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Alinson S. Xavier 2 years ago
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0.2/.buildinfo
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# Sphinx build info version 1
# This file hashes the configuration used when building these files. When it is not found, a full rebuild will be done.
config: 3772558d35a82a60dc512dba5e805386
tags: d77d1c0d9ca2f4c8421862c7c5a0d620

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0.2/_sources/benchmarks/facility.ipynb.txt
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{
"cells": [
{
"cell_type": "markdown",
"id": "792bbfa2",
"metadata": {},
"source": [
"# Facility Location\n",
"\n",
"TODO"
]
}
],
"metadata": {
"kernelspec": {
"display_name": "Julia 1.6.0",
"language": "julia",
"name": "julia-1.6"
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{
"cells": [
{
"cell_type": "markdown",
"id": "d236e2a0",
"metadata": {},
"source": [
"# Multidimensional Knapsack\n",
"\n",
"### Problem definition\n",
"\n",
"Given a set of $n$ items and $m$ types of resources (also called *knapsacks*), the problem is to find a subset of items that maximizes profit without consuming more resources than it is available. More precisely, the problem is:\n",
"\n",
"$$\n",
"\\begin{align*}\n",
" \\text{maximize}\n",
" & \\sum_{j=1}^n p_j x_j\n",
" \\\\\n",
" \\text{subject to}\n",
" & \\sum_{j=1}^n w_{ij} x_j \\leq b_i\n",
" & \\forall i=1,\\ldots,m \\\\\n",
" & x_j \\in \\{0,1\\}\n",
" & \\forall j=1,\\ldots,n\n",
"\\end{align*}\n",
"$$\n",
"\n",
"### Random instance generator\n",
"\n",
"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\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.\n",
"\n",
"\n",
"<div class=\"alert alert-info\">\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",
"</div>\n",
" \n",
"### Challenge A\n",
"\n",
"* 250 variables, 10 constraints, fixed weights\n",
"* $w \\sim U(0, 1000), \\gamma \\sim U(0.95, 1.05)$\n",
"* $K = 500, u \\sim U(0, 1), \\alpha = 0.25$\n",
"* 500 training instances, 50 test instances\n"
]
},
{
"cell_type": "code",
"execution_count": null,
"id": "39be5cda",
"metadata": {},
"outputs": [],
"source": [
"MultiKnapsackGenerator(\n",
" n=randint(low=250, high=251),\n",
" m=randint(low=10, high=11),\n",
" w=uniform(loc=0.0, scale=1000.0),\n",
" K=uniform(loc=500.0, scale=0.0),\n",
" u=uniform(loc=0.0, scale=1.0),\n",
" alpha=uniform(loc=0.25, scale=0.0),\n",
" fix_w=True,\n",
" w_jitter=uniform(loc=0.95, scale=0.1),\n",
")"
]
}
],
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"kernelspec": {
"display_name": "miplearn",
"language": "python",
"name": "miplearn"
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"language_info": {
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"name": "ipython",
"version": 3
},
"file_extension": ".py",
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0.2/_sources/benchmarks/preliminaries.ipynb.txt
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{
"cells": [
{
"cell_type": "markdown",
"id": "423ee254",
"metadata": {},
"source": [
"# Preliminaries\n",
"\n",
"## Benchmark challenges\n",
"\n",
"When evaluating the performance of a conventional MIP solver, *benchmark sets*, such as MIPLIB and TSPLIB, are typically used. The performance of newly proposed solvers or solution techniques are typically measured as the average (or total) running time the solver takes to solve the entire benchmark set. For Learning-Enhanced MIP solvers, it is also necessary to specify what instances should the solver be trained on (the *training instances*) before solving the actual set of instances we are interested in (the *test instances*). If the training instances are very similar to the test instances, we would expect a Learning-Enhanced Solver to present stronger perfomance benefits.\n",
"\n",
"In MIPLearn, each optimization problem comes with a set of **benchmark challenges**, which specify how should the training and test instances be generated. The first challenges are typically easier, in the sense that training and test instances are very similar. Later challenges gradually make the sets more distinct, and therefore harder to learn from.\n",
"\n",
"## Baseline results\n",
"\n",
"To illustrate the performance of `LearningSolver`, and to set a baseline for newly proposed techniques, we present in this page, for each benchmark challenge, a small set of computational results measuring the solution speed of the solver and the solution quality with default parameters. For more detailed computational studies, see [references](index.md#references). We compare three solvers:\n",
"\n",
"* **baseline:** Gurobi 9.1 with default settings (a conventional state-of-the-art MIP solver)\n",
"* **ml-exact:** `LearningSolver` with default settings, using Gurobi 9.0 as internal MIP solver\n",
"* **ml-heuristic:** Same as above, but with `mode=\"heuristic\"`\n",
"\n",
"All experiments presented here were performed on a Linux server (Ubuntu Linux 18.04 LTS) with Intel Xeon Gold 6230s (2 processors, 40 cores, 80 threads) and 256 GB RAM (DDR4, 2933 MHz). All solvers were restricted to use 4 threads, with no time limits, and 10 instances were solved simultaneously at a time."
