input: (i) a list of problem data filenames, in gzipped pickle format, ending with .pkl.gz; (ii) a function that builds the optimization model, such as build_tsp_model. After processing is done, collectors store the training data in a HDF5 file located alongside with the problem data. For example, if +the problem data is stored in file problem.pkl.gz, then the collector writes to problem.h5. Collectors are, in general, very time consuming, as they may need to solve the problem to optimality, potentially multiple times.

+
+
+

2.2. HDF5 Format

+

MIPLearn stores all training data in HDF5 (Hierarchical Data Format, Version 5) files. The HDF format was originally developed by the National Center for Supercomputing Applications (NCSA) for storing and organizing large amounts of data, and supports a variety of data types, including integers, floating-point numbers, strings, and arrays. Compared to other formats, such as CSV, JSON or SQLite, the +HDF5 format provides several advantages for MIPLearn, including:

+
    +

  • Storage of multiple scalars, vectors and matrices in a single file — This allows MIPLearn to store all training data related to a given problem instance in a single file, which makes training data easier to store, organize and transfer.

    • +

  • High-performance partial I/O — Partial I/O allows MIPLearn to read a single element from the training data (e.g. value of the optimal solution) without loading the entire file to memory or reading it from beginning to end, which dramatically improves performance and reduces memory requirements. This is especially important when processing a large number of training data files.

    • +

  • On-the-fly compression — HDF5 files can be transparently compressed, using the gzip method, which reduces storage requirements and accelerates network transfers.

    • +

  • Stable, portable and well-supported data format — Training data files are typically expensive to generate. Having a stable and well supported data format ensures that these files remain usable in the future, potentially even by other non-Python MIP/ML frameworks.

    • +
+

MIPLearn currently uses HDF5 as simple key-value storage for numerical data; more advanced features of the format, such as metadata, are not currently used. Although files generated by MIPLearn can be read with any HDF5 library, such as h5py, some convenience functions are provided to make the access more simple and less error-prone. Specifically, the class H5File, which is built on top of h5py, provides the methods +put_scalar, put_array, put_sparse, put_bytes to store, respectively, scalar values, dense multi-dimensional arrays, sparse multi-dimensional arrays and arbitrary binary data. The corresponding get methods are also provided. Compared to pure h5py methods, these methods +automatically perform type-checking and gzip compression. The example below shows their usage.

+
+

Example

+
+
[1]:
+
+
+
import numpy as np
+import scipy.sparse
+
+from miplearn.h5 import H5File
+
+# Set random seed to make example reproducible
+np.random.seed(42)
+
+# Create a new empty HDF5 file
+with H5File("test.h5", "w") as h5:
+    # Store a scalar
+    h5.put_scalar("x1", 1)
+    h5.put_scalar("x2", "hello world")
+
+    # Store a dense array and a dense matrix
+    h5.put_array("x3", np.array([1, 2, 3]))
+    h5.put_array("x4", np.random.rand(3, 3))
+
+    # Store a sparse matrix
+    h5.put_sparse("x5", scipy.sparse.random(5, 5, 0.5))
+
+# Re-open the file we just created and print
+# previously-stored data
+with H5File("test.h5", "r") as h5:
+    print("x1 =", h5.get_scalar("x1"))
+    print("x2 =", h5.get_scalar("x2"))
+    print("x3 =", h5.get_array("x3"))
+    print("x4 =", h5.get_array("x4"))
+    print("x5 =", h5.get_sparse("x5"))
+
+
+
+
+
+
+
+
+x1 = 1
+x2 = hello world
+x3 = [1 2 3]
+x4 = [[0.37454012 0.9507143  0.7319939 ]
+ [0.5986585  0.15601864 0.15599452]
+ [0.05808361 0.8661761  0.601115  ]]
+x5 =   (2, 3)   0.68030757
+  (3, 2)        0.45049927
+  (4, 0)        0.013264962
+  (0, 2)        0.94220173
+  (4, 2)        0.5632882
+  (2, 1)        0.3854165
+  (1, 1)        0.015966251
+  (3, 0)        0.23089382
+  (4, 4)        0.24102546
+  (1, 3)        0.68326354
+  (3, 1)        0.6099967
+  (0, 3)        0.8331949
+
+
+
+
+
+

2.3. Basic collector

+

BasicCollector is the most fundamental collector, and performs the following steps:

+
    +

  1. Extracts all model data, such as objective function and constraint right-hand sides into numpy arrays, which can later be easily and efficiently accessed without rebuilding the model or invoking the solver;

    2. +

  2. Solves the linear relaxation of the problem and stores its optimal solution, basis status and sensitivity information, among other information;

    3. +

  3. Solves the original mixed-integer optimization problem to optimality and stores its optimal solution, along with solve statistics, such as number of explored nodes and wallclock time.

    4. +
+

Data extracted in Phases 1, 2 and 3 above are prefixed, respectively as static_, lp_ and mip_. The entire set of fields is shown in the table below.

+
+

Data fields

+ +++++ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +

Field

Type

Description

static_constr_lhs

(nconstrs, nvars)

Constraint left-hand sides, in sparse matrix format

static_constr_names

(nconstrs,)

Constraint names

static_constr_rhs

(nconstrs,)

Constraint right-hand sides

static_constr_sense

(nconstrs,)

Constraint senses ("<", ">" or "=")

static_obj_offset

float

Constant value added to the objective function

static_sense

str

"min" if minimization problem or "max" otherwise

static_var_lower_bounds

(nvars,)

Variable lower bounds

static_var_names

(nvars,)

Variable names

static_var_obj_coeffs

(nvars,)

Objective coefficients

static_var_types

(nvars,)

Types of the decision variables ("C", "B" and "I" for continuous, binary and integer, respectively)

static_var_upper_bounds

(nvars,)

Variable upper bounds

lp_constr_basis_status

(nconstr,)

Constraint basis status (0 for basic, -1 for non-basic)

lp_constr_dual_values

(nconstr,)

Constraint dual value (or shadow price)

lp_constr_sa_rhs_{up,down}

(nconstr,)

Sensitivity information for the constraint RHS

lp_constr_slacks

(nconstr,)

Constraint slack in the solution to the LP relaxation

lp_obj_value

float

Optimal value of the LP relaxation

lp_var_basis_status

(nvars,)

Variable basis status (0, -1, -2 or -3 for basic, non-basic at lower bound, non-basic at upper bound, and superbasic, respectively)

lp_var_reduced_costs

(nvars,)

Variable reduced costs

lp_var_sa_{obj,ub,lb}_{up,down}

(nvars,)

Sensitivity information for the variable objective coefficient, lower and upper bound.

lp_var_values

(nvars,)

Optimal solution to the LP relaxation

lp_wallclock_time

float

Time taken to solve the LP relaxation (in seconds)

mip_constr_slacks

(nconstrs,)

Constraint slacks in the best MIP solution

mip_gap

float

Relative MIP optimality gap

mip_node_count

float

Number of explored branch-and-bound nodes

mip_obj_bound

float

Dual bound

mip_obj_value

float

Value of the best MIP solution

mip_var_values

(nvars,)

Best MIP solution

mip_wallclock_time

float

Time taken to solve the MIP (in seconds)

+
+
+

Example

+

The example below shows how to generate a few random instances of the traveling salesman problem, store its problem data, run the collector and print some of the training data to screen.

+
+
[2]:
+
+
+
import random
+import numpy as np
+from scipy.stats import uniform, randint
+from glob import glob
+
+from miplearn.problems.tsp import (
+    TravelingSalesmanGenerator,
+    build_tsp_model,
+)
+from miplearn.io import save
+from miplearn.h5 import H5File
+from miplearn.collectors.basic import BasicCollector
+
+# Set random seed to make example reproducible.
+random.seed(42)
+np.random.seed(42)
+
+# Generate a few instances of the traveling salesman problem.
+data = TravelingSalesmanGenerator(
+    n=randint(low=10, high=11),
+    x=uniform(loc=0.0, scale=1000.0),
+    y=uniform(loc=0.0, scale=1000.0),
+    gamma=uniform(loc=0.90, scale=0.20),
+    fix_cities=True,
+    round=True,
+).generate(10)
+
+# Save instance data to data/tsp/00000.pkl.gz, data/tsp/00001.pkl.gz, ...
+save(data, "data/tsp")
+
+# Solve all instances and collect basic solution information. Process at most four
+# instances in parallel, with a per-instance time limit of one hour.
+bc = BasicCollector(time_limit_sec=3600)
+bc.collect(glob("data/tsp/*.pkl.gz"), build_tsp_model, n_jobs=4)
+
+# Read and print some training data for the first instance.
+with H5File("data/tsp/00000.h5", "r") as h5:
+    print("lp_obj_value = ", h5.get_scalar("lp_obj_value"))
+    print("mip_obj_value = ", h5.get_scalar("mip_obj_value"))
+
+
+
+
+
+
+
+
+/home/axavier/Software/anaconda3/envs/miplearn/lib/python3.8/site-packages/tqdm/auto.py:22: TqdmWarning: IProgress not found. Please update jupyter and ipywidgets. See https://ipywidgets.readthedocs.io/en/stable/user_install.html
+  from .autonotebook import tqdm as notebook_tqdm
+
+
+
+
+
+
+
+Removing empty/corrupted h5 file: data/tsp/00000.h5
+lp_obj_value =  2909.0
+mip_obj_value =  2921.0
+
+
+
+
[2]:
+
+
+

+
+
+
+
+
+
+ + +
+ + +
+ + 1. Benchmark Problems + 3. Feature Extractors + +
+ +
+
+
+
+

+ + © Copyright 2020-2022, UChicago Argonne, LLC.
+

+
+
+
+ + +
+
+ + + + + + \ No newline at end of file diff --git a/0.3/guide/features.ipynb b/0.3/guide/features.ipynb new file mode 100644 index 0000000..bcf0d47 --- /dev/null +++ b/0.3/guide/features.ipynb @@ -0,0 +1,343 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "id": "cdc6ebe9-d1d4-4de1-9b5a-4fc8ef57b11b", + "metadata": {}, + "source": [ + "# Feature Extractors\n", + "\n", + "In the previous page, we introduced *training data collectors*, which solve the optimization problem and collect raw training data, such as the optimal solution. In this page, we introduce **feature extractors**, which take the raw training data, stored in HDF5 files, and extract relevant information in order to train a machine learning model. We describe the extractors readily available in MIPLearn." + ] + }, + { + "cell_type": "markdown", + "id": "599ac2f7", + "metadata": { + "collapsed": false + }, + "source": [ + "\n", + "## Overview\n", + "\n", + "Feature extraction is an important step of the process of building a machine learning model because it helps to reduce the complexity of the data and convert it into a format that is more easily processed. Previous research has proposed converting absolute variable coefficients, for example, into relative values which are invariant to various transformations, such as problem scaling, making them more amenable to learning. Various other transformations have also been described.\n", + "\n", + "In the framework, we treat data collection and feature extraction as two separate steps to accelerate the model development cycle. Specifically, collectors are typically time-consuming, as they often need to solve the problem to optimality, and therefore focus on collecting and storing all data that may or may not be relevant, in its raw format. Feature extractors, on the other hand, focus entirely on filtering the data and improving its representation, and are therefore much faster to run. Experimenting with new data representations, therefore, can be done without resolving the instances.\n", + "\n", + "In MIPLearn, extractors implement the abstract class [FeatureExtractor][FeatureExtractor], which has methods that take as input an [H5File][H5File] and produce either: (i) instance features, which describe the entire instances; (ii) variable features, which describe a particular decision variables; or (iii) constraint features, which describe a particular constraint. The extractor is free to implement only a subset of these methods, if it is known that it will not be used with a machine learning component that requires the other types of features.\n", + "\n", + "[FeatureExtractor]: ../../api/collectors/#miplearn.features.fields.FeaturesExtractor\n", + "[H5File]: ../../api/helpers/#miplearn.h5.H5File" + ] + }, + { + "cell_type": "markdown", + "id": "60efe8f5", + "metadata": { + "collapsed": false + }, + "source": [ + "\n", + "## H5FieldsExtractor\n", + "\n", + "[H5FieldsExtractor][H5FieldsExtractor], the most simple extractor in MIPLearn, simple extracts data that is already available in the HDF5 file, assembles it into a matrix and returns it as-is. The fields used to build instance, variable and constraint features are user-specified. The class also performs checks to ensure that the shapes of the returned matrices make sense." + ] + }, + { + "cell_type": "markdown", + "id": "dfc32e59", + "metadata": { + "collapsed": false + }, + "source": [ + "### Example\n", + "\n", + "The example below demonstrates the usage of H5FieldsExtractor in a randomly generated instance of the multi-dimensional knapsack problem." + ] + }, + { + "cell_type": "code", + "execution_count": 1, + "id": "ed2f5006", + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "instance features (11,) \n", + " [-1531.24308771 -350. -692. -454.\n", + " -709. -605. -543. -321.\n", + " -674. -571. -341. ]\n", + "variable features (10, 4) \n", + " [[-1.53124309e+03 -3.50000000e+02 0.00000000e+00 9.43468018e+01]\n", + " [-1.53124309e+03 -6.92000000e+02 2.51703322e-01 0.00000000e+00]\n", + " [-1.53124309e+03 -4.54000000e+02 0.00000000e+00 8.25504150e+01]\n", + " [-1.53124309e+03 -7.09000000e+02 1.11373022e-01 0.00000000e+00]\n", + " [-1.53124309e+03 -6.05000000e+02 1.00000000e+00 -1.26055283e+02]\n", + " [-1.53124309e+03 -5.43000000e+02 0.00000000e+00 1.68693771e+02]\n", + " [-1.53124309e+03 -3.21000000e+02 1.07488781e-01 0.00000000e+00]\n", + " [-1.53124309e+03 -6.74000000e+02 8.82293701e-01 0.00000000e+00]\n", + " [-1.53124309e+03 -5.71000000e+02 0.00000000e+00 1.41129074e+02]\n", + " [-1.53124309e+03 -3.41000000e+02 1.28830120e-01 0.00000000e+00]]\n", + "constraint features (5, 3) \n", + " [[ 1.3100000e+03 -1.5978307e-01 0.0000000e+00]\n", + " [ 9.8800000e+02 -3.2881632e-01 0.0000000e+00]\n", + " [ 1.0040000e+03 -4.0601316e-01 0.0000000e+00]\n", + " [ 1.2690000e+03 -1.3659772e-01 0.0000000e+00]\n", + " [ 1.0070000e+03 -2.8800571e-01 0.0000000e+00]]\n" + ] + } + ], + "source": [ + "from glob import glob\n", + "from shutil import rmtree\n", + "\n", + "import numpy as np\n", + "from scipy.stats import uniform, randint\n", + "\n", + "from miplearn.collectors.basic import BasicCollector\n", + "from miplearn.features.fields import H5FieldsExtractor\n", + "from miplearn.h5 import H5File\n", + "from miplearn.io import save\n", + "from miplearn.problems.multiknapsack import (\n", + " MultiKnapsackGenerator,\n", + " build_multiknapsack_model\n", + ")\n", + "\n", + "# Set random seed to make example reproducible\n", + "np.random.seed(42)\n", + "\n", + "# Generate some random multiknapsack instances\n", + "rmtree(\"data/multiknapsack/\", ignore_errors=True)\n", + "save(\n", + " MultiKnapsackGenerator(\n", + " n=randint(low=10, high=11),\n", + " m=randint(low=5, high=6),\n", + " w=uniform(loc=0, scale=1000),\n", + " K=uniform(loc=100, scale=0),\n", + " u=uniform(loc=1, scale=0),\n", + " alpha=uniform(loc=0.25, scale=0),\n", + " w_jitter=uniform(loc=0.95, scale=0.1),\n", + " p_jitter=uniform(loc=0.75, scale=0.5),\n", + " fix_w=True,\n", + " ).generate(10),\n", + " \"data/multiknapsack\"\n", + ")\n", + "\n", + "# Run the basic collector\n", + "BasicCollector().collect(\n", + " glob(\"data/multiknapsack/*\"),\n", + " build_multiknapsack_model,\n", + " n_jobs=4,\n", + ")\n", + "\n", + "ext = H5FieldsExtractor(\n", + " # Use as instance features the value of the LP relaxation and the\n", + " # vector of objective coefficients.\n", + " instance_fields=[\n", + " \"lp_obj_value\",\n", + " \"static_var_obj_coeffs\",\n", + " ],\n", + " # For each variable, use as features the optimal value of the LP\n", + " # relaxation, the variable objective coefficient, the variable's\n", + " # value its reduced cost.\n", + " var_fields=[\n", + " \"lp_obj_value\",\n", + " \"static_var_obj_coeffs\",\n", + " \"lp_var_values\",\n", + " \"lp_var_reduced_costs\",\n", + " ],\n", + " # For each constraint, use as features the RHS, dual value and slack.\n", + " constr_fields=[\n", + " \"static_constr_rhs\",\n", + " \"lp_constr_dual_values\",\n", + " \"lp_constr_slacks\",\n", + " ]\n", + ")\n", + "\n", + "with H5File(\"data/multiknapsack/00000.h5\") as h5:\n", + " # Extract and print instance features\n", + " x1 = ext.get_instance_features(h5)\n", + " print(\"instance features\", x1.shape, \"\\n\", x1)\n", + "\n", + " # Extract and print variable features\n", + " x2 = ext.get_var_features(h5)\n", + " print(\"variable features\", x2.shape, \"\\n\", x2)\n", + "\n", + " # Extract and print constraint features\n", + " x3 = ext.get_constr_features(h5)\n", + " print(\"constraint features\", x3.shape, \"\\n\", x3)\n" + ] + }, + { + "cell_type": "markdown", + "id": "35dc7ce3", + "metadata": { + "collapsed": false + }, + "source": [ + "\n", + "[H5FieldsExtractor]: ../../api/collectors/#miplearn.features.fields.H5FieldsExtractor" + ] + }, + { + "cell_type": "markdown", + "id": "cc32efd6", + "metadata": { + "collapsed": false + }, + "source": [ + "
\n", + "Warning\n", + "\n", + "You should ensure that the number of features remains the same for all relevant HDF5 files. In the previous example, to illustrate this issue, we used variable objective coefficients as instance features. While this is allowed, note that this requires all problem instances to have the same number of variables; otherwise the number of features would vary from instance to instance and MIPLearn would be unable to concatenate the matrices.\n", + "
" + ] + }, + { + "cell_type": "markdown", + "id": "2e3ba4fe", + "metadata": { + "collapsed": false + }, + "source": [ + "## AlvLouWeh2017Extractor\n", + "\n", + "Alvarez, Louveaux and Wehenkel (2017) proposed a set features to describe a particular decision variable in a given node of the branch-and-bound tree, and applied it to the problem of mimicking strong branching decisions. The class [AlvLouWeh2017Extractor][] implements a subset of these features (40 out of 64), which are available outside of the branch-and-bound tree. Some features are derived from the static defintion of the problem (i.e. from objective function and constraint data), while some features are derived from the solution to the LP relaxation. The features have been designed to be: (i) independent of the size of the problem; (ii) invariant with respect to irrelevant problem transformations, such as row and column permutation; and (iii) independent of the scale of the problem. We refer to the paper for a more complete description.\n", + "\n", + "### Example" + ] + }, + { + "cell_type": "code", + "execution_count": 5, + "id": "4944a4a4", + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "x1 (10, 40) \n", + " [[-1.00e+00 1.00e+20 1.00e-01 1.00e+00 0.00e+00 1.00e+00 6.00e-01\n", + " 0.00e+00 0.00e+00 0.00e+00 0.00e+00 0.00e+00 0.00e+00 0.00e+00\n", + " 0.00e+00 1.00e+00 6.00e-01 1.00e+00 1.75e+01 1.00e+00 2.00e-01\n", + " 1.00e+00 0.00e+00 0.00e+00 0.00e+00 0.00e+00 0.00e+00 0.00e+00\n", + " 0.00e+00 0.00e+00 0.00e+00 0.00e+00 0.00e+00 0.00e+00 0.00e+00\n", + " 0.00e+00 1.00e+00 -1.00e+00 0.00e+00 1.00e+20]\n", + " [-1.00e+00 1.00e+20 1.00e-01 1.00e+00 1.00e-01 1.00e+00 1.00e+00\n", + " 0.00e+00 0.00e+00 0.00e+00 0.00e+00 0.00e+00 0.00e+00 0.00e+00\n", + " 0.00e+00 1.00e+00 7.00e-01 1.00e+00 5.10e+00 1.00e+00 2.00e-01\n", + " 1.00e+00 0.00e+00 0.00e+00 0.00e+00 0.00e+00 0.00e+00 0.00e+00\n", + " 0.00e+00 0.00e+00 0.00e+00 0.00e+00 0.00e+00 0.00e+00 0.00e+00\n", + " 3.00e-01 -1.00e+00 -1.00e+00 0.00e+00 0.00e+00]\n", + " [-1.00e+00 1.00e+20 1.00e-01 1.00e+00 0.00e+00 1.00e+00 9.00e-01\n", + " 0.00e+00 0.00e+00 0.00e+00 0.00e+00 0.00e+00 0.00e+00 0.00e+00\n", + " 0.00e+00 1.00e+00 5.00e-01 1.00e+00 1.30e+01 1.00e+00 2.00e-01\n", + " 1.00e+00 0.00e+00 0.00e+00 0.00e+00 0.00e+00 0.00e+00 0.00e+00\n", + " 0.00e+00 0.00e+00 0.00e+00 0.00e+00 0.00e+00 0.00e+00 0.00e+00\n", + " 0.00e+00 1.00e+00 -1.00e+00 0.00e+00 1.00e+20]\n", + " [-1.00e+00 1.00e+20 1.00e-01 1.00e+00 2.00e-01 1.00e+00 9.00e-01\n", + " 0.00e+00 0.00e+00 0.00e+00 0.00e+00 0.00e+00 0.00e+00 0.00e+00\n", + " 0.00e+00 1.00e+00 8.00e-01 1.00e+00 3.40e+00 1.00e+00 2.00e-01\n", + " 1.00e+00 1.00e-01 0.00e+00 0.00e+00 0.00e+00 0.00e+00 0.00e+00\n", + " 0.00e+00 0.00e+00 0.00e+00 0.00e+00 0.00e+00 0.00e+00 0.00e+00\n", + " 1.00e-01 -1.00e+00 -1.00e+00 0.00e+00 0.00e+00]\n", + " [-1.00e+00 1.00e+20 1.00e-01 1.00e+00 1.00e-01 1.00e+00 7.00e-01\n", + " 0.00e+00 0.00e+00 0.00e+00 0.00e+00 0.00e+00 0.00e+00 0.00e+00\n", + " 0.00e+00 1.00e+00 6.00e-01 1.00e+00 3.80e+00 1.00e+00 2.00e-01\n", + " 1.00e+00 0.00e+00 0.00e+00 0.00e+00 0.00e+00 0.00e+00 0.00e+00\n", + " 0.00e+00 0.00e+00 0.00e+00 0.00e+00 0.00e+00 0.00e+00 0.00e+00\n", + " 0.00e+00 -1.00e+00 -1.00e+00 0.00e+00 0.00e+00]\n", + " [-1.00e+00 1.00e+20 1.00e-01 1.00e+00 1.00e-01 1.00e+00 8.00e-01\n", + " 0.00e+00 0.00e+00 0.00e+00 0.00e+00 0.00e+00 0.00e+00 0.00e+00\n", + " 0.00e+00 1.00e+00 7.00e-01 1.00e+00 3.30e+00 1.00e+00 2.00e-01\n", + " 1.00e+00 0.00e+00 0.00e+00 0.00e+00 0.00e+00 0.00e+00 0.00e+00\n", + " 0.00e+00 0.00e+00 0.00e+00 0.00e+00 0.00e+00 0.00e+00 0.00e+00\n", + " 0.00e+00 1.00e+00 -1.00e+00 0.00e+00 1.00e+20]\n", + " [-1.00e+00 1.00e+20 1.00e-01 1.00e+00 0.00e+00 1.00e+00 3.00e-01\n", + " 0.00e+00 0.00e+00 0.00e+00 0.00e+00 0.00e+00 0.00e+00 0.00e+00\n", + " 0.00e+00 1.00e+00 1.00e+00 1.00e+00 5.70e+00 1.00e+00 1.00e-01\n", + " 1.00e+00 0.00e+00 0.00e+00 0.00e+00 0.00e+00 0.00e+00 0.00e+00\n", + " 0.00e+00 0.00e+00 0.00e+00 0.00e+00 0.00e+00 0.00e+00 0.00e+00\n", + " 1.00e-01 -1.00e+00 -1.00e+00 0.00e+00 0.00e+00]\n", + " [-1.00e+00 1.00e+20 1.00e-01 1.00e+00 1.00e-01 1.00e+00 6.00e-01\n", + " 0.00e+00 0.00e+00 0.00e+00 0.00e+00 0.00e+00 0.00e+00 0.00e+00\n", + " 0.00e+00 1.00e+00 8.00e-01 1.00e+00 6.80e+00 1.00e+00 2.00e-01\n", + " 1.00e+00 0.00e+00 0.00e+00 0.00e+00 0.00e+00 0.00e+00 0.00e+00\n", + " 0.00e+00 0.00e+00 0.00e+00 0.00e+00 0.00e+00 0.00e+00 0.00e+00\n", + " 1.00e-01 -1.00e+00 -1.00e+00 0.00e+00 0.00e+00]\n", + " [-1.00e+00 1.00e+20 1.00e-01 1.00e+00 4.00e-01 1.00e+00 6.00e-01\n", + " 0.00e+00 0.00e+00 0.00e+00 0.00e+00 0.00e+00 0.00e+00 0.00e+00\n", + " 0.00e+00 1.00e+00 8.00e-01 1.00e+00 1.40e+00 1.00e+00 1.00e-01\n", + " 1.00e+00 1.00e-01 0.00e+00 0.00e+00 0.00e+00 0.00e+00 0.00e+00\n", + " 0.00e+00 0.00e+00 0.00e+00 0.00e+00 0.00e+00 0.00e+00 0.00e+00\n", + " 0.00e+00 1.00e+00 -1.00e+00 0.00e+00 1.00e+20]\n", + " [-1.00e+00 1.00e+20 1.00e-01 1.00e+00 0.00e+00 1.00e+00 5.00e-01\n", + " 0.00e+00 0.00e+00 0.00e+00 0.00e+00 0.00e+00 0.00e+00 0.00e+00\n", + " 0.00e+00 1.00e+00 5.00e-01 1.00e+00 7.60e+00 1.00e+00 1.00e-01\n", + " 1.00e+00 0.00e+00 0.00e+00 0.00e+00 0.00e+00 0.00e+00 0.00e+00\n", + " 0.00e+00 0.00e+00 0.00e+00 0.00e+00 0.00e+00 0.00e+00 0.00e+00\n", + " 1.00e-01 -1.00e+00 -1.00e+00 0.00e+00 0.00e+00]]\n" + ] + } + ], + "source": [ + "from miplearn.features.AlvLouWeh2017 import AlvLouWeh2017Extractor\n", + "from miplearn.h5 import H5File\n", + "\n", + "# Build the extractor\n", + "ext = AlvLouWeh2017Extractor()\n", + "\n", + "# Open previously-created multiknapsack training data\n", + "with H5File(\"data/multiknapsack/00000.h5\") as h5:\n", + "\n", + " # Extract and print variable features\n", + " x1 = ext.get_var_features(h5)\n", + " print(\"x1\", x1.shape, \"\\n\", x1.round(1))" + ] + }, + { + "cell_type": "markdown", + "id": "04eab813", + "metadata": { + "collapsed": false + }, + "source": [ + "
\n", + "References\n", + "\n", + "* **Alvarez, Alejandro Marcos.** *Computational and theoretical synergies between linear optimization and supervised machine learning.* (2016). University of Liège.\n", + "* **Alvarez, Alejandro Marcos, Quentin Louveaux, and Louis Wehenkel.** *A machine learning-based approximation of strong branching.* INFORMS Journal on Computing 29.1 (2017): 185-195.\n", + "\n", + "
" + ] + } + ], + "metadata": { + "kernelspec": { + "display_name": "Python 3", + "language": "python", + "name": "python3" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.8.13" + } + }, + "nbformat": 4, + "nbformat_minor": 5 +} diff --git a/0.3/guide/features/index.html b/0.3/guide/features/index.html new file mode 100644 index 0000000..6842ba4 --- /dev/null +++ b/0.3/guide/features/index.html @@ -0,0 +1,768 @@ + + + + + + + + 3. Feature Extractors — MIPLearn 0.3 + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
+
+ + + + + + + + +
+ +
+
+
+
+ + + + +
+ + +
+ + + + + + +
+
+ + + + + + + + + +
+ + +
+ +
+ Contents +
+ +
+
+
+
+
+ +
+ + + +
+

3. Feature Extractors

+

In the previous page, we introduced training data collectors, which solve the optimization problem and collect raw training data, such as the optimal solution. In this page, we introduce feature extractors, which take the raw training data, stored in HDF5 files, and extract relevant information in order to train a machine learning model. We describe the extractors readily available in MIPLearn.

+
+

3.1. Overview

+

Feature extraction is an important step of the process of building a machine learning model because it helps to reduce the complexity of the data and convert it into a format that is more easily processed. Previous research has proposed converting absolute variable coefficients, for example, into relative values which are invariant to various transformations, such as problem scaling, making them more amenable to learning. Various other transformations have also been described.

+

In the framework, we treat data collection and feature extraction as two separate steps to accelerate the model development cycle. Specifically, collectors are typically time-consuming, as they often need to solve the problem to optimality, and therefore focus on collecting and storing all data that may or may not be relevant, in its raw format. Feature extractors, on the other hand, focus entirely on filtering the data and improving its representation, and are therefore much faster to run. +Experimenting with new data representations, therefore, can be done without resolving the instances.

+

In MIPLearn, extractors implement the abstract class FeatureExtractor, which has methods that take as input an H5File and produce either: (i) instance features, which describe the entire instances; (ii) variable features, which describe a particular decision variables; or (iii) constraint features, which describe a particular constraint. The extractor is free to implement only a +subset of these methods, if it is known that it will not be used with a machine learning component that requires the other types of features.

+
+
+

3.2. H5FieldsExtractor

+

H5FieldsExtractor, the most simple extractor in MIPLearn, simple extracts data that is already available in the HDF5 file, assembles it into a matrix and returns it as-is. The fields used to build instance, variable and constraint features are user-specified. The class also performs checks to ensure that the shapes of the returned matrices make sense.

+
+

Example

+

The example below demonstrates the usage of H5FieldsExtractor in a randomly generated instance of the multi-dimensional knapsack problem.

+
+
[1]:
+
+
+
from glob import glob
+from shutil import rmtree
+
+import numpy as np
+from scipy.stats import uniform, randint
+
+from miplearn.collectors.basic import BasicCollector
+from miplearn.features.fields import H5FieldsExtractor
+from miplearn.h5 import H5File
+from miplearn.io import save
+from miplearn.problems.multiknapsack import (
+    MultiKnapsackGenerator,
+    build_multiknapsack_model
+)
+
+# Set random seed to make example reproducible
+np.random.seed(42)
+
+# Generate some random multiknapsack instances
+rmtree("data/multiknapsack/", ignore_errors=True)
+save(
+    MultiKnapsackGenerator(
+        n=randint(low=10, high=11),
+        m=randint(low=5, high=6),
+        w=uniform(loc=0, scale=1000),
+        K=uniform(loc=100, scale=0),
+        u=uniform(loc=1, scale=0),
+        alpha=uniform(loc=0.25, scale=0),
+        w_jitter=uniform(loc=0.95, scale=0.1),
+        p_jitter=uniform(loc=0.75, scale=0.5),
+        fix_w=True,
+    ).generate(10),
+    "data/multiknapsack"
+)
+
+# Run the basic collector
+BasicCollector().collect(
+    glob("data/multiknapsack/*"),
+    build_multiknapsack_model,
+    n_jobs=4,
+)
+
+ext = H5FieldsExtractor(
+    # Use as instance features the value of the LP relaxation and the
+    # vector of objective coefficients.
+    instance_fields=[
+        "lp_obj_value",
+        "static_var_obj_coeffs",
+    ],
+    # For each variable, use as features the optimal value of the LP
+    # relaxation, the variable objective coefficient, the variable's
+    # value its reduced cost.
+    var_fields=[
+        "lp_obj_value",
+        "static_var_obj_coeffs",
+        "lp_var_values",
+        "lp_var_reduced_costs",
+    ],
+    # For each constraint, use as features the RHS, dual value and slack.
+    constr_fields=[
+        "static_constr_rhs",
+        "lp_constr_dual_values",
+        "lp_constr_slacks",
+    ]
+)
+
+with H5File("data/multiknapsack/00000.h5") as h5:
+    # Extract and print instance features
+    x1 = ext.get_instance_features(h5)
+    print("instance features", x1.shape, "\n", x1)
+
+    # Extract and print variable features
+    x2 = ext.get_var_features(h5)
+    print("variable features", x2.shape, "\n", x2)
+
+    # Extract and print constraint features
+    x3 = ext.get_constr_features(h5)
+    print("constraint features", x3.shape, "\n", x3)
+
+
+
+
+
+
+
+
+instance features (11,)
+ [-1531.24308771  -350.          -692.          -454.
+  -709.          -605.          -543.          -321.
+  -674.          -571.          -341.        ]
+variable features (10, 4)
+ [[-1.53124309e+03 -3.50000000e+02  0.00000000e+00  9.43468018e+01]
+ [-1.53124309e+03 -6.92000000e+02  2.51703322e-01  0.00000000e+00]
+ [-1.53124309e+03 -4.54000000e+02  0.00000000e+00  8.25504150e+01]
+ [-1.53124309e+03 -7.09000000e+02  1.11373022e-01  0.00000000e+00]
+ [-1.53124309e+03 -6.05000000e+02  1.00000000e+00 -1.26055283e+02]
+ [-1.53124309e+03 -5.43000000e+02  0.00000000e+00  1.68693771e+02]
+ [-1.53124309e+03 -3.21000000e+02  1.07488781e-01  0.00000000e+00]
+ [-1.53124309e+03 -6.74000000e+02  8.82293701e-01  0.00000000e+00]
+ [-1.53124309e+03 -5.71000000e+02  0.00000000e+00  1.41129074e+02]
+ [-1.53124309e+03 -3.41000000e+02  1.28830120e-01  0.00000000e+00]]
+constraint features (5, 3)
+ [[ 1.3100000e+03 -1.5978307e-01  0.0000000e+00]
+ [ 9.8800000e+02 -3.2881632e-01  0.0000000e+00]
+ [ 1.0040000e+03 -4.0601316e-01  0.0000000e+00]
+ [ 1.2690000e+03 -1.3659772e-01  0.0000000e+00]
+ [ 1.0070000e+03 -2.8800571e-01  0.0000000e+00]]
+
+
+
+

Warning

+

You should ensure that the number of features remains the same for all relevant HDF5 files. In the previous example, to illustrate this issue, we used variable objective coefficients as instance features. While this is allowed, note that this requires all problem instances to have the same number of variables; otherwise the number of features would vary from instance to instance and MIPLearn would be unable to concatenate the matrices.

+
+
+
+
+

3.3. AlvLouWeh2017Extractor

+

Alvarez, Louveaux and Wehenkel (2017) proposed a set features to describe a particular decision variable in a given node of the branch-and-bound tree, and applied it to the problem of mimicking strong branching decisions. The class AlvLouWeh2017Extractor implements a subset of these features (40 out of 64), which are available outside of the branch-and-bound tree. Some features are derived from the static defintion of the problem (i.e. from objective function and +constraint data), while some features are derived from the solution to the LP relaxation. The features have been designed to be: (i) independent of the size of the problem; (ii) invariant with respect to irrelevant problem transformations, such as row and column permutation; and (iii) independent of the scale of the problem. We refer to the paper for a more complete description.

+
+

Example

+
+
[5]:
+
+
+
from miplearn.features.AlvLouWeh2017 import AlvLouWeh2017Extractor
+from miplearn.h5 import H5File
+
+# Build the extractor
+ext = AlvLouWeh2017Extractor()
+
+# Open previously-created multiknapsack training data
+with H5File("data/multiknapsack/00000.h5") as h5:
+
+    # Extract and print variable features
+    x1 = ext.get_var_features(h5)
+    print("x1", x1.shape, "\n", x1.round(1))
+
+
+
+
+
+
+
+
+x1 (10, 40)
+ [[-1.00e+00  1.00e+20  1.00e-01  1.00e+00  0.00e+00  1.00e+00  6.00e-01
+   0.00e+00  0.00e+00  0.00e+00  0.00e+00  0.00e+00  0.00e+00  0.00e+00
+   0.00e+00  1.00e+00  6.00e-01  1.00e+00  1.75e+01  1.00e+00  2.00e-01
+   1.00e+00  0.00e+00  0.00e+00  0.00e+00  0.00e+00  0.00e+00  0.00e+00
+   0.00e+00  0.00e+00  0.00e+00  0.00e+00  0.00e+00  0.00e+00  0.00e+00
+   0.00e+00  1.00e+00 -1.00e+00  0.00e+00  1.00e+20]
+ [-1.00e+00  1.00e+20  1.00e-01  1.00e+00  1.00e-01  1.00e+00  1.00e+00
+   0.00e+00  0.00e+00  0.00e+00  0.00e+00  0.00e+00  0.00e+00  0.00e+00
+   0.00e+00  1.00e+00  7.00e-01  1.00e+00  5.10e+00  1.00e+00  2.00e-01
+   1.00e+00  0.00e+00  0.00e+00  0.00e+00  0.00e+00  0.00e+00  0.00e+00
+   0.00e+00  0.00e+00  0.00e+00  0.00e+00  0.00e+00  0.00e+00  0.00e+00
+   3.00e-01 -1.00e+00 -1.00e+00  0.00e+00  0.00e+00]
+ [-1.00e+00  1.00e+20  1.00e-01  1.00e+00  0.00e+00  1.00e+00  9.00e-01
+   0.00e+00  0.00e+00  0.00e+00  0.00e+00  0.00e+00  0.00e+00  0.00e+00
+   0.00e+00  1.00e+00  5.00e-01  1.00e+00  1.30e+01  1.00e+00  2.00e-01
+   1.00e+00  0.00e+00  0.00e+00  0.00e+00  0.00e+00  0.00e+00  0.00e+00
+   0.00e+00  0.00e+00  0.00e+00  0.00e+00  0.00e+00  0.00e+00  0.00e+00
+   0.00e+00  1.00e+00 -1.00e+00  0.00e+00  1.00e+20]
+ [-1.00e+00  1.00e+20  1.00e-01  1.00e+00  2.00e-01  1.00e+00  9.00e-01
+   0.00e+00  0.00e+00  0.00e+00  0.00e+00  0.00e+00  0.00e+00  0.00e+00
+   0.00e+00  1.00e+00  8.00e-01  1.00e+00  3.40e+00  1.00e+00  2.00e-01
+   1.00e+00  1.00e-01  0.00e+00  0.00e+00  0.00e+00  0.00e+00  0.00e+00
+   0.00e+00  0.00e+00  0.00e+00  0.00e+00  0.00e+00  0.00e+00  0.00e+00
+   1.00e-01 -1.00e+00 -1.00e+00  0.00e+00  0.00e+00]
+ [-1.00e+00  1.00e+20  1.00e-01  1.00e+00  1.00e-01  1.00e+00  7.00e-01
+   0.00e+00  0.00e+00  0.00e+00  0.00e+00  0.00e+00  0.00e+00  0.00e+00
+   0.00e+00  1.00e+00  6.00e-01  1.00e+00  3.80e+00  1.00e+00  2.00e-01
+   1.00e+00  0.00e+00  0.00e+00  0.00e+00  0.00e+00  0.00e+00  0.00e+00
+   0.00e+00  0.00e+00  0.00e+00  0.00e+00  0.00e+00  0.00e+00  0.00e+00
+   0.00e+00 -1.00e+00 -1.00e+00  0.00e+00  0.00e+00]
+ [-1.00e+00  1.00e+20  1.00e-01  1.00e+00  1.00e-01  1.00e+00  8.00e-01
+   0.00e+00  0.00e+00  0.00e+00  0.00e+00  0.00e+00  0.00e+00  0.00e+00
+   0.00e+00  1.00e+00  7.00e-01  1.00e+00  3.30e+00  1.00e+00  2.00e-01
+   1.00e+00  0.00e+00  0.00e+00  0.00e+00  0.00e+00  0.00e+00  0.00e+00
+   0.00e+00  0.00e+00  0.00e+00  0.00e+00  0.00e+00  0.00e+00  0.00e+00
+   0.00e+00  1.00e+00 -1.00e+00  0.00e+00  1.00e+20]
+ [-1.00e+00  1.00e+20  1.00e-01  1.00e+00  0.00e+00  1.00e+00  3.00e-01
+   0.00e+00  0.00e+00  0.00e+00  0.00e+00  0.00e+00  0.00e+00  0.00e+00
+   0.00e+00  1.00e+00  1.00e+00  1.00e+00  5.70e+00  1.00e+00  1.00e-01
+   1.00e+00  0.00e+00  0.00e+00  0.00e+00  0.00e+00  0.00e+00  0.00e+00
+   0.00e+00  0.00e+00  0.00e+00  0.00e+00  0.00e+00  0.00e+00  0.00e+00
+   1.00e-01 -1.00e+00 -1.00e+00  0.00e+00  0.00e+00]
+ [-1.00e+00  1.00e+20  1.00e-01  1.00e+00  1.00e-01  1.00e+00  6.00e-01
+   0.00e+00  0.00e+00  0.00e+00  0.00e+00  0.00e+00  0.00e+00  0.00e+00
+   0.00e+00  1.00e+00  8.00e-01  1.00e+00  6.80e+00  1.00e+00  2.00e-01
+   1.00e+00  0.00e+00  0.00e+00  0.00e+00  0.00e+00  0.00e+00  0.00e+00
+   0.00e+00  0.00e+00  0.00e+00  0.00e+00  0.00e+00  0.00e+00  0.00e+00
+   1.00e-01 -1.00e+00 -1.00e+00  0.00e+00  0.00e+00]
+ [-1.00e+00  1.00e+20  1.00e-01  1.00e+00  4.00e-01  1.00e+00  6.00e-01
+   0.00e+00  0.00e+00  0.00e+00  0.00e+00  0.00e+00  0.00e+00  0.00e+00
+   0.00e+00  1.00e+00  8.00e-01  1.00e+00  1.40e+00  1.00e+00  1.00e-01
+   1.00e+00  1.00e-01  0.00e+00  0.00e+00  0.00e+00  0.00e+00  0.00e+00
+   0.00e+00  0.00e+00  0.00e+00  0.00e+00  0.00e+00  0.00e+00  0.00e+00
+   0.00e+00  1.00e+00 -1.00e+00  0.00e+00  1.00e+20]
+ [-1.00e+00  1.00e+20  1.00e-01  1.00e+00  0.00e+00  1.00e+00  5.00e-01
+   0.00e+00  0.00e+00  0.00e+00  0.00e+00  0.00e+00  0.00e+00  0.00e+00
+   0.00e+00  1.00e+00  5.00e-01  1.00e+00  7.60e+00  1.00e+00  1.00e-01
+   1.00e+00  0.00e+00  0.00e+00  0.00e+00  0.00e+00  0.00e+00  0.00e+00
+   0.00e+00  0.00e+00  0.00e+00  0.00e+00  0.00e+00  0.00e+00  0.00e+00
+   1.00e-01 -1.00e+00 -1.00e+00  0.00e+00  0.00e+00]]
+
+
+
+

References

+
    +

  • Alvarez, Alejandro Marcos. Computational and theoretical synergies between linear optimization and supervised machine learning. (2016). University of Liège.

    • +

  • Alvarez, Alejandro Marcos, Quentin Louveaux, and Louis Wehenkel. A machine learning-based approximation of strong branching. INFORMS Journal on Computing 29.1 (2017): 185-195.

    • +
+
+
+
+
+ + +
+ + +
+ + 2. Training Data Collectors + 4. Primal Components + +
+ +
+
+
+
+

+ + © Copyright 2020-2022, UChicago Argonne, LLC.
+

+
+
+
+ + +
+
+ + + + + + \ No newline at end of file diff --git a/0.3/guide/primal.ipynb b/0.3/guide/primal.ipynb new file mode 100644 index 0000000..db74fb1 --- /dev/null +++ b/0.3/guide/primal.ipynb @@ -0,0 +1,290 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "id": "880cf4c7-d3c4-4b92-85c7-04a32264cdae", + "metadata": {}, + "source": [ + "# Primal Components\n", + "\n", + "In MIPLearn, a **primal component** is class that uses machine learning to predict a (potentially partial) assignment of values to the decision variables of the problem. Predicting high-quality primal solutions may be beneficial, as they allow the MIP solver to prune potentially large portions of the search space. Alternatively, if proof of optimality is not required, the MIP solver can be used to complete the partial solution generated by the machine learning model and and double-check its feasibility. MIPLearn allows both of these usage patterns.\n", + "\n", + "In this page, we describe the four primal components currently included in MIPLearn, which employ machine learning in different ways. Each component is highly configurable, and accepts an user-provided machine learning model, which it uses for all predictions. Each component can also be configured to provide the solution to the solver in multiple ways, depending on whether proof of optimality is required.\n", + "\n", + "## Primal component actions\n", + "\n", + "Before presenting the primal components themselves, we briefly discuss the three ways a solution may be provided to the solver. Each approach has benefits and limitations, which we also discuss in this section. All primal components can be configured to use any of the following approaches.\n", + "\n", + "The first approach is to provide the solution to the solver as a **warm start**. This is implemented by the class [SetWarmStart](SetWarmStart). The main advantage is that this method maintains all optimality and feasibility guarantees of the MIP solver, while still providing significant performance benefits for various classes of problems. If the machine learning model is able to predict multiple solutions, it is also possible to set multiple warm starts. In this case, the solver evaluates each warm start, discards the infeasible ones, then proceeds with the one that has the best objective value. The main disadvantage of this approach, compared to the next two, is that it provides relatively modest speedups for most problem classes, and no speedup at all for many others, even when the machine learning predictions are 100% accurate.\n", + "\n", + "[SetWarmStart]: ../../api/components/#miplearn.components.primal.actions.SetWarmStart\n", + "\n", + "The second approach is to **fix the decision variables** to their predicted values, then solve a restricted optimization problem on the remaining variables. This approach is implemented by the class `FixVariables`. The main advantage is its potential speedup: if machine learning can accurately predict values for a significant portion of the decision variables, then the MIP solver can typically complete the solution in a small fraction of the time it would take to find the same solution from scratch. The main disadvantage of this approach is that it loses optimality guarantees; that is, the complete solution found by the MIP solver may no longer be globally optimal. Also, if the machine learning predictions are not sufficiently accurate, there might not even be a feasible assignment for the variables that were left free.\n", + "\n", + "Finally, the third approach, which tries to strike a balance between the two previous ones, is to **enforce proximity** to a given solution. This strategy is implemented by the class `EnforceProximity`. More precisely, given values $\\bar{x}_1,\\ldots,\\bar{x}_n$ for a subset of binary decision variables $x_1,\\ldots,x_n$, this approach adds the constraint\n", + "\n", + "$$\n", + "\\sum_{i : \\bar{x}_i=0} x_i + \\sum_{i : \\bar{x}_i=1} \\left(1 - x_i\\right) \\leq k,\n", + "$$\n", + "to the problem, where $k$ is a user-defined parameter, which indicates how many of the predicted variables are allowed to deviate from the machine learning suggestion. The main advantage of this approach, compared to fixing variables, is its tolerance to lower-quality machine learning predictions. Its main disadvantage is that it typically leads to smaller speedups, especially for larger values of $k$. This approach also loses optimality guarantees.\n", + "\n", + "## Memorizing primal component\n", + "\n", + "A simple machine learning strategy for the prediction of primal solutions is to memorize all distinct solutions seen during training, then try to predict, during inference time, which of those memorized solutions are most likely to be feasible and to provide a good objective value for the current instance. The most promising solutions may alternatively be combined into a single partial solution, which is then provided to the MIP solver. Both variations of this strategy are implemented by the `MemorizingPrimalComponent` class. Note that it is only applicable if the problem size, and in fact if the meaning of the decision variables, remains the same across problem instances.\n", + "\n", + "More precisely, let $I_1,\\ldots,I_n$ be the training instances, and let $\\bar{x}^1,\\ldots,\\bar{x}^n$ be their respective optimal solutions. Given a new instance $I_{n+1}$, `MemorizingPrimalComponent` expects a user-provided binary classifier that assigns (through the `predict_proba` method, following scikit-learn's conventions) a score $\\delta_i$ to each solution $\\bar{x}^i$, such that solutions with higher score are more likely to be good solutions for $I_{n+1}$. The features provided to the classifier are the instance features computed by an user-provided extractor. Given these scores, the component then performs one of the following to actions, as decided by the user:\n", + "\n", + "1. Selects the top $k$ solutions with the highest scores and provides them to the solver; this is implemented by `SelectTopSolutions`, and it is typically used with the `SetWarmStart` action.\n", + "\n", + "2. Merges the top $k$ solutions into a single partial solution, then provides it to the solver. This is implemented by `MergeTopSolutions`. More precisely, suppose that the machine learning regressor ordered the solutions in the sequence $\\bar{x}^{i_1},\\ldots,\\bar{x}^{i_n}$, with the most promising solutions appearing first, and with ties being broken arbitrarily. The component starts by keeping only the $k$ most promising solutions $\\bar{x}^{i_1},\\ldots,\\bar{x}^{i_k}$. Then it computes, for each binary decision variable $x_l$, its average assigned value $\\tilde{x}_l$:\n", + "$$\n", + " \\tilde{x}_l = \\frac{1}{k} \\sum_{j=1}^k \\bar{x}^{i_j}_l.\n", + "$$\n", + " Finally, the component constructs a merged solution $y$, defined as:\n", + "$$\n", + " y_j = \\begin{cases}\n", + " 0 & \\text{ if } \\tilde{x}_l \\le \\theta_0 \\\\\n", + " 1 & \\text{ if } \\tilde{x}_l \\ge \\theta_1 \\\\\n", + " \\square & \\text{otherwise,}\n", + " \\end{cases}\n", + "$$\n", + " where $\\theta_0$ and $\\theta_1$ are user-specified parameters, and where $\\square$ indicates that the variable is left undefined. The solution $y$ is then provided by the solver using any of the three approaches defined in the previous section.\n", + "\n", + "The above specification of `MemorizingPrimalComponent` is meant to be as general as possible. Simpler strategies can be implemented by configuring this component in specific ways. For example, a simpler approach employed in the literature is to collect all optimal solutions, then provide the entire list of solutions to the solver as warm starts, without any filtering or post-processing. This strategy can be implemented with `MemorizingPrimalComponent` by using a model that returns a constant value for all solutions (e.g. [scikit-learn's DummyClassifier][DummyClassifier]), then selecting the top $n$ (instead of $k$) solutions. See example below. Another simple approach is taking the solution to the most similar instance, and using it, by itself, as a warm start. This can be implemented by using a model that computes distances between the current instance and the training ones (e.g. [scikit-learn's KNeighborsClassifier][KNeighborsClassifier]), then select the solution to the nearest one. See also example below. More complex strategies, of course, can also be configured.\n", + "\n", + "[DummyClassifier]: https://scikit-learn.org/stable/modules/generated/sklearn.dummy.DummyClassifier.html\n", + "[KNeighborsClassifier]: https://scikit-learn.org/stable/modules/generated/sklearn.neighbors.KNeighborsClassifier.html\n", + "\n", + "### Examples" + ] + }, + { + "cell_type": "code", + "execution_count": 3, + "id": "94907996", + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "\n", + "from sklearn.dummy import DummyClassifier\n", + "from sklearn.neighbors import KNeighborsClassifier\n", + "\n", + "from miplearn.components.primal.actions import (\n", + " SetWarmStart,\n", + " FixVariables,\n", + " EnforceProximity,\n", + ")\n", + "from miplearn.components.primal.mem import (\n", + " MemorizingPrimalComponent,\n", + " SelectTopSolutions,\n", + " MergeTopSolutions,\n", + ")\n", + "from miplearn.extractors.dummy import DummyExtractor\n", + "from miplearn.extractors.fields import H5FieldsExtractor\n", + "\n", + "# Configures a memorizing primal component that collects\n", + "# all distinct solutions seen during training and provides\n", + "# them to the solver without any filtering or post-processing.\n", + "comp1 = MemorizingPrimalComponent(\n", + " clf=DummyClassifier(),\n", + " extractor=DummyExtractor(),\n", + " constructor=SelectTopSolutions(1_000_000),\n", + " action=SetWarmStart(),\n", + ")\n", + "\n", + "# Configures a memorizing primal component that finds the\n", + "# training instance with the closest objective function, then\n", + "# fixes the decision variables to the values they assumed\n", + "# at the optimal solution for that instance.\n", + "comp2 = MemorizingPrimalComponent(\n", + " clf=KNeighborsClassifier(n_neighbors=1),\n", + " extractor=H5FieldsExtractor(\n", + " instance_fields=[\"static_var_obj_coeffs\"],\n", + " ),\n", + " constructor=SelectTopSolutions(1),\n", + " action=FixVariables(),\n", + ")\n", + "\n", + "# Configures a memorizing primal component that finds the distinct\n", + "# solutions to the 10 most similar training problem instances,\n", + "# selects the 3 solutions that were most often optimal to these\n", + "# training instances, combines them into a single partial solution,\n", + "# then enforces proximity, allowing at most 3 variables to deviate\n", + "# from the machine learning suggestion.\n", + "comp3 = MemorizingPrimalComponent(\n", + " clf=KNeighborsClassifier(n_neighbors=10),\n", + " extractor=H5FieldsExtractor(instance_fields=[\"static_var_obj_coeffs\"]),\n", + " constructor=MergeTopSolutions(k=3, thresholds=[0.25, 0.75]),\n", + " action=EnforceProximity(3),\n", + ")" + ] + }, + { + "cell_type": "markdown", + "id": "6b854305", + "metadata": { + "collapsed": false + }, + "source": [ + "## Independent vars primal component\n", + "\n", + "Instead of memorizing previously-seen primal solutions, it is also natural to use machine learning models to directly predict the values of the decision variables, constructing a solution from scratch. This approach has the benefit of potentially constructing novel high-quality solutions, never observed in the training data. Two variations of this strategy are supported by MIPLearn: (i) predicting the values of the decision variables independently, using multiple ML models; or (ii) predicting the values jointly, with a single model. We describe the first variation in this section, and the second variation in the next section.\n", + "\n", + "Let $I_1,\\ldots,I_n$ be the training instances, and let $\\bar{x}^1,\\ldots,\\bar{x}^n$ be their respective optimal solutions. For each binary decision variable $x_j$, the component `IndependentVarsPrimalComponent` creates a copy of a user-provided binary classifier and trains it to predict the optimal value of $x_j$, given $\\bar{x}^1_j,\\ldots,\\bar{x}^n_j$ as training labels. The features provided to the model are the variable features computed by an user-provided extractor. During inference time, the component uses these $n$ binary classifiers to construct a solution and provides it to the solver using one of the available actions.\n", + "\n", + "Three issues often arise in practice when using this approach:\n", + "\n", + " 1. For certain binary variables $x_j$, it is frequently the case that its optimal value is either always zero or always one in the training dataset, which poses problems to some standard scikit-learn classifiers, since they do not expect a single class. The wrapper `SingleClassFix` can be used to fix this issue (see example below).\n", + "2. It is also frequently the case that machine learning classifier can only reliably predict the values of some variables with high accuracy, not all of them. In this situation, instead of computing a complete primal solution, it may be more beneficial to construct a partial solution containing values only for the variables for which the ML made a high-confidence prediction. The meta-classifier `MinProbabilityClassifier` can be used for this purpose. It asks the base classifier for the probability of the value being zero or one (using the `predict_proba` method) and erases from the primal solution all values whose probabilities are below a given threshold.\n", + "3. To make multiple copies of the provided ML classifier, MIPLearn uses the standard `sklearn.base.clone` method, which may not be suitable for classifiers from other frameworks. To handle this, it is possible to override the clone function using the `clone_fn` constructor argument.\n", + "\n", + "### Examples" + ] + }, + { + "cell_type": "code", + "execution_count": 4, + "id": "f5024983", + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "from sklearn.linear_model import LogisticRegression\n", + "from miplearn.classifiers.minprob import MinProbabilityClassifier\n", + "from miplearn.classifiers.singleclass import SingleClassFix\n", + "from miplearn.components.primal.indep import IndependentVarsPrimalComponent\n", + "from miplearn.extractors.AlvLouWeh2017 import AlvLouWeh2017Extractor\n", + "from miplearn.solvers.learning import LearningSolver\n", + "from miplearn.components.primal.actions import SetWarmStart\n", + "\n", + "# Configures a primal component that independently predicts the value of each\n", + "# binary variable using logistic regression and provides it to the solver as\n", + "# warm start. Erases predictions with probability less than 99%; applies\n", + "# single-class fix; and uses AlvLouWeh2017 features.\n", + "comp = IndependentVarsPrimalComponent(\n", + " base_clf=SingleClassFix(\n", + " MinProbabilityClassifier(\n", + " base_clf=LogisticRegression(),\n", + " thresholds=[0.99, 0.99],\n", + " ),\n", + " ),\n", + " extractor=AlvLouWeh2017Extractor(),\n", + " action=SetWarmStart(),\n", + ")" + ] + }, + { + "cell_type": "markdown", + "id": "dcb10079", + "metadata": { + "collapsed": false + }, + "source": [ + "## Joint vars primal component\n", + "In the previous subsection, we used multiple machine learning models to independently predict the values of the binary decision variables. When these values are correlated, an alternative approach is to jointly predict the values of all binary variables using a single machine learning model. This strategy is implemented by `JointVarsPrimalComponent`. Compared to the previous ones, this component is much more straightforwad. It simply extracts instance features, using the user-provided feature extractor, then directly trains the user-provided binary classifier (using the `fit` method), without making any copies. The trained classifier is then used to predict entire solutions (using the `predict` method), which are given to the solver using one of the previously discussed methods. In the example below, we illustrate the usage of this component with a simple feed-forward neural network.\n", + "\n", + "`JointVarsPrimalComponent` can also be used to implement strategies that use multiple machine learning models, but not indepedently. For example, a common strategy in multioutput prediction is building a *classifier chain*. In this approach, the first decision variable is predicted using the instance features alone; but the $n$-th decision variable is predicted using the instance features plus the predicted values of the $n-1$ previous variables. This can be easily implemented using scikit-learn's `ClassifierChain` estimator, as shown in the example below.\n", + "\n", + "### Examples" + ] + }, + { + "cell_type": "code", + "execution_count": 5, + "id": "c98f7eb8", + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "from sklearn.multioutput import ClassifierChain\n", + "from sklearn.neural_network import MLPClassifier\n", + "from miplearn.components.primal.joint import JointVarsPrimalComponent\n", + "from miplearn.extractors.fields import H5FieldsExtractor\n", + "from miplearn.solvers.learning import LearningSolver\n", + "from miplearn.components.primal.actions import SetWarmStart\n", + "\n", + "# Configures a primal component that uses a feedforward neural network\n", + "# to jointly predict the values of the binary variables, based on the\n", + "# objective cost function, and provides the solution to the solver as\n", + "# a warm start.\n", + "comp = JointVarsPrimalComponent(\n", + " clf=MLPClassifier(),\n", + " extractor=H5FieldsExtractor(\n", + " instance_fields=['static_var_obj_coeffs'],\n", + " ),\n", + " action=SetWarmStart(),\n", + ")\n", + "\n", + "# Configures a primal component that uses a chain of logistic regression\n", + "# models to jointly predict the values of the binary variables, based on\n", + "# the objective function.\n", + "comp = JointVarsPrimalComponent(\n", + " clf=ClassifierChain(SingleClassFix(LogisticRegression())),\n", + " extractor=H5FieldsExtractor(\n", + " instance_fields=['static_var_obj_coeffs'],\n", + " ),\n", + " action=SetWarmStart(),\n", + ")" + ] + }, + { + "cell_type": "markdown", + "id": "92461394", + "metadata": { + "collapsed": false + }, + "source": [ + "## Expert primal component\n", + "\n", + "Before spending time and effort choosing a machine learning strategy and tweaking its parameters, it is usually a good idea to evaluate what would be the performance impact of the model if its predictions were 100% accurate. This is especially important for the prediction of warm starts, since they are not always very beneficial. To simplify this task, MIPLearn provides `ExpertPrimalComponent`, a component which simply loads the optimal solution from the HDF5 file, assuming that it has already been computed, then directly provides it to the solver using one of the available methods. This component is useful in benchmarks, to evaluate how close to the best theoretical performance the machine learning components are.\n", + "\n", + "### Example" + ] + }, + { + "cell_type": "code", + "execution_count": 4, + "id": "fb7dbdd0", + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "from miplearn.components.primal.expert import ExpertPrimalComponent\n", + "from miplearn.components.primal.actions import SetWarmStart\n", + "\n", + "# Configures an expert primal component, which reads a pre-computed\n", + "# optimal solution from the HDF5 file and provides it to the solver\n", + "# as warm start.\n", + "comp = ExpertPrimalComponent(\n", + " action=SetWarmStart()\n", + ")" + ] + } + ], + "metadata": { + "kernelspec": { + "display_name": "Python 3", + "language": "python", + "name": "python3" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.8.13" + } + }, + "nbformat": 4, + "nbformat_minor": 5 +} diff --git a/0.3/guide/primal/index.html b/0.3/guide/primal/index.html new file mode 100644 index 0000000..8d64ef3 --- /dev/null +++ b/0.3/guide/primal/index.html @@ -0,0 +1,774 @@ + + + + + + + + 4. Primal Components — MIPLearn 0.3 + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
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+

4. Primal Components

+

In MIPLearn, a primal component is class that uses machine learning to predict a (potentially partial) assignment of values to the decision variables of the problem. Predicting high-quality primal solutions may be beneficial, as they allow the MIP solver to prune potentially large portions of the search space. Alternatively, if proof of optimality is not required, the MIP solver can be used to complete the partial solution generated by the machine learning model and and double-check its +feasibility. MIPLearn allows both of these usage patterns.

+

In this page, we describe the four primal components currently included in MIPLearn, which employ machine learning in different ways. Each component is highly configurable, and accepts an user-provided machine learning model, which it uses for all predictions. Each component can also be configured to provide the solution to the solver in multiple ways, depending on whether proof of optimality is required.

+
+

4.1. Primal component actions

+

Before presenting the primal components themselves, we briefly discuss the three ways a solution may be provided to the solver. Each approach has benefits and limitations, which we also discuss in this section. All primal components can be configured to use any of the following approaches.

+

The first approach is to provide the solution to the solver as a warm start. This is implemented by the class SetWarmStart. The main advantage is that this method maintains all optimality and feasibility guarantees of the MIP solver, while still providing significant performance benefits for various classes of problems. If the machine learning model is able to predict multiple solutions, it is also possible to set multiple warm starts. In this case, the solver evaluates +each warm start, discards the infeasible ones, then proceeds with the one that has the best objective value. The main disadvantage of this approach, compared to the next two, is that it provides relatively modest speedups for most problem classes, and no speedup at all for many others, even when the machine learning predictions are 100% accurate.

+

The second approach is to fix the decision variables to their predicted values, then solve a restricted optimization problem on the remaining variables. This approach is implemented by the class FixVariables. The main advantage is its potential speedup: if machine learning can accurately predict values for a significant portion of the decision variables, then the MIP solver can typically complete the solution in a small fraction of the time it would take to find the same solution from +scratch. The main disadvantage of this approach is that it loses optimality guarantees; that is, the complete solution found by the MIP solver may no longer be globally optimal. Also, if the machine learning predictions are not sufficiently accurate, there might not even be a feasible assignment for the variables that were left free.

+

Finally, the third approach, which tries to strike a balance between the two previous ones, is to enforce proximity to a given solution. This strategy is implemented by the class EnforceProximity. More precisely, given values \(\bar{x}_1,\ldots,\bar{x}_n\) for a subset of binary decision variables \(x_1,\ldots,x_n\), this approach adds the constraint

+
+\[\sum_{i : \bar{x}_i=0} x_i + \sum_{i : \bar{x}_i=1} \left(1 - x_i\right) \leq k,\]
+

to the problem, where \(k\) is a user-defined parameter, which indicates how many of the predicted variables are allowed to deviate from the machine learning suggestion. The main advantage of this approach, compared to fixing variables, is its tolerance to lower-quality machine learning predictions. Its main disadvantage is that it typically leads to smaller speedups, especially for larger values of \(k\). This approach also loses optimality guarantees.

+
+
+

4.2. Memorizing primal component

+

A simple machine learning strategy for the prediction of primal solutions is to memorize all distinct solutions seen during training, then try to predict, during inference time, which of those memorized solutions are most likely to be feasible and to provide a good objective value for the current instance. The most promising solutions may alternatively be combined into a single partial solution, which is then provided to the MIP solver. Both variations of this strategy are implemented by the +MemorizingPrimalComponent class. Note that it is only applicable if the problem size, and in fact if the meaning of the decision variables, remains the same across problem instances.

+

More precisely, let \(I_1,\ldots,I_n\) be the training instances, and let \(\bar{x}^1,\ldots,\bar{x}^n\) be their respective optimal solutions. Given a new instance \(I_{n+1}\), MemorizingPrimalComponent expects a user-provided binary classifier that assigns (through the predict_proba method, following scikit-learn’s conventions) a score \(\delta_i\) to each solution \(\bar{x}^i\), such that solutions with higher score are more likely to be good solutions for +\(I_{n+1}\). The features provided to the classifier are the instance features computed by an user-provided extractor. Given these scores, the component then performs one of the following to actions, as decided by the user:

+
    +

  1. Selects the top \(k\) solutions with the highest scores and provides them to the solver; this is implemented by SelectTopSolutions, and it is typically used with the SetWarmStart action.

    2. +

  2. Merges the top \(k\) solutions into a single partial solution, then provides it to the solver. This is implemented by MergeTopSolutions. More precisely, suppose that the machine learning regressor ordered the solutions in the sequence \(\bar{x}^{i_1},\ldots,\bar{x}^{i_n}\), with the most promising solutions appearing first, and with ties being broken arbitrarily. The component starts by keeping only the \(k\) most promising solutions \(\bar{x}^{i_1},\ldots,\bar{x}^{i_k}\). +Then it computes, for each binary decision variable \(x_l\), its average assigned value \(\tilde{x}_l\):

    +
    +\[\tilde{x}_l = \frac{1}{k} \sum_{j=1}^k \bar{x}^{i_j}_l.\]
    +

    Finally, the component constructs a merged solution \(y\), defined as:

    +
    +\[\begin{split}y_j = \begin{cases} + 0 & \text{ if } \tilde{x}_l \le \theta_0 \\ + 1 & \text{ if } \tilde{x}_l \ge \theta_1 \\ + \square & \text{otherwise,} +\end{cases}\end{split}\]
    +

    where \(\theta_0\) and \(\theta_1\) are user-specified parameters, and where \(\square\) indicates that the variable is left undefined. The solution \(y\) is then provided by the solver using any of the three approaches defined in the previous section.

    +
    3. +
+

The above specification of MemorizingPrimalComponent is meant to be as general as possible. Simpler strategies can be implemented by configuring this component in specific ways. For example, a simpler approach employed in the literature is to collect all optimal solutions, then provide the entire list of solutions to the solver as warm starts, without any filtering or post-processing. This strategy can be implemented with MemorizingPrimalComponent by using a model that returns a constant +value for all solutions (e.g. scikit-learn’s DummyClassifier), then selecting the top \(n\) (instead of \(k\)) solutions. See example below. Another simple approach is taking the solution to the most similar instance, and using it, by itself, as a warm start. This can be implemented by using a model that computes distances between the current instance and the training ones (e.g. scikit-learn’s +KNeighborsClassifier), then select the solution to the nearest one. See also example below. More complex strategies, of course, can also be configured.

+
+

Examples

+
+
[3]:
+
+
+

from sklearn.dummy import DummyClassifier
+from sklearn.neighbors import KNeighborsClassifier
+
+from miplearn.components.primal.actions import (
+    SetWarmStart,
+    FixVariables,
+    EnforceProximity,
+)
+from miplearn.components.primal.mem import (
+    MemorizingPrimalComponent,
+    SelectTopSolutions,
+    MergeTopSolutions,
+)
+from miplearn.extractors.dummy import DummyExtractor
+from miplearn.extractors.fields import H5FieldsExtractor
+
+# Configures a memorizing primal component that collects
+# all distinct solutions seen during training and provides
+# them to the solver without any filtering or post-processing.
+comp1 = MemorizingPrimalComponent(
+    clf=DummyClassifier(),
+    extractor=DummyExtractor(),
+    constructor=SelectTopSolutions(1_000_000),
+    action=SetWarmStart(),
+)
+
+# Configures a memorizing primal component that finds the
+# training instance with the closest objective function, then
+# fixes the decision variables to the values they assumed
+# at the optimal solution for that instance.
+comp2 = MemorizingPrimalComponent(
+    clf=KNeighborsClassifier(n_neighbors=1),
+    extractor=H5FieldsExtractor(
+        instance_fields=["static_var_obj_coeffs"],
+    ),
+    constructor=SelectTopSolutions(1),
+    action=FixVariables(),
+)
+
+# Configures a memorizing primal component that finds the distinct
+# solutions to the 10 most similar training problem instances,
+# selects the 3 solutions that were most often optimal to these
+# training instances, combines them into a single partial solution,
+# then enforces proximity, allowing at most 3 variables to deviate
+# from the machine learning suggestion.
+comp3 = MemorizingPrimalComponent(
+    clf=KNeighborsClassifier(n_neighbors=10),
+    extractor=H5FieldsExtractor(instance_fields=["static_var_obj_coeffs"]),
+    constructor=MergeTopSolutions(k=3, thresholds=[0.25, 0.75]),
+    action=EnforceProximity(3),
+)
+
+
+
+
+
+
+

4.3. Independent vars primal component

+

Instead of memorizing previously-seen primal solutions, it is also natural to use machine learning models to directly predict the values of the decision variables, constructing a solution from scratch. This approach has the benefit of potentially constructing novel high-quality solutions, never observed in the training data. Two variations of this strategy are supported by MIPLearn: (i) predicting the values of the decision variables independently, using multiple ML models; or (ii) predicting +the values jointly, with a single model. We describe the first variation in this section, and the second variation in the next section.

+

Let \(I_1,\ldots,I_n\) be the training instances, and let \(\bar{x}^1,\ldots,\bar{x}^n\) be their respective optimal solutions. For each binary decision variable \(x_j\), the component IndependentVarsPrimalComponent creates a copy of a user-provided binary classifier and trains it to predict the optimal value of \(x_j\), given \(\bar{x}^1_j,\ldots,\bar{x}^n_j\) as training labels. The features provided to the model are the variable features computed by an user-provided +extractor. During inference time, the component uses these \(n\) binary classifiers to construct a solution and provides it to the solver using one of the available actions.

+

Three issues often arise in practice when using this approach:

+
    +

  1. For certain binary variables \(x_j\), it is frequently the case that its optimal value is either always zero or always one in the training dataset, which poses problems to some standard scikit-learn classifiers, since they do not expect a single class. The wrapper SingleClassFix can be used to fix this issue (see example below).

    2. +

  2. It is also frequently the case that machine learning classifier can only reliably predict the values of some variables with high accuracy, not all of them. In this situation, instead of computing a complete primal solution, it may be more beneficial to construct a partial solution containing values only for the variables for which the ML made a high-confidence prediction. The meta-classifier MinProbabilityClassifier can be used for this purpose. It asks the base classifier for the +probability of the value being zero or one (using the predict_proba method) and erases from the primal solution all values whose probabilities are below a given threshold.

    3. +

  3. To make multiple copies of the provided ML classifier, MIPLearn uses the standard sklearn.base.clone method, which may not be suitable for classifiers from other frameworks. To handle this, it is possible to override the clone function using the clone_fn constructor argument.

    4. +
+
+

Examples

+
+
[4]:
+
+
+
from sklearn.linear_model import LogisticRegression
+from miplearn.classifiers.minprob import MinProbabilityClassifier
+from miplearn.classifiers.singleclass import SingleClassFix
+from miplearn.components.primal.indep import IndependentVarsPrimalComponent
+from miplearn.extractors.AlvLouWeh2017 import AlvLouWeh2017Extractor
+from miplearn.solvers.learning import LearningSolver
+from miplearn.components.primal.actions import SetWarmStart
+
+# Configures a primal component that independently predicts the value of each
+# binary variable using logistic regression and provides it to the solver as
+# warm start. Erases predictions with probability less than 99%; applies
+# single-class fix; and uses AlvLouWeh2017 features.
+comp = IndependentVarsPrimalComponent(
+    base_clf=SingleClassFix(
+        MinProbabilityClassifier(
+            base_clf=LogisticRegression(),
+            thresholds=[0.99, 0.99],
+        ),
+    ),
+    extractor=AlvLouWeh2017Extractor(),
+    action=SetWarmStart(),
+)
+
+
+
+
+
+
+

4.4. Joint vars primal component

+

In the previous subsection, we used multiple machine learning models to independently predict the values of the binary decision variables. When these values are correlated, an alternative approach is to jointly predict the values of all binary variables using a single machine learning model. This strategy is implemented by JointVarsPrimalComponent. Compared to the previous ones, this component is much more straightforwad. It simply extracts instance features, using the user-provided feature +extractor, then directly trains the user-provided binary classifier (using the fit method), without making any copies. The trained classifier is then used to predict entire solutions (using the predict method), which are given to the solver using one of the previously discussed methods. In the example below, we illustrate the usage of this component with a simple feed-forward neural network.

+

JointVarsPrimalComponent can also be used to implement strategies that use multiple machine learning models, but not indepedently. For example, a common strategy in multioutput prediction is building a classifier chain. In this approach, the first decision variable is predicted using the instance features alone; but the \(n\)-th decision variable is predicted using the instance features plus the predicted values of the \(n-1\) previous variables. This can be easily implemented +using scikit-learn’s ClassifierChain estimator, as shown in the example below.

+
+

Examples

+
+
[5]:
+
+
+
from sklearn.multioutput import ClassifierChain
+from sklearn.neural_network import MLPClassifier
+from miplearn.components.primal.joint import JointVarsPrimalComponent
+from miplearn.extractors.fields import H5FieldsExtractor
+from miplearn.solvers.learning import LearningSolver
+from miplearn.components.primal.actions import SetWarmStart
+
+# Configures a primal component that uses a feedforward neural network
+# to jointly predict the values of the binary variables, based on the
+# objective cost function, and provides the solution to the solver as
+# a warm start.
+comp = JointVarsPrimalComponent(
+    clf=MLPClassifier(),
+    extractor=H5FieldsExtractor(
+        instance_fields=['static_var_obj_coeffs'],
+    ),
+    action=SetWarmStart(),
+)
+
+# Configures a primal component that uses a chain of logistic regression
+# models to jointly predict the values of the binary variables, based on
+# the objective function.
+comp = JointVarsPrimalComponent(
+    clf=ClassifierChain(SingleClassFix(LogisticRegression())),
+    extractor=H5FieldsExtractor(
+        instance_fields=['static_var_obj_coeffs'],
+    ),
+    action=SetWarmStart(),
+)
+
+
+
+
+
+
+

4.5. Expert primal component

+

Before spending time and effort choosing a machine learning strategy and tweaking its parameters, it is usually a good idea to evaluate what would be the performance impact of the model if its predictions were 100% accurate. This is especially important for the prediction of warm starts, since they are not always very beneficial. To simplify this task, MIPLearn provides ExpertPrimalComponent, a component which simply loads the optimal solution from the HDF5 file, assuming that it has already +been computed, then directly provides it to the solver using one of the available methods. This component is useful in benchmarks, to evaluate how close to the best theoretical performance the machine learning components are.