]
}
],
"metadata": {
"kernelspec": {
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"language": "julia",
"name": "julia-1.6"
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"file_extension": ".jl",
"mimetype": "application/julia",
"name": "julia",
"version": "1.6.0"
}
},
"nbformat": 4,
"nbformat_minor": 5
}

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{
"cells": [
{
"cell_type": "markdown",
"id": "23083bd9",
"metadata": {},
"source": [
"# Maximum Weight Stable Set\n",
"\n",
"## Problem definition\n",
"\n",
"Given a simple undirected graph $G=(V,E)$ and weights $w \\in \\mathbb{R}^V$, the problem is to find a stable set $S \\subseteq V$ that maximizes $ \\sum_{v \\in V} w_v$. We recall that a subset $S \\subseteq V$ is a *stable set* if no two vertices of $S$ are adjacent. This is one of Karp's 21 NP-complete problems.\n",
"\n",
"## Random instance generator\n",
"\n",
"The class `MaxWeightStableSetGenerator` can be used to generate random instances of this problem, with user-specified probability distributions. When the constructor parameter `fix_graph=True` is provided, one random Erdős-Rényi graph $G_{n,p}$ is generated during 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, while the remaining parameters are sampled in the same way.\n",
"\n",
"## Challenge A\n",
"\n",
"* Fixed random Erdős-Rényi graph $G_{n,p}$ with $n=200$ and $p=5\\%$\n",
"* Random vertex weights $w_v \\sim U(100, 150)$\n",
"* 500 training instances, 50 test instances"
]
},
{
"cell_type": "code",
"execution_count": null,
"id": "207c7846",
"metadata": {},
"outputs": [],
"source": [
"MaxWeightStableSetGenerator(\n",
" w=uniform(loc=100., scale=50.),\n",
" n=randint(low=200, high=201),\n",
" p=uniform(loc=0.05, scale=0.0),\n",
" fix_graph=True,\n",
")"
]
}
],
"metadata": {
"kernelspec": {
"display_name": "miplearn",
"language": "python",
"name": "miplearn"
},
"language_info": {
"codemirror_mode": {
"name": "ipython",
"version": 3
},
"file_extension": ".py",
"mimetype": "text/x-python",
"name": "python",
"nbconvert_exporter": "python",
"pygments_lexer": "ipython3",
"version": "3.8.10"
}
},
"nbformat": 4,
"nbformat_minor": 5
}

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{
"cells": [
{
"cell_type": "markdown",
"id": "2f39414b",
"metadata": {},
"source": [
"# Traveling Salesman\n",
"\n",
"### Problem definition\n",
"\n",
"Given a list of cities and the distance between each pair of cities, the problem asks for the\n",
"shortest route starting at the first city, visiting each other city exactly once, then returning\n",
"to the first city. This problem is a generalization of the Hamiltonian path problem, one of Karp's\n",
"21 NP-complete problems.\n",
"\n",
"### Random problem generator\n",
"\n",
"The class `TravelingSalesmanGenerator` can be used to generate random instances of this\n",
"problem. Initially, the generator creates $n$ cities $(x_1,y_1),\\ldots,(x_n,y_n) \\in \\mathbb{R}^2$,\n",
"where $n, x_i$ and $y_i$ are sampled independently from the provided probability distributions `n`,\n",
"`x` and `y`. For each pair of cities $(i,j)$, the distance $d_{i,j}$ between them is set to:\n",
"$$\n",
" d_{i,j} = \\gamma_{i,j} \\sqrt{(x_i-x_j)^2 + (y_i - y_j)^2}\n",
"$$\n",
"where $\\gamma_{i,j}$ is sampled from the distribution `gamma`.\n",
"\n",
"If `fix_cities=True` is provided, the list of cities is kept the same for all generated instances.\n",
"The $gamma$ values, and therefore also the distances, are still different.\n",
"\n",
"By default, all distances $d_{i,j}$ are rounded to the nearest integer. If `round=False`\n",
"is provided, this rounding will be disabled.\n",
"\n",
"### Challenge A\n",
"\n",
"* Fixed list of 350 cities in the $[0, 1000]^2$ square\n",
"* $\\gamma_{i,j} \\sim U(0.95, 1.05)$\n",
"* 500 training instances, 50 test instances"
]
},
{
"cell_type": "code",
"execution_count": null,
"id": "6b2c4ff9",
"metadata": {},
"outputs": [],
"source": [
"TravelingSalesmanGenerator(\n",
" x=uniform(loc=0.0, scale=1000.0),\n",
" y=uniform(loc=0.0, scale=1000.0),\n",
" n=randint(low=350, high=351),\n",
" gamma=uniform(loc=0.95, scale=0.1),\n",
" fix_cities=True,\n",
" round=True,\n",
")"
]
},
{
"cell_type": "code",
"execution_count": null,
"id": "cc125860",
"metadata": {},
"outputs": [],
"source": []
}
],
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"display_name": "miplearn",
"language": "python",
"name": "miplearn"
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"name": "ipython",
"version": 3
},
"file_extension": ".py",
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"pygments_lexer": "ipython3",
"version": "3.8.10"
}
},
"nbformat": 4,
"nbformat_minor": 5
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{
"cells": [
{
"cell_type": "markdown",
"id": "ed7d4bdc",
"metadata": {},
"source": [
"# Unit Commitment\n",
"\n",
"TODO"
]
}
],
"metadata": {
"kernelspec": {
"display_name": "Julia 1.6.0",
"language": "julia",
"name": "julia-1.6"
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# MIPLearn
**MIPLearn** is an extensible framework for solving discrete optimization problems using a combination of Mixed-Integer Linear Programming (MIP) and Machine Learning (ML). The framework 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).
## Table of Contents
```{toctree}
---
maxdepth: 1
caption: Julia Tutorials
numbered: true
---
jump-tutorials/getting-started.ipynb
#jump-tutorials/lazy-constraints.ipynb
#jump-tutorials/user-cuts.ipynb
#jump-tutorials/customizing-ml.ipynb
```
```{toctree}
---
maxdepth: 1
caption: Benchmarks
numbered: true
---
benchmarks/preliminaries.ipynb
benchmarks/stab.ipynb
#benchmarks/uc.ipynb
#benchmarks/facility.ipynb
benchmarks/knapsack.ipynb
benchmarks/tsp.ipynb
```
```{toctree}
---
maxdepth: 1
caption: MIPLearn Internals
numbered: true
---
#internals/solver-interfaces.ipynb
#internals/data-collection.ipynb
#internals/abstract-component.ipynb
#internals/primal.ipynb
#internals/static-lazy.ipynb
#internals/dynamic-lazy.ipynb
```
## Source Code
* [https://github.com/ANL-CEEESA/MIPLearn](https://github.com/ANL-CEEESA/MIPLearn)
## Authors
* **Alinson S. Xavier,** Argonne National Laboratory <<axavier@anl.gov>>
* **Feng Qiu,** Argonne National Laboratory <<fqiu@anl.gov>>
## Acknowledgments
* Based upon work supported by **Laboratory Directed Research and Development** (LDRD) funding from Argonne National Laboratory, provided by the Director, Office of Science, of the U.S. Department of Energy under Contract No. DE-AC02-06CH11357, and the **U.S. Department of Energy Advanced Grid Modeling Program** under Grant DE-OE0000875.
## References
If you use MIPLearn in your research, or the included problem generators, we kindly request that you cite the package as follows:
- **Alinson S. Xavier, Feng Qiu.** *MIPLearn: An Extensible Framework for Learning-Enhanced Optimization*. Zenodo (2020). DOI: [10.5281/zenodo.4287567](https://doi.org/10.5281/zenodo.4287567)
If you use MIPLearn in the field of power systems optimization, we kindly request that you cite the reference below, in which the main techniques implemented in MIPLearn were first developed:
- **Alinson S. Xavier, Feng Qiu, Shabbir Ahmed.** *Learning to Solve Large-Scale Unit Commitment Problems.* INFORMS Journal on Computing (2021). DOI: [10.1287/ijoc.2020.0976](https://doi.org/10.1287/ijoc.2020.0976)
## License
```text
MIPLearn, an extensible framework for Learning-Enhanced Mixed-Integer Optimization
Copyright © 2020, UChicago Argonne, LLC. All Rights Reserved.
Redistribution and use in source and binary forms, with or without modification, are permitted
provided that the following conditions are met:
1. Redistributions of source code must retain the above copyright notice, this list of
conditions and the following disclaimer.
2. Redistributions in binary form must reproduce the above copyright notice, this list of
conditions and the following disclaimer in the documentation and/or other materials provided
with the distribution.
3. Neither the name of the copyright holder nor the names of its contributors may be used to
endorse or promote products derived from this software without specific prior written
permission.
THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS" AND ANY EXPRESS OR
IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY
AND FITNESS FOR A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT HOLDER OR
CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR
CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR
SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY
THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR
OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE
POSSIBILITY OF SUCH DAMAGE.
```

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{
"cells": [
{
"cell_type": "markdown",
"id": "ad9274ff",
"metadata": {},
"source": [
"# Abstract component\n",
"\n",
"TODO"
]
}
],
"metadata": {
"kernelspec": {
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"language": "julia",
"name": "julia-1.6"
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{
"cells": [
{
"cell_type": "markdown",
"id": "780b4172",
"metadata": {},
"source": [
"# Training data collection\n",
"\n",
"TODO"
]
}
],
"metadata": {
"kernelspec": {
"display_name": "Julia 1.6.0",
"language": "julia",
"name": "julia-1.6"
},
"language_info": {
"file_extension": ".jl",
"mimetype": "application/julia",
"name": "julia",
"version": "1.6.0"
}
},
"nbformat": 4,
"nbformat_minor": 5
}

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{
"cells": [
{
"cell_type": "markdown",
"id": "5e3dd4c0",
"metadata": {},
"source": [
"# Dynamic lazy constraints & user cuts\n",
"\n",
"TODO"
]
}
],
"metadata": {
"kernelspec": {
"display_name": "Julia 1.6.0",
"language": "julia",
"name": "julia-1.6"
},
"language_info": {
"file_extension": ".jl",
"mimetype": "application/julia",
"name": "julia",
"version": "1.6.0"
}
},
"nbformat": 4,
"nbformat_minor": 5
}

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{
"cells": [
{
"cell_type": "markdown",
"id": "c6d0d8dc",
"metadata": {},
"source": [
"# Primal solutions\n",
"\n",
"TODO"
]
}
],
"metadata": {
"kernelspec": {
"display_name": "Julia 1.6.0",
"language": "julia",
"name": "julia-1.6"
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"mimetype": "application/julia",
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"version": "1.6.0"
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"nbformat": 4,
"nbformat_minor": 5
}

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{
"cells": [
{
"cell_type": "markdown",
"id": "ac509ea5",
"metadata": {},
"source": [
"# Solver interfaces\n",
"\n",
"TODO"
]
}
],
"metadata": {
"kernelspec": {
"display_name": "Julia 1.6.0",
"language": "julia",
"name": "julia-1.6"
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"version": "1.6.0"
}
},
"nbformat": 4,
"nbformat_minor": 5
}

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{
"cells": [
{
"cell_type": "markdown",
"id": "ae350662",
"metadata": {},
"source": [
"# Static lazy constraints\n",
"\n",
"TODO"
]
}
],
"metadata": {
"kernelspec": {
"display_name": "Julia 1.6.0",
"language": "julia",
"name": "julia-1.6"
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"version": "1.6.0"
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"nbformat_minor": 5
}

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{
"cells": [
{
"cell_type": "markdown",
"id": "ea2dc06a",
"metadata": {},
"source": [
"# Customizing the ML models\n",
"\n",
"TODO"
]
}
],
"metadata": {
"kernelspec": {
"display_name": "Julia 1.6.0",
"language": "julia",
"name": "julia-1.6"
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"file_extension": ".jl",
"mimetype": "application/julia",
"name": "julia",
"version": "1.6.0"
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},
"nbformat": 4,
"nbformat_minor": 5
}

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{
"cells": [
{
"cell_type": "markdown",
"id": "546635ee",
"metadata": {},
"source": [
"# Getting started with MIPLearn\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 Julia/JuMP 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 with SCIP to solve new instances\n",
"\n",
"<div class=\"alert alert-info\">\n",
"Note\n",
" \n",
"In this tutorial, we use SCIP because it is more widely available than commercial MIP solvers. However, all the steps below should work for Gurobi, CPLEX or XPRESS, as long as you have a license for these solvers. The performance impact of MIPLearn may also change for different solvers.\n",
"</div>\n",
"\n",
"<div class=\"alert alert-warning\">\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",
"</div>\n"
]
},
{
"cell_type": "markdown",
"id": "8b97258c",
"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 Julia/JuMP version of the package. The first step is to install the Julia programming language in your computer. [See the official instructions for more details](https://julialang.org/downloads/). Note that MIPLearn was developed and tested with Julia 1.6, and may not be compatible with newer versions of the language. After Julia is installed, launch its console and run the following commands to download and install the package:"
]
},
{
"cell_type": "code",
"execution_count": 1,
"id": "2dbeacbc",
"metadata": {},
"outputs": [
{
"name": "stderr",
"output_type": "stream",
"text": [
"\u001b[32m\u001b[1m Updating\u001b[22m\u001b[39m git-repo `https://github.com/ANL-CEEESA/MIPLearn.jl.git`\n",
"\u001b[32m\u001b[1m Updating\u001b[22m\u001b[39m registry at `~/.julia/registries/General`\n",
"\u001b[32m\u001b[1m Updating\u001b[22m\u001b[39m git-repo `https://github.com/JuliaRegistries/General.git`\n",
"\u001b[32m\u001b[1m Resolving\u001b[22m\u001b[39m package versions...\n",
"\u001b[32m\u001b[1m No Changes\u001b[22m\u001b[39m to `~/Packages/MIPLearn/dev/docs/jump-tutorials/Project.toml`\n",
"\u001b[32m\u001b[1m No Changes\u001b[22m\u001b[39m to `~/Packages/MIPLearn/dev/docs/jump-tutorials/Manifest.toml`\n"
]
}
],
"source": [
"using Pkg\n",
"Pkg.add(PackageSpec(url=\"https://github.com/ANL-CEEESA/MIPLearn.jl.git\"))"
]
},
{
"cell_type": "markdown",
"id": "b2f449e7",
"metadata": {},
"source": [
"In addition to MIPLearn itself, we will also install a few other packages that are required for this tutorial:\n",
"\n",
"- [**SCIP**](https://www.scipopt.org/), one of the fastest non-commercial MIP solvers currently available\n",
"- [**JuMP**](https://jump.dev/), an open source modeling language for Julia\n",
"- [**Distributions.jl**](https://github.com/JuliaStats/Distributions.jl), a statistics package that we will use to generate random inputs\n",
"- [**Glob.jl**](https://github.com/vtjnash/Glob.jl), a package that retrieves all files in a directory matching a certain pattern"
]
},
{
"cell_type": "code",
"execution_count": 2,
"id": "68f99568",
"metadata": {},
"outputs": [
{
"name": "stderr",
"output_type": "stream",
"text": [
"\u001b[32m\u001b[1m Resolving\u001b[22m\u001b[39m package versions...\n",
"\u001b[32m\u001b[1m No Changes\u001b[22m\u001b[39m to `~/Packages/MIPLearn/dev/docs/jump-tutorials/Project.toml`\n",
"\u001b[32m\u001b[1m No Changes\u001b[22m\u001b[39m to `~/Packages/MIPLearn/dev/docs/jump-tutorials/Manifest.toml`\n"
]
}
],
"source": [
"using Pkg\n",
"Pkg.add([\n",
" PackageSpec(url=\"https://github.com/scipopt/SCIP.jl.git\", rev=\"7aa79aaa\"),\n",
" PackageSpec(name=\"JuMP\", version=\"0.21\"),\n",
" PackageSpec(name=\"Distributions\", version=\"0.25\"),\n",
" PackageSpec(name=\"Glob\", version=\"1\"),\n",
"])"
]
},
{
"cell_type": "markdown",
"id": "51e09fc9",
"metadata": {},
"source": [
"<div class=\"alert alert-info\">\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 Julia projects.\n",
" \n",
"</div>"
]
},
{
"cell_type": "markdown",
"id": "18c300c4",
"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",
"<div class=\"alert alert-info\">\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",
"</div>\n",
"\n",
"Next, let us convert this abstract mathematical formulation into a concrete optimization model, using Julia and JuMP. We start by defining a data structure that holds all the input data."