+
+

Example

+
+
[4]:
+
+
+
from miplearn.components.primal.expert import ExpertPrimalComponent
+from miplearn.components.primal.actions import SetWarmStart
+
+# Configures an expert primal component, which reads a pre-computed
+# optimal solution from the HDF5 file and provides it to the solver
+# as warm start.
+comp = ExpertPrimalComponent(
+    action=SetWarmStart()
+)
+
+
+
+
+
+
+ + +
+ + +
+ + 3. Feature Extractors + 5. Solvers + +
+ +
+
+
+
+

+ + © Copyright 2020-2022, UChicago Argonne, LLC.
+

+
+
+
+ + +
+
+ + + + + + \ No newline at end of file diff --git a/0.3/guide/problems.ipynb b/0.3/guide/problems.ipynb new file mode 100644 index 0000000..5f0a4f3 --- /dev/null +++ b/0.3/guide/problems.ipynb @@ -0,0 +1,1565 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "id": "f89436b4-5bc5-4ae3-a20a-522a2cd65274", + "metadata": {}, + "source": [ + "# Benchmark Problems\n", + "\n", + "## Overview\n", + "\n", + "Benchmark sets such as [MIPLIB](https://miplib.zib.de/) or [TSPLIB](http://comopt.ifi.uni-heidelberg.de/software/TSPLIB95/) are usually employed to evaluate the performance of conventional MIP solvers. Two shortcomings, unfortunately, make existing benchmark sets less than ideal for evaluating the performance of learning-enhanced MIP solvers: (i) while existing benchmark sets typically contain hundreds or thousands of instances, machine learning (ML) methods typically benefit from having orders of magnitude more instances available for training; (ii) current machine learning methods typically provide best performance on sets of homogeneous instances, buch general-purpose benchmark sets contain relatively few examples of each problem type.\n", + "\n", + "To tackle this challenge, MIPLearn provides random instance generators for a wide variety of classical optimization problems, covering applications from different fields, that can be used to evaluate new learning-enhanced MIP techniques in a measurable and reproducible way. As of MIPLearn 0.3, nine problem generators are available, each customizable with user-provided probability distribution and flexible parameters. The generators can be configured, for example, to produce large sets of very similar instances of same size, where only the objective function changes, or more diverse sets of instances, with various sizes and characteristics, belonging to a particular problem class.\n", + "\n", + "In the following, we describe the problems included in the library, their MIP formulation and the generation algorithm." + ] + }, + { + "cell_type": "markdown", + "id": "fbfe86db", + "metadata": { + "collapsed": false + }, + "source": [ + "
\n", + "Warning\n", + "\n", + "The random instance generators and formulations shown below are subject to change. If you use them in your research, for reproducibility, you should specify the MIPLearn version and all parameters.\n", + "
\n", + "\n", + "
\n", + "Note\n", + "\n", + "- To make the instances easier to process, all formulations are written as a minimization problem.\n", + "- Some problem formulations, such as the one for the *traveling salesman problem*, contain an exponential number of constraints, which are enforced through constraint generation. The MPS files for these problems contain only the constraints that were generated during a trial run, not the entire set of constraints. Resolving the MPS file, therefore, may not generate a feasible primal solution for the problem.\n", + "
" + ] + }, + { + "cell_type": "markdown", + "id": "830f3784-a3fc-4e2f-a484-e7808841ffe8", + "metadata": { + "jp-MarkdownHeadingCollapsed": true, + "tags": [] + }, + "source": [ + "## Bin Packing\n", + "\n", + "**Bin packing** is a combinatorial optimization problem that asks for the optimal way to pack a given set of items into a finite number of containers (or bins) of fixed capacity. More specifically, the problem is to assign indivisible items of different sizes to identical bins, while minimizing the number of bins used. The problem is NP-hard and has many practical applications, including logistics and warehouse management, where it is used to determine how to best store and transport goods using a limited amount of space." + ] + }, + { + "cell_type": "markdown", + "id": "af933298-92a9-4c5d-8d07-0d4918dedbb8", + "metadata": { + "tags": [] + }, + "source": [ + "### Formulation\n", + "\n", + "Let $n$ be the number of items, and $s_i$ the size of the $i$-th item. Also let $B$ be the size of the bins. For each bin $j$, let $y_j$ be a binary decision variable which equals one if the bin is used. For every item-bin pair $(i,j)$, let $x_{ij}$ be a binary decision variable which equals one if item $i$ is assigned to bin $j$. The bin packing problem is formulated as:" + ] + }, + { + "cell_type": "markdown", + "id": "0dcc6210", + "metadata": { + "collapsed": false + }, + "source": [ + "\n", + "$$\n", + "\\begin{align*}\n", + "\\text{minimize} \\;\\;\\;\n", + " & \\sum_{j=1}^n y_j \\\\\n", + "\\text{subject to} \\;\\;\\;\n", + " & \\sum_{i=1}^n s_i x_{ij} \\leq B y_j & \\forall j=1,\\ldots,n \\\\\n", + " & \\sum_{j=1}^n x_{ij} = 1 & \\forall i=1,\\ldots,n \\\\\n", + " & y_i \\in \\{0,1\\} & \\forall i=1,\\ldots,n \\\\\n", + " & x_{ij} \\in \\{0,1\\} & \\forall i,j=1,\\ldots,n \\\\\n", + "\\end{align*}\n", + "$$" + ] + }, + { + "cell_type": "markdown", + "id": "3e09abef", + "metadata": { + "collapsed": false + }, + "source": [ + "### Random instance generator\n", + "\n", + "Random instances of the bin packing problem can be generated using the class [BinPackGenerator][BinPackGenerator].\n", + "\n", + "If `fix_items=False`, the class samples the user-provided probability distributions `n`, `sizes` and `capacity` to decide, respectively, the number of items, the sizes of the items and capacity of the bin. All values are sampled independently.\n", + "\n", + "If `fix_items=True`, the class creates a reference instance, using the method previously described, then generates additional instances by perturbing its item sizes and bin capacity. More specifically, the sizes of the items are set to $s_i \\gamma_i$, where $s_i$ is the size of the $i$-th item in the reference instance and $\\gamma_i$ is sampled from `sizes_jitter`. Similarly, the bin size is set to $B \\beta$, where $B$ is the reference bin size and $\\beta$ is sampled from `capacity_jitter`. The number of items remains the same across all generated instances.\n", + "\n", + "[BinPackGenerator]: ../../api/problems/#miplearn.problems.binpack.BinPackGenerator" + ] + }, + { + "cell_type": "markdown", + "id": "c48da99f", + "metadata": { + "collapsed": false + }, + "source": [ + "### Example" + ] + }, + { + "cell_type": "code", + "execution_count": 1, + "id": "f14e560c-ef9f-4c48-8467-72d6acce5f9f", + "metadata": { + "tags": [] + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "0 [ 8.47 26. 19.52 14.11 3.65 3.65 1.4 21.76 14.82 16.96] 102.24\n", + "1 [ 8.69 22.78 17.81 14.83 4.12 3.67 1.46 22.05 13.66 18.08] 93.41\n", + "2 [ 8.55 25.9 20. 15.89 3.75 3.59 1.51 21.4 13.89 17.68] 90.69\n", + "3 [10.13 22.62 18.89 14.4 3.92 3.94 1.36 23.69 15.85 19.26] 107.9\n", + "4 [ 9.55 25.77 16.79 14.06 3.55 3.76 1.42 20.66 16.02 17.19] 95.62\n", + "5 [ 9.44 22.06 19.41 13.69 4.28 4.11 1.36 19.51 15.98 18.43] 104.58\n", + "6 [ 9.87 21.74 17.78 13.82 4.18 4. 1.4 19.76 14.46 17.08] 104.59\n", + "7 [ 9.62 25.61 18.2 13.83 4.07 4.1 1.47 22.83 15.01 17.78] 98.55\n", + "8 [ 8.47 21.9 16.58 15.37 3.76 3.91 1.57 20.57 14.76 18.61] 94.58\n", + "9 [ 8.57 22.77 17.06 16.25 4.14 4. 1.56 22.97 14.09 19.09] 100.79\n", + "\n", + "Restricted license - for non-production use only - expires 2023-10-25\n", + "Gurobi Optimizer version 9.5.2 build v9.5.2rc0 (linux64)\n", + "Thread count: 16 physical cores, 32 logical processors, using up to 32 threads\n", + "Optimize a model with 20 rows, 110 columns and 210 nonzeros\n", + "Model fingerprint: 0x1ff9913f\n", + "Variable types: 0 continuous, 110 integer (110 binary)\n", + "Coefficient statistics:\n", + " Matrix range [1e+00, 1e+02]\n", + " Objective range [1e+00, 1e+00]\n", + " Bounds range [1e+00, 1e+00]\n", + " RHS range [1e+00, 1e+00]\n", + "Found heuristic solution: objective 5.0000000\n", + "Presolve time: 0.00s\n", + "Presolved: 20 rows, 110 columns, 210 nonzeros\n", + "Variable types: 0 continuous, 110 integer (110 binary)\n", + "\n", + "Root relaxation: objective 1.274844e+00, 38 iterations, 0.00 seconds (0.00 work units)\n", + "\n", + " Nodes | Current Node | Objective Bounds | Work\n", + " Expl Unexpl | Obj Depth IntInf | Incumbent BestBd Gap | It/Node Time\n", + "\n", + " 0 0 1.27484 0 4 5.00000 1.27484 74.5% - 0s\n", + "H 0 0 4.0000000 1.27484 68.1% - 0s\n", + "H 0 0 2.0000000 1.27484 36.3% - 0s\n", + " 0 0 1.27484 0 4 2.00000 1.27484 36.3% - 0s\n", + "\n", + "Explored 1 nodes (38 simplex iterations) in 0.00 seconds (0.00 work units)\n", + "Thread count was 32 (of 32 available processors)\n", + "\n", + "Solution count 3: 2 4 5 \n", + "\n", + "Optimal solution found (tolerance 1.00e-04)\n", + "Best objective 2.000000000000e+00, best bound 2.000000000000e+00, gap 0.0000%\n" + ] + } + ], + "source": [ + "import numpy as np\n", + "from scipy.stats import uniform, randint\n", + "from miplearn.problems.binpack import BinPackGenerator, build_binpack_model\n", + "\n", + "# Set random seed, to make example reproducible\n", + "np.random.seed(42)\n", + "\n", + "# Generate random instances of the binpack problem with ten items\n", + "data = BinPackGenerator(\n", + " n=randint(low=10, high=11),\n", + " sizes=uniform(loc=0, scale=25),\n", + " capacity=uniform(loc=100, scale=0),\n", + " sizes_jitter=uniform(loc=0.9, scale=0.2),\n", + " capacity_jitter=uniform(loc=0.9, scale=0.2),\n", + " fix_items=True,\n", + ").generate(10)\n", + "\n", + "# Print sizes and capacities\n", + "for i in range(10):\n", + " print(i, data[i].sizes, data[i].capacity)\n", + "print()\n", + "\n", + "# Optimize first instance\n", + "model = build_binpack_model(data[0])\n", + "model.optimize()" + ] + }, + { + "cell_type": "markdown", + "id": "9a3df608-4faf-444b-b5c2-18d3e90cbb5a", + "metadata": { + "tags": [] + }, + "source": [ + "## Multi-Dimensional Knapsack\n", + "\n", + "The **multi-dimensional knapsack problem** is a generalization of the classic knapsack problem, which involves selecting a subset of items to be placed in a knapsack such that the total value of the items is maximized without exceeding a maximum weight. In this generalization, items have multiple weights (representing multiple resources), and multiple weight constraints must be satisfied." + ] + }, + { + "cell_type": "markdown", + "id": "8d989002-d837-4ccf-a224-0504a6d66473", + "metadata": { + "tags": [] + }, + "source": [ + "### Formulation\n", + "\n", + "Let $n$ be the number of items and $m$ be the number of resources. For each item $j$ and resource $i$, let $p_j$ be the price of the item, let $w_{ij}$ be the amount of resource $j$ item $i$ consumes (i.e. the $j$-th weight of the item), and let $b_i$ be the total amount of resource $i$ available (or the size of the $j$-th knapsack). The formulation is given by:" + ] + }, + { + "cell_type": "markdown", + "id": "021bbcef", + "metadata": { + "collapsed": false + }, + "source": [ + "\n", + "$$\n", + "\\begin{align*}\n", + " \\text{minimize}\\;\\;\\;\n", + " & - \\sum_{j=1}^n p_j x_j\n", + " \\\\\n", + " \\text{subject to}\\;\\;\\;\n", + " & \\sum_{j=1}^n w_{ij} x_j \\leq b_i\n", + " & \\forall i=1,\\ldots,m \\\\\n", + " & x_j \\in \\{0,1\\}\n", + " & \\forall j=1,\\ldots,n\n", + "\\end{align*}\n", + "$$" + ] + }, + { + "cell_type": "markdown", + "id": "81b5b085-cfa9-45ce-9682-3aeb9be96cba", + "metadata": {}, + "source": [ + "### Random instance generator\n", + "\n", + "The class [MultiKnapsackGenerator][MultiKnapsackGenerator] can be used to generate random instances of this problem. The number of items $n$ and knapsacks $m$ are sampled from the user-provided probability distributions `n` and `m`. The weights $w_{ij}$ are sampled independently from the provided distribution `w`. The capacity of knapsack $i$ is set to\n", + "\n", + "[MultiKnapsackGenerator]: ../../api/problems/#miplearn.problems.multiknapsack.MultiKnapsackGenerator\n", + "\n", + "$$\n", + " b_i = \\alpha_i \\sum_{j=1}^n w_{ij}\n", + "$$\n", + "\n", + "where $\\alpha_i$, the tightness ratio, is sampled from the provided probability\n", + "distribution `alpha`. To make the instances more challenging, the costs of the items\n", + "are linearly correlated to their average weights. More specifically, the price of each\n", + "item $j$ is set to:\n", + "\n", + "$$\n", + " p_j = \\sum_{i=1}^m \\frac{w_{ij}}{m} + K u_j,\n", + "$$\n", + "\n", + "where $K$, the correlation coefficient, and $u_j$, the correlation multiplier, are sampled\n", + "from the provided probability distributions `K` and `u`.\n", + "\n", + "If `fix_w=True` is provided, then $w_{ij}$ are kept the same in all generated instances. This also implies that $n$ and $m$ are kept fixed. Although the prices and capacities are derived from $w_{ij}$, as long as `u` and `K` are not constants, the generated instances will still not be completely identical.\n", + "\n", + "\n", + "If a probability distribution `w_jitter` is provided, then item weights will be set to $w_{ij} \\gamma_{ij}$ where $\\gamma_{ij}$ is sampled from `w_jitter`. When combined with `fix_w=True`, this argument may be used to generate instances where the weight of each item is roughly the same, but not exactly identical, across all instances. The prices of the items and the capacities of the knapsacks will be calculated as above, but using these perturbed weights instead.\n", + "\n", + "By default, all generated prices, weights and capacities are rounded to the nearest integer number. If `round=False` is provided, this rounding will be disabled." + ] + }, + { + "cell_type": "markdown", + "id": "f92135b8-67e7-4ec5-aeff-2fc17ad5e46d", + "metadata": {}, + "source": [ + "
\n", + "References\n", + "\n", + "* **Freville, Arnaud, and Gérard Plateau.** *An efficient preprocessing procedure for the multidimensional 0–1 knapsack problem.* Discrete applied mathematics 49.1-3 (1994): 189-212.\n", + "* **Fréville, Arnaud.** *The multidimensional 0–1 knapsack problem: An overview.* European Journal of Operational Research 155.1 (2004): 1-21.\n", + "
" + ] + }, + { + "cell_type": "markdown", + "id": "bfcb9910", + "metadata": { + "collapsed": false + }, + "source": [ + "### Example" + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "id": "1ce5f8fb-2769-4fbd-a40c-fd62b897690a", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "prices\n", + " [350. 692. 454. 709. 605. 543. 321. 674. 571. 341.]\n", + "weights\n", + " [[392. 977. 764. 622. 158. 163. 56. 840. 574. 696.]\n", + " [ 20. 948. 860. 209. 178. 184. 293. 541. 414. 305.]\n", + " [629. 135. 278. 378. 466. 803. 205. 492. 584. 45.]\n", + " [630. 173. 64. 907. 947. 794. 312. 99. 711. 439.]\n", + " [117. 506. 35. 915. 266. 662. 312. 516. 521. 178.]]\n", + "capacities\n", + " [1310. 988. 1004. 1269. 1007.]\n", + "\n", + "Gurobi Optimizer version 9.5.2 build v9.5.2rc0 (linux64)\n", + "Thread count: 16 physical cores, 32 logical processors, using up to 32 threads\n", + "Optimize a model with 5 rows, 10 columns and 50 nonzeros\n", + "Model fingerprint: 0xaf3ac15e\n", + "Variable types: 0 continuous, 10 integer (10 binary)\n", + "Coefficient statistics:\n", + " Matrix range [2e+01, 1e+03]\n", + " Objective range [3e+02, 7e+02]\n", + " Bounds range [1e+00, 1e+00]\n", + " RHS range [1e+03, 1e+03]\n", + "Found heuristic solution: objective -804.0000000\n", + "Presolve removed 0 rows and 3 columns\n", + "Presolve time: 0.00s\n", + "Presolved: 5 rows, 7 columns, 34 nonzeros\n", + "Variable types: 0 continuous, 7 integer (7 binary)\n", + "\n", + "Root relaxation: objective -1.428726e+03, 4 iterations, 0.00 seconds (0.00 work units)\n", + "\n", + " Nodes | Current Node | Objective Bounds | Work\n", + " Expl Unexpl | Obj Depth IntInf | Incumbent BestBd Gap | It/Node Time\n", + "\n", + " 0 0 -1428.7265 0 4 -804.00000 -1428.7265 77.7% - 0s\n", + "H 0 0 -1279.000000 -1428.7265 11.7% - 0s\n", + "\n", + "Cutting planes:\n", + " Cover: 1\n", + "\n", + "Explored 1 nodes (4 simplex iterations) in 0.00 seconds (0.00 work units)\n", + "Thread count was 32 (of 32 available processors)\n", + "\n", + "Solution count 2: -1279 -804 \n", + "No other solutions better than -1279\n", + "\n", + "Optimal solution found (tolerance 1.00e-04)\n", + "Best objective -1.279000000000e+03, best bound -1.279000000000e+03, gap 0.0000%\n" + ] + } + ], + "source": [ + "import numpy as np\n", + "from scipy.stats import uniform, randint\n", + "from miplearn.problems.multiknapsack import (\n", + " MultiKnapsackGenerator,\n", + " build_multiknapsack_model,\n", + ")\n", + "\n", + "# Set random seed, to make example reproducible\n", + "np.random.seed(42)\n", + "\n", + "# Generate ten similar random instances of the multiknapsack problem with\n", + "# ten items, five resources and weights around [0, 1000].\n", + "data = MultiKnapsackGenerator(\n", + " n=randint(low=10, high=11),\n", + " m=randint(low=5, high=6),\n", + " w=uniform(loc=0, scale=1000),\n", + " K=uniform(loc=100, scale=0),\n", + " u=uniform(loc=1, scale=0),\n", + " alpha=uniform(loc=0.25, scale=0),\n", + " w_jitter=uniform(loc=0.95, scale=0.1),\n", + " p_jitter=uniform(loc=0.75, scale=0.5),\n", + " fix_w=True,\n", + ").generate(10)\n", + "\n", + "# Print data for one of the instances\n", + "print(\"prices\\n\", data[0].prices)\n", + "print(\"weights\\n\", data[0].weights)\n", + "print(\"capacities\\n\", data[0].capacities)\n", + "print()\n", + "\n", + "# Build model and optimize\n", + "model = build_multiknapsack_model(data[0])\n", + "model.optimize()" + ] + }, + { + "cell_type": "markdown", + "id": "e20376b0-0781-4bfa-968f-ded5fa47e176", + "metadata": { + "tags": [] + }, + "source": [ + "## Capacitated P-Median\n", + "\n", + "The **capacitated p-median** problem is a variation of the classic $p$-median problem, in which a set of customers must be served by a set of facilities. In the capacitated $p$-Median problem, each facility has a fixed capacity, and the goal is to minimize the total cost of serving the customers while ensuring that the capacity of each facility is not exceeded. Variations of problem are often used in logistics and supply chain management to determine the most efficient locations for warehouses or distribution centers." + ] + }, + { + "cell_type": "markdown", + "id": "2af65137-109e-4ca0-8753-bd999825204f", + "metadata": { + "tags": [] + }, + "source": [ + "### Formulation\n", + "\n", + "Let $I=\\{1,\\ldots,n\\}$ be the set of customers. For each customer $i \\in I$, let $d_i$ be its demand and let $y_i$ be a binary decision variable that equals one if we decide to open a facility at that customer's location. For each pair $(i,j) \\in I \\times I$, let $x_{ij}$ be a binary decision variable that equals one if customer $i$ is assigned to facility $j$. Furthermore, let $w_{ij}$ be the cost of serving customer $i$ from facility $j$, let $p$ be the number of facilities we must open, and let $c_j$ be the capacity of facility $j$. The problem is formulated as:" + ] + }, + { + "cell_type": "markdown", + "id": "a2494ab1-d306-4db7-a100-8f1dfd4a55d7", + "metadata": { + "tags": [] + }, + "source": [ + "$$\n", + "\\begin{align*}\n", + " \\text{minimize}\\;\\;\\;\n", + " & \\sum_{i \\in I} \\sum_{j \\in I} w_{ij} x_{ij}\n", + " \\\\\n", + " \\text{subject to}\\;\\;\\;\n", + " & \\sum_{j \\in I} x_{ij} = 1 & \\forall i \\in I \\\\\n", + " & \\sum_{j \\in I} y_j = p \\\\\n", + " & \\sum_{i \\in I} d_i x_{ij} \\leq c_j y_j & \\forall j \\in I \\\\\n", + " & x_{ij} \\in \\{0, 1\\} & \\forall i, j \\in I \\\\\n", + " & y_j \\in \\{0, 1\\} & \\forall j \\in I\n", + "\\end{align*}\n", + "$$" + ] + }, + { + "cell_type": "markdown", + "id": "9dddf0d6-1f86-40d4-93a8-ccfe93d38e0d", + "metadata": {}, + "source": [ + "### Random instance generator\n", + "\n", + "The class [PMedianGenerator][PMedianGenerator] can be used to generate random instances of this problem. First, it decides the number of customers and the parameter $p$ by sampling the provided `n` and `p` distributions, respectively. Then, for each customer $i$, the class builds its geographical location $(x_i, y_i)$ by sampling the provided `x` and `y` distributions. For each $i$, the demand for customer $i$ and the capacity of facility $i$ are decided by sampling the provided distributions `demands` and `capacities`, respectively. Finally, the costs $w_{ij}$ are set to the Euclidean distance between the locations of customers $i$ and $j$.\n", + "\n", + "If `fixed=True`, then the number of customers, their locations, the parameter $p$, the demands and the capacities are only sampled from their respective distributions exactly once, to build a reference instance which is then randomly perturbed. Specifically, in each perturbation, the distances, demands and capacities are multiplied by random scaling factors sampled from the distributions `distances_jitter`, `demands_jitter` and `capacities_jitter`, respectively. The result is a list of instances that have the same set of customers, but slightly different demands, capacities and distances.\n", + "\n", + "[PMedianGenerator]: ../../api/problems/#miplearn.problems.pmedian.PMedianGenerator" + ] + }, + { + "cell_type": "markdown", + "id": "f58d88e5", + "metadata": { + "collapsed": false + }, + "source": [ + "### Example" + ] + }, + { + "cell_type": "code", + "execution_count": 3, + "id": "4e0e4223-b4e0-4962-a157-82a23a86e37d", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "p = 5\n", + "distances =\n", + " [[ 0. 50.17 82.42 32.76 33.2 35.45 86.88 79.11 43.17 66.2 ]\n", + " [ 50.17 0. 72.64 72.51 17.06 80.25 39.92 68.93 43.41 42.96]\n", + " [ 82.42 72.64 0. 71.69 70.92 82.51 67.88 3.76 39.74 30.73]\n", + " [ 32.76 72.51 71.69 0. 56.56 11.03 101.35 69.39 42.09 68.58]\n", + " [ 33.2 17.06 70.92 56.56 0. 63.68 54.71 67.16 34.89 44.99]\n", + " [ 35.45 80.25 82.51 11.03 63.68 0. 111.04 80.29 52.78 79.36]\n", + " [ 86.88 39.92 67.88 101.35 54.71 111.04 0. 65.13 61.37 40.82]\n", + " [ 79.11 68.93 3.76 69.39 67.16 80.29 65.13 0. 36.26 27.24]\n", + " [ 43.17 43.41 39.74 42.09 34.89 52.78 61.37 36.26 0. 26.62]\n", + " [ 66.2 42.96 30.73 68.58 44.99 79.36 40.82 27.24 26.62 0. ]]\n", + "demands = [6.12 1.39 2.92 3.66 4.56 7.85 2. 5.14 5.92 0.46]\n", + "capacities = [151.89 42.63 16.26 237.22 241.41 202.1 76.15 24.42 171.06 110.04]\n", + "\n", + "Gurobi Optimizer version 9.5.2 build v9.5.2rc0 (linux64)\n", + "Thread count: 16 physical cores, 32 logical processors, using up to 32 threads\n", + "Optimize a model with 21 rows, 110 columns and 220 nonzeros\n", + "Model fingerprint: 0x8d8d9346\n", + "Variable types: 0 continuous, 110 integer (110 binary)\n", + "Coefficient statistics:\n", + " Matrix range [5e-01, 2e+02]\n", + " Objective range [4e+00, 1e+02]\n", + " Bounds range [1e+00, 1e+00]\n", + " RHS range [1e+00, 5e+00]\n", + "Found heuristic solution: objective 368.7900000\n", + "Presolve time: 0.00s\n", + "Presolved: 21 rows, 110 columns, 220 nonzeros\n", + "Variable types: 0 continuous, 110 integer (110 binary)\n", + "Found heuristic solution: objective 245.6400000\n", + "\n", + "Root relaxation: objective 0.000000e+00, 18 iterations, 0.00 seconds (0.00 work units)\n", + "\n", + " Nodes | Current Node | Objective Bounds | Work\n", + " Expl Unexpl | Obj Depth IntInf | Incumbent BestBd Gap | It/Node Time\n", + "\n", + " 0 0 0.00000 0 6 245.64000 0.00000 100% - 0s\n", + "H 0 0 185.1900000 0.00000 100% - 0s\n", + "H 0 0 148.6300000 17.14595 88.5% - 0s\n", + "H 0 0 113.1800000 17.14595 84.9% - 0s\n", + " 0 0 17.14595 0 10 113.18000 17.14595 84.9% - 0s\n", + "H 0 0 99.5000000 17.14595 82.8% - 0s\n", + "H 0 0 98.3900000 17.14595 82.6% - 0s\n", + "H 0 0 93.9800000 64.28872 31.6% - 0s\n", + " 0 0 64.28872 0 15 93.98000 64.28872 31.6% - 0s\n", + "H 0 0 93.9200000 64.28872 31.5% - 0s\n", + " 0 0 86.06884 0 15 93.92000 86.06884 8.36% - 0s\n", + "* 0 0 0 91.2300000 91.23000 0.00% - 0s\n", + "\n", + "Explored 1 nodes (60 simplex iterations) in 0.01 seconds (0.00 work units)\n", + "Thread count was 32 (of 32 available processors)\n", + "\n", + "Solution count 10: 91.23 93.92 93.98 ... 368.79\n", + "\n", + "Optimal solution found (tolerance 1.00e-04)\n", + "Best objective 9.123000000000e+01, best bound 9.123000000000e+01, gap 0.0000%\n" + ] + } + ], + "source": [ + "import numpy as np\n", + "from scipy.stats import uniform, randint\n", + "from miplearn.problems.pmedian import PMedianGenerator, build_pmedian_model\n", + "\n", + "# Set random seed, to make example reproducible\n", + "np.random.seed(42)\n", + "\n", + "# Generate random instances with ten customers located in a\n", + "# 100x100 square, with demands in [0,10], capacities in [0, 250].\n", + "data = PMedianGenerator(\n", + " x=uniform(loc=0.0, scale=100.0),\n", + " y=uniform(loc=0.0, scale=100.0),\n", + " n=randint(low=10, high=11),\n", + " p=randint(low=5, high=6),\n", + " demands=uniform(loc=0, scale=10),\n", + " capacities=uniform(loc=0, scale=250),\n", + " distances_jitter=uniform(loc=0.9, scale=0.2),\n", + " demands_jitter=uniform(loc=0.9, scale=0.2),\n", + " capacities_jitter=uniform(loc=0.9, scale=0.2),\n", + " fixed=True,\n", + ").generate(10)\n", + "\n", + "# Print data for one of the instances\n", + "print(\"p =\", data[0].p)\n", + "print(\"distances =\\n\", data[0].distances)\n", + "print(\"demands =\", data[0].demands)\n", + "print(\"capacities =\", data[0].capacities)\n", + "print()\n", + "\n", + "# Build and optimize model\n", + "model = build_pmedian_model(data[0])\n", + "model.optimize()" + ] + }, + { + "cell_type": "markdown", + "id": "36129dbf-ecba-4026-ad4d-f2356bad4a26", + "metadata": {}, + "source": [ + "## Set cover\n", + "\n", + "The **set cover problem** is a classical NP-hard optimization problem which aims to minimize the number of sets needed to cover all elements in a given universe. Each set may contain a different number of elements, and sets may overlap with each other. This problem can be useful in various real-world scenarios such as scheduling, resource allocation, and network design." + ] + }, + { + "cell_type": "markdown", + "id": "5e02b717", + "metadata": { + "collapsed": false + }, + "source": [ + "### Formulation\n", + "\n", + "Let $U = \\{1,\\ldots,n\\}$ be a given universe set, and let $S=\\{S_1,\\ldots,S_m\\}$ be a collection of sets whose union equal $U$. For each $j \\in \\{1,\\ldots,m\\}$, let $w_j$ be the weight of set $S_j$, and let $x_j$ be a binary decision variable that equals one if set $S_j$ is chosen. The set cover problem is formulated as:" + ] + }, + { + "cell_type": "markdown", + "id": "5062d606-678c-45ba-9a45-d3c8b7401ad1", + "metadata": {}, + "source": [ + "$$\n", + "\\begin{align*}\n", + " \\text{minimize}\\;\\;\\;\n", + " & \\sum_{j=1}^m w_j x_j\n", + " \\\\\n", + " \\text{subject to}\\;\\;\\;\n", + " & \\sum_{j : i \\in S_j} x_j \\geq 1 & \\forall i \\in \\{1,\\ldots,n\\} \\\\\n", + " & x_j \\in \\{0, 1\\} & \\forall j \\in \\{1,\\ldots,m\\}\n", + "\\end{align*}\n", + "$$" + ] + }, + { + "cell_type": "markdown", + "id": "2732c050-2e11-44fc-bdd1-1b804a60f166", + "metadata": {}, + "source": [ + "### Random instance generator\n", + "\n", + "The class [SetCoverGenerator] can generate random instances of this problem. The class first decides the number of elements and sets by sampling the provided distributions `n_elements` and `n_sets`, respectively. Then it generates a random incidence matrix $M$, as follows:\n", + "\n", + "1. The density $d$ of $M$ is decided by sampling the provided probability distribution `density`.\n", + "2. Each entry of $M$ is then sampled from the Bernoulli distribution, with probability $d$.\n", + "3. To ensure that each element belongs to at least one set, the class identifies elements that are not contained in any set, then assigns them to a random set (chosen uniformly).\n", + "4. Similarly, to ensure that each set contains at least one element, the class identifies empty sets, then modifies them to include one random element (chosen uniformly).\n", + "\n", + "Finally, the weight of set $j$ is set to $w_j + K | S_j |$, where $w_j$ and $k$ are sampled from `costs` and `K`, respectively, and where $|S_j|$ denotes the size of set $S_j$. The parameter $K$ is used to introduce some correlation between the size of the set and its weight, making the instance more challenging. Note that `K` is only sampled once for the entire instance.\n", + "\n", + "If `fix_sets=True`, then all generated instances have exactly the same sets and elements. The costs of the sets, however, are multiplied by random scaling factors sampled from the provided probability distribution `costs_jitter`.\n", + "\n", + "[SetCoverGenerator]: ../../api/problems/#miplearn.problems.setcover.SetCoverGenerator" + ] + }, + { + "cell_type": "markdown", + "id": "569aa5ec-d475-41fa-a5d9-0b1a675fdf95", + "metadata": {}, + "source": [ + "### Example" + ] + }, + { + "cell_type": "code", + "execution_count": 4, + "id": "3224845b-9afd-463e-abf4-e0e93d304859", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "matrix\n", + " [[1 0 0 0 1 1 1 0 0 0]\n", + " [1 0 0 1 1 1 1 0 1 1]\n", + " [0 1 1 1 1 0 1 0 0 1]\n", + " [0 1 1 0 0 0 1 1 0 1]\n", + " [1 1 1 0 1 0 1 0 0 1]]\n", + "costs [1044.58 850.13 1014.5 944.83 697.9 971.87 213.49 220.98 70.23\n", + " 425.33]\n", + "\n", + "Gurobi Optimizer version 9.5.2 build v9.5.2rc0 (linux64)\n", + "Thread count: 16 physical cores, 32 logical processors, using up to 32 threads\n", + "Optimize a model with 5 rows, 10 columns and 28 nonzeros\n", + "Model fingerprint: 0xe5c2d4fa\n", + "Variable types: 0 continuous, 10 integer (10 binary)\n", + "Coefficient statistics:\n", + " Matrix range [1e+00, 1e+00]\n", + " Objective range [7e+01, 1e+03]\n", + " Bounds range [1e+00, 1e+00]\n", + " RHS range [1e+00, 1e+00]\n", + "Found heuristic solution: objective 213.4900000\n", + "Presolve removed 5 rows and 10 columns\n", + "Presolve time: 0.00s\n", + "Presolve: All rows and columns removed\n", + "\n", + "Explored 0 nodes (0 simplex iterations) in 0.00 seconds (0.00 work units)\n", + "Thread count was 1 (of 32 available processors)\n", + "\n", + "Solution count 1: 213.49 \n", + "\n", + "Optimal solution found (tolerance 1.00e-04)\n", + "Best objective 2.134900000000e+02, best bound 2.134900000000e+02, gap 0.0000%\n" + ] + } + ], + "source": [ + "import numpy as np\n", + "from scipy.stats import uniform, randint\n", + "from miplearn.problems.setcover import SetCoverGenerator, build_setcover_model\n", + "\n", + "# Set random seed, to make example reproducible\n", + "np.random.seed(42)\n", + "\n", + "# Build random instances with five elements, ten sets and costs\n", + "# in the [0, 1000] interval, with a correlation factor of 25 and\n", + "# an incidence matrix with 25% density.\n", + "data = SetCoverGenerator(\n", + " n_elements=randint(low=5, high=6),\n", + " n_sets=randint(low=10, high=11),\n", + " costs=uniform(loc=0.0, scale=1000.0),\n", + " costs_jitter=uniform(loc=0.90, scale=0.20),\n", + " density=uniform(loc=0.5, scale=0.00),\n", + " K=uniform(loc=25.0, scale=0.0),\n", + " fix_sets=True,\n", + ").generate(10)\n", + "\n", + "# Print problem data for one instance\n", + "print(\"matrix\\n\", data[0].incidence_matrix)\n", + "print(\"costs\", data[0].costs)\n", + "print()\n", + "\n", + "# Build and optimize model\n", + "model = build_setcover_model(data[0])\n", + "model.optimize()" + ] + }, + { + "cell_type": "markdown", + "id": "255a4e88-2e38-4a1b-ba2e-806b6bd4c815", + "metadata": {}, + "source": [ + "## Set Packing\n", + "\n", + "**Set packing** is a classical optimization problem that asks for the maximum number of disjoint sets within a given list. This problem often arises in real-world situations where a finite number of resources need to be allocated to tasks, such as airline flight crew scheduling." + ] + }, + { + "cell_type": "markdown", + "id": "fe2d24e5", + "metadata": { + "collapsed": false + }, + "source": [ + "### Formulation\n", + "\n", + "Let $U=\\{1,\\ldots,n\\}$ be a given universe set, and let $S = \\{S_1, \\ldots, S_m\\}$ be a collection of subsets of $U$. For each subset $j \\in \\{1, \\ldots, m\\}$, let $w_j$ be the weight of $S_j$ and let $x_j$ be a binary decision variable which equals one if set $S_j$ is chosen. The problem is formulated as:" + ] + }, + { + "cell_type": "markdown", + "id": "679ae3f5", + "metadata": { + "collapsed": false + }, + "source": [ + "$$\n", + "\\begin{align*}\n", + " \\text{minimize}\\;\\;\\;\n", + " & -\\sum_{j=1}^m w_j x_j\n", + " \\\\\n", + " \\text{subject to}\\;\\;\\;\n", + " & \\sum_{j : i \\in S_j} x_j \\leq 1 & \\forall i \\in \\{1,\\ldots,n\\} \\\\\n", + " & x_j \\in \\{0, 1\\} & \\forall j \\in \\{1,\\ldots,m\\}\n", + "\\end{align*}\n", + "$$" + ] + }, + { + "cell_type": "markdown", + "id": "66306263", + "metadata": { + "collapsed": false + }, + "source": [ + "### Random instance generator\n", + "\n", + "The class [SetPackGenerator][SetPackGenerator] can generate random instances of this problem. It accepts exactly the same arguments, and generates instance data in exactly the same way as [SetCoverGenerator][SetCoverGenerator]. For more details, please see the documentation for that class.\n", + "\n", + "[SetPackGenerator]: ../../api/problems/#miplearn.problems.setpack.SetPackGenerator\n", + "[SetCoverGenerator]: ../../api/problems/#miplearn.problems.setcover.SetCoverGenerator\n", + "\n", + "### Example" + ] + }, + { + "cell_type": "code", + "execution_count": 5, + "id": "9d0ee846", + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "matrix\n", + " [[1 0 0 0 1 1 1 0 0 0]\n", + " [1 0 0 1 1 1 1 0 1 1]\n", + " [0 1 1 1 1 0 1 0 0 1]\n", + " [0 1 1 0 0 0 1 1 0 1]\n", + " [1 1 1 0 1 0 1 0 0 1]]\n", + "costs [1044.58 850.13 1014.5 944.83 697.9 971.87 213.49 220.98 70.23\n", + " 425.33]\n", + "\n", + "Gurobi Optimizer version 9.5.2 build v9.5.2rc0 (linux64)\n", + "Thread count: 16 physical cores, 32 logical processors, using up to 32 threads\n", + "Optimize a model with 5 rows, 10 columns and 28 nonzeros\n", + "Model fingerprint: 0x4ee91388\n", + "Variable types: 0 continuous, 10 integer (10 binary)\n", + "Coefficient statistics:\n", + " Matrix range [1e+00, 1e+00]\n", + " Objective range [7e+01, 1e+03]\n", + " Bounds range [1e+00, 1e+00]\n", + " RHS range [1e+00, 1e+00]\n", + "Found heuristic solution: objective -1265.560000\n", + "Presolve removed 5 rows and 10 columns\n", + "Presolve time: 0.00s\n", + "Presolve: All rows and columns removed\n", + "\n", + "Explored 0 nodes (0 simplex iterations) in 0.00 seconds (0.00 work units)\n", + "Thread count was 1 (of 32 available processors)\n", + "\n", + "Solution count 2: -1986.37 -1265.56 \n", + "No other solutions better than -1986.37\n", + "\n", + "Optimal solution found (tolerance 1.00e-04)\n", + "Best objective -1.986370000000e+03, best bound -1.986370000000e+03, gap 0.0000%\n" + ] + } + ], + "source": [ + "import numpy as np\n", + "from scipy.stats import uniform, randint\n", + "from miplearn.problems.setpack import SetPackGenerator, build_setpack_model\n", + "\n", + "# Set random seed, to make example reproducible\n", + "np.random.seed(42)\n", + "\n", + "# Build random instances with five elements, ten sets and costs\n", + "# in the [0, 1000] interval, with a correlation factor of 25 and\n", + "# an incidence matrix with 25% density.\n", + "data = SetPackGenerator(\n", + " n_elements=randint(low=5, high=6),\n", + " n_sets=randint(low=10, high=11),\n", + " costs=uniform(loc=0.0, scale=1000.0),\n", + " costs_jitter=uniform(loc=0.90, scale=0.20),\n", + " density=uniform(loc=0.5, scale=0.00),\n", + " K=uniform(loc=25.0, scale=0.0),\n", + " fix_sets=True,\n", + ").generate(10)\n", + "\n", + "# Print problem data for one instance\n", + "print(\"matrix\\n\", data[0].incidence_matrix)\n", + "print(\"costs\", data[0].costs)\n", + "print()\n", + "\n", + "# Build and optimize model\n", + "model = build_setpack_model(data[0])\n", + "model.optimize()" + ] + }, + { + "cell_type": "markdown", + "id": "373e450c-8f8b-4b59-bf73-251bdd6ff67e", + "metadata": {}, + "source": [ + "## Stable Set\n", + "\n", + "The **maximum-weight stable set problem** is a classical optimization problem in graph theory which asks for the maximum-weight subset of vertices in a graph such that no two vertices in the subset are adjacent. The problem often arises in real-world scheduling or resource allocation situations, where stable sets represent tasks or resources that can be chosen simultaneously without conflicts.\n", + "\n", + "### Formulation\n", + "\n", + "Let $G=(V,E)$ be a simple undirected graph, and for each vertex $v \\in V$, let $w_v$ be its weight. The problem is formulated as:" + ] + }, + { + "cell_type": "markdown", + "id": "31bc4be9", + "metadata": { + "collapsed": false + }, + "source": [ + "$$\n", + "\\begin{align*}\n", + "\\text{minimize} \\;\\;\\; & -\\sum_{v \\in V} w_v x_v \\\\\n", + "\\text{such that} \\;\\;\\; & \\sum_{v \\in C} x_v \\leq 1 & \\forall C \\in \\mathcal{C} \\\\\n", + "& x_v \\in \\{0, 1\\} & \\forall v \\in V\n", + "\\end{align*}\n", + "$$\n", + "where $\\mathcal{C}$ is the set of cliques in $G$. We recall that a clique is a subset of vertices in which every pair of vertices is adjacent." + ] + }, + { + "cell_type": "markdown", + "id": "135f311f", + "metadata": { + "collapsed": false + }, + "source": [ + "\n", + "### Random instance generator\n", + "\n", + "The class [MaxWeightStableSetGenerator][MaxWeightStableSetGenerator] can be used to generate random instances of this problem. The class first samples the user-provided probability distributions `n` and `p` to decide the number of vertices and the density of the graph. Then, it generates a random Erdős-Rényi graph $G_{n,p}$. We recall that, in such a graph, each potential edge is included with probabilty $p$, independently for each other. The class then samples the provided probability distribution `w` to decide the vertex weights.\n", + "\n", + "[MaxWeightStableSetGenerator]: ../../api/problems/#miplearn.problems.stab.MaxWeightStableSetGenerator\n", + "\n", + "If `fix_graph=True`, then all generated instances have the same random graph. For each instance, the weights are decided by sampling `w`, as described above.\n", + "\n", + "### Example" + ] + }, + { + "cell_type": "code", + "execution_count": 24, + "id": "0f996e99-0ec9-472b-be8a-30c9b8556931", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "graph [(0, 2), (0, 4), (0, 8), (1, 2), (1, 3), (1, 5), (1, 6), (1, 9), (2, 5), (2, 9), (3, 6), (3, 7), (6, 9), (7, 8), (8, 9)]\n", + "weights[0] [37.45 95.07 73.2 59.87 15.6 15.6 5.81 86.62 60.11 70.81]\n", + "weights[1] [ 2.06 96.99 83.24 21.23 18.18 18.34 30.42 52.48 43.19 29.12]\n", + "\n", + "Gurobi Optimizer version 9.5.2 build v9.5.2rc0 (linux64)\n", + "Thread count: 16 physical cores, 32 logical processors, using up to 32 threads\n", + "Optimize a model with 10 rows, 10 columns and 24 nonzeros\n", + "Model fingerprint: 0xf4c21689\n", + "Variable types: 0 continuous, 10 integer (10 binary)\n", + "Coefficient statistics:\n", + " Matrix range [1e+00, 1e+00]\n", + " Objective range [6e+00, 1e+02]\n", + " Bounds range [1e+00, 1e+00]\n", + " RHS range [1e+00, 1e+00]\n", + "Found heuristic solution: objective -219.1400000\n", + "Presolve removed 2 rows and 2 columns\n", + "Presolve time: 0.00s\n", + "Presolved: 8 rows, 8 columns, 19 nonzeros\n", + "Variable types: 0 continuous, 8 integer (8 binary)\n", + "\n", + "Root relaxation: objective -2.205650e+02, 4 iterations, 0.00 seconds (0.00 work units)\n", + "\n", + " Nodes | Current Node | Objective Bounds | Work\n", + " Expl Unexpl | Obj Depth IntInf | Incumbent BestBd Gap | It/Node Time\n", + "\n", + " 0 0 infeasible 0 -219.14000 -219.14000 0.00% - 0s\n", + "\n", + "Explored 1 nodes (4 simplex iterations) in 0.00 seconds (0.00 work units)\n", + "Thread count was 32 (of 32 available processors)\n", + "\n", + "Solution count 1: -219.14 \n", + "No other solutions better than -219.14\n", + "\n", + "Optimal solution found (tolerance 1.00e-04)\n", + "Best objective -2.191400000000e+02, best bound -2.191400000000e+02, gap 0.0000%\n" + ] + } + ], + "source": [ + "import random\n", + "import numpy as np\n", + "from scipy.stats import uniform, randint\n", + "from miplearn.problems.stab import MaxWeightStableSetGenerator, build_stab_model\n", + "\n", + "# Set random seed to make example reproducible\n", + "random.seed(42)\n", + "np.random.seed(42)\n", + "\n", + "# Generate random instances with a fixed 10-node graph,\n", + "# 25% density and random weights in the [0, 100] interval.\n", + "data = MaxWeightStableSetGenerator(\n", + " w=uniform(loc=0.0, scale=100.0),\n", + " n=randint(low=10, high=11),\n", + " p=uniform(loc=0.25, scale=0.0),\n", + " fix_graph=True,\n", + ").generate(10)\n", + "\n", + "# Print the graph and weights for two instances\n", + "print(\"graph\", data[0].graph.edges)\n", + "print(\"weights[0]\", data[0].weights)\n", + "print(\"weights[1]\", data[1].weights)\n", + "print()\n", + "\n", + "# Load and optimize the first instance\n", + "model = build_stab_model(data[0])\n", + "model.optimize()" + ] + }, + { + "cell_type": "markdown", + "id": "444d1092-fd83-4957-b691-a198d56ba066", + "metadata": {}, + "source": [ + "## Traveling Salesman\n", + "\n", + "Given a list of cities and the distances between them, the **traveling salesman problem** asks for the shortest route starting at the first city, visiting each other city exactly once, then returning to the first city. This problem is a generalization of the Hamiltonian path problem, one of Karp's 21 NP-complete problems, and has many practical applications, including routing delivery trucks and scheduling airline routes." + ] + }, + { + "cell_type": "markdown", + "id": "4074551b", + "metadata": { + "collapsed": false + }, + "source": [ + "### Formulation\n", + "\n", + "Let $G=(V,E)$ be a simple undirected graph. For each edge $e \\in E$, let $d_e$ be its weight (or distance) and let $x_e$ be a binary decision variable which equals one if $e$ is included in the route. The problem is formulated as:" + ] + }, + { + "cell_type": "markdown", + "id": "5672fbab", + "metadata": { + "collapsed": false + }, + "source": [ + "$$\n", + "\\begin{align*}\n", + "\\text{minimize} \\;\\;\\;\n", + " & \\sum_{e \\in E} d_e x_e \\\\\n", + "\\text{such that} \\;\\;\\;\n", + " & \\sum_{e : \\delta(v)} x_e = 2 & \\forall v \\in V, \\\\\n", + " & \\sum_{e \\in \\delta(S)} x_e \\geq 2 & \\forall S \\subsetneq V, |S| \\neq \\emptyset, \\\\\n", + " & x_e \\in \\{0, 1\\} & \\forall e \\in E,\n", + "\\end{align*}\n", + "$$\n", + "where $\\delta(v)$ denotes the set of edges adjacent to vertex $v$, and $\\delta(S)$ denotes the set of edges that have one extremity in $S$ and one in $V \\setminus S$. Because of its exponential size, we enforce the second set of inequalities as lazy constraints." + ] + }, + { + "cell_type": "markdown", + "id": "257111e2", + "metadata": { + "collapsed": false + }, + "source": [ + "### Random instance generator\n", + "\n", + "The class [TravelingSalesmanGenerator][TravelingSalesmanGenerator] can be used to generate random instances of this problem. Initially, the class samples the user-provided probability distribution `n` to decide how many cities to generate. Then, for each city $i$, the class generates its geographical location $(x_i, y_i)$ by sampling the provided distributions `x` and `y`. The distance $d_{ij}$ between cities $i$ and $j$ is then set to\n", + "$$\n", + "\\gamma_{ij} \\sqrt{(x_i - x_j)^2 + (y_i - y_j)^2},\n", + "$$\n", + "where $\\gamma$ is a random scaling factor sampled from the provided probability distribution `gamma`.\n", + "\n", + "If `fix_cities=True`, then the list of cities is kept the same for all generated instances. The $\\gamma$ values, however, and therefore also the distances, are still different. By default, all distances $d_{ij}$ are rounded to the nearest integer. If `round=False` is provided, this rounding will be disabled.\n", + "\n", + "[TravelingSalesmanGenerator]: ../../api/problems/#miplearn.problems.tsp.TravelingSalesmanGenerator" + ] + }, + { + "cell_type": "markdown", + "id": "3c20e302", + "metadata": { + "collapsed": false + }, + "source": [ + "### Example" + ] + }, + { + "cell_type": "code", + "execution_count": 32, + "id": "e08346b5", + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "distances[0]\n", + " [[ 0. 513. 762. 358. 325. 374. 932. 731. 391. 634.]\n", + " [ 513. 0. 726. 765. 163. 754. 409. 719. 446. 400.]\n", + " [ 762. 726. 0. 780. 756. 744. 656. 40. 383. 334.]\n", + " [ 358. 765. 780. 0. 549. 117. 925. 702. 422. 728.]\n", + " [ 325. 163. 756. 549. 0. 663. 526. 708. 377. 462.]\n", + " [ 374. 754. 744. 117. 663. 0. 1072. 802. 501. 853.]\n", + " [ 932. 409. 656. 925. 526. 1072. 0. 654. 603. 433.]\n", + " [ 731. 719. 40. 702. 708. 802. 654. 0. 381. 255.]\n", + " [ 391. 446. 383. 422. 377. 501. 603. 381. 0. 287.]\n", + " [ 634. 400. 334. 728. 462. 853. 433. 255. 287. 0.]]\n", + "distances[1]\n", + " [[ 0. 493. 900. 354. 323. 367. 841. 727. 444. 668.]\n", + " [ 493. 0. 690. 687. 175. 725. 368. 744. 398. 446.]\n", + " [ 900. 690. 0. 666. 728. 827. 736. 41. 371. 317.]\n", + " [ 354. 687. 666. 0. 570. 104. 1090. 712. 454. 648.]\n", + " [ 323. 175. 728. 570. 0. 655. 521. 650. 356. 469.]\n", + " [ 367. 725. 827. 104. 655. 0. 1146. 779. 476. 752.]\n", + " [ 841. 368. 736. 1090. 521. 1146. 0. 681. 565. 394.]\n", + " [ 727. 744. 41. 712. 650. 779. 681. 0. 374. 286.]\n", + " [ 444. 398. 371. 454. 356. 476. 565. 374. 0. 274.]\n", + " [ 668. 446. 317. 648. 469. 752. 394. 286. 274. 0.]]\n", + "\n", + "Set parameter LazyConstraints to value 1\n", + "Gurobi Optimizer version 9.5.2 build v9.5.2rc0 (linux64)\n", + "Thread count: 16 physical cores, 32 logical processors, using up to 32 threads\n", + "Optimize a model with 10 rows, 45 columns and 90 nonzeros\n", + "Model fingerprint: 0x719675e5\n", + "Variable types: 0 continuous, 45 integer (45 binary)\n", + "Coefficient statistics:\n", + " Matrix range [1e+00, 1e+00]\n", + " Objective range [4e+01, 1e+03]\n", + " Bounds range [1e+00, 1e+00]\n", + " RHS range [2e+00, 2e+00]\n", + "Presolve time: 0.00s\n", + "Presolved: 10 rows, 45 columns, 90 nonzeros\n", + "Variable types: 0 continuous, 45 integer (45 binary)\n", + "\n", + "Root relaxation: objective 2.921000e+03, 17 iterations, 0.00 seconds (0.00 work units)\n", + "\n", + " Nodes | Current Node | Objective Bounds | Work\n", + " Expl Unexpl | Obj Depth IntInf | Incumbent BestBd Gap | It/Node Time\n", + "\n", + "* 0 0 0 2921.0000000 2921.00000 0.00% - 0s\n", + "\n", + "Cutting planes:\n", + " Lazy constraints: 3\n", + "\n", + "Explored 1 nodes (17 simplex iterations) in 0.01 seconds (0.00 work units)\n", + "Thread count was 32 (of 32 available processors)\n", + "\n", + "Solution count 1: 2921 \n", + "\n", + "Optimal solution found (tolerance 1.00e-04)\n", + "Best objective 2.921000000000e+03, best bound 2.921000000000e+03, gap 0.0000%\n", + "\n", + "User-callback calls 100, time in user-callback 0.00 sec\n" + ] + } + ], + "source": [ + "import random\n", + "import numpy as np\n", + "from scipy.stats import uniform, randint\n", + "from miplearn.problems.tsp import TravelingSalesmanGenerator, build_tsp_model\n", + "\n", + "# Set random seed to make example reproducible\n", + "random.seed(42)\n", + "np.random.seed(42)\n", + "\n", + "# Generate random instances with a fixed ten cities in the 1000x1000 box\n", + "# and random distance scaling factors in the [0.90, 1.10] interval.\n", + "data = TravelingSalesmanGenerator(\n", + " n=randint(low=10, high=11),\n", + " x=uniform(loc=0.0, scale=1000.0),\n", + " y=uniform(loc=0.0, scale=1000.0),\n", + " gamma=uniform(loc=0.90, scale=0.20),\n", + " fix_cities=True,\n", + " round=True,\n", + ").generate(10)\n", + "\n", + "# Print distance matrices for the first two instances\n", + "print(\"distances[0]\\n\", data[0].distances)\n", + "print(\"distances[1]\\n\", data[1].distances)\n", + "print()\n", + "\n", + "# Load and optimize the first instance\n", + "model = build_tsp_model(data[0])\n", + "model.optimize()" + ] + }, + { + "cell_type": "markdown", + "id": "26dfc157-11f4-4564-b368-95ee8200875e", + "metadata": {}, + "source": [ + "## Unit Commitment\n", + "\n", + "The **unit commitment problem** is a mixed-integer optimization problem which asks which power generation units should be turned on and off, at what time, and at what capacity, in order to meet the demand for electricity generation at the lowest cost. Numerous operational constraints are typically enforced, such as *ramping constraints*, which prevent generation units from changing power output levels too quickly from one time step to the next, and *minimum-up* and *minimum-down* constraints, which prevent units from switching on and off too frequently. The unit commitment problem is widely used in power systems planning and operations." + ] + }, + { + "cell_type": "markdown", + "id": "b18b10c9", + "metadata": { + "collapsed": false + }, + "source": [ + "\n", + "
\n", + "Note\n", + "\n", + "MIPLearn includes a simple formulation for the unit commitment problem, which enforces only minimum and maximum power production, as well as minimum-up and minimum-down constraints. The formulation does not enforce, for example, ramping trajectories, piecewise-linear cost curves, start-up costs or transmission and n-1 security constraints. For a more complete set of formulations, solution methods and realistic benchmark instances for the problem, see [UnitCommitment.jl](https://github.com/ANL-CEEESA/UnitCommitment.jl).\n", + "
\n", + "\n", + "### Formulation\n", + "\n", + "Let $T$ be the number of time steps, $G$ be the number of generation units, and let $D_t$ be the power demand (in MW) at time $t$. For each generating unit $g$, let $P^\\max_g$ and $P^\\min_g$ be the maximum and minimum amount of power the unit is able to produce when switched on; let $L_g$ and $l_g$ be the minimum up- and down-time for unit $g$; let $C^\\text{fixed}$ be the cost to keep unit $g$ on for one time step, regardless of its power output level; let $C^\\text{start}$ be the cost to switch unit $g$ on; and let $C^\\text{var}$ be the cost for generator $g$ to produce 1 MW of power. In this formulation, we assume linear production costs. For each generator $g$ and time $t$, let $x_{gt}$ be a binary variable which equals one if unit $g$ is on at time $t$, let $w_{gt}$ be a binary variable which equals one if unit $g$ switches from being off at time $t-1$ to being on at time $t$, and let $p_{gt}$ be a continuous variable which indicates the amount of power generated. The formulation is given by:" + ] + }, + { + "cell_type": "markdown", + "id": "12739207", + "metadata": { + "collapsed": false + }, + "source": [ + "\n", + "$$\n", + "\\begin{align*}\n", + "\\text{minimize} \\;\\;\\;\n", + " & \\sum_{t=1}^T \\sum_{g=1}^G \\left(\n", + " x_{gt} C^\\text{fixed}_g\n", + " + w_{gt} C^\\text{start}_g\n", + " + p_{gt} C^\\text{var}_g\n", + " \\right)\n", + " \\\\\n", + "\\text{such that} \\;\\;\\;\n", + " & \\sum_{k=t-L_g+1}^t w_{gk} \\leq x_{gt}\n", + " & \\forall g\\; \\forall t=L_g-1,\\ldots,T-1 \\\\\n", + " & \\sum_{k=g-l_g+1}^T w_{gt} \\leq 1 - x_{g,t-l_g+1}\n", + " & \\forall g \\forall t=l_g-1,\\ldots,T-1 \\\\\n", + " & w_{gt} \\geq x_{gt} - x_{g,t-1}\n", + " & \\forall g \\forall t=1,\\ldots,T-1 \\\\\n", + " & \\sum_{g=1}^G p_{gt} \\geq D_t\n", + " & \\forall t \\\\\n", + " & P^\\text{min}_g x_{gt} \\leq p_{gt}\n", + " & \\forall g, t \\\\\n", + " & p_{gt} \\leq P^\\text{max}_g x_{gt}\n", + " & \\forall g, t \\\\\n", + " & x_{gt} \\in \\{0, 1\\}\n", + " & \\forall g, t.\n", + "\\end{align*}\n", + "$$" + ] + }, + { + "cell_type": "markdown", + "id": "b5d85554", + "metadata": { + "collapsed": false + }, + "source": [ + "\n", + "The first set of inequalities enforces minimum up-time constraints: if unit $g$ is down at time $t$, then it cannot start up during the previous $L_g$ time steps. The second set of inequalities enforces minimum down-time constraints, and is symmetrical to the previous one. The third set ensures that if unit $g$ starts up at time $t$, then the start up variable must be one. The fourth set ensures that demand is satisfied at each time period. The fifth and sixth sets enforce bounds to the quantity of power generated by each unit.\n", + "\n", + "
\n", + "References\n", + "\n", + "- *Bendotti, P., Fouilhoux, P. & Rottner, C.* **The min-up/min-down unit commitment polytope.** J Comb Optim 36, 1024-1058 (2018). https://doi.org/10.1007/s10878-018-0273-y\n", + "
" + ] + }, + { + "cell_type": "markdown", + "id": "a2f9e098", + "metadata": { + "collapsed": false + }, + "source": [ + "\n", + "### Random instance generator\n", + "\n", + "The class `UnitCommitmentGenerator` can be used to generate random instances of this problem.\n", + "\n", + "First, the user-provided probability distributions `n_units` and `n_periods` are sampled to determine the number of generating units and the number of time steps, respectively. Then, for each unit, the probabilities `max_power` and `min_power` are sampled to determine the unit's maximum and minimum power output. To make it easier to generate valid ranges, `min_power` is not specified as the absolute power level in MW, but rather as a multiplier of `max_power`; for example, if `max_power` samples to 100 and `min_power` samples to 0.5, then the unit's power range is set to `[50,100]`. Then, the distributions `cost_startup`, `cost_prod` and `cost_fixed` are sampled to determine the unit's startup, variable and fixed costs, while the distributions `min_uptime` and `min_downtime` are sampled to determine its minimum up/down-time.\n", + "\n", + "After parameters for the units have been generated, the class then generates a periodic demand curve, with a peak every 12 time steps, in the range $(0.4C, 0.8C)$, where $C$ is the sum of all units' maximum power output. Finally, all costs and demand values are perturbed by random scaling factors independently sampled from the distributions `cost_jitter` and `demand_jitter`, respectively.\n", + "\n", + "If `fix_units=True`, then the list of generators (with their respective parameters) is kept the same for all generated instances. If `cost_jitter` and `demand_jitter` are provided, the instances will still have slightly different costs and demands." + ] + }, + { + "cell_type": "markdown", + "id": "09e98292", + "metadata": { + "collapsed": false + }, + "source": [ + "### Example" + ] + }, + { + "cell_type": "code", + "execution_count": 8, + "id": "e7c16609", + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "min_power[0] [117.79 245.85 271.85 207.7 81.38]\n", + "max_power[0] [218.54 477.82 379.4 319.4 120.21]\n", + "min_uptime[0] [7 6 3 5 7]\n", + "min_downtime[0] [7 3 5 6 2]\n", + "min_power[0] [117.79 245.85 271.85 207.7 81.38]\n", + "cost_startup[0] [3042.42 5247.56 4319.45 2912.29 6118.53]\n", + "cost_prod[0] [ 6.97 14.61 18.32 22.8 39.26]\n", + "cost_fixed[0] [199.67 514.23 592.41 46.45 607.54]\n", + "demand[0]\n", + " [ 905.06 915.41 1166.52 1212.29 1127.81 953.52 905.06 796.21 783.78\n", + " 866.23 768.62 899.59 905.06 946.23 1087.61 1004.24 1048.36 992.03\n", + " 905.06 750.82 691.48 606.15 658.5 809.95]\n", + "\n", + "min_power[1] [117.79 245.85 271.85 207.7 81.38]\n", + "max_power[1] [218.54 477.82 379.4 319.4 120.21]\n", + "min_uptime[1] [7 6 3 5 7]\n", + "min_downtime[1] [7 3 5 6 2]\n", + "min_power[1] [117.79 245.85 271.85 207.7 81.38]\n", + "cost_startup[1] [2458.08 6200.26 4585.74 2666.05 4783.34]\n", + "cost_prod[1] [ 6.31 13.33 20.42 24.37 46.86]\n", + "cost_fixed[1] [196.9 416.42 655.57 52.51 626.15]\n", + "demand[1]\n", + " [ 981.42 840.07 1095.59 1102.03 1088.41 932.29 863.67 848.56 761.33\n", + " 828.28 775.18 834.99 959.76 865.72 1193.52 1058.92 985.19 893.92\n", + " 962.16 781.88 723.15 639.04 602.4 787.02]\n", + "\n", + "Gurobi Optimizer version 9.5.2 build v9.5.2rc0 (linux64)\n", + "Thread count: 6 physical cores, 12 logical processors, using up to 12 threads\n", + "Optimize a model with 578 rows, 360 columns and 2128 nonzeros\n", + "Model fingerprint: 0x4dc1c661\n", + "Variable types: 120 continuous, 240 integer (240 binary)\n", + "Coefficient statistics:\n", + " Matrix range [1e+00, 5e+02]\n", + " Objective range [7e+00, 6e+03]\n", + " Bounds range [1e+00, 1e+00]\n", + " RHS range [1e+00, 1e+03]\n", + "Presolve removed 244 rows and 131 columns\n", + "Presolve time: 0.01s\n", + "Presolved: 334 rows, 229 columns, 842 nonzeros\n", + "Variable types: 116 continuous, 113 integer (113 binary)\n", + "Found heuristic solution: objective 441426.66550\n", + "Found heuristic solution: objective 429461.97680\n", + "Found heuristic solution: objective 374043.64040\n", + "\n", + "Root relaxation: objective 3.361348e+05, 139 iterations, 0.00 seconds (0.00 work units)\n", + "\n", + " Nodes | Current Node | Objective Bounds | Work\n", + " Expl Unexpl | Obj Depth IntInf | Incumbent BestBd Gap | It/Node Time\n", + "\n", + " 0 0 336134.820 0 18 374043.640 336134.820 10.1% - 0s\n", + "H 0 0 368600.14450 336134.820 8.81% - 0s\n", + "H 0 0 364721.76610 364721.766 0.00% - 0s\n", + " 0 0 - 0 364721.766 364721.766 0.00% - 0s\n", + "\n", + "Cutting planes:\n", + " Gomory: 3\n", + " Cover: 8\n", + " Implied bound: 29\n", + " Clique: 222\n", + " MIR: 7\n", + " Flow cover: 7\n", + " RLT: 1\n", + " Relax-and-lift: 7\n", + "\n", + "Explored 1 nodes (232 simplex iterations) in 0.04 seconds (0.02 work units)\n", + "Thread count was 12 (of 12 available processors)\n", + "\n", + "Solution count 5: 364722 368600 374044 ... 441427\n", + "\n", + "Optimal solution found (tolerance 1.00e-04)\n", + "Best objective 3.647217661000e+05, best bound 3.647217661000e+05, gap 0.0000%\n" + ] + } + ], + "source": [ + "import random\n", + "import numpy as np\n", + "from scipy.stats import uniform, randint\n", + "from miplearn.problems.uc import UnitCommitmentGenerator, build_uc_model\n", + "\n", + "# Set random seed to make example reproducible\n", + "random.seed(42)\n", + "np.random.seed(42)\n", + "\n", + "# Generate a random instance with 5 generators and 24 time steps\n", + "data = UnitCommitmentGenerator(\n", + " n_units=randint(low=5, high=6),\n", + " n_periods=randint(low=24, high=25),\n", + " max_power=uniform(loc=50, scale=450),\n", + " min_power=uniform(loc=0.5, scale=0.25),\n", + " cost_startup=uniform(loc=0, scale=10_000),\n", + " cost_prod=uniform(loc=0, scale=50),\n", + " cost_fixed=uniform(loc=0, scale=1_000),\n", + " min_uptime=randint(low=2, high=8),\n", + " min_downtime=randint(low=2, high=8),\n", + " cost_jitter=uniform(loc=0.75, scale=0.5),\n", + " demand_jitter=uniform(loc=0.9, scale=0.2),\n", + " fix_units=True,\n", + ").generate(10)\n", + "\n", + "# Print problem data for the two first instances\n", + "for i in range(2):\n", + " print(f\"min_power[{i}]\", data[i].min_power)\n", + " print(f\"max_power[{i}]\", data[i].max_power)\n", + " print(f\"min_uptime[{i}]\", data[i].min_uptime)\n", + " print(f\"min_downtime[{i}]\", data[i].min_downtime)\n", + " print(f\"min_power[{i}]\", data[i].min_power)\n", + " print(f\"cost_startup[{i}]\", data[i].cost_startup)\n", + " print(f\"cost_prod[{i}]\", data[i].cost_prod)\n", + " print(f\"cost_fixed[{i}]\", data[i].cost_fixed)\n", + " print(f\"demand[{i}]\\n\", data[i].demand)\n", + " print()\n", + "\n", + "# Load and optimize the first instance\n", + "model = build_uc_model(data[0])\n", + "model.optimize()" + ] + }, + { + "cell_type": "markdown", + "id": "169293c7-33e1-4d28-8d39-9982776251d7", + "metadata": {}, + "source": [ + "## Vertex Cover\n", + "\n", + "**Minimum weight vertex cover** is a classical optimization problem in graph theory where the goal is to find the minimum-weight set of vertices that are connected to all of the edges in the graph. The problem generalizes one of Karp's 21 NP-complete problems and has applications in various fields, including bioinformatics and machine learning." + ] + }, + { + "cell_type": "markdown", + "id": "238e9968", + "metadata": { + "collapsed": false + }, + "source": [ + "\n", + "### Formulation\n", + "\n", + "Let $G=(V,E)$ be a simple graph. For each vertex $v \\in V$, let $w_g$ be its weight, and let $x_v$ be a binary decision variable which equals one if $v$ is included in the cover. The mixed-integer linear formulation for the problem is given by:" + ] + }, + { + "cell_type": "markdown", + "id": "d1f1cced", + "metadata": { + "collapsed": false + }, + "source": [ + " $$\n", + "\\begin{align*}\n", + "\\text{minimize} \\;\\;\\;\n", + " & \\sum_{v \\in V} w_v \\\\\n", + "\\text{such that} \\;\\;\\;\n", + " & x_i + x_j \\ge 1 & \\forall \\{i, j\\} \\in E, \\\\\n", + " & x_{i,j} \\in \\{0, 1\\}\n", + " & \\forall \\{i,j\\} \\in E.\n", + "\\end{align*}\n", + "$$" + ] + }, + { + "cell_type": "markdown", + "id": "cbcb1ae0", + "metadata": { + "collapsed": false + }, + "source": [ + "### Random instance generator\n", + "\n", + "The class [MinWeightVertexCoverGenerator][MinWeightVertexCoverGenerator] can be used to generate random instances of this problem. The class accepts exactly the same parameters and behaves exactly in the same way as [MaxWeightStableSetGenerator][MaxWeightStableSetGenerator]. See the [stable set section](#Stable-Set) for more details.\n", + "\n", + "[MinWeightVertexCoverGenerator]: ../../api/problems/#module-miplearn.problems.vertexcover\n", + "[MaxWeightStableSetGenerator]: ../../api/problems/#miplearn.problems.stab.MaxWeightStableSetGenerator\n", + "\n", + "### Example" + ] + }, + { + "cell_type": "code", + "execution_count": 9, + "id": "5fff7afe-5b7a-4889-a502-66751ec979bf", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "graph [(0, 2), (0, 4), (0, 8), (1, 2), (1, 3), (1, 5), (1, 6), (1, 9), (2, 5), (2, 9), (3, 6), (3, 7), (6, 9), (7, 8), (8, 9)]\n", + "weights[0] [37.45 95.07 73.2 59.87 15.6 15.6 5.81 86.62 60.11 70.81]\n", + "weights[1] [ 2.06 96.99 83.24 21.23 18.18 18.34 30.42 52.48 43.19 29.12]\n", + "\n", + "Gurobi Optimizer version 9.5.2 build v9.5.2rc0 (linux64)\n", + "Thread count: 6 physical cores, 12 logical processors, using up to 12 threads\n", + "Optimize a model with 15 rows, 10 columns and 30 nonzeros\n", + "Model fingerprint: 0x2d2d1390\n", + "Variable types: 0 continuous, 10 integer (10 binary)\n", + "Coefficient statistics:\n", + " Matrix range [1e+00, 1e+00]\n", + " Objective range [6e+00, 1e+02]\n", + " Bounds range [1e+00, 1e+00]\n", + " RHS range [1e+00, 1e+00]\n", + "Found heuristic solution: objective 301.0000000\n", + "Presolve removed 7 rows and 2 columns\n", + "Presolve time: 0.00s\n", + "Presolved: 8 rows, 8 columns, 19 nonzeros\n", + "Variable types: 0 continuous, 8 integer (8 binary)\n", + "\n", + "Root relaxation: objective 2.995750e+02, 8 iterations, 0.00 seconds (0.00 work units)\n", + "\n", + " Nodes | Current Node | Objective Bounds | Work\n", + " Expl Unexpl | Obj Depth IntInf | Incumbent BestBd Gap | It/Node Time\n", + "\n", + " 0 0 infeasible 0 301.00000 301.00000 0.00% - 0s\n", + "\n", + "Explored 1 nodes (8 simplex iterations) in 0.01 seconds (0.00 work units)\n", + "Thread count was 12 (of 12 available processors)\n", + "\n", + "Solution count 1: 301 \n", + "\n", + "Optimal solution found (tolerance 1.00e-04)\n", + "Best objective 3.010000000000e+02, best bound 3.010000000000e+02, gap 0.0000%\n" + ] + } + ], + "source": [ + "import random\n", + "import numpy as np\n", + "from scipy.stats import uniform, randint\n", + "from miplearn.problems.vertexcover import MinWeightVertexCoverGenerator, build_vertexcover_model\n", + "\n", + "# Set random seed to make example reproducible\n", + "random.seed(42)\n", + "np.random.seed(42)\n", + "\n", + "# Generate random instances with a fixed 10-node graph,\n", + "# 25% density and random weights in the [0, 100] interval.\n", + "data = MinWeightVertexCoverGenerator(\n", + " w=uniform(loc=0.0, scale=100.0),\n", + " n=randint(low=10, high=11),\n", + " p=uniform(loc=0.25, scale=0.0),\n", + " fix_graph=True,\n", + ").generate(10)\n", + "\n", + "# Print the graph and weights for two instances\n", + "print(\"graph\", data[0].graph.edges)\n", + "print(\"weights[0]\", data[0].weights)\n", + "print(\"weights[1]\", data[1].weights)\n", + "print()\n", + "\n", + "# Load and optimize the first instance\n", + "model = build_vertexcover_model(data[0])\n", + "model.optimize()\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "d1d25734", + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [] + } + ], + "metadata": { + "kernelspec": { + "display_name": "Python 3", + "language": "python", + "name": "python3" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.8.13" + } + }, + "nbformat": 4, + "nbformat_minor": 5 +} diff --git a/0.3/guide/problems/index.html b/0.3/guide/problems/index.html new file mode 100644 index 0000000..9b8df5a --- /dev/null +++ b/0.3/guide/problems/index.html @@ -0,0 +1,1831 @@ + + + + + + + + 1. Benchmark Problems — MIPLearn 0.3 + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
+
+ + + + + + + + +
+ +
+
+
+
+ + + + +
+ + +
+ + + + + + +
+
+ + + + + + + + + +
+ + +
+ +
+ Contents +
+ +
+
+
+
+
+ +
+ + + +
+

1. Benchmark Problems

+
+

1.1. Overview

+

Benchmark sets such as MIPLIB or TSPLIB are usually employed to evaluate the performance of conventional MIP solvers. Two shortcomings, unfortunately, make existing benchmark sets less than ideal for evaluating the performance of learning-enhanced MIP solvers: (i) while existing benchmark sets typically contain hundreds or thousands of instances, machine learning (ML) methods typically benefit from having +orders of magnitude more instances available for training; (ii) current machine learning methods typically provide best performance on sets of homogeneous instances, buch general-purpose benchmark sets contain relatively few examples of each problem type.

+

To tackle this challenge, MIPLearn provides random instance generators for a wide variety of classical optimization problems, covering applications from different fields, that can be used to evaluate new learning-enhanced MIP techniques in a measurable and reproducible way. As of MIPLearn 0.3, nine problem generators are available, each customizable with user-provided probability distribution and flexible parameters. The generators can be configured, for example, to produce large sets of very +similar instances of same size, where only the objective function changes, or more diverse sets of instances, with various sizes and characteristics, belonging to a particular problem class.

+

In the following, we describe the problems included in the library, their MIP formulation and the generation algorithm.

+
+

Warning

+

The random instance generators and formulations shown below are subject to change. If you use them in your research, for reproducibility, you should specify the MIPLearn version and all parameters.

+
+
+

Note

+
    +

  • To make the instances easier to process, all formulations are written as a minimization problem.

    • +

  • Some problem formulations, such as the one for the traveling salesman problem, contain an exponential number of constraints, which are enforced through constraint generation. The MPS files for these problems contain only the constraints that were generated during a trial run, not the entire set of constraints. Resolving the MPS file, therefore, may not generate a feasible primal solution for the problem.

    • +
+
+
+
+

1.2. Bin Packing

+

Bin packing is a combinatorial optimization problem that asks for the optimal way to pack a given set of items into a finite number of containers (or bins) of fixed capacity. More specifically, the problem is to assign indivisible items of different sizes to identical bins, while minimizing the number of bins used. The problem is NP-hard and has many practical applications, including logistics and warehouse management, where it is used to determine how to best store and transport goods using +a limited amount of space.

+
+

Formulation

+

Let \(n\) be the number of items, and \(s_i\) the size of the \(i\)-th item. Also let \(B\) be the size of the bins. For each bin \(j\), let \(y_j\) be a binary decision variable which equals one if the bin is used. For every item-bin pair \((i,j)\), let \(x_{ij}\) be a binary decision variable which equals one if item \(i\) is assigned to bin \(j\). The bin packing problem is formulated as:

+
+\[\begin{split}\begin{align*} +\text{minimize} \;\;\; + & \sum_{j=1}^n y_j \\ +\text{subject to} \;\;\; + & \sum_{i=1}^n s_i x_{ij} \leq B y_j & \forall j=1,\ldots,n \\ + & \sum_{j=1}^n x_{ij} = 1 & \forall i=1,\ldots,n \\ + & y_i \in \{0,1\} & \forall i=1,\ldots,n \\ + & x_{ij} \in \{0,1\} & \forall i,j=1,\ldots,n \\ +\end{align*}\end{split}\]
+
+
+

Random instance generator

+

Random instances of the bin packing problem can be generated using the class BinPackGenerator.

+

If fix_items=False, the class samples the user-provided probability distributions n, sizes and capacity to decide, respectively, the number of items, the sizes of the items and capacity of the bin. All values are sampled independently.

+

If fix_items=True, the class creates a reference instance, using the method previously described, then generates additional instances by perturbing its item sizes and bin capacity. More specifically, the sizes of the items are set to \(s_i \gamma_i\), where \(s_i\) is the size of the \(i\)-th item in the reference instance and \(\gamma_i\) is sampled from sizes_jitter. Similarly, the bin size is set to \(B \beta\), where \(B\) is the reference bin size and +\(\beta\) is sampled from capacity_jitter. The number of items remains the same across all generated instances.

+
+
+

Example

+
+
[1]:
+
+
+
import numpy as np
+from scipy.stats import uniform, randint
+from miplearn.problems.binpack import BinPackGenerator, build_binpack_model
+
+# Set random seed, to make example reproducible
+np.random.seed(42)
+
+# Generate random instances of the binpack problem with ten items
+data = BinPackGenerator(
+    n=randint(low=10, high=11),
+    sizes=uniform(loc=0, scale=25),
+    capacity=uniform(loc=100, scale=0),
+    sizes_jitter=uniform(loc=0.9, scale=0.2),
+    capacity_jitter=uniform(loc=0.9, scale=0.2),
+    fix_items=True,
+).generate(10)
+
+# Print sizes and capacities
+for i in range(10):
+    print(i, data[i].sizes, data[i].capacity)
+print()
+
+# Optimize first instance
+model = build_binpack_model(data[0])
+model.optimize()
+
+
+
+
+
+
+
+
+0 [ 8.47 26.   19.52 14.11  3.65  3.65  1.4  21.76 14.82 16.96] 102.24
+1 [ 8.69 22.78 17.81 14.83  4.12  3.67  1.46 22.05 13.66 18.08] 93.41
+2 [ 8.55 25.9  20.   15.89  3.75  3.59  1.51 21.4  13.89 17.68] 90.69
+3 [10.13 22.62 18.89 14.4   3.92  3.94  1.36 23.69 15.85 19.26] 107.9
+4 [ 9.55 25.77 16.79 14.06  3.55  3.76  1.42 20.66 16.02 17.19] 95.62
+5 [ 9.44 22.06 19.41 13.69  4.28  4.11  1.36 19.51 15.98 18.43] 104.58
+6 [ 9.87 21.74 17.78 13.82  4.18  4.    1.4  19.76 14.46 17.08] 104.59
+7 [ 9.62 25.61 18.2  13.83  4.07  4.1   1.47 22.83 15.01 17.78] 98.55
+8 [ 8.47 21.9  16.58 15.37  3.76  3.91  1.57 20.57 14.76 18.61] 94.58
+9 [ 8.57 22.77 17.06 16.25  4.14  4.    1.56 22.97 14.09 19.09] 100.79
+
+Restricted license - for non-production use only - expires 2023-10-25
+Gurobi Optimizer version 9.5.2 build v9.5.2rc0 (linux64)
+Thread count: 16 physical cores, 32 logical processors, using up to 32 threads
+Optimize a model with 20 rows, 110 columns and 210 nonzeros
+Model fingerprint: 0x1ff9913f
+Variable types: 0 continuous, 110 integer (110 binary)
+Coefficient statistics:
+  Matrix range     [1e+00, 1e+02]
+  Objective range  [1e+00, 1e+00]
+  Bounds range     [1e+00, 1e+00]
+  RHS range        [1e+00, 1e+00]
+Found heuristic solution: objective 5.0000000
+Presolve time: 0.00s
+Presolved: 20 rows, 110 columns, 210 nonzeros
+Variable types: 0 continuous, 110 integer (110 binary)
+
+Root relaxation: objective 1.274844e+00, 38 iterations, 0.00 seconds (0.00 work units)
+
+    Nodes    |    Current Node    |     Objective Bounds      |     Work
+ Expl Unexpl |  Obj  Depth IntInf | Incumbent    BestBd   Gap | It/Node Time
+
+     0     0    1.27484    0    4    5.00000    1.27484  74.5%     -    0s
+H    0     0                       4.0000000    1.27484  68.1%     -    0s
+H    0     0                       2.0000000    1.27484  36.3%     -    0s
+     0     0    1.27484    0    4    2.00000    1.27484  36.3%     -    0s
+
+Explored 1 nodes (38 simplex iterations) in 0.00 seconds (0.00 work units)
+Thread count was 32 (of 32 available processors)
+
+Solution count 3: 2 4 5
+
+Optimal solution found (tolerance 1.00e-04)
+Best objective 2.000000000000e+00, best bound 2.000000000000e+00, gap 0.0000%
+
+
+
+
+
+

1.3. Multi-Dimensional Knapsack

+

The multi-dimensional knapsack problem is a generalization of the classic knapsack problem, which involves selecting a subset of items to be placed in a knapsack such that the total value of the items is maximized without exceeding a maximum weight. In this generalization, items have multiple weights (representing multiple resources), and multiple weight constraints must be satisfied.

+
+

Formulation

+

Let \(n\) be the number of items and \(m\) be the number of resources. For each item \(j\) and resource \(i\), let \(p_j\) be the price of the item, let \(w_{ij}\) be the amount of resource \(j\) item \(i\) consumes (i.e. the \(j\)-th weight of the item), and let \(b_i\) be the total amount of resource \(i\) available (or the size of the \(j\)-th knapsack). The formulation is given by:

+
+\[\begin{split}\begin{align*} + \text{minimize}\;\;\; + & - \sum_{j=1}^n p_j x_j + \\ + \text{subject to}\;\;\; + & \sum_{j=1}^n w_{ij} x_j \leq b_i + & \forall i=1,\ldots,m \\ + & x_j \in \{0,1\} + & \forall j=1,\ldots,n +\end{align*}\end{split}\]
+
+
+

Random instance generator

+

The class MultiKnapsackGenerator can be used to generate random instances of this problem. The number of items \(n\) and knapsacks \(m\) are sampled from the user-provided probability distributions n and m. The weights \(w_{ij}\) are sampled independently from the provided distribution w. The capacity of knapsack \(i\) is set to

+
+\[b_i = \alpha_i \sum_{j=1}^n w_{ij}\]
+

where \(\alpha_i\), the tightness ratio, is sampled from the provided probability distribution alpha. To make the instances more challenging, the costs of the items are linearly correlated to their average weights. More specifically, the price of each item \(j\) is set to:

+
+\[p_j = \sum_{i=1}^m \frac{w_{ij}}{m} + K u_j,\]
+

where \(K\), the correlation coefficient, and \(u_j\), the correlation multiplier, are sampled from the provided probability distributions K and u.

+

If fix_w=True is provided, then \(w_{ij}\) are kept the same in all generated instances. This also implies that \(n\) and \(m\) are kept fixed. Although the prices and capacities are derived from \(w_{ij}\), as long as u and K are not constants, the generated instances will still not be completely identical.

+

If a probability distribution w_jitter is provided, then item weights will be set to \(w_{ij} \gamma_{ij}\) where \(\gamma_{ij}\) is sampled from w_jitter. When combined with fix_w=True, this argument may be used to generate instances where the weight of each item is roughly the same, but not exactly identical, across all instances. The prices of the items and the capacities of the knapsacks will be calculated as above, but using these perturbed weights instead.

+

By default, all generated prices, weights and capacities are rounded to the nearest integer number. If round=False is provided, this rounding will be disabled.

+
+

References

+
    +

  • Freville, Arnaud, and Gérard Plateau. An efficient preprocessing procedure for the multidimensional 0–1 knapsack problem. Discrete applied mathematics 49.1-3 (1994): 189-212.