]
},
{
"cell_type": "code",
"execution_count": 3,
"id": "b12d6483",
"metadata": {},
"outputs": [],
"source": [
"Base.@kwdef struct UnitCommitmentData\n",
" demand::Float64\n",
" pmin::Vector{Float64}\n",
" pmax::Vector{Float64}\n",
" cfix::Vector{Float64}\n",
" cvar::Vector{Float64}\n",
"end;"
]
},
{
"cell_type": "markdown",
"id": "55cdb64b",
"metadata": {},
"source": [
"Next, we create a function that converts this data structure into a concrete JuMP model. For more details on the JuMP syntax, see [the official JuMP documentation](https://jump.dev/JuMP.jl/stable/)."
]
},
{
"cell_type": "code",
"execution_count": 4,
"id": "1e38a266",
"metadata": {},
"outputs": [],
"source": [
"using JuMP\n",
"\n",
"function build_uc_model(data::UnitCommitmentData)::Model\n",
" model = Model()\n",
" n = length(data.pmin)\n",
" @variable(model, x[1:n], Bin)\n",
" @variable(model, y[1:n] >= 0)\n",
" @objective(\n",
" model,\n",
" Min,\n",
" sum(\n",
" data.cfix[i] * x[i] +\n",
" data.cvar[i] * y[i]\n",
" for i in 1:n\n",
" )\n",
" )\n",
" @constraint(model, eq_max_power[i in 1:n], y[i] <= data.pmax[i] * x[i])\n",
" @constraint(model, eq_min_power[i in 1:n], y[i] >= data.pmin[i] * x[i])\n",
" @constraint(model, eq_demand, sum(y[i] for i in 1:n) == data.demand)\n",
" return model\n",
"end;"
]
},
{
"cell_type": "markdown",
"id": "d28c4d5a",
"metadata": {},
"source": [
"At this point, we can already use JuMP 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, using SCIP:"
]
},
{
"cell_type": "code",
"execution_count": 5,
"id": "9ff9f05c",
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"obj = 1320.0\n",
" x = [0.0, 1.0, 1.0]\n",
" y = [0.0, 60.0, 40.0]\n"
]
}
],
"source": [
"using SCIP\n",
"\n",
"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",
"scip = optimizer_with_attributes(SCIP.Optimizer, \"limits/gap\" => 1e-4)\n",
"set_optimizer(model, scip)\n",
"set_silent(model)\n",
"optimize!(model)\n",
"\n",
"println(\"obj = \", objective_value(model))\n",
"println(\" x = \", round.(value.(model[:x])))\n",
"println(\" y = \", round.(value.(model[:y]), digits=2));"
]
},
{
"cell_type": "markdown",
"id": "345de591",
"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": "eb8904ef",
"metadata": {},
"source": [
"## Generating training data\n",
"\n",
"Although SCIP 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 SCIP, 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 can be used to accelerate SCIP's performance on a particular set of instances. More specifically, MIPLearn will train a model that is able to predict the optimal solution for instances that follow a given probability distribution, then it will provide this predicted solution to SCIP as a warm start.\n",
"\n",
"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": "7298bb0d",
"metadata": {},
"outputs": [],
"source": [
"using Distributions\n",
"using Random\n",
"\n",
"function random_uc_data(; samples::Int, n::Int, seed=42)\n",
" Random.seed!(seed)\n",
" pmin = rand(Uniform(100, 500.0), n)\n",
" pmax = pmin .* rand(Uniform(2.0, 2.5), n)\n",
" cfix = pmin .* rand(Uniform(100.0, 125.0), n)\n",
" cvar = rand(Uniform(1.25, 1.5), n)\n",
" return [\n",
" UnitCommitmentData(;\n",
" pmin,\n",
" pmax,\n",
" cfix,\n",
" cvar,\n",
" demand = sum(pmax) * rand(Uniform(0.5, 0.75)),\n",
" )\n",
" for i in 1:samples\n",
" ]\n",
"end;"
]
},
{
"cell_type": "markdown",
"id": "c1feed43",
"metadata": {},
"source": [
"In this example, for simplicity, only the demands change from one instance to the next. We could also have made the prices and the production limits random. 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 100 instances of this problem, each one with 1,000 generators. We will use the first 90 instances for training, and the remaining 10 instances to evaluate SCIP's performance."
]
},
{
"cell_type": "code",
"execution_count": 7,
"id": "61d43994",
"metadata": {},
"outputs": [],
"source": [
"data = random_uc_data(samples=100, n=1000);\n",
"train_data = data[1:90]\n",
"test_data = data[91:100];"
]
},
{
"cell_type": "markdown",
"id": "3fdeb8cd",
"metadata": {},
"source": [
"Next, we write these data structures to individual files. MIPLearn uses files during the training process because, for large-scale optimization problems, it is often impractical to hold the entire training data, as well as the concrete JuMP models, in memory. 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.\n",
"\n",
"The code below generates the files `uc/train/000001.jld2`, `uc/train/000002.jld2`, etc., which contain the input data in [JLD2 format](https://github.com/JuliaIO/JLD2.jl)."
]
},
{
"cell_type": "code",
"execution_count": 8,
"id": "31b48701",
"metadata": {},
"outputs": [],
"source": [
"using MIPLearn\n",
"MIPLearn.save(data[1:90], \"uc/train/\")\n",
"MIPLearn.save(data[91:100], \"uc/test/\")\n",
"\n",
"using Glob\n",
"train_files = glob(\"uc/train/*.jld2\")\n",
"test_files = glob(\"uc/test/*.jld2\");"
]
},
{
"cell_type": "markdown",
"id": "5cecea59",
"metadata": {},
"source": [
"Finally, we use `MIPLearn.LearningSolver` and `MIPLearn.solve!` to solve all the training instances. `LearningSolver` is the main component provided by MIPLearn, which integrates MIP solvers and ML. The `solve!` function can be used to solve either one or multiple instances, and requires: (i) the list of files containing the training data; and (ii) the function that converts the data structure into a concrete JuMP model:"
]
},
{
"cell_type": "code",
"execution_count": 9,
"id": "60732af0",
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"103.808547 seconds (93.52 M allocations: 3.604 GiB, 1.19% gc time, 0.52% compilation time)\n"
]
},
{
"name": "stderr",
"output_type": "stream",
"text": [
"WARNING: Dual bound 1.98665e+07 is larger than the objective of the primal solution 1.98665e+07. The solution might not be optimal.\n"
]
}
],
"source": [
"using Glob\n",
"solver = LearningSolver(scip)\n",
"@time solve!(solver, train_files, build_uc_model);"
]
},
{
"cell_type": "markdown",
"id": "bbc7ad82",
"metadata": {},
"source": [
"The macro `@time` shows us how long did the code take to run. We can see that SCIP was able to solve all training instances in about 2 minutes. The solutions, and other useful training data, are stored by MIPLearn in `.h5` files, stored side-by-side with the original `.jld2` files."
]
},
{
"cell_type": "markdown",
"id": "73379180",
"metadata": {},
"source": [
"## Solving new instances\n",
"\n",
"With training data in hand, we can now fit the ML models using `MIPLearn.fit!`, then solve the test instances with `MIPLearn.solve!`, as shown below:"
]
},
{
"cell_type": "code",
"execution_count": 10,
"id": "e045d644",
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
" 5.951264 seconds (9.33 M allocations: 334.657 MiB, 1.51% gc time)\n"
]
}
],
"source": [
"solver_ml = LearningSolver(scip)\n",
"fit!(solver_ml, train_files, build_uc_model)\n",
"@time solve!(solver_ml, test_files, build_uc_model);"
]
},
{
"cell_type": "markdown",
"id": "d8de7b26",
"metadata": {},
"source": [
"The trained MIP solver was able to solve all test instances in about 6 seconds. To see that ML is being helpful here, let us repeat the code above, but remove the `fit!` line:"
]
},
{
"cell_type": "code",
"execution_count": 11,
"id": "cf2a989e",
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
" 10.390325 seconds (8.17 M allocations: 278.042 MiB, 0.89% gc time)\n"
]
}
],
"source": [
"solver_baseline = LearningSolver(scip)\n",
"@time solve!(solver_baseline, test_files, build_uc_model);"
]
},
{
"cell_type": "markdown",
"id": "e100b25d",
"metadata": {},
"source": [
"Without the help of the ML models, SCIP took around 10 seconds to solve the same test instances.\n",
"\n",
"<div class=\"alert alert-info\">\n",
"Note\n",
" \n",
"Note that is 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",
"</div>"
]
},
{
"cell_type": "markdown",
"id": "af451e87",
"metadata": {},
"source": [
"## Understanding the acceleration\n",
"\n",
"Let us go a bit deeper and try to understand how exactly did MIPLearn accelerate SCIP's performance. First, we are going to solve one of the test instances again, using the trained solver, but this time using the `tee=true` parameter, so that we can see SCIP's log:"
]
},
{
"cell_type": "code",
"execution_count": 12,
"id": "0c675452",
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"presolving:\n",
"(round 1, fast) 861 del vars, 861 del conss, 0 add conss, 2000 chg bounds, 0 chg sides, 0 chg coeffs, 0 upgd conss, 0 impls, 0 clqs\n",
"(round 2, fast) 861 del vars, 1722 del conss, 0 add conss, 2000 chg bounds, 0 chg sides, 0 chg coeffs, 0 upgd conss, 0 impls, 0 clqs\n",
"(round 3, fast) 862 del vars, 1722 del conss, 0 add conss, 2000 chg bounds, 0 chg sides, 0 chg coeffs, 0 upgd conss, 0 impls, 0 clqs\n",
"presolving (4 rounds: 4 fast, 1 medium, 1 exhaustive):\n",
" 862 deleted vars, 1722 deleted constraints, 0 added constraints, 2000 tightened bounds, 0 added holes, 0 changed sides, 0 changed coefficients\n",
" 0 implications, 0 cliques\n",
"presolved problem has 1138 variables (0 bin, 0 int, 0 impl, 1138 cont) and 279 constraints\n",
" 279 constraints of type <linear>\n",
"Presolving Time: 0.03\n",
"\n",
" time | node | left |LP iter|LP it/n|mem/heur|mdpt |vars |cons |rows |cuts |sepa|confs|strbr| dualbound | primalbound | gap | compl. \n",
"* 0.0s| 1 | 0 | 203 | - | LP | 0 |1138 | 279 | 279 | 0 | 0 | 0 | 0 | 1.705035e+07 | 1.705035e+07 | 0.00%| unknown\n",
" 0.0s| 1 | 0 | 203 | - | 8950k | 0 |1138 | 279 | 279 | 0 | 0 | 0 | 0 | 1.705035e+07 | 1.705035e+07 | 0.00%| unknown\n",
"\n",
"SCIP Status : problem is solved [optimal solution found]\n",
"Solving Time (sec) : 0.04\n",
"Solving Nodes : 1\n",
"Primal Bound : +1.70503465600131e+07 (1 solutions)\n",
"Dual Bound : +1.70503465600131e+07\n",
"Gap : 0.00 %\n",
"\n",
"violation: integrality condition of variable <> = 0.338047247943162\n",
"all 1 solutions given by solution candidate storage are infeasible\n",
"\n",
"feasible solution found by completesol heuristic after 0.1 seconds, objective value 1.705169e+07\n",
"presolving:\n",
"(round 1, fast) 0 del vars, 0 del conss, 0 add conss, 3000 chg bounds, 0 chg sides, 0 chg coeffs, 0 upgd conss, 0 impls, 0 clqs\n",
"(round 2, exhaustive) 0 del vars, 0 del conss, 0 add conss, 3000 chg bounds, 0 chg sides, 0 chg coeffs, 1000 upgd conss, 0 impls, 0 clqs\n",
"(round 3, exhaustive) 0 del vars, 0 del conss, 0 add conss, 3000 chg bounds, 0 chg sides, 0 chg coeffs, 2000 upgd conss, 1000 impls, 0 clqs\n",
" (0.1s) probing: 51/1000 (5.1%) - 0 fixings, 0 aggregations, 0 implications, 0 bound changes\n",
" (0.1s) probing aborted: 50/50 successive totally useless probings\n",
" (0.1s) symmetry computation started: requiring (bin +, int -, cont +), (fixed: bin -, int +, cont -)\n",
" (0.1s) no symmetry present\n",
"presolving (4 rounds: 4 fast, 3 medium, 3 exhaustive):\n",
" 0 deleted vars, 0 deleted constraints, 0 added constraints, 3000 tightened bounds, 0 added holes, 0 changed sides, 0 changed coefficients\n",
" 2000 implications, 0 cliques\n",
"presolved problem has 2000 variables (1000 bin, 0 int, 0 impl, 1000 cont) and 2001 constraints\n",
" 2000 constraints of type <varbound>\n",
" 1 constraints of type <linear>\n",
"Presolving Time: 0.11\n",
"transformed 1/1 original solutions to the transformed problem space\n",
"\n",
" time | node | left |LP iter|LP it/n|mem/heur|mdpt |vars |cons |rows |cuts |sepa|confs|strbr| dualbound | primalbound | gap | compl. \n",
" 0.2s| 1 | 0 | 1201 | - | 20M | 0 |2000 |2001 |2001 | 0 | 0 | 0 | 0 | 1.705035e+07 | 1.705169e+07 | 0.01%| unknown\n",
"\n",
"SCIP Status : solving was interrupted [gap limit reached]\n",
"Solving Time (sec) : 0.21\n",
"Solving Nodes : 1\n",
"Primal Bound : +1.70516871251443e+07 (1 solutions)\n",
"Dual Bound : +1.70503465600130e+07\n",
"Gap : 0.01 %\n",
"\n"
]
}
],
"source": [
"solve!(solver_ml, test_files[1], build_uc_model, tee=true);"