    • +

  • Fréville, Arnaud. The multidimensional 0–1 knapsack problem: An overview. European Journal of Operational Research 155.1 (2004): 1-21.

    • +
+
+
+
+

Example

+
+
[2]:
+
+
+
import numpy as np
+from scipy.stats import uniform, randint
+from miplearn.problems.multiknapsack import (
+    MultiKnapsackGenerator,
+    build_multiknapsack_model,
+)
+
+# Set random seed, to make example reproducible
+np.random.seed(42)
+
+# Generate ten similar random instances of the multiknapsack problem with
+# ten items, five resources and weights around [0, 1000].
+data = MultiKnapsackGenerator(
+    n=randint(low=10, high=11),
+    m=randint(low=5, high=6),
+    w=uniform(loc=0, scale=1000),
+    K=uniform(loc=100, scale=0),
+    u=uniform(loc=1, scale=0),
+    alpha=uniform(loc=0.25, scale=0),
+    w_jitter=uniform(loc=0.95, scale=0.1),
+    p_jitter=uniform(loc=0.75, scale=0.5),
+    fix_w=True,
+).generate(10)
+
+# Print data for one of the instances
+print("prices\n", data[0].prices)
+print("weights\n", data[0].weights)
+print("capacities\n", data[0].capacities)
+print()
+
+# Build model and optimize
+model = build_multiknapsack_model(data[0])
+model.optimize()
+
+
+
+
+
+
+
+
+prices
+ [350. 692. 454. 709. 605. 543. 321. 674. 571. 341.]
+weights
+ [[392. 977. 764. 622. 158. 163.  56. 840. 574. 696.]
+ [ 20. 948. 860. 209. 178. 184. 293. 541. 414. 305.]
+ [629. 135. 278. 378. 466. 803. 205. 492. 584.  45.]
+ [630. 173.  64. 907. 947. 794. 312.  99. 711. 439.]
+ [117. 506.  35. 915. 266. 662. 312. 516. 521. 178.]]
+capacities
+ [1310.  988. 1004. 1269. 1007.]
+
+Gurobi Optimizer version 9.5.2 build v9.5.2rc0 (linux64)
+Thread count: 16 physical cores, 32 logical processors, using up to 32 threads
+Optimize a model with 5 rows, 10 columns and 50 nonzeros
+Model fingerprint: 0xaf3ac15e
+Variable types: 0 continuous, 10 integer (10 binary)
+Coefficient statistics:
+  Matrix range     [2e+01, 1e+03]
+  Objective range  [3e+02, 7e+02]
+  Bounds range     [1e+00, 1e+00]
+  RHS range        [1e+03, 1e+03]
+Found heuristic solution: objective -804.0000000
+Presolve removed 0 rows and 3 columns
+Presolve time: 0.00s
+Presolved: 5 rows, 7 columns, 34 nonzeros
+Variable types: 0 continuous, 7 integer (7 binary)
+
+Root relaxation: objective -1.428726e+03, 4 iterations, 0.00 seconds (0.00 work units)
+
+    Nodes    |    Current Node    |     Objective Bounds      |     Work
+ Expl Unexpl |  Obj  Depth IntInf | Incumbent    BestBd   Gap | It/Node Time
+
+     0     0 -1428.7265    0    4 -804.00000 -1428.7265  77.7%     -    0s
+H    0     0                    -1279.000000 -1428.7265  11.7%     -    0s
+
+Cutting planes:
+  Cover: 1
+
+Explored 1 nodes (4 simplex iterations) in 0.00 seconds (0.00 work units)
+Thread count was 32 (of 32 available processors)
+
+Solution count 2: -1279 -804
+No other solutions better than -1279
+
+Optimal solution found (tolerance 1.00e-04)
+Best objective -1.279000000000e+03, best bound -1.279000000000e+03, gap 0.0000%
+
+
+
+
+
+

1.4. Capacitated P-Median

+

The capacitated p-median problem is a variation of the classic \(p\)-median problem, in which a set of customers must be served by a set of facilities. In the capacitated \(p\)-Median problem, each facility has a fixed capacity, and the goal is to minimize the total cost of serving the customers while ensuring that the capacity of each facility is not exceeded. Variations of problem are often used in logistics and supply chain management to determine the most efficient locations for +warehouses or distribution centers.

+
+

Formulation

+

Let \(I=\{1,\ldots,n\}\) be the set of customers. For each customer \(i \in I\), let \(d_i\) be its demand and let \(y_i\) be a binary decision variable that equals one if we decide to open a facility at that customer’s location. For each pair \((i,j) \in I \times I\), let \(x_{ij}\) be a binary decision variable that equals one if customer \(i\) is assigned to facility \(j\). Furthermore, let \(w_{ij}\) be the cost of serving customer \(i\) from facility +\(j\), let \(p\) be the number of facilities we must open, and let \(c_j\) be the capacity of facility \(j\). The problem is formulated as:

+
+\[\begin{split}\begin{align*} + \text{minimize}\;\;\; + & \sum_{i \in I} \sum_{j \in I} w_{ij} x_{ij} + \\ + \text{subject to}\;\;\; + & \sum_{j \in I} x_{ij} = 1 & \forall i \in I \\ + & \sum_{j \in I} y_j = p \\ + & \sum_{i \in I} d_i x_{ij} \leq c_j y_j & \forall j \in I \\ + & x_{ij} \in \{0, 1\} & \forall i, j \in I \\ + & y_j \in \{0, 1\} & \forall j \in I +\end{align*}\end{split}\]
+
+
+

Random instance generator

+

The class PMedianGenerator can be used to generate random instances of this problem. First, it decides the number of customers and the parameter \(p\) by sampling the provided n and p distributions, respectively. Then, for each customer \(i\), the class builds its geographical location \((x_i, y_i)\) by sampling the provided x and y distributions. For each \(i\), the demand for customer \(i\) +and the capacity of facility \(i\) are decided by sampling the provided distributions demands and capacities, respectively. Finally, the costs \(w_{ij}\) are set to the Euclidean distance between the locations of customers \(i\) and \(j\).

+

If fixed=True, then the number of customers, their locations, the parameter \(p\), the demands and the capacities are only sampled from their respective distributions exactly once, to build a reference instance which is then randomly perturbed. Specifically, in each perturbation, the distances, demands and capacities are multiplied by random scaling factors sampled from the distributions distances_jitter, demands_jitter and capacities_jitter, respectively. The result is a +list of instances that have the same set of customers, but slightly different demands, capacities and distances.

+
+
+

Example

+
+
[3]:
+
+
+
import numpy as np
+from scipy.stats import uniform, randint
+from miplearn.problems.pmedian import PMedianGenerator, build_pmedian_model
+
+# Set random seed, to make example reproducible
+np.random.seed(42)
+
+# Generate random instances with ten customers located in a
+# 100x100 square, with demands in [0,10], capacities in [0, 250].
+data = PMedianGenerator(
+    x=uniform(loc=0.0, scale=100.0),
+    y=uniform(loc=0.0, scale=100.0),
+    n=randint(low=10, high=11),
+    p=randint(low=5, high=6),
+    demands=uniform(loc=0, scale=10),
+    capacities=uniform(loc=0, scale=250),
+    distances_jitter=uniform(loc=0.9, scale=0.2),
+    demands_jitter=uniform(loc=0.9, scale=0.2),
+    capacities_jitter=uniform(loc=0.9, scale=0.2),
+    fixed=True,
+).generate(10)
+
+# Print data for one of the instances
+print("p =", data[0].p)
+print("distances =\n", data[0].distances)
+print("demands =", data[0].demands)
+print("capacities =", data[0].capacities)
+print()
+
+# Build and optimize model
+model = build_pmedian_model(data[0])
+model.optimize()
+
+
+
+
+
+
+
+
+p = 5
+distances =
+ [[  0.    50.17  82.42  32.76  33.2   35.45  86.88  79.11  43.17  66.2 ]
+ [ 50.17   0.    72.64  72.51  17.06  80.25  39.92  68.93  43.41  42.96]
+ [ 82.42  72.64   0.    71.69  70.92  82.51  67.88   3.76  39.74  30.73]
+ [ 32.76  72.51  71.69   0.    56.56  11.03 101.35  69.39  42.09  68.58]
+ [ 33.2   17.06  70.92  56.56   0.    63.68  54.71  67.16  34.89  44.99]
+ [ 35.45  80.25  82.51  11.03  63.68   0.   111.04  80.29  52.78  79.36]
+ [ 86.88  39.92  67.88 101.35  54.71 111.04   0.    65.13  61.37  40.82]
+ [ 79.11  68.93   3.76  69.39  67.16  80.29  65.13   0.    36.26  27.24]
+ [ 43.17  43.41  39.74  42.09  34.89  52.78  61.37  36.26   0.    26.62]
+ [ 66.2   42.96  30.73  68.58  44.99  79.36  40.82  27.24  26.62   0.  ]]
+demands = [6.12 1.39 2.92 3.66 4.56 7.85 2.   5.14 5.92 0.46]
+capacities = [151.89  42.63  16.26 237.22 241.41 202.1   76.15  24.42 171.06 110.04]
+
+Gurobi Optimizer version 9.5.2 build v9.5.2rc0 (linux64)
+Thread count: 16 physical cores, 32 logical processors, using up to 32 threads
+Optimize a model with 21 rows, 110 columns and 220 nonzeros
+Model fingerprint: 0x8d8d9346
+Variable types: 0 continuous, 110 integer (110 binary)
+Coefficient statistics:
+  Matrix range     [5e-01, 2e+02]
+  Objective range  [4e+00, 1e+02]
+  Bounds range     [1e+00, 1e+00]
+  RHS range        [1e+00, 5e+00]
+Found heuristic solution: objective 368.7900000
+Presolve time: 0.00s
+Presolved: 21 rows, 110 columns, 220 nonzeros
+Variable types: 0 continuous, 110 integer (110 binary)
+Found heuristic solution: objective 245.6400000
+
+Root relaxation: objective 0.000000e+00, 18 iterations, 0.00 seconds (0.00 work units)
+
+    Nodes    |    Current Node    |     Objective Bounds      |     Work
+ Expl Unexpl |  Obj  Depth IntInf | Incumbent    BestBd   Gap | It/Node Time
+
+     0     0    0.00000    0    6  245.64000    0.00000   100%     -    0s
+H    0     0                     185.1900000    0.00000   100%     -    0s
+H    0     0                     148.6300000   17.14595  88.5%     -    0s
+H    0     0                     113.1800000   17.14595  84.9%     -    0s
+     0     0   17.14595    0   10  113.18000   17.14595  84.9%     -    0s
+H    0     0                      99.5000000   17.14595  82.8%     -    0s
+H    0     0                      98.3900000   17.14595  82.6%     -    0s
+H    0     0                      93.9800000   64.28872  31.6%     -    0s
+     0     0   64.28872    0   15   93.98000   64.28872  31.6%     -    0s
+H    0     0                      93.9200000   64.28872  31.5%     -    0s
+     0     0   86.06884    0   15   93.92000   86.06884  8.36%     -    0s
+*    0     0               0      91.2300000   91.23000  0.00%     -    0s
+
+Explored 1 nodes (60 simplex iterations) in 0.01 seconds (0.00 work units)
+Thread count was 32 (of 32 available processors)
+
+Solution count 10: 91.23 93.92 93.98 ... 368.79
+
+Optimal solution found (tolerance 1.00e-04)
+Best objective 9.123000000000e+01, best bound 9.123000000000e+01, gap 0.0000%
+
+
+
+
+
+

1.5. Set cover

+

The set cover problem is a classical NP-hard optimization problem which aims to minimize the number of sets needed to cover all elements in a given universe. Each set may contain a different number of elements, and sets may overlap with each other. This problem can be useful in various real-world scenarios such as scheduling, resource allocation, and network design.

+
+

Formulation

+

Let \(U = \{1,\ldots,n\}\) be a given universe set, and let \(S=\{S_1,\ldots,S_m\}\) be a collection of sets whose union equal \(U\). For each \(j \in \{1,\ldots,m\}\), let \(w_j\) be the weight of set \(S_j\), and let \(x_j\) be a binary decision variable that equals one if set \(S_j\) is chosen. The set cover problem is formulated as:

+
+\[\begin{split}\begin{align*} + \text{minimize}\;\;\; + & \sum_{j=1}^m w_j x_j + \\ + \text{subject to}\;\;\; + & \sum_{j : i \in S_j} x_j \geq 1 & \forall i \in \{1,\ldots,n\} \\ + & x_j \in \{0, 1\} & \forall j \in \{1,\ldots,m\} +\end{align*}\end{split}\]
+
+
+

Random instance generator

+

The class SetCoverGenerator can generate random instances of this problem. The class first decides the number of elements and sets by sampling the provided distributions n_elements and n_sets, respectively. Then it generates a random incidence matrix \(M\), as follows:

+
    +

  1. The density \(d\) of \(M\) is decided by sampling the provided probability distribution density.

    2. +

  2. Each entry of \(M\) is then sampled from the Bernoulli distribution, with probability \(d\).

    3. +

  3. To ensure that each element belongs to at least one set, the class identifies elements that are not contained in any set, then assigns them to a random set (chosen uniformly).

    4. +

  4. Similarly, to ensure that each set contains at least one element, the class identifies empty sets, then modifies them to include one random element (chosen uniformly).

    5. +
+

Finally, the weight of set \(j\) is set to \(w_j + K | S_j |\), where \(w_j\) and \(k\) are sampled from costs and K, respectively, and where \(|S_j|\) denotes the size of set \(S_j\). The parameter \(K\) is used to introduce some correlation between the size of the set and its weight, making the instance more challenging. Note that K is only sampled once for the entire instance.

+

If fix_sets=True, then all generated instances have exactly the same sets and elements. The costs of the sets, however, are multiplied by random scaling factors sampled from the provided probability distribution costs_jitter.

+
+
+

Example

+
+
[4]:
+
+
+
import numpy as np
+from scipy.stats import uniform, randint
+from miplearn.problems.setcover import SetCoverGenerator, build_setcover_model
+
+# Set random seed, to make example reproducible
+np.random.seed(42)
+
+# Build random instances with five elements, ten sets and costs
+# in the [0, 1000] interval, with a correlation factor of 25 and
+# an incidence matrix with 25% density.
+data = SetCoverGenerator(
+    n_elements=randint(low=5, high=6),
+    n_sets=randint(low=10, high=11),
+    costs=uniform(loc=0.0, scale=1000.0),
+    costs_jitter=uniform(loc=0.90, scale=0.20),
+    density=uniform(loc=0.5, scale=0.00),
+    K=uniform(loc=25.0, scale=0.0),
+    fix_sets=True,
+).generate(10)
+
+# Print problem data for one instance
+print("matrix\n", data[0].incidence_matrix)
+print("costs", data[0].costs)
+print()
+
+# Build and optimize model
+model = build_setcover_model(data[0])
+model.optimize()
+
+
+
+
+
+
+
+
+matrix
+ [[1 0 0 0 1 1 1 0 0 0]
+ [1 0 0 1 1 1 1 0 1 1]
+ [0 1 1 1 1 0 1 0 0 1]
+ [0 1 1 0 0 0 1 1 0 1]
+ [1 1 1 0 1 0 1 0 0 1]]
+costs [1044.58  850.13 1014.5   944.83  697.9   971.87  213.49  220.98   70.23
+  425.33]
+
+Gurobi Optimizer version 9.5.2 build v9.5.2rc0 (linux64)
+Thread count: 16 physical cores, 32 logical processors, using up to 32 threads
+Optimize a model with 5 rows, 10 columns and 28 nonzeros
+Model fingerprint: 0xe5c2d4fa
+Variable types: 0 continuous, 10 integer (10 binary)
+Coefficient statistics:
+  Matrix range     [1e+00, 1e+00]
+  Objective range  [7e+01, 1e+03]
+  Bounds range     [1e+00, 1e+00]
+  RHS range        [1e+00, 1e+00]
+Found heuristic solution: objective 213.4900000
+Presolve removed 5 rows and 10 columns
+Presolve time: 0.00s
+Presolve: All rows and columns removed
+
+Explored 0 nodes (0 simplex iterations) in 0.00 seconds (0.00 work units)
+Thread count was 1 (of 32 available processors)
+
+Solution count 1: 213.49
+
+Optimal solution found (tolerance 1.00e-04)
+Best objective 2.134900000000e+02, best bound 2.134900000000e+02, gap 0.0000%
+
+
+
+
+
+

1.6. Set Packing

+

Set packing is a classical optimization problem that asks for the maximum number of disjoint sets within a given list. This problem often arises in real-world situations where a finite number of resources need to be allocated to tasks, such as airline flight crew scheduling.

+
+

Formulation

+

Let \(U=\{1,\ldots,n\}\) be a given universe set, and let \(S = \{S_1, \ldots, S_m\}\) be a collection of subsets of \(U\). For each subset \(j \in \{1, \ldots, m\}\), let \(w_j\) be the weight of \(S_j\) and let \(x_j\) be a binary decision variable which equals one if set \(S_j\) is chosen. The problem is formulated as:

+
+\[\begin{split}\begin{align*} + \text{minimize}\;\;\; + & -\sum_{j=1}^m w_j x_j + \\ + \text{subject to}\;\;\; + & \sum_{j : i \in S_j} x_j \leq 1 & \forall i \in \{1,\ldots,n\} \\ + & x_j \in \{0, 1\} & \forall j \in \{1,\ldots,m\} +\end{align*}\end{split}\]
+
+
+

Random instance generator

+

The class SetPackGenerator can generate random instances of this problem. It accepts exactly the same arguments, and generates instance data in exactly the same way as SetCoverGenerator. For more details, please see the documentation for that class.

+
+
+

Example

+
+
[5]:
+
+
+
import numpy as np
+from scipy.stats import uniform, randint
+from miplearn.problems.setpack import SetPackGenerator, build_setpack_model
+
+# Set random seed, to make example reproducible
+np.random.seed(42)
+
+# Build random instances with five elements, ten sets and costs
+# in the [0, 1000] interval, with a correlation factor of 25 and
+# an incidence matrix with 25% density.
+data = SetPackGenerator(
+    n_elements=randint(low=5, high=6),
+    n_sets=randint(low=10, high=11),
+    costs=uniform(loc=0.0, scale=1000.0),
+    costs_jitter=uniform(loc=0.90, scale=0.20),
+    density=uniform(loc=0.5, scale=0.00),
+    K=uniform(loc=25.0, scale=0.0),
+    fix_sets=True,
+).generate(10)
+
+# Print problem data for one instance
+print("matrix\n", data[0].incidence_matrix)
+print("costs", data[0].costs)
+print()
+
+# Build and optimize model
+model = build_setpack_model(data[0])
+model.optimize()
+
+
+
+
+
+
+
+
+matrix
+ [[1 0 0 0 1 1 1 0 0 0]
+ [1 0 0 1 1 1 1 0 1 1]
+ [0 1 1 1 1 0 1 0 0 1]
+ [0 1 1 0 0 0 1 1 0 1]
+ [1 1 1 0 1 0 1 0 0 1]]
+costs [1044.58  850.13 1014.5   944.83  697.9   971.87  213.49  220.98   70.23
+  425.33]
+
+Gurobi Optimizer version 9.5.2 build v9.5.2rc0 (linux64)
+Thread count: 16 physical cores, 32 logical processors, using up to 32 threads
+Optimize a model with 5 rows, 10 columns and 28 nonzeros
+Model fingerprint: 0x4ee91388
+Variable types: 0 continuous, 10 integer (10 binary)
+Coefficient statistics:
+  Matrix range     [1e+00, 1e+00]
+  Objective range  [7e+01, 1e+03]
+  Bounds range     [1e+00, 1e+00]
+  RHS range        [1e+00, 1e+00]
+Found heuristic solution: objective -1265.560000
+Presolve removed 5 rows and 10 columns
+Presolve time: 0.00s
+Presolve: All rows and columns removed
+
+Explored 0 nodes (0 simplex iterations) in 0.00 seconds (0.00 work units)
+Thread count was 1 (of 32 available processors)
+
+Solution count 2: -1986.37 -1265.56
+No other solutions better than -1986.37
+
+Optimal solution found (tolerance 1.00e-04)
+Best objective -1.986370000000e+03, best bound -1.986370000000e+03, gap 0.0000%
+
+
+
+
+
+

1.7. Stable Set

+

The maximum-weight stable set problem is a classical optimization problem in graph theory which asks for the maximum-weight subset of vertices in a graph such that no two vertices in the subset are adjacent. The problem often arises in real-world scheduling or resource allocation situations, where stable sets represent tasks or resources that can be chosen simultaneously without conflicts.

+
+

Formulation

+

Let \(G=(V,E)\) be a simple undirected graph, and for each vertex \(v \in V\), let \(w_v\) be its weight. The problem is formulated as:

+
+\[\begin{split}\begin{align*} +\text{minimize} \;\;\; & -\sum_{v \in V} w_v x_v \\ +\text{such that} \;\;\; & \sum_{v \in C} x_v \leq 1 & \forall C \in \mathcal{C} \\ +& x_v \in \{0, 1\} & \forall v \in V +\end{align*}\end{split}\]
+

where \(\mathcal{C}\) is the set of cliques in \(G\). We recall that a clique is a subset of vertices in which every pair of vertices is adjacent.

+
+
+

Random instance generator

+

The class MaxWeightStableSetGenerator can be used to generate random instances of this problem. The class first samples the user-provided probability distributions n and p to decide the number of vertices and the density of the graph. Then, it generates a random Erdős-Rényi graph \(G_{n,p}\). We recall that, in such a graph, each potential edge is included with probabilty \(p\), independently for each +other. The class then samples the provided probability distribution w to decide the vertex weights.

+

If fix_graph=True, then all generated instances have the same random graph. For each instance, the weights are decided by sampling w, as described above.

+
+
+

Example

+
+
[24]:
+
+
+
import random
+import numpy as np
+from scipy.stats import uniform, randint
+from miplearn.problems.stab import MaxWeightStableSetGenerator, build_stab_model
+
+# Set random seed to make example reproducible
+random.seed(42)
+np.random.seed(42)
+
+# Generate random instances with a fixed 10-node graph,
+# 25% density and random weights in the [0, 100] interval.
+data = MaxWeightStableSetGenerator(
+    w=uniform(loc=0.0, scale=100.0),
+    n=randint(low=10, high=11),
+    p=uniform(loc=0.25, scale=0.0),
+    fix_graph=True,
+).generate(10)
+
+# Print the graph and weights for two instances
+print("graph", data[0].graph.edges)
+print("weights[0]", data[0].weights)
+print("weights[1]", data[1].weights)
+print()
+
+# Load and optimize the first instance
+model = build_stab_model(data[0])
+model.optimize()
+
+
+
+
+
+
+
+
+graph [(0, 2), (0, 4), (0, 8), (1, 2), (1, 3), (1, 5), (1, 6), (1, 9), (2, 5), (2, 9), (3, 6), (3, 7), (6, 9), (7, 8), (8, 9)]
+weights[0] [37.45 95.07 73.2  59.87 15.6  15.6   5.81 86.62 60.11 70.81]
+weights[1] [ 2.06 96.99 83.24 21.23 18.18 18.34 30.42 52.48 43.19 29.12]
+
+Gurobi Optimizer version 9.5.2 build v9.5.2rc0 (linux64)
+Thread count: 16 physical cores, 32 logical processors, using up to 32 threads
+Optimize a model with 10 rows, 10 columns and 24 nonzeros
+Model fingerprint: 0xf4c21689
+Variable types: 0 continuous, 10 integer (10 binary)
+Coefficient statistics:
+  Matrix range     [1e+00, 1e+00]
+  Objective range  [6e+00, 1e+02]
+  Bounds range     [1e+00, 1e+00]
+  RHS range        [1e+00, 1e+00]
+Found heuristic solution: objective -219.1400000
+Presolve removed 2 rows and 2 columns
+Presolve time: 0.00s
+Presolved: 8 rows, 8 columns, 19 nonzeros
+Variable types: 0 continuous, 8 integer (8 binary)
+
+Root relaxation: objective -2.205650e+02, 4 iterations, 0.00 seconds (0.00 work units)
+
+    Nodes    |    Current Node    |     Objective Bounds      |     Work
+ Expl Unexpl |  Obj  Depth IntInf | Incumbent    BestBd   Gap | It/Node Time
+
+     0     0 infeasible    0      -219.14000 -219.14000  0.00%     -    0s
+
+Explored 1 nodes (4 simplex iterations) in 0.00 seconds (0.00 work units)
+Thread count was 32 (of 32 available processors)
+
+Solution count 1: -219.14
+No other solutions better than -219.14
+
+Optimal solution found (tolerance 1.00e-04)
+Best objective -2.191400000000e+02, best bound -2.191400000000e+02, gap 0.0000%
+
+
+
+
+
+

1.8. Traveling Salesman

+

Given a list of cities and the distances between them, the traveling salesman problem asks for the shortest route starting at the first city, visiting each other city exactly once, then returning to the first city. This problem is a generalization of the Hamiltonian path problem, one of Karp’s 21 NP-complete problems, and has many practical applications, including routing delivery trucks and scheduling airline routes.

+
+

Formulation

+

Let \(G=(V,E)\) be a simple undirected graph. For each edge \(e \in E\), let \(d_e\) be its weight (or distance) and let \(x_e\) be a binary decision variable which equals one if \(e\) is included in the route. The problem is formulated as:

+
+\[\begin{split}\begin{align*} +\text{minimize} \;\;\; + & \sum_{e \in E} d_e x_e \\ +\text{such that} \;\;\; + & \sum_{e : \delta(v)} x_e = 2 & \forall v \in V, \\ + & \sum_{e \in \delta(S)} x_e \geq 2 & \forall S \subsetneq V, |S| \neq \emptyset, \\ + & x_e \in \{0, 1\} & \forall e \in E, +\end{align*}\end{split}\]
+

where \(\delta(v)\) denotes the set of edges adjacent to vertex \(v\), and \(\delta(S)\) denotes the set of edges that have one extremity in \(S\) and one in \(V \setminus S\). Because of its exponential size, we enforce the second set of inequalities as lazy constraints.

+
+
+

Random instance generator

+

The class TravelingSalesmanGenerator can be used to generate random instances of this problem. Initially, the class samples the user-provided probability distribution n to decide how many cities to generate. Then, for each city \(i\), the class generates its geographical location \((x_i, y_i)\) by sampling the provided distributions x and y. The distance \(d_{ij}\) between cities \(i\) and +\(j\) is then set to

+
+\[\gamma_{ij} \sqrt{(x_i - x_j)^2 + (y_i - y_j)^2},\]
+

where \(\gamma\) is a random scaling factor sampled from the provided probability distribution gamma.

+

If fix_cities=True, then the list of cities is kept the same for all generated instances. The \(\gamma\) values, however, and therefore also the distances, are still different. By default, all distances \(d_{ij}\) are rounded to the nearest integer. If round=False is provided, this rounding will be disabled.

+
+
+

Example

+
+
[32]:
+
+
+
import random
+import numpy as np
+from scipy.stats import uniform, randint
+from miplearn.problems.tsp import TravelingSalesmanGenerator, build_tsp_model
+
+# Set random seed to make example reproducible
+random.seed(42)
+np.random.seed(42)
+
+# Generate random instances with a fixed ten cities in the 1000x1000 box
+# and random distance scaling factors in the [0.90, 1.10] interval.
+data = TravelingSalesmanGenerator(
+    n=randint(low=10, high=11),
+    x=uniform(loc=0.0, scale=1000.0),
+    y=uniform(loc=0.0, scale=1000.0),
+    gamma=uniform(loc=0.90, scale=0.20),
+    fix_cities=True,
+    round=True,
+).generate(10)
+
+# Print distance matrices for the first two instances
+print("distances[0]\n", data[0].distances)
+print("distances[1]\n", data[1].distances)
+print()
+
+# Load and optimize the first instance
+model = build_tsp_model(data[0])
+model.optimize()
+
+
+
+
+
+
+
+
+distances[0]
+ [[   0.  513.  762.  358.  325.  374.  932.  731.  391.  634.]
+ [ 513.    0.  726.  765.  163.  754.  409.  719.  446.  400.]
+ [ 762.  726.    0.  780.  756.  744.  656.   40.  383.  334.]
+ [ 358.  765.  780.    0.  549.  117.  925.  702.  422.  728.]
+ [ 325.  163.  756.  549.    0.  663.  526.  708.  377.  462.]
+ [ 374.  754.  744.  117.  663.    0. 1072.  802.  501.  853.]
+ [ 932.  409.  656.  925.  526. 1072.    0.  654.  603.  433.]
+ [ 731.  719.   40.  702.  708.  802.  654.    0.  381.  255.]
+ [ 391.  446.  383.  422.  377.  501.  603.  381.    0.  287.]
+ [ 634.  400.  334.  728.  462.  853.  433.  255.  287.    0.]]
+distances[1]
+ [[   0.  493.  900.  354.  323.  367.  841.  727.  444.  668.]
+ [ 493.    0.  690.  687.  175.  725.  368.  744.  398.  446.]
+ [ 900.  690.    0.  666.  728.  827.  736.   41.  371.  317.]
+ [ 354.  687.  666.    0.  570.  104. 1090.  712.  454.  648.]
+ [ 323.  175.  728.  570.    0.  655.  521.  650.  356.  469.]
+ [ 367.  725.  827.  104.  655.    0. 1146.  779.  476.  752.]
+ [ 841.  368.  736. 1090.  521. 1146.    0.  681.  565.  394.]
+ [ 727.  744.   41.  712.  650.  779.  681.    0.  374.  286.]
+ [ 444.  398.  371.  454.  356.  476.  565.  374.    0.  274.]
+ [ 668.  446.  317.  648.  469.  752.  394.  286.  274.    0.]]
+
+Set parameter LazyConstraints to value 1
+Gurobi Optimizer version 9.5.2 build v9.5.2rc0 (linux64)
+Thread count: 16 physical cores, 32 logical processors, using up to 32 threads
+Optimize a model with 10 rows, 45 columns and 90 nonzeros
+Model fingerprint: 0x719675e5
+Variable types: 0 continuous, 45 integer (45 binary)
+Coefficient statistics:
+  Matrix range     [1e+00, 1e+00]
+  Objective range  [4e+01, 1e+03]
+  Bounds range     [1e+00, 1e+00]
+  RHS range        [2e+00, 2e+00]
+Presolve time: 0.00s
+Presolved: 10 rows, 45 columns, 90 nonzeros
+Variable types: 0 continuous, 45 integer (45 binary)
+
+Root relaxation: objective 2.921000e+03, 17 iterations, 0.00 seconds (0.00 work units)
+
+    Nodes    |    Current Node    |     Objective Bounds      |     Work
+ Expl Unexpl |  Obj  Depth IntInf | Incumbent    BestBd   Gap | It/Node Time
+
+*    0     0               0    2921.0000000 2921.00000  0.00%     -    0s
+
+Cutting planes:
+  Lazy constraints: 3
+
+Explored 1 nodes (17 simplex iterations) in 0.01 seconds (0.00 work units)
+Thread count was 32 (of 32 available processors)
+
+Solution count 1: 2921
+
+Optimal solution found (tolerance 1.00e-04)
+Best objective 2.921000000000e+03, best bound 2.921000000000e+03, gap 0.0000%
+
+User-callback calls 100, time in user-callback 0.00 sec
+
+
+
+
+
+

1.9. Unit Commitment

+

The unit commitment problem is a mixed-integer optimization problem which asks which power generation units should be turned on and off, at what time, and at what capacity, in order to meet the demand for electricity generation at the lowest cost. Numerous operational constraints are typically enforced, such as ramping constraints, which prevent generation units from changing power output levels too quickly from one time step to the next, and minimum-up and minimum-down constraints, +which prevent units from switching on and off too frequently. The unit commitment problem is widely used in power systems planning and operations.

+
+

Note

+

MIPLearn includes a simple formulation for the unit commitment problem, which enforces only minimum and maximum power production, as well as minimum-up and minimum-down constraints. The formulation does not enforce, for example, ramping trajectories, piecewise-linear cost curves, start-up costs or transmission and n-1 security constraints. For a more complete set of formulations, solution methods and realistic benchmark instances for the problem, see +UnitCommitment.jl.

+
+
+

Formulation

+

Let \(T\) be the number of time steps, \(G\) be the number of generation units, and let \(D_t\) be the power demand (in MW) at time \(t\). For each generating unit \(g\), let \(P^\max_g\) and \(P^\min_g\) be the maximum and minimum amount of power the unit is able to produce when switched on; let \(L_g\) and \(l_g\) be the minimum up- and down-time for unit \(g\); let \(C^\text{fixed}\) be the cost to keep unit \(g\) on for one time step, +regardless of its power output level; let \(C^\text{start}\) be the cost to switch unit \(g\) on; and let \(C^\text{var}\) be the cost for generator \(g\) to produce 1 MW of power. In this formulation, we assume linear production costs. For each generator \(g\) and time \(t\), let \(x_{gt}\) be a binary variable which equals one if unit \(g\) is on at time \(t\), let \(w_{gt}\) be a binary variable which equals one if unit \(g\) switches from being off +at time \(t-1\) to being on at time \(t\), and let \(p_{gt}\) be a continuous variable which indicates the amount of power generated. The formulation is given by:

+
+\[\begin{split}\begin{align*} +\text{minimize} \;\;\; + & \sum_{t=1}^T \sum_{g=1}^G \left( + x_{gt} C^\text{fixed}_g + + w_{gt} C^\text{start}_g + + p_{gt} C^\text{var}_g + \right) + \\ +\text{such that} \;\;\; + & \sum_{k=t-L_g+1}^t w_{gk} \leq x_{gt} + & \forall g\; \forall t=L_g-1,\ldots,T-1 \\ + & \sum_{k=g-l_g+1}^T w_{gt} \leq 1 - x_{g,t-l_g+1} + & \forall g \forall t=l_g-1,\ldots,T-1 \\ + & w_{gt} \geq x_{gt} - x_{g,t-1} + & \forall g \forall t=1,\ldots,T-1 \\ + & \sum_{g=1}^G p_{gt} \geq D_t + & \forall t \\ + & P^\text{min}_g x_{gt} \leq p_{gt} + & \forall g, t \\ + & p_{gt} \leq P^\text{max}_g x_{gt} + & \forall g, t \\ + & x_{gt} \in \{0, 1\} + & \forall g, t. +\end{align*}\end{split}\]
+

The first set of inequalities enforces minimum up-time constraints: if unit \(g\) is down at time \(t\), then it cannot start up during the previous \(L_g\) time steps. The second set of inequalities enforces minimum down-time constraints, and is symmetrical to the previous one. The third set ensures that if unit \(g\) starts up at time \(t\), then the start up variable must be one. The fourth set ensures that demand is satisfied at each time period. The fifth and sixth sets +enforce bounds to the quantity of power generated by each unit.

+
+

References

+ +
+
+
+

Random instance generator

+

The class UnitCommitmentGenerator can be used to generate random instances of this problem.

+

First, the user-provided probability distributions n_units and n_periods are sampled to determine the number of generating units and the number of time steps, respectively. Then, for each unit, the probabilities max_power and min_power are sampled to determine the unit’s maximum and minimum power output. To make it easier to generate valid ranges, min_power is not specified as the absolute power level in MW, but rather as a multiplier of max_power; for example, if +max_power samples to 100 and min_power samples to 0.5, then the unit’s power range is set to [50,100]. Then, the distributions cost_startup, cost_prod and cost_fixed are sampled to determine the unit’s startup, variable and fixed costs, while the distributions min_uptime and min_downtime are sampled to determine its minimum up/down-time.

+

After parameters for the units have been generated, the class then generates a periodic demand curve, with a peak every 12 time steps, in the range \((0.4C, 0.8C)\), where \(C\) is the sum of all units’ maximum power output. Finally, all costs and demand values are perturbed by random scaling factors independently sampled from the distributions cost_jitter and demand_jitter, respectively.

+

If fix_units=True, then the list of generators (with their respective parameters) is kept the same for all generated instances. If cost_jitter and demand_jitter are provided, the instances will still have slightly different costs and demands.

+
+
+

Example

+
+
[8]:
+
+
+
import random
+import numpy as np
+from scipy.stats import uniform, randint
+from miplearn.problems.uc import UnitCommitmentGenerator, build_uc_model
+
+# Set random seed to make example reproducible
+random.seed(42)
+np.random.seed(42)
+
+# Generate a random instance with 5 generators and 24 time steps
+data = UnitCommitmentGenerator(
+    n_units=randint(low=5, high=6),
+    n_periods=randint(low=24, high=25),
+    max_power=uniform(loc=50, scale=450),
+    min_power=uniform(loc=0.5, scale=0.25),
+    cost_startup=uniform(loc=0, scale=10_000),
+    cost_prod=uniform(loc=0, scale=50),
+    cost_fixed=uniform(loc=0, scale=1_000),
+    min_uptime=randint(low=2, high=8),
+    min_downtime=randint(low=2, high=8),
+    cost_jitter=uniform(loc=0.75, scale=0.5),
+    demand_jitter=uniform(loc=0.9, scale=0.2),
+    fix_units=True,
+).generate(10)
+
+# Print problem data for the two first instances
+for i in range(2):
+    print(f"min_power[{i}]", data[i].min_power)
+    print(f"max_power[{i}]", data[i].max_power)
+    print(f"min_uptime[{i}]", data[i].min_uptime)
+    print(f"min_downtime[{i}]", data[i].min_downtime)
+    print(f"min_power[{i}]", data[i].min_power)
+    print(f"cost_startup[{i}]", data[i].cost_startup)
+    print(f"cost_prod[{i}]", data[i].cost_prod)
+    print(f"cost_fixed[{i}]", data[i].cost_fixed)
+    print(f"demand[{i}]\n", data[i].demand)
+    print()
+
+# Load and optimize the first instance
+model = build_uc_model(data[0])
+model.optimize()
+
+
+
+
+
+
+
+
+min_power[0] [117.79 245.85 271.85 207.7   81.38]
+max_power[0] [218.54 477.82 379.4  319.4  120.21]
+min_uptime[0] [7 6 3 5 7]
+min_downtime[0] [7 3 5 6 2]
+min_power[0] [117.79 245.85 271.85 207.7   81.38]
+cost_startup[0] [3042.42 5247.56 4319.45 2912.29 6118.53]
+cost_prod[0] [ 6.97 14.61 18.32 22.8  39.26]
+cost_fixed[0] [199.67 514.23 592.41  46.45 607.54]
+demand[0]
+ [ 905.06  915.41 1166.52 1212.29 1127.81  953.52  905.06  796.21  783.78
+  866.23  768.62  899.59  905.06  946.23 1087.61 1004.24 1048.36  992.03
+  905.06  750.82  691.48  606.15  658.5   809.95]
+
+min_power[1] [117.79 245.85 271.85 207.7   81.38]
+max_power[1] [218.54 477.82 379.4  319.4  120.21]
+min_uptime[1] [7 6 3 5 7]
+min_downtime[1] [7 3 5 6 2]
+min_power[1] [117.79 245.85 271.85 207.7   81.38]
+cost_startup[1] [2458.08 6200.26 4585.74 2666.05 4783.34]
+cost_prod[1] [ 6.31 13.33 20.42 24.37 46.86]
+cost_fixed[1] [196.9  416.42 655.57  52.51 626.15]
+demand[1]
+ [ 981.42  840.07 1095.59 1102.03 1088.41  932.29  863.67  848.56  761.33
+  828.28  775.18  834.99  959.76  865.72 1193.52 1058.92  985.19  893.92
+  962.16  781.88  723.15  639.04  602.4   787.02]
+
+Gurobi Optimizer version 9.5.2 build v9.5.2rc0 (linux64)
+Thread count: 6 physical cores, 12 logical processors, using up to 12 threads
+Optimize a model with 578 rows, 360 columns and 2128 nonzeros
+Model fingerprint: 0x4dc1c661
+Variable types: 120 continuous, 240 integer (240 binary)
+Coefficient statistics:
+  Matrix range     [1e+00, 5e+02]
+  Objective range  [7e+00, 6e+03]
+  Bounds range     [1e+00, 1e+00]
+  RHS range        [1e+00, 1e+03]
+Presolve removed 244 rows and 131 columns
+Presolve time: 0.01s
+Presolved: 334 rows, 229 columns, 842 nonzeros
+Variable types: 116 continuous, 113 integer (113 binary)
+Found heuristic solution: objective 441426.66550
+Found heuristic solution: objective 429461.97680
+Found heuristic solution: objective 374043.64040
+
+Root relaxation: objective 3.361348e+05, 139 iterations, 0.00 seconds (0.00 work units)
+
+    Nodes    |    Current Node    |     Objective Bounds      |     Work
+ Expl Unexpl |  Obj  Depth IntInf | Incumbent    BestBd   Gap | It/Node Time
+
+     0     0 336134.820    0   18 374043.640 336134.820  10.1%     -    0s
+H    0     0                    368600.14450 336134.820  8.81%     -    0s
+H    0     0                    364721.76610 364721.766  0.00%     -    0s
+     0     0          -    0      364721.766 364721.766  0.00%     -    0s
+
+Cutting planes:
+  Gomory: 3
+  Cover: 8
+  Implied bound: 29
+  Clique: 222
+  MIR: 7
+  Flow cover: 7
+  RLT: 1
+  Relax-and-lift: 7
+
+Explored 1 nodes (232 simplex iterations) in 0.04 seconds (0.02 work units)
+Thread count was 12 (of 12 available processors)
+
+Solution count 5: 364722 368600 374044 ... 441427
+
+Optimal solution found (tolerance 1.00e-04)
+Best objective 3.647217661000e+05, best bound 3.647217661000e+05, gap 0.0000%
+
+
+
+
+
+

1.10. Vertex Cover

+

Minimum weight vertex cover is a classical optimization problem in graph theory where the goal is to find the minimum-weight set of vertices that are connected to all of the edges in the graph. The problem generalizes one of Karp’s 21 NP-complete problems and has applications in various fields, including bioinformatics and machine learning.

+
+

Formulation

+

Let \(G=(V,E)\) be a simple graph. For each vertex \(v \in V\), let \(w_g\) be its weight, and let \(x_v\) be a binary decision variable which equals one if \(v\) is included in the cover. The mixed-integer linear formulation for the problem is given by:

+
+\[\begin{split}\begin{align*} +\text{minimize} \;\;\; + & \sum_{v \in V} w_v \\ +\text{such that} \;\;\; + & x_i + x_j \ge 1 & \forall \{i, j\} \in E, \\ + & x_{i,j} \in \{0, 1\} + & \forall \{i,j\} \in E. +\end{align*}\end{split}\]
+
+
+

Random instance generator

+

The class MinWeightVertexCoverGenerator can be used to generate random instances of this problem. The class accepts exactly the same parameters and behaves exactly in the same way as MaxWeightStableSetGenerator. See the stable set section for more details.

+
+
+

Example

+
+
[9]:
+
+
+
import random
+import numpy as np
+from scipy.stats import uniform, randint
+from miplearn.problems.vertexcover import MinWeightVertexCoverGenerator, build_vertexcover_model
+
+# Set random seed to make example reproducible
+random.seed(42)
+np.random.seed(42)
+
+# Generate random instances with a fixed 10-node graph,
+# 25% density and random weights in the [0, 100] interval.
+data = MinWeightVertexCoverGenerator(
+    w=uniform(loc=0.0, scale=100.0),
+    n=randint(low=10, high=11),
+    p=uniform(loc=0.25, scale=0.0),
+    fix_graph=True,
+).generate(10)
+
+# Print the graph and weights for two instances
+print("graph", data[0].graph.edges)
+print("weights[0]", data[0].weights)
+print("weights[1]", data[1].weights)
+print()
+
+# Load and optimize the first instance
+model = build_vertexcover_model(data[0])
+model.optimize()
+
+
+
+
+
+
+
+
+graph [(0, 2), (0, 4), (0, 8), (1, 2), (1, 3), (1, 5), (1, 6), (1, 9), (2, 5), (2, 9), (3, 6), (3, 7), (6, 9), (7, 8), (8, 9)]
+weights[0] [37.45 95.07 73.2  59.87 15.6  15.6   5.81 86.62 60.11 70.81]
+weights[1] [ 2.06 96.99 83.24 21.23 18.18 18.34 30.42 52.48 43.19 29.12]
+
+Gurobi Optimizer version 9.5.2 build v9.5.2rc0 (linux64)
+Thread count: 6 physical cores, 12 logical processors, using up to 12 threads
+Optimize a model with 15 rows, 10 columns and 30 nonzeros
+Model fingerprint: 0x2d2d1390
+Variable types: 0 continuous, 10 integer (10 binary)
+Coefficient statistics:
+  Matrix range     [1e+00, 1e+00]
+  Objective range  [6e+00, 1e+02]
+  Bounds range     [1e+00, 1e+00]
+  RHS range        [1e+00, 1e+00]
+Found heuristic solution: objective 301.0000000
+Presolve removed 7 rows and 2 columns
+Presolve time: 0.00s
+Presolved: 8 rows, 8 columns, 19 nonzeros
+Variable types: 0 continuous, 8 integer (8 binary)
+
+Root relaxation: objective 2.995750e+02, 8 iterations, 0.00 seconds (0.00 work units)
+
+    Nodes    |    Current Node    |     Objective Bounds      |     Work
+ Expl Unexpl |  Obj  Depth IntInf | Incumbent    BestBd   Gap | It/Node Time
+
+     0     0 infeasible    0       301.00000  301.00000  0.00%     -    0s
+
+Explored 1 nodes (8 simplex iterations) in 0.01 seconds (0.00 work units)
+Thread count was 12 (of 12 available processors)
+
+Solution count 1: 301
+
+Optimal solution found (tolerance 1.00e-04)
+Best objective 3.010000000000e+02, best bound 3.010000000000e+02, gap 0.0000%
+
+
+
+
[ ]:
+
+
+

+
+
+
+
+
+
+ + +
+ + +
+ + MIPLearn + 2. Training Data Collectors + +
+ +
+
+
+
+

+ + © Copyright 2020-2022, UChicago Argonne, LLC.
+

+
+
+
+ + +
+
+ + + + + + \ No newline at end of file diff --git a/0.3/guide/solvers.ipynb b/0.3/guide/solvers.ipynb new file mode 100644 index 0000000..33c2e56 --- /dev/null +++ b/0.3/guide/solvers.ipynb @@ -0,0 +1,211 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "id": "3371f072-be1e-4c47-b765-b5d30fdbfae6", + "metadata": {}, + "source": [ + "# Solvers\n", + "\n", + "## LearningSolver\n", + "\n", + "### Example" + ] + }, + { + "cell_type": "code", + "execution_count": 3, + "id": "dac704b5", + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Gurobi Optimizer version 9.5.2 build v9.5.2rc0 (linux64)\n", + "Thread count: 6 physical cores, 12 logical processors, using up to 12 threads\n", + "Optimize a model with 10 rows, 45 columns and 90 nonzeros\n", + "Model fingerprint: 0x6ddcd141\n", + "Coefficient statistics:\n", + " Matrix range [1e+00, 1e+00]\n", + " Objective range [4e+01, 1e+03]\n", + " Bounds range [1e+00, 1e+00]\n", + " RHS range [2e+00, 2e+00]\n", + "Presolve time: 0.00s\n", + "Presolved: 10 rows, 45 columns, 90 nonzeros\n", + "\n", + "Iteration Objective Primal Inf. Dual Inf. Time\n", + " 0 6.3600000e+02 1.700000e+01 0.000000e+00 0s\n", + " 15 2.7610000e+03 0.000000e+00 0.000000e+00 0s\n", + "\n", + "Solved in 15 iterations and 0.01 seconds (0.00 work units)\n", + "Optimal objective 2.761000000e+03\n", + "Set parameter LazyConstraints to value 1\n", + "Gurobi Optimizer version 9.5.2 build v9.5.2rc0 (linux64)\n", + "Thread count: 6 physical cores, 12 logical processors, using up to 12 threads\n", + "Optimize a model with 10 rows, 45 columns and 90 nonzeros\n", + "Model fingerprint: 0x74ca3d0a\n", + "Variable types: 0 continuous, 45 integer (45 binary)\n", + "Coefficient statistics:\n", + " Matrix range [1e+00, 1e+00]\n", + " Objective range [4e+01, 1e+03]\n", + " Bounds range [1e+00, 1e+00]\n", + " RHS range [2e+00, 2e+00]\n", + "\n", + "User MIP start produced solution with objective 2796 (0.01s)\n", + "Loaded user MIP start with objective 2796\n", + "\n", + "Presolve time: 0.00s\n", + "Presolved: 10 rows, 45 columns, 90 nonzeros\n", + "Variable types: 0 continuous, 45 integer (45 binary)\n", + "\n", + "Root relaxation: objective 2.761000e+03, 14 iterations, 0.00 seconds (0.00 work units)\n", + "\n", + " Nodes | Current Node | Objective Bounds | Work\n", + " Expl Unexpl | Obj Depth IntInf | Incumbent BestBd Gap | It/Node Time\n", + "\n", + " 0 0 cutoff 0 2796.00000 2796.00000 0.00% - 0s\n", + "\n", + "Cutting planes:\n", + " Lazy constraints: 3\n", + "\n", + "Explored 1 nodes (15 simplex iterations) in 0.02 seconds (0.00 work units)\n", + "Thread count was 12 (of 12 available processors)\n", + "\n", + "Solution count 1: 2796 \n", + "\n", + "Optimal solution found (tolerance 1.00e-04)\n", + "Best objective 2.796000000000e+03, best bound 2.796000000000e+03, gap 0.0000%\n", + "\n", + "User-callback calls 103, time in user-callback 0.00 sec\n", + "Gurobi Optimizer version 9.5.2 build v9.5.2rc0 (linux64)\n", + "Thread count: 6 physical cores, 12 logical processors, using up to 12 threads\n", + "Optimize a model with 10 rows, 45 columns and 90 nonzeros\n", + "Model fingerprint: 0x74ca3d0a\n", + "Variable types: 0 continuous, 45 integer (45 binary)\n", + "Coefficient statistics:\n", + " Matrix range [1e+00, 1e+00]\n", + " Objective range [4e+01, 1e+03]\n", + " Bounds range [1e+00, 1e+00]\n", + " RHS range [2e+00, 2e+00]\n", + "Presolved: 10 rows, 45 columns, 90 nonzeros\n", + "\n", + "Continuing optimization...\n", + "\n", + "\n", + "Cutting planes:\n", + " Lazy constraints: 3\n", + "\n", + "Explored 1 nodes (15 simplex iterations) in 0.01 seconds (0.00 work units)\n", + "Thread count was 12 (of 12 available processors)\n", + "\n", + "Solution count 1: 2796 \n", + "\n", + "Optimal solution found (tolerance 1.00e-04)\n", + "Best objective 2.796000000000e+03, best bound 2.796000000000e+03, gap 0.0000%\n", + "\n", + "User-callback calls 27, time in user-callback 0.00 sec\n" + ] + } + ], + "source": [ + "import random\n", + "\n", + "import numpy as np\n", + "from scipy.stats import uniform, randint\n", + "from sklearn.linear_model import LogisticRegression\n", + "\n", + "from miplearn.classifiers.minprob import MinProbabilityClassifier\n", + "from miplearn.classifiers.singleclass import SingleClassFix\n", + "from miplearn.collectors.basic import BasicCollector\n", + "from miplearn.components.primal.actions import SetWarmStart\n", + "from miplearn.components.primal.indep import IndependentVarsPrimalComponent\n", + "from miplearn.extractors.AlvLouWeh2017 import AlvLouWeh2017Extractor\n", + "from miplearn.io import save\n", + "from miplearn.problems.tsp import (\n", + " TravelingSalesmanGenerator,\n", + " build_tsp_model,\n", + ")\n", + "from miplearn.solvers.learning import LearningSolver\n", + "\n", + "# Set random seed to make example reproducible.\n", + "random.seed(42)\n", + "np.random.seed(42)\n", + "\n", + "# Generate a few instances of the traveling salesman problem.\n", + "data = TravelingSalesmanGenerator(\n", + " n=randint(low=10, high=11),\n", + " x=uniform(loc=0.0, scale=1000.0),\n", + " y=uniform(loc=0.0, scale=1000.0),\n", + " gamma=uniform(loc=0.90, scale=0.20),\n", + " fix_cities=True,\n", + " round=True,\n", + ").generate(50)\n", + "\n", + "# Save instance data to data/tsp/00000.pkl.gz, data/tsp/00001.pkl.gz, ...\n", + "all_data = save(data, \"data/tsp\")\n", + "\n", + "# Split train/test data\n", + "train_data = all_data[:40]\n", + "test_data = all_data[40:]\n", + "\n", + "# Collect training data\n", + "bc = BasicCollector(time_limit_sec=3600)\n", + "bc.collect(train_data, build_tsp_model, n_jobs=4)\n", + "\n", + "# Build learning solver\n", + "solver = LearningSolver(\n", + " components=[\n", + " IndependentVarsPrimalComponent(\n", + " base_clf=SingleClassFix(\n", + " MinProbabilityClassifier(\n", + " base_clf=LogisticRegression(),\n", + " thresholds=[0.95, 0.95],\n", + " ),\n", + " ),\n", + " extractor=AlvLouWeh2017Extractor(),\n", + " action=SetWarmStart(),\n", + " )\n", + " ]\n", + ")\n", + "\n", + "# Train ML models\n", + "solver.fit(train_data)\n", + "\n", + "# Solve a test instance\n", + "solver.optimize(test_data[0], build_tsp_model);" + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "id": "e27d2cbd-5341-461d-bbc1-8131aee8d949", + "metadata": {}, + "outputs": [], + "source": [] + } + ], + "metadata": { + "kernelspec": { + "display_name": "Python 3", + "language": "python", + "name": "python3" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.8.13" + } + }, + "nbformat": 4, + "nbformat_minor": 5 +} diff --git a/0.3/guide/solvers/index.html b/0.3/guide/solvers/index.html new file mode 100644 index 0000000..f3f9a4f --- /dev/null +++ b/0.3/guide/solvers/index.html @@ -0,0 +1,691 @@ + + + + + + + + 5. Solvers — MIPLearn 0.3 + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
+
+ + + + + + + + +
+ +
+
+
+
+ + + + +
+ + +
+ + + + + + +
+
+ + + + + + + + + +
+ + +
+ +
+ Contents +
+ +
+
+
+
+
+ +
+ + + +
+

5. Solvers

+
+

5.1. LearningSolver

+
+

Example

+
+
[3]:
+
+
+
import random
+
+import numpy as np
+from scipy.stats import uniform, randint
+from sklearn.linear_model import LogisticRegression
+
+from miplearn.classifiers.minprob import MinProbabilityClassifier
+from miplearn.classifiers.singleclass import SingleClassFix
+from miplearn.collectors.basic import BasicCollector
+from miplearn.components.primal.actions import SetWarmStart
+from miplearn.components.primal.indep import IndependentVarsPrimalComponent
+from miplearn.extractors.AlvLouWeh2017 import AlvLouWeh2017Extractor
+from miplearn.io import save
+from miplearn.problems.tsp import (
+    TravelingSalesmanGenerator,
+    build_tsp_model,
+)
+from miplearn.solvers.learning import LearningSolver
+
+# Set random seed to make example reproducible.
+random.seed(42)
+np.random.seed(42)
+
+# Generate a few instances of the traveling salesman problem.
+data = TravelingSalesmanGenerator(
+    n=randint(low=10, high=11),
+    x=uniform(loc=0.0, scale=1000.0),
+    y=uniform(loc=0.0, scale=1000.0),
+    gamma=uniform(loc=0.90, scale=0.20),
+    fix_cities=True,
+    round=True,
+).generate(50)
+
+# Save instance data to data/tsp/00000.pkl.gz, data/tsp/00001.pkl.gz, ...
+all_data = save(data, "data/tsp")
+
+# Split train/test data
+train_data = all_data[:40]
+test_data = all_data[40:]
+
+# Collect training data
+bc = BasicCollector(time_limit_sec=3600)
+bc.collect(train_data, build_tsp_model, n_jobs=4)
+
+# Build learning solver
+solver = LearningSolver(
+    components=[
+        IndependentVarsPrimalComponent(
+            base_clf=SingleClassFix(
+                MinProbabilityClassifier(
+                    base_clf=LogisticRegression(),
+                    thresholds=[0.95, 0.95],
+                ),
+            ),
+            extractor=AlvLouWeh2017Extractor(),
+            action=SetWarmStart(),
+        )
+    ]
+)
+
+# Train ML models
+solver.fit(train_data)
+
+# Solve a test instance
+solver.optimize(test_data[0], build_tsp_model);
+
+
+
+
+
+
+
+
+Gurobi Optimizer version 9.5.2 build v9.5.2rc0 (linux64)
+Thread count: 6 physical cores, 12 logical processors, using up to 12 threads
+Optimize a model with 10 rows, 45 columns and 90 nonzeros
+Model fingerprint: 0x6ddcd141
+Coefficient statistics:
+  Matrix range     [1e+00, 1e+00]
+  Objective range  [4e+01, 1e+03]
+  Bounds range     [1e+00, 1e+00]
+  RHS range        [2e+00, 2e+00]
+Presolve time: 0.00s
+Presolved: 10 rows, 45 columns, 90 nonzeros
+
+Iteration    Objective       Primal Inf.    Dual Inf.      Time
+       0    6.3600000e+02   1.700000e+01   0.000000e+00      0s
+      15    2.7610000e+03   0.000000e+00   0.000000e+00      0s
+
+Solved in 15 iterations and 0.01 seconds (0.00 work units)
+Optimal objective  2.761000000e+03
+Set parameter LazyConstraints to value 1
+Gurobi Optimizer version 9.5.2 build v9.5.2rc0 (linux64)
+Thread count: 6 physical cores, 12 logical processors, using up to 12 threads
+Optimize a model with 10 rows, 45 columns and 90 nonzeros
+Model fingerprint: 0x74ca3d0a
+Variable types: 0 continuous, 45 integer (45 binary)
+Coefficient statistics:
+  Matrix range     [1e+00, 1e+00]
+  Objective range  [4e+01, 1e+03]
+  Bounds range     [1e+00, 1e+00]
+  RHS range        [2e+00, 2e+00]
+
+User MIP start produced solution with objective 2796 (0.01s)
+Loaded user MIP start with objective 2796
+
+Presolve time: 0.00s
+Presolved: 10 rows, 45 columns, 90 nonzeros
+Variable types: 0 continuous, 45 integer (45 binary)
+
+Root relaxation: objective 2.761000e+03, 14 iterations, 0.00 seconds (0.00 work units)
+
+    Nodes    |    Current Node    |     Objective Bounds      |     Work
+ Expl Unexpl |  Obj  Depth IntInf | Incumbent    BestBd   Gap | It/Node Time
+
+     0     0     cutoff    0      2796.00000 2796.00000  0.00%     -    0s
+
+Cutting planes:
+  Lazy constraints: 3
+
+Explored 1 nodes (15 simplex iterations) in 0.02 seconds (0.00 work units)
+Thread count was 12 (of 12 available processors)
+
+Solution count 1: 2796
+
+Optimal solution found (tolerance 1.00e-04)
+Best objective 2.796000000000e+03, best bound 2.796000000000e+03, gap 0.0000%
+
+User-callback calls 103, time in user-callback 0.00 sec
+Gurobi Optimizer version 9.5.2 build v9.5.2rc0 (linux64)
+Thread count: 6 physical cores, 12 logical processors, using up to 12 threads
+Optimize a model with 10 rows, 45 columns and 90 nonzeros
+Model fingerprint: 0x74ca3d0a
+Variable types: 0 continuous, 45 integer (45 binary)
+Coefficient statistics:
+  Matrix range     [1e+00, 1e+00]
+  Objective range  [4e+01, 1e+03]
+  Bounds range     [1e+00, 1e+00]
+  RHS range        [2e+00, 2e+00]
+Presolved: 10 rows, 45 columns, 90 nonzeros
+
+Continuing optimization...
+
+
+Cutting planes:
+  Lazy constraints: 3
+
+Explored 1 nodes (15 simplex iterations) in 0.01 seconds (0.00 work units)
+Thread count was 12 (of 12 available processors)
+
+Solution count 1: 2796
+
+Optimal solution found (tolerance 1.00e-04)
+Best objective 2.796000000000e+03, best bound 2.796000000000e+03, gap 0.0000%
+
+User-callback calls 27, time in user-callback 0.00 sec
+
+
+
+
[2]:
+
+
+

+
+
+
+
+
+
+ + +
+ + +
+ + 4. Primal Components + 6. Benchmark Problems + +
+ +
+
+
+
+

+ + © Copyright 2020-2022, UChicago Argonne, LLC.
+

+
+
+
+ + +
+
+ + + + + + \ No newline at end of file diff --git a/0.3/index.html b/0.3/index.html new file mode 100644 index 0000000..c764e63 --- /dev/null +++ b/0.3/index.html @@ -0,0 +1,413 @@ + + + + + + + + MIPLearn — MIPLearn 0.3 + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
+
+ + + + + + + + +
+ +
+
+
+
+ + + + +
+ + +
+ + + + + + +
+
+ + + + + + + + + +
+ + +
+ +
+ Contents +
+ +
+
+
+
+
+ +
+ +
+

MIPLearn

+

MIPLearn is an extensible framework for solving discrete optimization problems using a combination of Mixed-Integer Linear Programming (MIP) and Machine Learning (ML). MIPLearn uses ML methods to automatically identify patterns in previously solved instances of the problem, then uses these patterns to accelerate the performance of conventional state-of-the-art MIP solvers such as CPLEX, Gurobi or XPRESS.

+

Unlike pure ML methods, MIPLearn is not only able to find high-quality solutions to discrete optimization problems, but it can also prove the optimality and feasibility of these solutions. Unlike conventional MIP solvers, MIPLearn can take full advantage of very specific observations that happen to be true in a particular family of instances (such as the observation that a particular constraint is typically redundant, or that a particular variable typically assumes a certain value). For certain classes of problems, this approach has been shown to provide significant performance benefits (see benchmarks and references).

+
+

Contents

+
+

User Guide

+ +
+
+

API Reference

+ +
+
+
+ + +
+ + +
+ + 1. Benchmark Problems + +
+ +
+
+
+
+

+ + © Copyright 2020-2022, UChicago Argonne, LLC.
+

+
+
+
+ + +
+
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+ miplearn +
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Collectors & Extractors","8. Components","10. Helpers","6. Benchmark Problems","9. Solvers","2. Training Data Collectors","3. Feature Extractors","4. Primal Components","1. Benchmark Problems","5. Solvers","MIPLearn","Getting started (JuMP)","Getting started (Pyomo)"],titleterms:{"1000x1000":[],"abstract":4,"var":7,access:[11,12],action:[1,7],alvlouweh2017:0,alvlouweh2017extractor:6,api:10,background:[],basic:[0,5],benchmark:[3,8],bin:8,binpack:3,box:[],capacit:8,citi:[],classifi:0,collector:[0,5],commit:8,compon:[1,7],content:10,cover:8,data:[5,11,12],dimension:8,distanc:[],exampl:[5,6,7,8,9],expert:[1,7],expertprimalcompon:[],extractor:[0,6],factor:[],featur:[0,6],field:[0,5],first:[],fix:[],format:5,formul:8,gener:[8,11,12],get:[11,12],guid:10,gurobi:4,h5fieldsextractor:6,hdf5:5,helper:2,indep:1,independ:7,independentvarsprimalcompon:[],instal:[11,12],instanc:[8,11,12],interv:[],introduct:[11,12],joint:[1,7],jointvarsprimalcompon:[],jump:11,knapsack:8,learn:4,learningsolv:9,load:[],make:[],matric:[],maximum:[],median:8,mem:1,memor:7,memorizingprimalcompon:[],minimum:[],minprob:0,miplearn:[0,1,2,3,4,10],model:[11,12],multi:8,multiknapsack:3,optim:[11,12],overview:[5,6,8],pack:8,pmedian:3,primal:[1,7],print:[],problem:[3,8,11,12],pyomo:12,random:8,refer:10,reproduc:[],salesman:8,scale:[],seed:[],set:8,setcov:3,setpack:3,simpl:[11,12],singleclass:0,solut:[11,12],solv:[11,12],solver:[4,9],stab:3,stabl:8,start:[11,12],ten:[],test:[11,12],train:[5,11,12],travel:8,tsp:3,two:[],unit:8,user:10,variabl:[],vertex:8,vertexcov:3,weight:[]}}) \ No newline at end of file diff --git a/0.3/tutorials/getting-started-jl.ipynb b/0.3/tutorials/getting-started-jl.ipynb new file mode 100644 index 0000000..5b3ee60 --- /dev/null +++ b/0.3/tutorials/getting-started-jl.ipynb @@ -0,0 +1,625 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "id": "6b8983b1", + "metadata": { + "tags": [] + }, + "source": [ + "# Getting started (JuMP)\n", + "\n", + "## Introduction\n", + "\n", + "**MIPLearn** is an open source framework that uses machine learning (ML) to accelerate the performance of both commercial and open source mixed-integer programming solvers (e.g. Gurobi, CPLEX, XPRESS, Cbc or SCIP). In this tutorial, we will:\n", + "\n", + "1. Install the Python/Pyomo version of MIPLearn\n", + "2. Model a simple optimization problem using JuMP\n", + "3. Generate training data and train the ML models\n", + "4. Use the ML models together Gurobi to solve new instances\n", + "\n", + "
\n", + "Note\n", + " \n", + "The Python/Pyomo version of MIPLearn is currently only compatible with with Gurobi, CPLEX and XPRESS. For broader solver compatibility, see the Julia/JuMP version of the package.\n", + "
\n", + "\n", + "
\n", + "Warning\n", + " \n", + "MIPLearn is still in early development stage. If run into any bugs or issues, please submit a bug report in our GitHub repository. Comments, suggestions and pull requests are also very welcome!\n", + " \n", + "
\n" + ] + }, + { + "cell_type": "markdown", + "id": "02f0a927", + "metadata": {}, + "source": [ + "## Installation\n", + "\n", + "MIPLearn is available in two versions:\n", + "\n", + "- Python version, compatible with the Pyomo modeling language,\n", + "- Julia version, compatible with the JuMP modeling language.\n", + "\n", + "In this tutorial, we will demonstrate how to use and install the Python/Pyomo version of the package. The first step is to install Python 3.8+ in your computer. See the [official Python website for more instructions](https://www.python.org/downloads/). After Python is installed, we proceed to install MIPLearn using `pip`:" + ] + }, + { + "cell_type": "code", + "execution_count": 1, + "id": "cd8a69c1", + "metadata": {}, + "outputs": [], + "source": [ + "# !pip install MIPLearn==0.2.0.dev13" + ] + }, + { + "cell_type": "markdown", + "id": "e8274543", + "metadata": {}, + "source": [ + "In addition to MIPLearn itself, we will also install Gurobi 9.5, a state-of-the-art commercial MILP solver. This step also install a demo license for Gurobi, which should able to solve the small optimization problems in this tutorial. A paid license is required for solving large-scale problems." + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "id": "dcc8756c", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Looking in indexes: https://pypi.gurobi.com\n", + "Requirement already satisfied: gurobipy<9.6,>=9.5 in /opt/anaconda3/envs/miplearn/lib/python3.8/site-packages (9.5.1)\n" + ] + } + ], + "source": [ + "!pip install --upgrade -i https://pypi.gurobi.com 'gurobipy>=9.5,<9.6'" + ] + }, + { + "cell_type": "markdown", + "id": "a14e4550", + "metadata": {}, + "source": [ + "
\n", + " \n", + "Note\n", + " \n", + "In the code above, we install specific version of all packages to ensure that this tutorial keeps running in the future, even when newer (and possibly incompatible) versions of the packages are released. This is usually a recommended practice for all Python projects.\n", + " \n", + "
" + ] + }, + { + "cell_type": "markdown", + "id": "16b86823", + "metadata": {}, + "source": [ + "## Modeling a simple optimization problem\n", + "\n", + "To illustrate how can MIPLearn be used, we will model and solve a small optimization problem related to power systems optimization. The problem we discuss below is a simplification of the **unit commitment problem,** a practical optimization problem solved daily by electric grid operators around the world. \n", + "\n", + "Suppose that you work at a utility company, and that it is your job to decide which electrical generators should be online at a certain hour of the day, as well as how much power should each generator produce. More specifically, assume that your company owns $n$ generators, denoted by $g_1, \\ldots, g_n$. Each generator can either be online or offline. An online generator $g_i$ can produce between $p^\\text{min}_i$ to $p^\\text{max}_i$ megawatts of power, and it costs your company $c^\\text{fix}_i + c^\\text{var}_i y_i$, where $y_i$ is the amount of power produced. An offline generator produces nothing and costs nothing. You also know that the total amount of power to be produced needs to be exactly equal to the total demand $d$ (in megawatts). To minimize the costs to your company, which generators should be online, and how much power should they produce?\n", + "\n", + "This simple problem can be modeled as a *mixed-integer linear optimization* problem as follows. For each generator $g_i$, let $x_i \\in \\{0,1\\}$ be a decision variable indicating whether $g_i$ is online, and let $y_i \\geq 0$ be a decision variable indicating how much power does $g_i$ produce. The problem is then given by:\n", + "\n", + "$$\n", + "\\begin{align}\n", + "\\text{minimize } \\quad & \\sum_{i=1}^n \\left( c^\\text{fix}_i x_i + c^\\text{var}_i y_i \\right) \\\\\n", + "\\text{subject to } \\quad & y_i \\leq p^\\text{max}_i x_i & i=1,\\ldots,n \\\\\n", + "& y_i \\geq p^\\text{min}_i x_i & i=1,\\ldots,n \\\\\n", + "& \\sum_{i=1}^n y_i = d \\\\\n", + "& x_i \\in \\{0,1\\} & i=1,\\ldots,n \\\\\n", + "& y_i \\geq 0 & i=1,\\ldots,n\n", + "\\end{align}\n", + "$$\n", + "\n", + "
\n", + " \n", + "Note\n", + " \n", + "We use a simplified version of the unit commitment problem in this tutorial just to make it easier to follow. MIPLearn can also handle realistic, large-scale versions of this problem. See benchmarks for more details.\n", + " \n", + "
\n", + "\n", + "Next, let us convert this abstract mathematical formulation into a concrete optimization model, using Python and Pyomo. We start by defining a data class `UnitCommitmentData`, which holds all the input data." + ] + }, + { + "cell_type": "code", + "execution_count": 3, + "id": "22a67170-10b4-43d3-8708-014d91141e73", + "metadata": { + "tags": [] + }, + "outputs": [], + "source": [ + "from dataclasses import dataclass\n", + "import numpy as np\n", + "\n", + "@dataclass\n", + "class UnitCommitmentData:\n", + " demand: float\n", + " pmin: np.ndarray\n", + " pmax: np.ndarray\n", + " cfix: np.ndarray\n", + " cvar: np.ndarray" + ] + }, + { + "cell_type": "markdown", + "id": "29f55efa-0751-465a-9b0a-a821d46a3d40", + "metadata": {}, + "source": [ + "Next, we write a `build_uc_model` function, which converts the input data into a concrete Pyomo model." + ] + }, + { + "cell_type": "code", + "execution_count": 4, + "id": "2f67032f-0d74-4317-b45c-19da0ec859e9", + "metadata": {}, + "outputs": [], + "source": [ + "import pyomo.environ as pe\n", + "\n", + "def build_uc_model(data: UnitCommitmentData) -> pe.ConcreteModel:\n", + " model = pe.ConcreteModel()\n", + " n = len(data.pmin)\n", + " model.x = pe.Var(range(n), domain=pe.Binary)\n", + " model.y = pe.Var(range(n), domain=pe.NonNegativeReals)\n", + " model.obj = pe.Objective(\n", + " expr=sum(\n", + " data.cfix[i] * model.x[i] +\n", + " data.cvar[i] * model.y[i]\n", + " for i in range(n)\n", + " )\n", + " )\n", + " model.eq_max_power = pe.ConstraintList()\n", + " model.eq_min_power = pe.ConstraintList()\n", + " for i in range(n):\n", + " model.eq_max_power.add(model.y[i] <= data.pmax[i] * model.x[i])\n", + " model.eq_min_power.add(model.y[i] >= data.pmin[i] * model.x[i])\n", + " model.eq_demand = pe.Constraint(\n", + " expr=sum(model.y[i] for i in range(n)) == data.demand,\n", + " )\n", + " return model" + ] + }, + { + "cell_type": "markdown", + "id": "c22714a3", + "metadata": {}, + "source": [ + "At this point, we can already use Pyomo and any mixed-integer linear programming solver to find optimal solutions to any instance of this problem. To illustrate this, let us solve a small instance with three generators:" + ] + }, + { + "cell_type": "code", + "execution_count": 5, + "id": "2a896f47", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Set parameter Threads to value 1\n", + "Set parameter Seed to value 42\n", + "Restricted license - for non-production use only - expires 2023-10-25\n", + "obj = 1320.0\n", + "x = [-0.0, 1.0, 1.0]\n", + "y = [0.0, 60.0, 40.0]\n" + ] + } + ], + "source": [ + "model = build_uc_model(\n", + " UnitCommitmentData(\n", + " demand = 100.0,\n", + " pmin = [10, 20, 30],\n", + " pmax = [50, 60, 70],\n", + " cfix = [700, 600, 500],\n", + " cvar = [1.5, 2.0, 2.5],\n", + " )\n", + ")\n", + "\n", + "solver = pe.SolverFactory(\"gurobi_persistent\")\n", + "solver.set_instance(model)\n", + "solver.solve()\n", + "print(\"obj =\", model.obj())\n", + "print(\"x =\", [model.x[i].value for i in range(3)])\n", + "print(\"y =\", [model.y[i].value for i in range(3)])" + ] + }, + { + "cell_type": "markdown", + "id": "41b03bbc", + "metadata": {}, + "source": [ + "Running the code above, we found that the optimal solution for our small problem instance costs \\$1320. It is achieve by keeping generators 2 and 3 online and producing, respectively, 60 MW and 40 MW of power." + ] + }, + { + "cell_type": "markdown", + "id": "cf60c1dd", + "metadata": {}, + "source": [ + "## Generating training data\n", + "\n", + "Although Gurobi could solve the small example above in a fraction of a second, it gets slower for larger and more complex versions of the problem. If this is a problem that needs to be solved frequently, as it is often the case in practice, it could make sense to spend some time upfront generating a **trained** version of Gurobi, which can solve new instances (similar to the ones it was trained on) faster.\n", + "\n", + "In the following, we will use MIPLearn to train machine learning models that is able to predict the optimal solution for instances that follow a given probability distribution, then it will provide this predicted solution to Gurobi as a warm start. Before we can train the model, we need to collect training data by solving a large number of instances. In real-world situations, we may construct these training instances based on historical data. In this tutorial, we will construct them using a random instance generator:" + ] + }, + { + "cell_type": "code", + "execution_count": 6, + "id": "5eb09fab", + "metadata": {}, + "outputs": [], + "source": [ + "from scipy.stats import uniform\n", + "from typing import List\n", + "import random\n", + "\n", + "def random_uc_data(samples: int, n: int, seed: int = 42) -> List[UnitCommitmentData]:\n", + " random.seed(seed)\n", + " np.random.seed(seed)\n", + " pmin = uniform(loc=100_000.0, scale=400_000.0).rvs(n)\n", + " pmax = pmin * uniform(loc=2.0, scale=2.5).rvs(n)\n", + " cfix = pmin * uniform(loc=100.0, scale=25.0).rvs(n)\n", + " cvar = uniform(loc=1.25, scale=0.25).rvs(n)\n", + " return [\n", + " UnitCommitmentData(\n", + " demand = pmax.sum() * uniform(loc=0.5, scale=0.25).rvs(),\n", + " pmin = pmin,\n", + " pmax = pmax,\n", + " cfix = cfix,\n", + " cvar = cvar,\n", + " )\n", + " for i in range(samples)\n", + " ]" + ] + }, + { + "cell_type": "markdown", + "id": "3a03a7ac", + "metadata": {}, + "source": [ + "In this example, for simplicity, only the demands change from one instance to the next. We could also have randomized the costs, production limits or even the number of units. The more randomization we have in the training data, however, the more challenging it is for the machine learning models to learn solution patterns.\n", + "\n", + "Now we generate 500 instances of this problem, each one with 50 generators, and we use 450 of these instances for training. After generating the instances, we write them to individual files. MIPLearn uses files during the training process because, for large-scale optimization problems, it is often impractical to hold in memory the entire training data, as well as the concrete Pyomo models. Files also make it much easier to solve multiple instances simultaneously, potentially even on multiple machines. We will cover parallel and distributed computing in a future tutorial. The code below generates the files `uc/train/00000.pkl.gz`, `uc/train/00001.pkl.gz`, etc., which contain the input data in compressed (gzipped) pickle format." + ] + }, + { + "cell_type": "code", + "execution_count": 7, + "id": "6156752c", + "metadata": {}, + "outputs": [], + "source": [ + "from miplearn import save\n", + "data = random_uc_data(samples=500, n=50)\n", + "train_files = save(data[0:450], \"uc/train/\")\n", + "test_files = save(data[450:500], \"uc/test/\")" + ] + }, + { + "cell_type": "markdown", + "id": "b17af877", + "metadata": {}, + "source": [ + "Finally, we use `LearningSolver` to solve all the training instances. `LearningSolver` is the main component provided by MIPLearn, which integrates MIP solvers and ML. The optimal solutions, along with other useful training data, are stored in HDF5 files `uc/train/00000.h5`, `uc/train/00001.h5`, etc." + ] + }, + { + "cell_type": "code", + "execution_count": 12, + "id": "7623f002", + "metadata": {}, + "outputs": [], + "source": [ + "from miplearn import LearningSolver\n", + "solver = LearningSolver()\n", + "solver.solve(train_files, build_uc_model);" + ] + }, + { + "cell_type": "markdown", + "id": "2f24ee83", + "metadata": {}, + "source": [ + "## Solving test instances\n", + "\n", + "With training data in hand, we can now fit the ML models, using the `LearningSolver.fit` method, then solve the test instances with `LearningSolver.solve`, as shown below. The `tee=True` parameter asks MIPLearn to print the solver log to the screen." + ] + }, + { + "cell_type": "code", + "execution_count": 9, + "id": "c8385030", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Set parameter LogFile to value \"/tmp/tmpvbaqbyty.log\"\n", + "Set parameter QCPDual to value 1\n", + "Gurobi Optimizer version 9.5.1 build v9.5.1rc2 (linux64)\n", + "Thread count: 16 physical cores, 32 logical processors, using up to 1 threads\n", + "Optimize a model with 101 rows, 100 columns and 250 nonzeros\n", + "Model fingerprint: 0x8de73876\n", + "Coefficient statistics:\n", + " Matrix range [1e+00, 2e+06]\n", + " Objective range [1e+00, 6e+07]\n", + " Bounds range [1e+00, 1e+00]\n", + " RHS range [2e+07, 2e+07]\n", + "Presolve removed 100 rows and 50 columns\n", + "Presolve time: 0.00s\n", + "Presolved: 1 rows, 50 columns, 50 nonzeros\n", + "\n", + "Iteration Objective Primal Inf. Dual Inf. Time\n", + " 0 5.7349081e+08 1.044003e+04 0.000000e+00 0s\n", + " 1 6.8268465e+08 0.000000e+00 0.000000e+00 0s\n", + "\n", + "Solved in 1 iterations and 0.00 seconds (0.00 work units)\n", + "Optimal objective 6.826846503e+08\n", + "Set parameter LogFile to value \"\"\n", + "Set parameter LogFile to value \"/tmp/tmp48j6n35b.log\"\n", + "Gurobi Optimizer version 9.5.1 build v9.5.1rc2 (linux64)\n", + "Thread count: 16 physical cores, 32 logical processors, using up to 1 threads\n", + "Optimize a model with 101 rows, 100 columns and 250 nonzeros\n", + "Model fingerprint: 0x200d64ba\n", + "Variable types: 50 continuous, 50 integer (50 binary)\n", + "Coefficient statistics:\n", + " Matrix range [1e+00, 2e+06]\n", + " Objective range [1e+00, 6e+07]\n", + " Bounds range [1e+00, 1e+00]\n", + " RHS range [2e+07, 2e+07]\n", + "\n", + "User MIP start produced solution with objective 6.84841e+08 (0.00s)\n", + "Loaded user MIP start with objective 6.84841e+08\n", + "\n", + "Presolve time: 0.00s\n", + "Presolved: 101 rows, 100 columns, 250 nonzeros\n", + "Variable types: 50 continuous, 50 integer (50 binary)\n", + "\n", + "Root relaxation: objective 6.826847e+08, 56 iterations, 0.00 seconds (0.00 work units)\n", + "\n", + " Nodes | Current Node | Objective Bounds | Work\n", + " Expl Unexpl | Obj Depth IntInf | Incumbent BestBd Gap | It/Node Time\n", + "\n", + " 0 0 6.8268e+08 0 1 6.8484e+08 6.8268e+08 0.31% - 0s\n", + " 0 0 6.8315e+08 0 3 6.8484e+08 6.8315e+08 0.25% - 0s\n", + " 0 0 6.8315e+08 0 1 6.8484e+08 6.8315e+08 0.25% - 0s\n", + " 0 0 6.8315e+08 0 3 6.8484e+08 6.8315e+08 0.25% - 0s\n", + " 0 0 6.8315e+08 0 4 6.8484e+08 6.8315e+08 0.25% - 0s\n", + " 0 0 6.8315e+08 0 4 6.8484e+08 6.8315e+08 0.25% - 0s\n", + " 0 2 6.8327e+08 0 4 6.8484e+08 6.8327e+08 0.23% - 0s\n", + "\n", + "Cutting planes:\n", + " Flow cover: 3\n", + "\n", + "Explored 32 nodes (155 simplex iterations) in 0.02 seconds (0.00 work units)\n", + "Thread count was 1 (of 32 available processors)\n", + "\n", + "Solution count 1: 6.84841e+08 \n", + "\n", + "Optimal solution found (tolerance 1.00e-04)\n", + "Best objective 6.848411655488e+08, best bound 6.848411655488e+08, gap 0.0000%\n", + "Set parameter LogFile to value \"\"\n", + "WARNING: Cannot get reduced costs for MIP.\n", + "WARNING: Cannot get duals for MIP.\n" + ] + } + ], + "source": [ + "solver_ml = LearningSolver()\n", + "solver_ml.fit(train_files, build_uc_model)\n", + "solver_ml.solve(test_files[0:1], build_uc_model, tee=True);" + ] + }, + { + "cell_type": "markdown", + "id": "61da6dad-7f56-4edb-aa26-c00eb5f946c0", + "metadata": {}, + "source": [ + "By examining the solve log above, specifically the line `Loaded user MIP start with objective...`, we can see that MIPLearn was able to construct an initial solution which turned out to be the optimal solution to the problem. Now let us repeat the code above, but using an untrained solver. Note that the `fit` line is omitted." + ] + }, + { + "cell_type": "code", + "execution_count": 10, + "id": "33d15d6c-6db4-477f-bd4b-fe8e84e5f023", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Set parameter LogFile to value \"/tmp/tmp3uhhdurw.log\"\n", + "Set parameter QCPDual to value 1\n", + "Gurobi Optimizer version 9.5.1 build v9.5.1rc2 (linux64)\n", + "Thread count: 16 physical cores, 32 logical processors, using up to 1 threads\n", + "Optimize a model with 101 rows, 100 columns and 250 nonzeros\n", + "Model fingerprint: 0x8de73876\n", + "Coefficient statistics:\n", + " Matrix range [1e+00, 2e+06]\n", + " Objective range [1e+00, 6e+07]\n", + " Bounds range [1e+00, 1e+00]\n", + " RHS range [2e+07, 2e+07]\n", + "Presolve removed 100 rows and 50 columns\n", + "Presolve time: 0.00s\n", + "Presolved: 1 rows, 50 columns, 50 nonzeros\n", + "\n", + "Iteration Objective Primal Inf. Dual Inf. Time\n", + " 0 5.7349081e+08 1.044003e+04 0.000000e+00 0s\n", + " 1 6.8268465e+08 0.000000e+00 0.000000e+00 0s\n", + "\n", + "Solved in 1 iterations and 0.01 seconds (0.00 work units)\n", + "Optimal objective 6.826846503e+08\n", + "Set parameter LogFile to value \"\"\n", + "Set parameter LogFile to value \"/tmp/tmp18aqg2ic.log\"\n", + "Gurobi Optimizer version 9.5.1 build v9.5.1rc2 (linux64)\n", + "Thread count: 16 physical cores, 32 logical processors, using up to 1 threads\n", + "Optimize a model with 101 rows, 100 columns and 250 nonzeros\n", + "Model fingerprint: 0xb90d1075\n", + "Variable types: 50 continuous, 50 integer (50 binary)\n", + "Coefficient statistics:\n", + " Matrix range [1e+00, 2e+06]\n", + " Objective range [1e+00, 6e+07]\n", + " Bounds range [1e+00, 1e+00]\n", + " RHS range [2e+07, 2e+07]\n", + "Found heuristic solution: objective 8.056576e+08\n", + "Presolve time: 0.00s\n", + "Presolved: 101 rows, 100 columns, 250 nonzeros\n", + "Variable types: 50 continuous, 50 integer (50 binary)\n", + "\n", + "Root relaxation: objective 6.826847e+08, 56 iterations, 0.00 seconds (0.00 work units)\n", + "\n", + " Nodes | Current Node | Objective Bounds | Work\n", + " Expl Unexpl | Obj Depth IntInf | Incumbent BestBd Gap | It/Node Time\n", + "\n", + " 0 0 6.8268e+08 0 1 8.0566e+08 6.8268e+08 15.3% - 0s\n", + "H 0 0 7.099498e+08 6.8268e+08 3.84% - 0s\n", + " 0 0 6.8315e+08 0 3 7.0995e+08 6.8315e+08 3.78% - 0s\n", + "H 0 0 6.883227e+08 6.8315e+08 0.75% - 0s\n", + " 0 0 6.8352e+08 0 4 6.8832e+08 6.8352e+08 0.70% - 0s\n", + " 0 0 6.8352e+08 0 4 6.8832e+08 6.8352e+08 0.70% - 0s\n", + " 0 0 6.8352e+08 0 1 6.8832e+08 6.8352e+08 0.70% - 0s\n", + "H 0 0 6.862582e+08 6.8352e+08 0.40% - 0s\n", + " 0 0 6.8352e+08 0 4 6.8626e+08 6.8352e+08 0.40% - 0s\n", + " 0 0 6.8352e+08 0 4 6.8626e+08 6.8352e+08 0.40% - 0s\n", + " 0 0 6.8352e+08 0 1 6.8626e+08 6.8352e+08 0.40% - 0s\n", + " 0 0 6.8352e+08 0 3 6.8626e+08 6.8352e+08 0.40% - 0s\n", + " 0 0 6.8352e+08 0 4 6.8626e+08 6.8352e+08 0.40% - 0s\n", + " 0 0 6.8352e+08 0 4 6.8626e+08 6.8352e+08 0.40% - 0s\n", + " 0 2 6.8354e+08 0 4 6.8626e+08 6.8354e+08 0.40% - 0s\n", + "* 18 5 6 6.849018e+08 6.8413e+08 0.11% 3.1 0s\n", + "H 24 1 6.848412e+08 6.8426e+08 0.09% 3.2 0s\n", + "\n", + "Cutting planes:\n", + " Gomory: 1\n", + " Flow cover: 2\n", + "\n", + "Explored 30 nodes (217 simplex iterations) in 0.02 seconds (0.00 work units)\n", + "Thread count was 1 (of 32 available processors)\n", + "\n", + "Solution count 6: 6.84841e+08 6.84902e+08 6.86258e+08 ... 8.05658e+08\n", + "\n", + "Optimal solution found (tolerance 1.00e-04)\n", + "Best objective 6.848411655488e+08, best bound 6.848411655488e+08, gap 0.0000%\n", + "Set parameter LogFile to value \"\"\n", + "WARNING: Cannot get reduced costs for MIP.\n", + "WARNING: Cannot get duals for MIP.\n" + ] + } + ], + "source": [ + "solver_baseline = LearningSolver()\n", + "solver_baseline.solve(test_files[0:1], build_uc_model, tee=True);" + ] + }, + { + "cell_type": "markdown", + "id": "b6d37b88-9fcc-43ee-ac1e-2a7b1e51a266", + "metadata": {}, + "source": [ + "In the log above, the `MIP start` line is missing, and Gurobi had to start with a significantly inferior initial solution. The solver was still able to find the optimal solution at the end, but it required using its own internal heuristic procedures. In this example, because we solve very small optimization problems, there was almost no difference in terms of running time. For larger problems, however, the difference can be significant. See benchmarks for more details.\n", + "\n", + "
\n", + "Note\n", + " \n", + "In addition to partial initial solutions, MIPLearn is also able to predict lazy constraints, cutting planes and branching priorities. See the next tutorials for more details.\n", + "
\n", + "\n", + "
\n", + "Note\n", + " \n", + "It is not necessary to specify what ML models to use. MIPLearn, by default, will try a number of classical ML models and will choose the one that performs the best, based on k-fold cross validation. MIPLearn is also able to automatically collect features based on the MIP formulation of the problem and the solution to the LP relaxation, among other things, so it does not require handcrafted features. If you do want to customize the models and features, however, that is also possible, as we will see in a later tutorial.\n", + "
" + ] + }, + { + "cell_type": "markdown", + "id": "eec97f06", + "metadata": { + "tags": [] + }, + "source": [ + "## Accessing the solution\n", + "\n", + "In the example above, we used `LearningSolver.solve` together with data files to solve both the training and the test instances. The optimal solutions were saved to HDF5 files in the train/test folders, and could be retrieved by reading theses files, but that is not very convenient. In the following example, we show how to build and solve a Pyomo model entirely in-memory, using our trained solver." + ] + }, + { + "cell_type": "code", + "execution_count": 11, + "id": "67a6cd18", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "obj = 903865807.3536932\n", + " x = [1.0, 1.0, 1.0, 1.0, 1.0]\n", + " y = [1105176.593734543, 1891284.5155055337, 1708177.4224033852, 1438329.610189608, 535496.3347187206]\n" + ] + } + ], + "source": [ + "# Construct model using previously defined functions\n", + "data = random_uc_data(samples=1, n=50)[0]\n", + "model = build_uc_model(data)\n", + "\n", + "# Solve model using ML + Gurobi\n", + "solver_ml.solve(model)\n", + "\n", + "# Print part of the optimal solution\n", + "print(\"obj =\", model.obj())\n", + "print(\" x =\", [model.x[i].value for i in range(5)])\n", + "print(\" y =\", [model.y[i].value for i in range(5)])" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "5593d23a-83bd-4e16-8253-6300f5e3f63b", + "metadata": {}, + "outputs": [], + "source": [] + } + ], + "metadata": { + "kernelspec": { + "display_name": "Python 3", + "language": "python", + "name": "python3" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.8.13" + } + }, + "nbformat": 4, + "nbformat_minor": 5 +} diff --git a/0.3/tutorials/getting-started-jl/index.html b/0.3/tutorials/getting-started-jl/index.html new file mode 100644 index 0000000..292b23a --- /dev/null +++ b/0.3/tutorials/getting-started-jl/index.html @@ -0,0 +1,982 @@ + + + + + + + + Getting started (JuMP) — MIPLearn 0.3 + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
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Getting started (JuMP)