]
},
{
"cell_type": "markdown",
"id": "ff0b6858",
"metadata": {},
"source": [
"The log above is quite complicated if you have never seen it before, but the important line is the one starting with `feasible solution found [...] objective value 1.705169e+07`. This line indicates that MIPLearn was able to construct a warm start with value `1.705169e+07`. Using this warm start, SCIP then used the branch-and-cut method to either prove its optimality or to find an even better solution. Very quickly, however, SCIP proved that the solution produced by MIPLearn was indeed optimal. It was able to do this without generating a single cutting plane or running any other heuristics; it could tell the optimality by the root LP relaxation alone, which was very fast. \n",
"\n",
"Let us now repeat the process, but using the untrained solver this time:"
]
},
{
"cell_type": "code",
"execution_count": 13,
"id": "1aa9230e",
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"presolving:\n",
"(round 1, fast) 861 del vars, 861 del conss, 0 add conss, 2000 chg bounds, 0 chg sides, 0 chg coeffs, 0 upgd conss, 0 impls, 0 clqs\n",
"(round 2, fast) 861 del vars, 1722 del conss, 0 add conss, 2000 chg bounds, 0 chg sides, 0 chg coeffs, 0 upgd conss, 0 impls, 0 clqs\n",
"(round 3, fast) 862 del vars, 1722 del conss, 0 add conss, 2000 chg bounds, 0 chg sides, 0 chg coeffs, 0 upgd conss, 0 impls, 0 clqs\n",
"presolving (4 rounds: 4 fast, 1 medium, 1 exhaustive):\n",
" 862 deleted vars, 1722 deleted constraints, 0 added constraints, 2000 tightened bounds, 0 added holes, 0 changed sides, 0 changed coefficients\n",
" 0 implications, 0 cliques\n",
"presolved problem has 1138 variables (0 bin, 0 int, 0 impl, 1138 cont) and 279 constraints\n",
" 279 constraints of type <linear>\n",
"Presolving Time: 0.03\n",
"\n",
" time | node | left |LP iter|LP it/n|mem/heur|mdpt |vars |cons |rows |cuts |sepa|confs|strbr| dualbound | primalbound | gap | compl. \n",
"* 0.0s| 1 | 0 | 203 | - | LP | 0 |1138 | 279 | 279 | 0 | 0 | 0 | 0 | 1.705035e+07 | 1.705035e+07 | 0.00%| unknown\n",
" 0.0s| 1 | 0 | 203 | - | 8950k | 0 |1138 | 279 | 279 | 0 | 0 | 0 | 0 | 1.705035e+07 | 1.705035e+07 | 0.00%| unknown\n",
"\n",
"SCIP Status : problem is solved [optimal solution found]\n",
"Solving Time (sec) : 0.04\n",
"Solving Nodes : 1\n",
"Primal Bound : +1.70503465600131e+07 (1 solutions)\n",
"Dual Bound : +1.70503465600131e+07\n",
"Gap : 0.00 %\n",
"\n",
"violation: integrality condition of variable <> = 0.338047247943162\n",
"all 1 solutions given by solution candidate storage are infeasible\n",
"\n",
"presolving:\n",
"(round 1, fast) 0 del vars, 0 del conss, 0 add conss, 2000 chg bounds, 0 chg sides, 0 chg coeffs, 0 upgd conss, 0 impls, 0 clqs\n",
"(round 2, exhaustive) 0 del vars, 0 del conss, 0 add conss, 2000 chg bounds, 0 chg sides, 0 chg coeffs, 1000 upgd conss, 0 impls, 0 clqs\n",
"(round 3, exhaustive) 0 del vars, 0 del conss, 0 add conss, 2000 chg bounds, 0 chg sides, 0 chg coeffs, 2000 upgd conss, 1000 impls, 0 clqs\n",
" (0.0s) probing: 51/1000 (5.1%) - 0 fixings, 0 aggregations, 0 implications, 0 bound changes\n",
" (0.0s) probing aborted: 50/50 successive totally useless probings\n",
" (0.0s) symmetry computation started: requiring (bin +, int -, cont +), (fixed: bin -, int +, cont -)\n",
" (0.0s) no symmetry present\n",
"presolving (4 rounds: 4 fast, 3 medium, 3 exhaustive):\n",
" 0 deleted vars, 0 deleted constraints, 0 added constraints, 2000 tightened bounds, 0 added holes, 0 changed sides, 0 changed coefficients\n",
" 2000 implications, 0 cliques\n",
"presolved problem has 2000 variables (1000 bin, 0 int, 0 impl, 1000 cont) and 2001 constraints\n",
" 2000 constraints of type <varbound>\n",
" 1 constraints of type <linear>\n",
"Presolving Time: 0.03\n",
"\n",
" time | node | left |LP iter|LP it/n|mem/heur|mdpt |vars |cons |rows |cuts |sepa|confs|strbr| dualbound | primalbound | gap | compl. \n",
"p 0.0s| 1 | 0 | 1 | - | locks| 0 |2000 |2001 |2001 | 0 | 0 | 0 | 0 | 0.000000e+00 | 2.335200e+07 | Inf | unknown\n",
"p 0.0s| 1 | 0 | 2 | - | vbounds| 0 |2000 |2001 |2001 | 0 | 0 | 0 | 0 | 0.000000e+00 | 1.839873e+07 | Inf | unknown\n",
" 0.1s| 1 | 0 | 1204 | - | 20M | 0 |2000 |2001 |2001 | 0 | 0 | 0 | 0 | 1.705035e+07 | 1.839873e+07 | 7.91%| unknown\n",
" 0.1s| 1 | 0 | 1207 | - | 22M | 0 |2000 |2001 |2002 | 1 | 1 | 0 | 0 | 1.705036e+07 | 1.839873e+07 | 7.91%| unknown\n",
"r 0.1s| 1 | 0 | 1207 | - |shifting| 0 |2000 |2001 |2002 | 1 | 1 | 0 | 0 | 1.705036e+07 | 1.711399e+07 | 0.37%| unknown\n",
" 0.1s| 1 | 0 | 1209 | - | 22M | 0 |2000 |2001 |2003 | 2 | 2 | 0 | 0 | 1.705037e+07 | 1.711399e+07 | 0.37%| unknown\n",
"r 0.1s| 1 | 0 | 1209 | - |shifting| 0 |2000 |2001 |2003 | 2 | 2 | 0 | 0 | 1.705037e+07 | 1.706492e+07 | 0.09%| unknown\n",
" 0.1s| 1 | 0 | 1210 | - | 22M | 0 |2000 |2001 |2004 | 3 | 3 | 0 | 0 | 1.705037e+07 | 1.706492e+07 | 0.09%| unknown\n",
" 0.1s| 1 | 0 | 1211 | - | 23M | 0 |2000 |2001 |2005 | 4 | 4 | 0 | 0 | 1.705037e+07 | 1.706492e+07 | 0.09%| unknown\n",
" 0.1s| 1 | 0 | 1212 | - | 23M | 0 |2000 |2001 |2006 | 5 | 5 | 0 | 0 | 1.705037e+07 | 1.706492e+07 | 0.09%| unknown\n",
"r 0.1s| 1 | 0 | 1212 | - |shifting| 0 |2000 |2001 |2006 | 5 | 5 | 0 | 0 | 1.705037e+07 | 1.706228e+07 | 0.07%| unknown\n",
" 0.1s| 1 | 0 | 1214 | - | 24M | 0 |2000 |2001 |2007 | 6 | 7 | 0 | 0 | 1.705037e+07 | 1.706228e+07 | 0.07%| unknown\n",
" 0.2s| 1 | 0 | 1216 | - | 24M | 0 |2000 |2001 |2009 | 8 | 8 | 0 | 0 | 1.705037e+07 | 1.706228e+07 | 0.07%| unknown\n",
" 0.2s| 1 | 0 | 1220 | - | 25M | 0 |2000 |2001 |2011 | 10 | 9 | 0 | 0 | 1.705037e+07 | 1.706228e+07 | 0.07%| unknown\n",
" 0.2s| 1 | 0 | 1223 | - | 25M | 0 |2000 |2001 |2014 | 13 | 10 | 0 | 0 | 1.705037e+07 | 1.706228e+07 | 0.07%| unknown\n",
" time | node | left |LP iter|LP it/n|mem/heur|mdpt |vars |cons |rows |cuts |sepa|confs|strbr| dualbound | primalbound | gap | compl. \n",
" 0.2s| 1 | 0 | 1229 | - | 26M | 0 |2000 |2001 |2015 | 14 | 11 | 0 | 0 | 1.705038e+07 | 1.706228e+07 | 0.07%| unknown\n",
"r 0.2s| 1 | 0 | 1403 | - |intshift| 0 |2000 |2001 |2015 | 14 | 11 | 0 | 0 | 1.705038e+07 | 1.705687e+07 | 0.04%| unknown\n",
"L 0.6s| 1 | 0 | 1707 | - | rens| 0 |2000 |2001 |2015 | 14 | 11 | 0 | 0 | 1.705038e+07 | 1.705332e+07 | 0.02%| unknown\n",
"L 0.7s| 1 | 0 | 1707 | - | alns| 0 |2000 |2001 |2015 | 14 | 11 | 0 | 0 | 1.705038e+07 | 1.705178e+07 | 0.01%| unknown\n",
"\n",
"SCIP Status : solving was interrupted [gap limit reached]\n",
"Solving Time (sec) : 0.68\n",
"Solving Nodes : 1\n",
"Primal Bound : +1.70517823853380e+07 (13 solutions)\n",
"Dual Bound : +1.70503798271962e+07\n",
"Gap : 0.01 %\n",
"\n"
]
}
],
"source": [
"solve!(solver_baseline, test_files[1], build_uc_model, tee=true);"
]
},
{
"cell_type": "markdown",
"id": "9417bb85",
"metadata": {},
"source": [
"In this log file, notice how the previous line about warm starts is missing. Since no warm starts were provided, SCIP had to find an initial solution using its own internal heuristics, which are not specifically tailored for this problem. The initial solution found by SCIP's heuristics has value `2.335200e+07`, which is significantly worse than the one constructed by MIPLearn. SCIP then proceeded to improve this solution, by generating cutting planes and repeatedly running additional primal heuristics. In the end, it was able to find the optimal solution, as expected, but it took longer.\n",
"\n",
"In summary, MIPLearn accelerated the solution process by constructing a high-quality initial solution. In the following tutorials, we will see other strategies that MIPLearn can use to accelerate MIP performance, besides warm starts."
]
},
{
"cell_type": "markdown",
"id": "ab9c1ff4",
"metadata": {},
"source": [
"## Accessing the solution\n",
"\n",
"In the example above, we used `MIPLearn.solve!` together with data files to solve both the training and the test instances. The solutions were saved to a `.h5` files in the train/test folders, and could be retrieved by reading theses files, but that is not very convenient. In this section we will use an easier method.\n",
"\n",
"We can use the function `MIPLearn.load!` to obtain a regular JuMP model:"
]
},
{
"cell_type": "code",
"execution_count": 14,
"id": "79759e87",
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"A JuMP Model\n",
"Minimization problem with:\n",
"Variables: 2000\n",
"Objective function type: AffExpr\n",
"`AffExpr`-in-`MathOptInterface.EqualTo{Float64}`: 1 constraint\n",
"`AffExpr`-in-`MathOptInterface.GreaterThan{Float64}`: 1000 constraints\n",
"`AffExpr`-in-`MathOptInterface.LessThan{Float64}`: 1000 constraints\n",
"`VariableRef`-in-`MathOptInterface.GreaterThan{Float64}`: 1000 constraints\n",
"`VariableRef`-in-`MathOptInterface.ZeroOne`: 1000 constraints\n",
"Model mode: AUTOMATIC\n",
"CachingOptimizer state: NO_OPTIMIZER\n",
"Solver name: No optimizer attached.\n",
"Names registered in the model: eq_demand, eq_max_power, eq_min_power, x, y"
]
},
"execution_count": 14,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"model = MIPLearn.load(\"uc/test/000001.jld2\", build_uc_model)"
]
},
{
"cell_type": "markdown",
"id": "b096dcf9",
"metadata": {},
"source": [
"We can then solve this model as before, with `MIPLearn.solve!`:"
]
},
{
"cell_type": "code",
"execution_count": 15,
"id": "1b668c12",
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"obj = 1.7051217395548128e7\n",
" x = [1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 0.0, 0.0, 0.0, 0.0]\n",
" y = [767.11, 646.61, 230.28, 365.46, 1150.99, 1103.36, 0.0, 0.0, 0.0, 0.0]\n"
]
}
],
"source": [
"solve!(solver_ml, model)\n",
"println(\"obj = \", objective_value(model))\n",
"println(\" x = \", round.(value.(model[:x][1:10])))\n",
"println(\" y = \", round.(value.(model[:y][1:10]), digits=2))"
]
}
],
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"kernelspec": {
"display_name": "Julia 1.6.0",
"language": "julia",
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"name": "julia",
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dl.citation > dt {
float: left;
margin-right: 0.5em;
}
dl.footnote > dd,
dl.citation > dd {
margin-bottom: 0em;
}
dl.footnote > dd:after,
dl.citation > dd:after {
content: "";
clear: both;
}
dl.field-list {
display: grid;
grid-template-columns: fit-content(30%) auto;
}
dl.field-list > dt {
font-weight: bold;
word-break: break-word;
padding-left: 0.5em;
padding-right: 5px;
}
dl.field-list > dt:after {
content: ":";
}
dl.field-list > dd {
padding-left: 0.5em;
margin-top: 0em;
margin-left: 0em;
margin-bottom: 0em;
}
dl {
margin-bottom: 15px;
}
dd > :first-child {
margin-top: 0px;
}
dd ul, dd table {
margin-bottom: 10px;
}
dd {
margin-top: 3px;
margin-bottom: 10px;
margin-left: 30px;
}
dl > dd:last-child,
dl > dd:last-child > :last-child {
margin-bottom: 0;
}
dt:target, span.highlighted {
background-color: #fbe54e;
}
rect.highlighted {
fill: #fbe54e;
}
dl.glossary dt {
font-weight: bold;
font-size: 1.1em;
}
.optional {
font-size: 1.3em;
}
.sig-paren {
font-size: larger;
}
.versionmodified {
font-style: italic;
}
.system-message {
background-color: #fda;
padding: 5px;
border: 3px solid red;
}
.footnote:target {
background-color: #ffa;
}
.line-block {