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Introduction

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MIPLearn is an open source framework that uses machine learning (ML) to accelerate the performance of both commercial and open source mixed-integer programming solvers (e.g. Gurobi, CPLEX, XPRESS, Cbc or SCIP). In this tutorial, we will:

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  1. Install the Python/Pyomo version of MIPLearn

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  2. Model a simple optimization problem using JuMP

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  3. Generate training data and train the ML models

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  4. Use the ML models together Gurobi to solve new instances

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Note

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The Python/Pyomo version of MIPLearn is currently only compatible with with Gurobi, CPLEX and XPRESS. For broader solver compatibility, see the Julia/JuMP version of the package.

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Warning

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MIPLearn is still in early development stage. If run into any bugs or issues, please submit a bug report in our GitHub repository. Comments, suggestions and pull requests are also very welcome!

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Installation

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MIPLearn is available in two versions:

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  • Python version, compatible with the Pyomo modeling language,

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  • Julia version, compatible with the JuMP modeling language.

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In this tutorial, we will demonstrate how to use and install the Python/Pyomo version of the package. The first step is to install Python 3.8+ in your computer. See the official Python website for more instructions. After Python is installed, we proceed to install MIPLearn using pip:

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# !pip install MIPLearn==0.2.0.dev13
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In addition to MIPLearn itself, we will also install Gurobi 9.5, a state-of-the-art commercial MILP solver. This step also install a demo license for Gurobi, which should able to solve the small optimization problems in this tutorial. A paid license is required for solving large-scale problems.

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!pip install --upgrade -i https://pypi.gurobi.com 'gurobipy>=9.5,<9.6'
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Note

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In the code above, we install specific version of all packages to ensure that this tutorial keeps running in the future, even when newer (and possibly incompatible) versions of the packages are released. This is usually a recommended practice for all Python projects.

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Modeling a simple optimization problem

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To illustrate how can MIPLearn be used, we will model and solve a small optimization problem related to power systems optimization. The problem we discuss below is a simplification of the unit commitment problem, a practical optimization problem solved daily by electric grid operators around the world.

+

Suppose that you work at a utility company, and that it is your job to decide which electrical generators should be online at a certain hour of the day, as well as how much power should each generator produce. More specifically, assume that your company owns \(n\) generators, denoted by \(g_1, \ldots, g_n\). Each generator can either be online or offline. An online generator \(g_i\) can produce between \(p^\text{min}_i\) to \(p^\text{max}_i\) megawatts of power, and it costs +your company \(c^\text{fix}_i + c^\text{var}_i y_i\), where \(y_i\) is the amount of power produced. An offline generator produces nothing and costs nothing. You also know that the total amount of power to be produced needs to be exactly equal to the total demand \(d\) (in megawatts). To minimize the costs to your company, which generators should be online, and how much power should they produce?

+

This simple problem can be modeled as a mixed-integer linear optimization problem as follows. For each generator \(g_i\), let \(x_i \in \{0,1\}\) be a decision variable indicating whether \(g_i\) is online, and let \(y_i \geq 0\) be a decision variable indicating how much power does \(g_i\) produce. The problem is then given by:

+
+\[\begin{split}\begin{align} +\text{minimize } \quad & \sum_{i=1}^n \left( c^\text{fix}_i x_i + c^\text{var}_i y_i \right) \\ +\text{subject to } \quad & y_i \leq p^\text{max}_i x_i & i=1,\ldots,n \\ +& y_i \geq p^\text{min}_i x_i & i=1,\ldots,n \\ +& \sum_{i=1}^n y_i = d \\ +& x_i \in \{0,1\} & i=1,\ldots,n \\ +& y_i \geq 0 & i=1,\ldots,n +\end{align}\end{split}\]
+
+

Note

+

We use a simplified version of the unit commitment problem in this tutorial just to make it easier to follow. MIPLearn can also handle realistic, large-scale versions of this problem. See benchmarks for more details.

+
+

Next, let us convert this abstract mathematical formulation into a concrete optimization model, using Python and Pyomo. We start by defining a data class UnitCommitmentData, which holds all the input data.

+
+
[3]:
+
+
+
from dataclasses import dataclass
+import numpy as np
+
+@dataclass
+class UnitCommitmentData:
+    demand: float
+    pmin: np.ndarray
+    pmax: np.ndarray
+    cfix: np.ndarray
+    cvar: np.ndarray
+
+
+
+

Next, we write a build_uc_model function, which converts the input data into a concrete Pyomo model.

+
+
[4]:
+
+
+
import pyomo.environ as pe
+
+def build_uc_model(data: UnitCommitmentData) -> pe.ConcreteModel:
+    model = pe.ConcreteModel()
+    n = len(data.pmin)
+    model.x = pe.Var(range(n), domain=pe.Binary)
+    model.y = pe.Var(range(n), domain=pe.NonNegativeReals)
+    model.obj = pe.Objective(
+        expr=sum(
+            data.cfix[i] * model.x[i] +
+            data.cvar[i] * model.y[i]
+            for i in range(n)
+        )
+    )
+    model.eq_max_power = pe.ConstraintList()
+    model.eq_min_power = pe.ConstraintList()
+    for i in range(n):
+        model.eq_max_power.add(model.y[i] <= data.pmax[i] * model.x[i])
+        model.eq_min_power.add(model.y[i] >= data.pmin[i] * model.x[i])
+    model.eq_demand = pe.Constraint(
+        expr=sum(model.y[i] for i in range(n)) == data.demand,
+    )
+    return model
+
+
+
+

At this point, we can already use Pyomo and any mixed-integer linear programming solver to find optimal solutions to any instance of this problem. To illustrate this, let us solve a small instance with three generators:

+
+
[5]:
+
+
+
model = build_uc_model(
+    UnitCommitmentData(
+        demand = 100.0,
+        pmin = [10, 20, 30],
+        pmax = [50, 60, 70],
+        cfix = [700, 600, 500],
+        cvar = [1.5, 2.0, 2.5],
+    )
+)
+
+solver = pe.SolverFactory("gurobi_persistent")
+solver.set_instance(model)
+solver.solve()
+print("obj =", model.obj())
+print("x =", [model.x[i].value for i in range(3)])
+print("y =", [model.y[i].value for i in range(3)])
+
+
+
+
+
+
+
+
+Set parameter Threads to value 1
+Set parameter Seed to value 42
+Restricted license - for non-production use only - expires 2023-10-25
+obj = 1320.0
+x = [-0.0, 1.0, 1.0]
+y = [0.0, 60.0, 40.0]
+
+
+

Running the code above, we found that the optimal solution for our small problem instance costs $1320. It is achieve by keeping generators 2 and 3 online and producing, respectively, 60 MW and 40 MW of power.

+
+
+

Generating training data

+

Although Gurobi could solve the small example above in a fraction of a second, it gets slower for larger and more complex versions of the problem. If this is a problem that needs to be solved frequently, as it is often the case in practice, it could make sense to spend some time upfront generating a trained version of Gurobi, which can solve new instances (similar to the ones it was trained on) faster.

+

In the following, we will use MIPLearn to train machine learning models that is able to predict the optimal solution for instances that follow a given probability distribution, then it will provide this predicted solution to Gurobi as a warm start. Before we can train the model, we need to collect training data by solving a large number of instances. In real-world situations, we may construct these training instances based on historical data. In this tutorial, we will construct them using a +random instance generator:

+
+
[6]:
+
+
+
from scipy.stats import uniform
+from typing import List
+import random
+
+def random_uc_data(samples: int, n: int, seed: int = 42) -> List[UnitCommitmentData]:
+    random.seed(seed)
+    np.random.seed(seed)
+    pmin = uniform(loc=100_000.0, scale=400_000.0).rvs(n)
+    pmax = pmin * uniform(loc=2.0, scale=2.5).rvs(n)
+    cfix = pmin * uniform(loc=100.0, scale=25.0).rvs(n)
+    cvar = uniform(loc=1.25, scale=0.25).rvs(n)
+    return [
+        UnitCommitmentData(
+            demand = pmax.sum() * uniform(loc=0.5, scale=0.25).rvs(),
+            pmin = pmin,
+            pmax = pmax,
+            cfix = cfix,
+            cvar = cvar,
+        )
+        for i in range(samples)
+    ]
+
+
+
+

In this example, for simplicity, only the demands change from one instance to the next. We could also have randomized the costs, production limits or even the number of units. The more randomization we have in the training data, however, the more challenging it is for the machine learning models to learn solution patterns.

+

Now we generate 500 instances of this problem, each one with 50 generators, and we use 450 of these instances for training. After generating the instances, we write them to individual files. MIPLearn uses files during the training process because, for large-scale optimization problems, it is often impractical to hold in memory the entire training data, as well as the concrete Pyomo models. Files also make it much easier to solve multiple instances simultaneously, potentially even on multiple +machines. We will cover parallel and distributed computing in a future tutorial. The code below generates the files uc/train/00000.pkl.gz, uc/train/00001.pkl.gz, etc., which contain the input data in compressed (gzipped) pickle format.

+
+
[7]:
+
+
+
from miplearn import save
+data = random_uc_data(samples=500, n=50)
+train_files = save(data[0:450], "uc/train/")
+test_files  = save(data[450:500], "uc/test/")
+
+
+
+

Finally, we use LearningSolver to solve all the training instances. LearningSolver is the main component provided by MIPLearn, which integrates MIP solvers and ML. The optimal solutions, along with other useful training data, are stored in HDF5 files uc/train/00000.h5, uc/train/00001.h5, etc.

+
+
[12]:
+
+
+
from miplearn import LearningSolver
+solver = LearningSolver()
+solver.solve(train_files, build_uc_model);
+
+
+
+
+
+

Solving test instances

+

With training data in hand, we can now fit the ML models, using the LearningSolver.fit method, then solve the test instances with LearningSolver.solve, as shown below. The tee=True parameter asks MIPLearn to print the solver log to the screen.

+
+
[9]:
+
+
+
solver_ml = LearningSolver()
+solver_ml.fit(train_files, build_uc_model)
+solver_ml.solve(test_files[0:1], build_uc_model, tee=True);
+
+
+
+
+
+
+
+
+Set parameter LogFile to value "/tmp/tmpvbaqbyty.log"
+Set parameter QCPDual to value 1
+Gurobi Optimizer version 9.5.1 build v9.5.1rc2 (linux64)
+Thread count: 16 physical cores, 32 logical processors, using up to 1 threads
+Optimize a model with 101 rows, 100 columns and 250 nonzeros
+Model fingerprint: 0x8de73876
+Coefficient statistics:
+  Matrix range     [1e+00, 2e+06]
+  Objective range  [1e+00, 6e+07]
+  Bounds range     [1e+00, 1e+00]
+  RHS range        [2e+07, 2e+07]
+Presolve removed 100 rows and 50 columns
+Presolve time: 0.00s
+Presolved: 1 rows, 50 columns, 50 nonzeros
+
+Iteration    Objective       Primal Inf.    Dual Inf.      Time
+       0    5.7349081e+08   1.044003e+04   0.000000e+00      0s
+       1    6.8268465e+08   0.000000e+00   0.000000e+00      0s
+
+Solved in 1 iterations and 0.00 seconds (0.00 work units)
+Optimal objective  6.826846503e+08
+Set parameter LogFile to value ""
+Set parameter LogFile to value "/tmp/tmp48j6n35b.log"
+Gurobi Optimizer version 9.5.1 build v9.5.1rc2 (linux64)
+Thread count: 16 physical cores, 32 logical processors, using up to 1 threads
+Optimize a model with 101 rows, 100 columns and 250 nonzeros
+Model fingerprint: 0x200d64ba
+Variable types: 50 continuous, 50 integer (50 binary)
+Coefficient statistics:
+  Matrix range     [1e+00, 2e+06]
+  Objective range  [1e+00, 6e+07]
+  Bounds range     [1e+00, 1e+00]
+  RHS range        [2e+07, 2e+07]
+
+User MIP start produced solution with objective 6.84841e+08 (0.00s)
+Loaded user MIP start with objective 6.84841e+08
+
+Presolve time: 0.00s
+Presolved: 101 rows, 100 columns, 250 nonzeros
+Variable types: 50 continuous, 50 integer (50 binary)
+
+Root relaxation: objective 6.826847e+08, 56 iterations, 0.00 seconds (0.00 work units)
+
+    Nodes    |    Current Node    |     Objective Bounds      |     Work
+ Expl Unexpl |  Obj  Depth IntInf | Incumbent    BestBd   Gap | It/Node Time
+
+     0     0 6.8268e+08    0    1 6.8484e+08 6.8268e+08  0.31%     -    0s
+     0     0 6.8315e+08    0    3 6.8484e+08 6.8315e+08  0.25%     -    0s
+     0     0 6.8315e+08    0    1 6.8484e+08 6.8315e+08  0.25%     -    0s
+     0     0 6.8315e+08    0    3 6.8484e+08 6.8315e+08  0.25%     -    0s
+     0     0 6.8315e+08    0    4 6.8484e+08 6.8315e+08  0.25%     -    0s
+     0     0 6.8315e+08    0    4 6.8484e+08 6.8315e+08  0.25%     -    0s
+     0     2 6.8327e+08    0    4 6.8484e+08 6.8327e+08  0.23%     -    0s
+
+Cutting planes:
+  Flow cover: 3
+
+Explored 32 nodes (155 simplex iterations) in 0.02 seconds (0.00 work units)
+Thread count was 1 (of 32 available processors)
+
+Solution count 1: 6.84841e+08
+
+Optimal solution found (tolerance 1.00e-04)
+Best objective 6.848411655488e+08, best bound 6.848411655488e+08, gap 0.0000%
+Set parameter LogFile to value ""
+WARNING: Cannot get reduced costs for MIP.
+WARNING: Cannot get duals for MIP.
+
+
+

By examining the solve log above, specifically the line Loaded user MIP start with objective..., we can see that MIPLearn was able to construct an initial solution which turned out to be the optimal solution to the problem. Now let us repeat the code above, but using an untrained solver. Note that the fit line is omitted.

+
+
[10]:
+
+
+
solver_baseline = LearningSolver()
+solver_baseline.solve(test_files[0:1], build_uc_model, tee=True);
+
+
+
+
+
+
+
+
+Set parameter LogFile to value "/tmp/tmp3uhhdurw.log"
+Set parameter QCPDual to value 1
+Gurobi Optimizer version 9.5.1 build v9.5.1rc2 (linux64)
+Thread count: 16 physical cores, 32 logical processors, using up to 1 threads
+Optimize a model with 101 rows, 100 columns and 250 nonzeros
+Model fingerprint: 0x8de73876
+Coefficient statistics:
+  Matrix range     [1e+00, 2e+06]
+  Objective range  [1e+00, 6e+07]
+  Bounds range     [1e+00, 1e+00]
+  RHS range        [2e+07, 2e+07]
+Presolve removed 100 rows and 50 columns
+Presolve time: 0.00s
+Presolved: 1 rows, 50 columns, 50 nonzeros
+
+Iteration    Objective       Primal Inf.    Dual Inf.      Time
+       0    5.7349081e+08   1.044003e+04   0.000000e+00      0s
+       1    6.8268465e+08   0.000000e+00   0.000000e+00      0s
+
+Solved in 1 iterations and 0.01 seconds (0.00 work units)
+Optimal objective  6.826846503e+08
+Set parameter LogFile to value ""
+Set parameter LogFile to value "/tmp/tmp18aqg2ic.log"
+Gurobi Optimizer version 9.5.1 build v9.5.1rc2 (linux64)
+Thread count: 16 physical cores, 32 logical processors, using up to 1 threads
+Optimize a model with 101 rows, 100 columns and 250 nonzeros
+Model fingerprint: 0xb90d1075
+Variable types: 50 continuous, 50 integer (50 binary)
+Coefficient statistics:
+  Matrix range     [1e+00, 2e+06]
+  Objective range  [1e+00, 6e+07]
+  Bounds range     [1e+00, 1e+00]
+  RHS range        [2e+07, 2e+07]
+Found heuristic solution: objective 8.056576e+08
+Presolve time: 0.00s
+Presolved: 101 rows, 100 columns, 250 nonzeros
+Variable types: 50 continuous, 50 integer (50 binary)
+
+Root relaxation: objective 6.826847e+08, 56 iterations, 0.00 seconds (0.00 work units)
+
+    Nodes    |    Current Node    |     Objective Bounds      |     Work
+ Expl Unexpl |  Obj  Depth IntInf | Incumbent    BestBd   Gap | It/Node Time
+
+     0     0 6.8268e+08    0    1 8.0566e+08 6.8268e+08  15.3%     -    0s
+H    0     0                    7.099498e+08 6.8268e+08  3.84%     -    0s
+     0     0 6.8315e+08    0    3 7.0995e+08 6.8315e+08  3.78%     -    0s
+H    0     0                    6.883227e+08 6.8315e+08  0.75%     -    0s
+     0     0 6.8352e+08    0    4 6.8832e+08 6.8352e+08  0.70%     -    0s
+     0     0 6.8352e+08    0    4 6.8832e+08 6.8352e+08  0.70%     -    0s
+     0     0 6.8352e+08    0    1 6.8832e+08 6.8352e+08  0.70%     -    0s
+H    0     0                    6.862582e+08 6.8352e+08  0.40%     -    0s
+     0     0 6.8352e+08    0    4 6.8626e+08 6.8352e+08  0.40%     -    0s
+     0     0 6.8352e+08    0    4 6.8626e+08 6.8352e+08  0.40%     -    0s
+     0     0 6.8352e+08    0    1 6.8626e+08 6.8352e+08  0.40%     -    0s
+     0     0 6.8352e+08    0    3 6.8626e+08 6.8352e+08  0.40%     -    0s
+     0     0 6.8352e+08    0    4 6.8626e+08 6.8352e+08  0.40%     -    0s
+     0     0 6.8352e+08    0    4 6.8626e+08 6.8352e+08  0.40%     -    0s
+     0     2 6.8354e+08    0    4 6.8626e+08 6.8354e+08  0.40%     -    0s
+*   18     5               6    6.849018e+08 6.8413e+08  0.11%   3.1    0s
+H   24     1                    6.848412e+08 6.8426e+08  0.09%   3.2    0s
+
+Cutting planes:
+  Gomory: 1
+  Flow cover: 2
+
+Explored 30 nodes (217 simplex iterations) in 0.02 seconds (0.00 work units)
+Thread count was 1 (of 32 available processors)
+
+Solution count 6: 6.84841e+08 6.84902e+08 6.86258e+08 ... 8.05658e+08
+
+Optimal solution found (tolerance 1.00e-04)
+Best objective 6.848411655488e+08, best bound 6.848411655488e+08, gap 0.0000%
+Set parameter LogFile to value ""
+WARNING: Cannot get reduced costs for MIP.
+WARNING: Cannot get duals for MIP.
+
+
+

In the log above, the MIP start line is missing, and Gurobi had to start with a significantly inferior initial solution. The solver was still able to find the optimal solution at the end, but it required using its own internal heuristic procedures. In this example, because we solve very small optimization problems, there was almost no difference in terms of running time. For larger problems, however, the difference can be significant. See benchmarks for more details.

+
+

Note

+

In addition to partial initial solutions, MIPLearn is also able to predict lazy constraints, cutting planes and branching priorities. See the next tutorials for more details.

+
+
+

Note

+

It is not necessary to specify what ML models to use. MIPLearn, by default, will try a number of classical ML models and will choose the one that performs the best, based on k-fold cross validation. MIPLearn is also able to automatically collect features based on the MIP formulation of the problem and the solution to the LP relaxation, among other things, so it does not require handcrafted features. If you do want to customize the models and features, however, that is also possible, as we will +see in a later tutorial.

+
+
+
+

Accessing the solution

+

In the example above, we used LearningSolver.solve together with data files to solve both the training and the test instances. The optimal solutions were saved to HDF5 files in the train/test folders, and could be retrieved by reading theses files, but that is not very convenient. In the following example, we show how to build and solve a Pyomo model entirely in-memory, using our trained solver.

+
+
[11]:
+
+
+
# Construct model using previously defined functions
+data = random_uc_data(samples=1, n=50)[0]
+model = build_uc_model(data)
+
+# Solve model using ML + Gurobi
+solver_ml.solve(model)
+
+# Print part of the optimal solution
+print("obj =", model.obj())
+print(" x =", [model.x[i].value for i in range(5)])
+print(" y =", [model.y[i].value for i in range(5)])
+
+
+
+
+
+
+
+
+obj = 903865807.3536932
+ x = [1.0, 1.0, 1.0, 1.0, 1.0]
+ y = [1105176.593734543, 1891284.5155055337, 1708177.4224033852, 1438329.610189608, 535496.3347187206]
+
+
+
+
[ ]:
+
+
+

+
+
+
+
+
+ + +
+ + +
+ + +
+ +
+
+
+
+

+ + © Copyright 2020-2022, UChicago Argonne, LLC.
+

+
+
+
+ + +
+
+ + + + + + \ No newline at end of file diff --git a/0.3/tutorials/getting-started-pyomo.ipynb b/0.3/tutorials/getting-started-pyomo.ipynb new file mode 100644 index 0000000..55c5830 --- /dev/null +++ b/0.3/tutorials/getting-started-pyomo.ipynb @@ -0,0 +1,625 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "id": "6b8983b1", + "metadata": { + "tags": [] + }, + "source": [ + "# Getting started (Pyomo)\n", + "\n", + "## Introduction\n", + "\n", + "**MIPLearn** is an open source framework that uses machine learning (ML) to accelerate the performance of both commercial and open source mixed-integer programming solvers (e.g. Gurobi, CPLEX, XPRESS, Cbc or SCIP). In this tutorial, we will:\n", + "\n", + "1. Install the Python/Pyomo version of MIPLearn\n", + "2. Model a simple optimization problem using JuMP\n", + "3. Generate training data and train the ML models\n", + "4. Use the ML models together Gurobi to solve new instances\n", + "\n", + "
\n", + "Note\n", + " \n", + "The Python/Pyomo version of MIPLearn is currently only compatible with with Gurobi, CPLEX and XPRESS. For broader solver compatibility, see the Julia/JuMP version of the package.\n", + "
\n", + "\n", + "
\n", + "Warning\n", + " \n", + "MIPLearn is still in early development stage. If run into any bugs or issues, please submit a bug report in our GitHub repository. Comments, suggestions and pull requests are also very welcome!\n", + " \n", + "
\n" + ] + }, + { + "cell_type": "markdown", + "id": "02f0a927", + "metadata": {}, + "source": [ + "## Installation\n", + "\n", + "MIPLearn is available in two versions:\n", + "\n", + "- Python version, compatible with the Pyomo modeling language,\n", + "- Julia version, compatible with the JuMP modeling language.\n", + "\n", + "In this tutorial, we will demonstrate how to use and install the Python/Pyomo version of the package. The first step is to install Python 3.8+ in your computer. See the [official Python website for more instructions](https://www.python.org/downloads/). After Python is installed, we proceed to install MIPLearn using `pip`:" + ] + }, + { + "cell_type": "code", + "execution_count": 1, + "id": "cd8a69c1", + "metadata": {}, + "outputs": [], + "source": [ + "# !pip install MIPLearn==0.2.0.dev13" + ] + }, + { + "cell_type": "markdown", + "id": "e8274543", + "metadata": {}, + "source": [ + "In addition to MIPLearn itself, we will also install Gurobi 9.5, a state-of-the-art commercial MILP solver. This step also install a demo license for Gurobi, which should able to solve the small optimization problems in this tutorial. A paid license is required for solving large-scale problems." + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "id": "dcc8756c", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Looking in indexes: https://pypi.gurobi.com\n", + "Requirement already satisfied: gurobipy<9.6,>=9.5 in /opt/anaconda3/envs/miplearn/lib/python3.8/site-packages (9.5.1)\n" + ] + } + ], + "source": [ + "!pip install --upgrade -i https://pypi.gurobi.com 'gurobipy>=9.5,<9.6'" + ] + }, + { + "cell_type": "markdown", + "id": "a14e4550", + "metadata": {}, + "source": [ + "
\n", + " \n", + "Note\n", + " \n", + "In the code above, we install specific version of all packages to ensure that this tutorial keeps running in the future, even when newer (and possibly incompatible) versions of the packages are released. This is usually a recommended practice for all Python projects.\n", + " \n", + "
" + ] + }, + { + "cell_type": "markdown", + "id": "16b86823", + "metadata": {}, + "source": [ + "## Modeling a simple optimization problem\n", + "\n", + "To illustrate how can MIPLearn be used, we will model and solve a small optimization problem related to power systems optimization. The problem we discuss below is a simplification of the **unit commitment problem,** a practical optimization problem solved daily by electric grid operators around the world. \n", + "\n", + "Suppose that you work at a utility company, and that it is your job to decide which electrical generators should be online at a certain hour of the day, as well as how much power should each generator produce. More specifically, assume that your company owns $n$ generators, denoted by $g_1, \\ldots, g_n$. Each generator can either be online or offline. An online generator $g_i$ can produce between $p^\\text{min}_i$ to $p^\\text{max}_i$ megawatts of power, and it costs your company $c^\\text{fix}_i + c^\\text{var}_i y_i$, where $y_i$ is the amount of power produced. An offline generator produces nothing and costs nothing. You also know that the total amount of power to be produced needs to be exactly equal to the total demand $d$ (in megawatts). To minimize the costs to your company, which generators should be online, and how much power should they produce?\n", + "\n", + "This simple problem can be modeled as a *mixed-integer linear optimization* problem as follows. For each generator $g_i$, let $x_i \\in \\{0,1\\}$ be a decision variable indicating whether $g_i$ is online, and let $y_i \\geq 0$ be a decision variable indicating how much power does $g_i$ produce. The problem is then given by:\n", + "\n", + "$$\n", + "\\begin{align}\n", + "\\text{minimize } \\quad & \\sum_{i=1}^n \\left( c^\\text{fix}_i x_i + c^\\text{var}_i y_i \\right) \\\\\n", + "\\text{subject to } \\quad & y_i \\leq p^\\text{max}_i x_i & i=1,\\ldots,n \\\\\n", + "& y_i \\geq p^\\text{min}_i x_i & i=1,\\ldots,n \\\\\n", + "& \\sum_{i=1}^n y_i = d \\\\\n", + "& x_i \\in \\{0,1\\} & i=1,\\ldots,n \\\\\n", + "& y_i \\geq 0 & i=1,\\ldots,n\n", + "\\end{align}\n", + "$$\n", + "\n", + "
\n", + " \n", + "Note\n", + " \n", + "We use a simplified version of the unit commitment problem in this tutorial just to make it easier to follow. MIPLearn can also handle realistic, large-scale versions of this problem. See benchmarks for more details.\n", + " \n", + "
\n", + "\n", + "Next, let us convert this abstract mathematical formulation into a concrete optimization model, using Python and Pyomo. We start by defining a data class `UnitCommitmentData`, which holds all the input data." + ] + }, + { + "cell_type": "code", + "execution_count": 3, + "id": "22a67170-10b4-43d3-8708-014d91141e73", + "metadata": { + "tags": [] + }, + "outputs": [], + "source": [ + "from dataclasses import dataclass\n", + "import numpy as np\n", + "\n", + "@dataclass\n", + "class UnitCommitmentData:\n", + " demand: float\n", + " pmin: np.ndarray\n", + " pmax: np.ndarray\n", + " cfix: np.ndarray\n", + " cvar: np.ndarray" + ] + }, + { + "cell_type": "markdown", + "id": "29f55efa-0751-465a-9b0a-a821d46a3d40", + "metadata": {}, + "source": [ + "Next, we write a `build_uc_model` function, which converts the input data into a concrete Pyomo model." + ] + }, + { + "cell_type": "code", + "execution_count": 4, + "id": "2f67032f-0d74-4317-b45c-19da0ec859e9", + "metadata": {}, + "outputs": [], + "source": [ + "import pyomo.environ as pe\n", + "\n", + "def build_uc_model(data: UnitCommitmentData) -> pe.ConcreteModel:\n", + " model = pe.ConcreteModel()\n", + " n = len(data.pmin)\n", + " model.x = pe.Var(range(n), domain=pe.Binary)\n", + " model.y = pe.Var(range(n), domain=pe.NonNegativeReals)\n", + " model.obj = pe.Objective(\n", + " expr=sum(\n", + " data.cfix[i] * model.x[i] +\n", + " data.cvar[i] * model.y[i]\n", + " for i in range(n)\n", + " )\n", + " )\n", + " model.eq_max_power = pe.ConstraintList()\n", + " model.eq_min_power = pe.ConstraintList()\n", + " for i in range(n):\n", + " model.eq_max_power.add(model.y[i] <= data.pmax[i] * model.x[i])\n", + " model.eq_min_power.add(model.y[i] >= data.pmin[i] * model.x[i])\n", + " model.eq_demand = pe.Constraint(\n", + " expr=sum(model.y[i] for i in range(n)) == data.demand,\n", + " )\n", + " return model" + ] + }, + { + "cell_type": "markdown", + "id": "c22714a3", + "metadata": {}, + "source": [ + "At this point, we can already use Pyomo and any mixed-integer linear programming solver to find optimal solutions to any instance of this problem. To illustrate this, let us solve a small instance with three generators:" + ] + }, + { + "cell_type": "code", + "execution_count": 5, + "id": "2a896f47", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Set parameter Threads to value 1\n", + "Set parameter Seed to value 42\n", + "Restricted license - for non-production use only - expires 2023-10-25\n", + "obj = 1320.0\n", + "x = [-0.0, 1.0, 1.0]\n", + "y = [0.0, 60.0, 40.0]\n" + ] + } + ], + "source": [ + "model = build_uc_model(\n", + " UnitCommitmentData(\n", + " demand = 100.0,\n", + " pmin = [10, 20, 30],\n", + " pmax = [50, 60, 70],\n", + " cfix = [700, 600, 500],\n", + " cvar = [1.5, 2.0, 2.5],\n", + " )\n", + ")\n", + "\n", + "solver = pe.SolverFactory(\"gurobi_persistent\")\n", + "solver.set_instance(model)\n", + "solver.solve()\n", + "print(\"obj =\", model.obj())\n", + "print(\"x =\", [model.x[i].value for i in range(3)])\n", + "print(\"y =\", [model.y[i].value for i in range(3)])" + ] + }, + { + "cell_type": "markdown", + "id": "41b03bbc", + "metadata": {}, + "source": [ + "Running the code above, we found that the optimal solution for our small problem instance costs \\$1320. It is achieve by keeping generators 2 and 3 online and producing, respectively, 60 MW and 40 MW of power." + ] + }, + { + "cell_type": "markdown", + "id": "cf60c1dd", + "metadata": {}, + "source": [ + "## Generating training data\n", + "\n", + "Although Gurobi could solve the small example above in a fraction of a second, it gets slower for larger and more complex versions of the problem. If this is a problem that needs to be solved frequently, as it is often the case in practice, it could make sense to spend some time upfront generating a **trained** version of Gurobi, which can solve new instances (similar to the ones it was trained on) faster.\n", + "\n", + "In the following, we will use MIPLearn to train machine learning models that is able to predict the optimal solution for instances that follow a given probability distribution, then it will provide this predicted solution to Gurobi as a warm start. Before we can train the model, we need to collect training data by solving a large number of instances. In real-world situations, we may construct these training instances based on historical data. In this tutorial, we will construct them using a random instance generator:" + ] + }, + { + "cell_type": "code", + "execution_count": 6, + "id": "5eb09fab", + "metadata": {}, + "outputs": [], + "source": [ + "from scipy.stats import uniform\n", + "from typing import List\n", + "import random\n", + "\n", + "def random_uc_data(samples: int, n: int, seed: int = 42) -> List[UnitCommitmentData]:\n", + " random.seed(seed)\n", + " np.random.seed(seed)\n", + " pmin = uniform(loc=100_000.0, scale=400_000.0).rvs(n)\n", + " pmax = pmin * uniform(loc=2.0, scale=2.5).rvs(n)\n", + " cfix = pmin * uniform(loc=100.0, scale=25.0).rvs(n)\n", + " cvar = uniform(loc=1.25, scale=0.25).rvs(n)\n", + " return [\n", + " UnitCommitmentData(\n", + " demand = pmax.sum() * uniform(loc=0.5, scale=0.25).rvs(),\n", + " pmin = pmin,\n", + " pmax = pmax,\n", + " cfix = cfix,\n", + " cvar = cvar,\n", + " )\n", + " for i in range(samples)\n", + " ]" + ] + }, + { + "cell_type": "markdown", + "id": "3a03a7ac", + "metadata": {}, + "source": [ + "In this example, for simplicity, only the demands change from one instance to the next. We could also have randomized the costs, production limits or even the number of units. The more randomization we have in the training data, however, the more challenging it is for the machine learning models to learn solution patterns.\n", + "\n", + "Now we generate 500 instances of this problem, each one with 50 generators, and we use 450 of these instances for training. After generating the instances, we write them to individual files. MIPLearn uses files during the training process because, for large-scale optimization problems, it is often impractical to hold in memory the entire training data, as well as the concrete Pyomo models. Files also make it much easier to solve multiple instances simultaneously, potentially even on multiple machines. We will cover parallel and distributed computing in a future tutorial. The code below generates the files `uc/train/00000.pkl.gz`, `uc/train/00001.pkl.gz`, etc., which contain the input data in compressed (gzipped) pickle format." + ] + }, + { + "cell_type": "code", + "execution_count": 7, + "id": "6156752c", + "metadata": {}, + "outputs": [], + "source": [ + "from miplearn import save\n", + "data = random_uc_data(samples=500, n=50)\n", + "train_files = save(data[0:450], \"uc/train/\")\n", + "test_files = save(data[450:500], \"uc/test/\")" + ] + }, + { + "cell_type": "markdown", + "id": "b17af877", + "metadata": {}, + "source": [ + "Finally, we use `LearningSolver` to solve all the training instances. `LearningSolver` is the main component provided by MIPLearn, which integrates MIP solvers and ML. The optimal solutions, along with other useful training data, are stored in HDF5 files `uc/train/00000.h5`, `uc/train/00001.h5`, etc." + ] + }, + { + "cell_type": "code", + "execution_count": 12, + "id": "7623f002", + "metadata": {}, + "outputs": [], + "source": [ + "from miplearn import LearningSolver\n", + "solver = LearningSolver()\n", + "solver.solve(train_files, build_uc_model);" + ] + }, + { + "cell_type": "markdown", + "id": "2f24ee83", + "metadata": {}, + "source": [ + "## Solving test instances\n", + "\n", + "With training data in hand, we can now fit the ML models, using the `LearningSolver.fit` method, then solve the test instances with `LearningSolver.solve`, as shown below. The `tee=True` parameter asks MIPLearn to print the solver log to the screen." + ] + }, + { + "cell_type": "code", + "execution_count": 9, + "id": "c8385030", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Set parameter LogFile to value \"/tmp/tmpvbaqbyty.log\"\n", + "Set parameter QCPDual to value 1\n", + "Gurobi Optimizer version 9.5.1 build v9.5.1rc2 (linux64)\n", + "Thread count: 16 physical cores, 32 logical processors, using up to 1 threads\n", + "Optimize a model with 101 rows, 100 columns and 250 nonzeros\n", + "Model fingerprint: 0x8de73876\n", + "Coefficient statistics:\n", + " Matrix range [1e+00, 2e+06]\n", + " Objective range [1e+00, 6e+07]\n", + " Bounds range [1e+00, 1e+00]\n", + " RHS range [2e+07, 2e+07]\n", + "Presolve removed 100 rows and 50 columns\n", + "Presolve time: 0.00s\n", + "Presolved: 1 rows, 50 columns, 50 nonzeros\n", + "\n", + "Iteration Objective Primal Inf. Dual Inf. Time\n", + " 0 5.7349081e+08 1.044003e+04 0.000000e+00 0s\n", + " 1 6.8268465e+08 0.000000e+00 0.000000e+00 0s\n", + "\n", + "Solved in 1 iterations and 0.00 seconds (0.00 work units)\n", + "Optimal objective 6.826846503e+08\n", + "Set parameter LogFile to value \"\"\n", + "Set parameter LogFile to value \"/tmp/tmp48j6n35b.log\"\n", + "Gurobi Optimizer version 9.5.1 build v9.5.1rc2 (linux64)\n", + "Thread count: 16 physical cores, 32 logical processors, using up to 1 threads\n", + "Optimize a model with 101 rows, 100 columns and 250 nonzeros\n", + "Model fingerprint: 0x200d64ba\n", + "Variable types: 50 continuous, 50 integer (50 binary)\n", + "Coefficient statistics:\n", + " Matrix range [1e+00, 2e+06]\n", + " Objective range [1e+00, 6e+07]\n", + " Bounds range [1e+00, 1e+00]\n", + " RHS range [2e+07, 2e+07]\n", + "\n", + "User MIP start produced solution with objective 6.84841e+08 (0.00s)\n", + "Loaded user MIP start with objective 6.84841e+08\n", + "\n", + "Presolve time: 0.00s\n", + "Presolved: 101 rows, 100 columns, 250 nonzeros\n", + "Variable types: 50 continuous, 50 integer (50 binary)\n", + "\n", + "Root relaxation: objective 6.826847e+08, 56 iterations, 0.00 seconds (0.00 work units)\n", + "\n", + " Nodes | Current Node | Objective Bounds | Work\n", + " Expl Unexpl | Obj Depth IntInf | Incumbent BestBd Gap | It/Node Time\n", + "\n", + " 0 0 6.8268e+08 0 1 6.8484e+08 6.8268e+08 0.31% - 0s\n", + " 0 0 6.8315e+08 0 3 6.8484e+08 6.8315e+08 0.25% - 0s\n", + " 0 0 6.8315e+08 0 1 6.8484e+08 6.8315e+08 0.25% - 0s\n", + " 0 0 6.8315e+08 0 3 6.8484e+08 6.8315e+08 0.25% - 0s\n", + " 0 0 6.8315e+08 0 4 6.8484e+08 6.8315e+08 0.25% - 0s\n", + " 0 0 6.8315e+08 0 4 6.8484e+08 6.8315e+08 0.25% - 0s\n", + " 0 2 6.8327e+08 0 4 6.8484e+08 6.8327e+08 0.23% - 0s\n", + "\n", + "Cutting planes:\n", + " Flow cover: 3\n", + "\n", + "Explored 32 nodes (155 simplex iterations) in 0.02 seconds (0.00 work units)\n", + "Thread count was 1 (of 32 available processors)\n", + "\n", + "Solution count 1: 6.84841e+08 \n", + "\n", + "Optimal solution found (tolerance 1.00e-04)\n", + "Best objective 6.848411655488e+08, best bound 6.848411655488e+08, gap 0.0000%\n", + "Set parameter LogFile to value \"\"\n", + "WARNING: Cannot get reduced costs for MIP.\n", + "WARNING: Cannot get duals for MIP.\n" + ] + } + ], + "source": [ + "solver_ml = LearningSolver()\n", + "solver_ml.fit(train_files, build_uc_model)\n", + "solver_ml.solve(test_files[0:1], build_uc_model, tee=True);" + ] + }, + { + "cell_type": "markdown", + "id": "61da6dad-7f56-4edb-aa26-c00eb5f946c0", + "metadata": {}, + "source": [ + "By examining the solve log above, specifically the line `Loaded user MIP start with objective...`, we can see that MIPLearn was able to construct an initial solution which turned out to be the optimal solution to the problem. Now let us repeat the code above, but using an untrained solver. Note that the `fit` line is omitted." + ] + }, + { + "cell_type": "code", + "execution_count": 10, + "id": "33d15d6c-6db4-477f-bd4b-fe8e84e5f023", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Set parameter LogFile to value \"/tmp/tmp3uhhdurw.log\"\n", + "Set parameter QCPDual to value 1\n", + "Gurobi Optimizer version 9.5.1 build v9.5.1rc2 (linux64)\n", + "Thread count: 16 physical cores, 32 logical processors, using up to 1 threads\n", + "Optimize a model with 101 rows, 100 columns and 250 nonzeros\n", + "Model fingerprint: 0x8de73876\n", + "Coefficient statistics:\n", + " Matrix range [1e+00, 2e+06]\n", + " Objective range [1e+00, 6e+07]\n", + " Bounds range [1e+00, 1e+00]\n", + " RHS range [2e+07, 2e+07]\n", + "Presolve removed 100 rows and 50 columns\n", + "Presolve time: 0.00s\n", + "Presolved: 1 rows, 50 columns, 50 nonzeros\n", + "\n", + "Iteration Objective Primal Inf. Dual Inf. Time\n", + " 0 5.7349081e+08 1.044003e+04 0.000000e+00 0s\n", + " 1 6.8268465e+08 0.000000e+00 0.000000e+00 0s\n", + "\n", + "Solved in 1 iterations and 0.01 seconds (0.00 work units)\n", + "Optimal objective 6.826846503e+08\n", + "Set parameter LogFile to value \"\"\n", + "Set parameter LogFile to value \"/tmp/tmp18aqg2ic.log\"\n", + "Gurobi Optimizer version 9.5.1 build v9.5.1rc2 (linux64)\n", + "Thread count: 16 physical cores, 32 logical processors, using up to 1 threads\n", + "Optimize a model with 101 rows, 100 columns and 250 nonzeros\n", + "Model fingerprint: 0xb90d1075\n", + "Variable types: 50 continuous, 50 integer (50 binary)\n", + "Coefficient statistics:\n", + " Matrix range [1e+00, 2e+06]\n", + " Objective range [1e+00, 6e+07]\n", + " Bounds range [1e+00, 1e+00]\n", + " RHS range [2e+07, 2e+07]\n", + "Found heuristic solution: objective 8.056576e+08\n", + "Presolve time: 0.00s\n", + "Presolved: 101 rows, 100 columns, 250 nonzeros\n", + "Variable types: 50 continuous, 50 integer (50 binary)\n", + "\n", + "Root relaxation: objective 6.826847e+08, 56 iterations, 0.00 seconds (0.00 work units)\n", + "\n", + " Nodes | Current Node | Objective Bounds | Work\n", + " Expl Unexpl | Obj Depth IntInf | Incumbent BestBd Gap | It/Node Time\n", + "\n", + " 0 0 6.8268e+08 0 1 8.0566e+08 6.8268e+08 15.3% - 0s\n", + "H 0 0 7.099498e+08 6.8268e+08 3.84% - 0s\n", + " 0 0 6.8315e+08 0 3 7.0995e+08 6.8315e+08 3.78% - 0s\n", + "H 0 0 6.883227e+08 6.8315e+08 0.75% - 0s\n", + " 0 0 6.8352e+08 0 4 6.8832e+08 6.8352e+08 0.70% - 0s\n", + " 0 0 6.8352e+08 0 4 6.8832e+08 6.8352e+08 0.70% - 0s\n", + " 0 0 6.8352e+08 0 1 6.8832e+08 6.8352e+08 0.70% - 0s\n", + "H 0 0 6.862582e+08 6.8352e+08 0.40% - 0s\n", + " 0 0 6.8352e+08 0 4 6.8626e+08 6.8352e+08 0.40% - 0s\n", + " 0 0 6.8352e+08 0 4 6.8626e+08 6.8352e+08 0.40% - 0s\n", + " 0 0 6.8352e+08 0 1 6.8626e+08 6.8352e+08 0.40% - 0s\n", + " 0 0 6.8352e+08 0 3 6.8626e+08 6.8352e+08 0.40% - 0s\n", + " 0 0 6.8352e+08 0 4 6.8626e+08 6.8352e+08 0.40% - 0s\n", + " 0 0 6.8352e+08 0 4 6.8626e+08 6.8352e+08 0.40% - 0s\n", + " 0 2 6.8354e+08 0 4 6.8626e+08 6.8354e+08 0.40% - 0s\n", + "* 18 5 6 6.849018e+08 6.8413e+08 0.11% 3.1 0s\n", + "H 24 1 6.848412e+08 6.8426e+08 0.09% 3.2 0s\n", + "\n", + "Cutting planes:\n", + " Gomory: 1\n", + " Flow cover: 2\n", + "\n", + "Explored 30 nodes (217 simplex iterations) in 0.02 seconds (0.00 work units)\n", + "Thread count was 1 (of 32 available processors)\n", + "\n", + "Solution count 6: 6.84841e+08 6.84902e+08 6.86258e+08 ... 8.05658e+08\n", + "\n", + "Optimal solution found (tolerance 1.00e-04)\n", + "Best objective 6.848411655488e+08, best bound 6.848411655488e+08, gap 0.0000%\n", + "Set parameter LogFile to value \"\"\n", + "WARNING: Cannot get reduced costs for MIP.\n", + "WARNING: Cannot get duals for MIP.\n" + ] + } + ], + "source": [ + "solver_baseline = LearningSolver()\n", + "solver_baseline.solve(test_files[0:1], build_uc_model, tee=True);" + ] + }, + { + "cell_type": "markdown", + "id": "b6d37b88-9fcc-43ee-ac1e-2a7b1e51a266", + "metadata": {}, + "source": [ + "In the log above, the `MIP start` line is missing, and Gurobi had to start with a significantly inferior initial solution. The solver was still able to find the optimal solution at the end, but it required using its own internal heuristic procedures. In this example, because we solve very small optimization problems, there was almost no difference in terms of running time. For larger problems, however, the difference can be significant. See benchmarks for more details.\n", + "\n", + "
\n", + "Note\n", + " \n", + "In addition to partial initial solutions, MIPLearn is also able to predict lazy constraints, cutting planes and branching priorities. See the next tutorials for more details.\n", + "
\n", + "\n", + "
\n", + "Note\n", + " \n", + "It is not necessary to specify what ML models to use. MIPLearn, by default, will try a number of classical ML models and will choose the one that performs the best, based on k-fold cross validation. MIPLearn is also able to automatically collect features based on the MIP formulation of the problem and the solution to the LP relaxation, among other things, so it does not require handcrafted features. If you do want to customize the models and features, however, that is also possible, as we will see in a later tutorial.\n", + "
" + ] + }, + { + "cell_type": "markdown", + "id": "eec97f06", + "metadata": { + "tags": [] + }, + "source": [ + "## Accessing the solution\n", + "\n", + "In the example above, we used `LearningSolver.solve` together with data files to solve both the training and the test instances. The optimal solutions were saved to HDF5 files in the train/test folders, and could be retrieved by reading theses files, but that is not very convenient. In the following example, we show how to build and solve a Pyomo model entirely in-memory, using our trained solver." + ] + }, + { + "cell_type": "code", + "execution_count": 11, + "id": "67a6cd18", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "obj = 903865807.3536932\n", + " x = [1.0, 1.0, 1.0, 1.0, 1.0]\n", + " y = [1105176.593734543, 1891284.5155055337, 1708177.4224033852, 1438329.610189608, 535496.3347187206]\n" + ] + } + ], + "source": [ + "# Construct model using previously defined functions\n", + "data = random_uc_data(samples=1, n=50)[0]\n", + "model = build_uc_model(data)\n", + "\n", + "# Solve model using ML + Gurobi\n", + "solver_ml.solve(model)\n", + "\n", + "# Print part of the optimal solution\n", + "print(\"obj =\", model.obj())\n", + "print(\" x =\", [model.x[i].value for i in range(5)])\n", + "print(\" y =\", [model.y[i].value for i in range(5)])" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "5593d23a-83bd-4e16-8253-6300f5e3f63b", + "metadata": {}, + "outputs": [], + "source": [] + } + ], + "metadata": { + "kernelspec": { + "display_name": "Python 3", + "language": "python", + "name": "python3" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.8.13" + } + }, + "nbformat": 4, + "nbformat_minor": 5 +} diff --git a/0.3/tutorials/getting-started-pyomo/index.html b/0.3/tutorials/getting-started-pyomo/index.html new file mode 100644 index 0000000..bfead2c --- /dev/null +++ b/0.3/tutorials/getting-started-pyomo/index.html @@ -0,0 +1,982 @@ + + + + + + + + Getting started (Pyomo) — MIPLearn 0.3 + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
+
+ + + + + + + + +
+ +
+
+
+
+ + + + +
+ + +
+ + + + + + +
+
+ + + + + + + + + +
+ + +
+ +
+ Contents +
+ +
+
+
+
+
+ +
+ + + +
+

Getting started (Pyomo)

+
+

Introduction

+

MIPLearn is an open source framework that uses machine learning (ML) to accelerate the performance of both commercial and open source mixed-integer programming solvers (e.g. Gurobi, CPLEX, XPRESS, Cbc or SCIP). In this tutorial, we will:

+
    +

  1. Install the Python/Pyomo version of MIPLearn

    2. +

  2. Model a simple optimization problem using JuMP

    3. +

  3. Generate training data and train the ML models

    4. +

  4. Use the ML models together Gurobi to solve new instances

    5. +
+
+

Note

+

The Python/Pyomo version of MIPLearn is currently only compatible with with Gurobi, CPLEX and XPRESS. For broader solver compatibility, see the Julia/JuMP version of the package.

+
+
+

Warning

+

MIPLearn is still in early development stage. If run into any bugs or issues, please submit a bug report in our GitHub repository. Comments, suggestions and pull requests are also very welcome!

+
+
+
+

Installation

+

MIPLearn is available in two versions:

+
    +

  • Python version, compatible with the Pyomo modeling language,

    • +

  • Julia version, compatible with the JuMP modeling language.

    • +
+

In this tutorial, we will demonstrate how to use and install the Python/Pyomo version of the package. The first step is to install Python 3.8+ in your computer. See the official Python website for more instructions. After Python is installed, we proceed to install MIPLearn using pip:

+
+
[1]:
+
+
+
# !pip install MIPLearn==0.2.0.dev13
+
+
+
+

In addition to MIPLearn itself, we will also install Gurobi 9.5, a state-of-the-art commercial MILP solver. This step also install a demo license for Gurobi, which should able to solve the small optimization problems in this tutorial. A paid license is required for solving large-scale problems.

+
+
[2]:
+
+
+
!pip install --upgrade -i https://pypi.gurobi.com 'gurobipy>=9.5,<9.6'
+
+
+
+
+
+
+
+
+Looking in indexes: https://pypi.gurobi.com
+Requirement already satisfied: gurobipy<9.6,>=9.5 in /opt/anaconda3/envs/miplearn/lib/python3.8/site-packages (9.5.1)
+
+
+
+

Note

+

In the code above, we install specific version of all packages to ensure that this tutorial keeps running in the future, even when newer (and possibly incompatible) versions of the packages are released. This is usually a recommended practice for all Python projects.

+
+
+
+

Modeling a simple optimization problem

+

To illustrate how can MIPLearn be used, we will model and solve a small optimization problem related to power systems optimization. The problem we discuss below is a simplification of the unit commitment problem, a practical optimization problem solved daily by electric grid operators around the world.

+

Suppose that you work at a utility company, and that it is your job to decide which electrical generators should be online at a certain hour of the day, as well as how much power should each generator produce. More specifically, assume that your company owns \(n\) generators, denoted by \(g_1, \ldots, g_n\). Each generator can either be online or offline. An online generator \(g_i\) can produce between \(p^\text{min}_i\) to \(p^\text{max}_i\) megawatts of power, and it costs +your company \(c^\text{fix}_i + c^\text{var}_i y_i\), where \(y_i\) is the amount of power produced. An offline generator produces nothing and costs nothing. You also know that the total amount of power to be produced needs to be exactly equal to the total demand \(d\) (in megawatts). To minimize the costs to your company, which generators should be online, and how much power should they produce?

+

This simple problem can be modeled as a mixed-integer linear optimization problem as follows. For each generator \(g_i\), let \(x_i \in \{0,1\}\) be a decision variable indicating whether \(g_i\) is online, and let \(y_i \geq 0\) be a decision variable indicating how much power does \(g_i\) produce. The problem is then given by:

+
+\[\begin{split}\begin{align} +\text{minimize } \quad & \sum_{i=1}^n \left( c^\text{fix}_i x_i + c^\text{var}_i y_i \right) \\ +\text{subject to } \quad & y_i \leq p^\text{max}_i x_i & i=1,\ldots,n \\ +& y_i \geq p^\text{min}_i x_i & i=1,\ldots,n \\ +& \sum_{i=1}^n y_i = d \\ +& x_i \in \{0,1\} & i=1,\ldots,n \\ +& y_i \geq 0 & i=1,\ldots,n +\end{align}\end{split}\]
+
+

Note

+

We use a simplified version of the unit commitment problem in this tutorial just to make it easier to follow. MIPLearn can also handle realistic, large-scale versions of this problem. See benchmarks for more details.

+
+

Next, let us convert this abstract mathematical formulation into a concrete optimization model, using Python and Pyomo. We start by defining a data class UnitCommitmentData, which holds all the input data.

+
+
[3]:
+
+
+
from dataclasses import dataclass
+import numpy as np
+
+@dataclass
+class UnitCommitmentData:
+    demand: float
+    pmin: np.ndarray
+    pmax: np.ndarray
+    cfix: np.ndarray
+    cvar: np.ndarray
+
+
+
+

Next, we write a build_uc_model function, which converts the input data into a concrete Pyomo model.

+
+
[4]:
+
+
+
import pyomo.environ as pe
+
+def build_uc_model(data: UnitCommitmentData) -> pe.ConcreteModel:
+    model = pe.ConcreteModel()
+    n = len(data.pmin)
+    model.x = pe.Var(range(n), domain=pe.Binary)
+    model.y = pe.Var(range(n), domain=pe.NonNegativeReals)
+    model.obj = pe.Objective(
+        expr=sum(
+            data.cfix[i] * model.x[i] +
+            data.cvar[i] * model.y[i]
+            for i in range(n)
+        )
+    )
+    model.eq_max_power = pe.ConstraintList()
+    model.eq_min_power = pe.ConstraintList()
+    for i in range(n):
+        model.eq_max_power.add(model.y[i] <= data.pmax[i] * model.x[i])
+        model.eq_min_power.add(model.y[i] >= data.pmin[i] * model.x[i])
+    model.eq_demand = pe.Constraint(
+        expr=sum(model.y[i] for i in range(n)) == data.demand,
+    )
+    return model
+
+
+
+

At this point, we can already use Pyomo and any mixed-integer linear programming solver to find optimal solutions to any instance of this problem. To illustrate this, let us solve a small instance with three generators:

+
+
[5]:
+
+
+
model = build_uc_model(
+    UnitCommitmentData(
+        demand = 100.0,
+        pmin = [10, 20, 30],
+        pmax = [50, 60, 70],
+        cfix = [700, 600, 500],
+        cvar = [1.5, 2.0, 2.5],
+    )
+)
+
+solver = pe.SolverFactory("gurobi_persistent")
+solver.set_instance(model)
+solver.solve()
+print("obj =", model.obj())
+print("x =", [model.x[i].value for i in range(3)])
+print("y =", [model.y[i].value for i in range(3)])
+
+
+
+
+
+
+
+
+Set parameter Threads to value 1
+Set parameter Seed to value 42
+Restricted license - for non-production use only - expires 2023-10-25
+obj = 1320.0
+x = [-0.0, 1.0, 1.0]
+y = [0.0, 60.0, 40.0]
+
+
+

Running the code above, we found that the optimal solution for our small problem instance costs $1320. It is achieve by keeping generators 2 and 3 online and producing, respectively, 60 MW and 40 MW of power.

+
+
+

Generating training data

+

Although Gurobi could solve the small example above in a fraction of a second, it gets slower for larger and more complex versions of the problem. If this is a problem that needs to be solved frequently, as it is often the case in practice, it could make sense to spend some time upfront generating a trained version of Gurobi, which can solve new instances (similar to the ones it was trained on) faster.

+

In the following, we will use MIPLearn to train machine learning models that is able to predict the optimal solution for instances that follow a given probability distribution, then it will provide this predicted solution to Gurobi as a warm start. Before we can train the model, we need to collect training data by solving a large number of instances. In real-world situations, we may construct these training instances based on historical data. In this tutorial, we will construct them using a +random instance generator:

+
+
[6]:
+
+
+
from scipy.stats import uniform
+from typing import List
+import random
+
+def random_uc_data(samples: int, n: int, seed: int = 42) -> List[UnitCommitmentData]:
+    random.seed(seed)
+    np.random.seed(seed)
+    pmin = uniform(loc=100_000.0, scale=400_000.0).rvs(n)
+    pmax = pmin * uniform(loc=2.0, scale=2.5).rvs(n)
+    cfix = pmin * uniform(loc=100.0, scale=25.0).rvs(n)
+    cvar = uniform(loc=1.25, scale=0.25).rvs(n)
+    return [
+        UnitCommitmentData(
+            demand = pmax.sum() * uniform(loc=0.5, scale=0.25).rvs(),
+            pmin = pmin,
+            pmax = pmax,
+            cfix = cfix,
+            cvar = cvar,
+        )
+        for i in range(samples)
+    ]
+
+
+
+

In this example, for simplicity, only the demands change from one instance to the next. We could also have randomized the costs, production limits or even the number of units. The more randomization we have in the training data, however, the more challenging it is for the machine learning models to learn solution patterns.

+

Now we generate 500 instances of this problem, each one with 50 generators, and we use 450 of these instances for training. After generating the instances, we write them to individual files. MIPLearn uses files during the training process because, for large-scale optimization problems, it is often impractical to hold in memory the entire training data, as well as the concrete Pyomo models. Files also make it much easier to solve multiple instances simultaneously, potentially even on multiple +machines. We will cover parallel and distributed computing in a future tutorial. The code below generates the files uc/train/00000.pkl.gz, uc/train/00001.pkl.gz, etc., which contain the input data in compressed (gzipped) pickle format.

+
+
[7]:
+
+
+
from miplearn import save
+data = random_uc_data(samples=500, n=50)
+train_files = save(data[0:450], "uc/train/")
+test_files  = save(data[450:500], "uc/test/")
+
+
+
+

Finally, we use LearningSolver to solve all the training instances. LearningSolver is the main component provided by MIPLearn, which integrates MIP solvers and ML. The optimal solutions, along with other useful training data, are stored in HDF5 files uc/train/00000.h5, uc/train/00001.h5, etc.

+
+
[12]:
+
+
+
from miplearn import LearningSolver
+solver = LearningSolver()
+solver.solve(train_files, build_uc_model);
+
+
+
+
+
+

Solving test instances

+

With training data in hand, we can now fit the ML models, using the LearningSolver.fit method, then solve the test instances with LearningSolver.solve, as shown below. The tee=True parameter asks MIPLearn to print the solver log to the screen.

+
+
[9]:
+
+
+
solver_ml = LearningSolver()
+solver_ml.fit(train_files, build_uc_model)
+solver_ml.solve(test_files[0:1], build_uc_model, tee=True);
+
+
+
+
+
+
+
+
+Set parameter LogFile to value "/tmp/tmpvbaqbyty.log"
+Set parameter QCPDual to value 1
+Gurobi Optimizer version 9.5.1 build v9.5.1rc2 (linux64)
+Thread count: 16 physical cores, 32 logical processors, using up to 1 threads
+Optimize a model with 101 rows, 100 columns and 250 nonzeros
+Model fingerprint: 0x8de73876
+Coefficient statistics:
+  Matrix range     [1e+00, 2e+06]
+  Objective range  [1e+00, 6e+07]
+  Bounds range     [1e+00, 1e+00]
+  RHS range        [2e+07, 2e+07]
+Presolve removed 100 rows and 50 columns
+Presolve time: 0.00s
+Presolved: 1 rows, 50 columns, 50 nonzeros
+
+Iteration    Objective       Primal Inf.    Dual Inf.      Time
+       0    5.7349081e+08   1.044003e+04   0.000000e+00      0s
+       1    6.8268465e+08   0.000000e+00   0.000000e+00      0s
+
+Solved in 1 iterations and 0.00 seconds (0.00 work units)
+Optimal objective  6.826846503e+08
+Set parameter LogFile to value ""
+Set parameter LogFile to value "/tmp/tmp48j6n35b.log"
+Gurobi Optimizer version 9.5.1 build v9.5.1rc2 (linux64)
+Thread count: 16 physical cores, 32 logical processors, using up to 1 threads
+Optimize a model with 101 rows, 100 columns and 250 nonzeros
+Model fingerprint: 0x200d64ba
+Variable types: 50 continuous, 50 integer (50 binary)
+Coefficient statistics:
+  Matrix range     [1e+00, 2e+06]
+  Objective range  [1e+00, 6e+07]
+  Bounds range     [1e+00, 1e+00]
+  RHS range        [2e+07, 2e+07]
+
+User MIP start produced solution with objective 6.84841e+08 (0.00s)
+Loaded user MIP start with objective 6.84841e+08
+
+Presolve time: 0.00s
+Presolved: 101 rows, 100 columns, 250 nonzeros
+Variable types: 50 continuous, 50 integer (50 binary)
+
+Root relaxation: objective 6.826847e+08, 56 iterations, 0.00 seconds (0.00 work units)
+
+    Nodes    |    Current Node    |     Objective Bounds      |     Work
+ Expl Unexpl |  Obj  Depth IntInf | Incumbent    BestBd   Gap | It/Node Time
+
+     0     0 6.8268e+08    0    1 6.8484e+08 6.8268e+08  0.31%     -    0s
+     0     0 6.8315e+08    0    3 6.8484e+08 6.8315e+08  0.25%     -    0s
+     0     0 6.8315e+08    0    1 6.8484e+08 6.8315e+08  0.25%     -    0s
+     0     0 6.8315e+08    0    3 6.8484e+08 6.8315e+08  0.25%     -    0s
+     0     0 6.8315e+08    0    4 6.8484e+08 6.8315e+08  0.25%     -    0s
+     0     0 6.8315e+08    0    4 6.8484e+08 6.8315e+08  0.25%     -    0s
+     0     2 6.8327e+08    0    4 6.8484e+08 6.8327e+08  0.23%     -    0s
+
+Cutting planes:
+  Flow cover: 3
+
+Explored 32 nodes (155 simplex iterations) in 0.02 seconds (0.00 work units)
+Thread count was 1 (of 32 available processors)
+
+Solution count 1: 6.84841e+08
+
+Optimal solution found (tolerance 1.00e-04)
+Best objective 6.848411655488e+08, best bound 6.848411655488e+08, gap 0.0000%
+Set parameter LogFile to value ""
+WARNING: Cannot get reduced costs for MIP.
+WARNING: Cannot get duals for MIP.
+
+
+

By examining the solve log above, specifically the line Loaded user MIP start with objective..., we can see that MIPLearn was able to construct an initial solution which turned out to be the optimal solution to the problem. Now let us repeat the code above, but using an untrained solver. Note that the fit line is omitted.

+
+
[10]:
+
+
+
solver_baseline = LearningSolver()
+solver_baseline.solve(test_files[0:1], build_uc_model, tee=True);
+
+
+
+
+
+
+
+
+Set parameter LogFile to value "/tmp/tmp3uhhdurw.log"
+Set parameter QCPDual to value 1
+Gurobi Optimizer version 9.5.1 build v9.5.1rc2 (linux64)
+Thread count: 16 physical cores, 32 logical processors, using up to 1 threads
+Optimize a model with 101 rows, 100 columns and 250 nonzeros
+Model fingerprint: 0x8de73876
+Coefficient statistics:
+  Matrix range     [1e+00, 2e+06]
+  Objective range  [1e+00, 6e+07]
+  Bounds range     [1e+00, 1e+00]
+  RHS range        [2e+07, 2e+07]
+Presolve removed 100 rows and 50 columns
+Presolve time: 0.00s
+Presolved: 1 rows, 50 columns, 50 nonzeros
+
+Iteration    Objective       Primal Inf.    Dual Inf.      Time
+       0    5.7349081e+08   1.044003e+04   0.000000e+00      0s
+       1    6.8268465e+08   0.000000e+00   0.000000e+00      0s
+
+Solved in 1 iterations and 0.01 seconds (0.00 work units)
+Optimal objective  6.826846503e+08
+Set parameter LogFile to value ""
+Set parameter LogFile to value "/tmp/tmp18aqg2ic.log"
+Gurobi Optimizer version 9.5.1 build v9.5.1rc2 (linux64)
+Thread count: 16 physical cores, 32 logical processors, using up to 1 threads
+Optimize a model with 101 rows, 100 columns and 250 nonzeros
+Model fingerprint: 0xb90d1075
+Variable types: 50 continuous, 50 integer (50 binary)
+Coefficient statistics:
+  Matrix range     [1e+00, 2e+06]
+  Objective range  [1e+00, 6e+07]
+  Bounds range     [1e+00, 1e+00]
+  RHS range        [2e+07, 2e+07]
+Found heuristic solution: objective 8.056576e+08
+Presolve time: 0.00s
+Presolved: 101 rows, 100 columns, 250 nonzeros
+Variable types: 50 continuous, 50 integer (50 binary)
+
+Root relaxation: objective 6.826847e+08, 56 iterations, 0.00 seconds (0.00 work units)
+
+    Nodes    |    Current Node    |     Objective Bounds      |     Work
+ Expl Unexpl |  Obj  Depth IntInf | Incumbent    BestBd   Gap | It/Node Time
+
+     0     0 6.8268e+08    0    1 8.0566e+08 6.8268e+08  15.3%     -    0s
+H    0     0                    7.099498e+08 6.8268e+08  3.84%     -    0s
+     0     0 6.8315e+08    0    3 7.0995e+08 6.8315e+08  3.78%     -    0s
+H    0     0                    6.883227e+08 6.8315e+08  0.75%     -    0s
+     0     0 6.8352e+08    0    4 6.8832e+08 6.8352e+08  0.70%     -    0s
+     0     0 6.8352e+08    0    4 6.8832e+08 6.8352e+08  0.70%     -    0s
+     0     0 6.8352e+08    0    1 6.8832e+08 6.8352e+08  0.70%     -    0s
+H    0     0                    6.862582e+08 6.8352e+08  0.40%     -    0s
+     0     0 6.8352e+08    0    4 6.8626e+08 6.8352e+08  0.40%     -    0s
+     0     0 6.8352e+08    0    4 6.8626e+08 6.8352e+08  0.40%     -    0s
+     0     0 6.8352e+08    0    1 6.8626e+08 6.8352e+08  0.40%     -    0s
+     0     0 6.8352e+08    0    3 6.8626e+08 6.8352e+08  0.40%     -    0s
+     0     0 6.8352e+08    0    4 6.8626e+08 6.8352e+08  0.40%     -    0s
+     0     0 6.8352e+08    0    4 6.8626e+08 6.8352e+08  0.40%     -    0s
+     0     2 6.8354e+08    0    4 6.8626e+08 6.8354e+08  0.40%     -    0s
+*   18     5               6    6.849018e+08 6.8413e+08  0.11%   3.1    0s
+H   24     1                    6.848412e+08 6.8426e+08  0.09%   3.2    0s
+
+Cutting planes:
+  Gomory: 1
+  Flow cover: 2
+
+Explored 30 nodes (217 simplex iterations) in 0.02 seconds (0.00 work units)
+Thread count was 1 (of 32 available processors)
+
+Solution count 6: 6.84841e+08 6.84902e+08 6.86258e+08 ... 8.05658e+08
+
+Optimal solution found (tolerance 1.00e-04)
+Best objective 6.848411655488e+08, best bound 6.848411655488e+08, gap 0.0000%
+Set parameter LogFile to value ""
+WARNING: Cannot get reduced costs for MIP.
+WARNING: Cannot get duals for MIP.
+
+
+

In the log above, the MIP start line is missing, and Gurobi had to start with a significantly inferior initial solution. The solver was still able to find the optimal solution at the end, but it required using its own internal heuristic procedures. In this example, because we solve very small optimization problems, there was almost no difference in terms of running time. For larger problems, however, the difference can be significant. See benchmarks for more details.

+
+

Note

+

In addition to partial initial solutions, MIPLearn is also able to predict lazy constraints, cutting planes and branching priorities. See the next tutorials for more details.

+
+
+

Note

+

It is not necessary to specify what ML models to use. MIPLearn, by default, will try a number of classical ML models and will choose the one that performs the best, based on k-fold cross validation. MIPLearn is also able to automatically collect features based on the MIP formulation of the problem and the solution to the LP relaxation, among other things, so it does not require handcrafted features. If you do want to customize the models and features, however, that is also possible, as we will +see in a later tutorial.

+
+
+
+

Accessing the solution

+

In the example above, we used LearningSolver.solve together with data files to solve both the training and the test instances. The optimal solutions were saved to HDF5 files in the train/test folders, and could be retrieved by reading theses files, but that is not very convenient. In the following example, we show how to build and solve a Pyomo model entirely in-memory, using our trained solver.

+
+
[11]:
+
+
+
# Construct model using previously defined functions
+data = random_uc_data(samples=1, n=50)[0]
+model = build_uc_model(data)
+
+# Solve model using ML + Gurobi
+solver_ml.solve(model)
+
+# Print part of the optimal solution
+print("obj =", model.obj())
+print(" x =", [model.x[i].value for i in range(5)])
+print(" y =", [model.y[i].value for i in range(5)])
+
+
+
+
+
+
+
+
+obj = 903865807.3536932
+ x = [1.0, 1.0, 1.0, 1.0, 1.0]
+ y = [1105176.593734543, 1891284.5155055337, 1708177.4224033852, 1438329.610189608, 535496.3347187206]
+
+
+
+
[ ]:
+
+
+

+
+
+
+
+
+ + +
+ + +
+ + +
+ +
+
+
+
+

+ + © Copyright 2020-2022, UChicago Argonne, LLC.
+

+
+
+
+ + +
+
+ + + + + + \ No newline at end of file