display: block;
margin-top: 1em;
margin-bottom: 1em;
}
.line-block .line-block {
margin-top: 0;
margin-bottom: 0;
margin-left: 1.5em;
}
.guilabel, .menuselection {
font-family: sans-serif;
}
.accelerator {
text-decoration: underline;
}
.classifier {
font-style: oblique;
}
.classifier:before {
font-style: normal;
margin: 0.5em;
content: ":";
}
abbr, acronym {
border-bottom: dotted 1px;
cursor: help;
}
/* -- code displays --------------------------------------------------------- */
pre {
overflow: auto;
overflow-y: hidden; /* fixes display issues on Chrome browsers */
}
pre, div[class*="highlight-"] {
clear: both;
}
span.pre {
-moz-hyphens: none;
-ms-hyphens: none;
-webkit-hyphens: none;
hyphens: none;
}
div[class*="highlight-"] {
margin: 1em 0;
}
td.linenos pre {
border: 0;
background-color: transparent;
color: #aaa;
}
table.highlighttable {
display: block;
}
table.highlighttable tbody {
display: block;
}
table.highlighttable tr {
display: flex;
}
table.highlighttable td {
margin: 0;
padding: 0;
}
table.highlighttable td.linenos {
padding-right: 0.5em;
}
table.highlighttable td.code {
flex: 1;
overflow: hidden;
}
.highlight .hll {
display: block;
}
div.highlight pre,
table.highlighttable pre {
margin: 0;
}
div.code-block-caption + div {
margin-top: 0;
}
div.code-block-caption {
margin-top: 1em;
padding: 2px 5px;
font-size: small;
}
div.code-block-caption code {
background-color: transparent;
}
table.highlighttable td.linenos,
span.linenos,
div.doctest > div.highlight span.gp { /* gp: Generic.Prompt */
user-select: none;
}
div.code-block-caption span.caption-number {
padding: 0.1em 0.3em;
font-style: italic;
}
div.code-block-caption span.caption-text {
}
div.literal-block-wrapper {
margin: 1em 0;
}
code.descname {
background-color: transparent;
font-weight: bold;
font-size: 1.2em;
}
code.descclassname {
background-color: transparent;
}
code.xref, a code {
background-color: transparent;
font-weight: bold;
}
h1 code, h2 code, h3 code, h4 code, h5 code, h6 code {
background-color: transparent;
}
.viewcode-link {
float: right;
}
.viewcode-back {
float: right;
font-family: sans-serif;
}
div.viewcode-block:target {
margin: -1px -10px;
padding: 0 10px;
}
/* -- math display ---------------------------------------------------------- */
img.math {
vertical-align: middle;
}
div.body div.math p {
text-align: center;
}
span.eqno {
float: right;
}
span.eqno a.headerlink {
position: absolute;
z-index: 1;
}
div.math:hover a.headerlink {
visibility: visible;
}
/* -- printout stylesheet --------------------------------------------------- */
@media print {
div.document,
div.documentwrapper,
div.bodywrapper {
margin: 0 !important;
width: 100%;
}
div.sphinxsidebar,
div.related,
div.footer,
#top-link {
display: none;
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}

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: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);
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h1.site-logo {
font-size: 30px !important;
}
h1.site-logo small {
font-size: 20px !important;
}
code {
display: inline-block;
color: #222 !important;
background-color: rgba(0 0 0 / 8%);
border-radius: 4px;
padding: 0 4px;
}
.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 {
border-radius: 8px !important;
border-width: 0 !important;
margin: 8px 0 8px 0;
}
.output_area {
padding: 12px;
background-color: hsl(227 60% 11% / 0.7) !important;
}
.output_area pre {
//overflow: hidden;
color: #fff;
}
.input_area pre {
background-color: rgba(0 0 0 / 3%) !important;
padding: 12px !important;
}
.ansi-green-intense-fg {
color: #64d88b !important;
}

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/*
* 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() {
$('<a class="headerlink">\u00B6</a>').
attr('href', '#' + this.id).
attr('title', _('Permalink to this headline')).
appendTo(this);
});
$('dt[id]').each(function() {
$('<a class="headerlink">\u00B6</a>').
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);
$('<p class="highlight-link"><a href="javascript:Documentation.' +
'hideSearchWords()">' + _('Hide Search Matches') + '</a></p>')
.appendTo($('#searchbox'));
}
},
/**
* init the domain index toggle buttons
*/
initIndexTable : function() {
var togglers = $('img.toggler').click(function() {
var src = $(this).attr('src');
var idnum = $(this).attr('id').substr(7);
$('tr.cg-' + idnum).toggle();
if (src.substr(-9) === 'minus.png')
$(this).attr('src', src.substr(0, src.length-9) + 'plus.png');
else
$(this).attr('src', src.substr(0, src.length-8) + 'minus.png');
}).css('display', '');
if (DOCUMENTATION_OPTIONS.COLLAPSE_INDEX) {
togglers.click();
}
},
/**
* helper function to hide the search marks again
*/
hideSearchWords : function() {
$('#searchbox .highlight-link').fadeOut(300);
$('span.highlighted').removeClass('highlighted');
},
/**
* make the url absolute
*/
makeURL : function(relativeURL) {
return DOCUMENTATION_OPTIONS.URL_ROOT + '/' + relativeURL;
},
/**
* get the current relative url
*/
getCurrentURL : function() {
var path = document.location.pathname;
var parts = path.split(/\//);
$.each(DOCUMENTATION_OPTIONS.URL_ROOT.split(/\//), function() {
if (this === '..')
parts.pop();
});
var url = parts.join('/');
return path.substring(url.lastIndexOf('/') + 1, path.length - 1);
},
initOnKeyListeners: function() {
$(document).keydown(function(event) {
var activeElementType = document.activeElement.tagName;
// don't navigate when in search box, textarea, dropdown or button
if (activeElementType !== 'TEXTAREA' && activeElementType !== 'INPUT' && activeElementType !== 'SELECT'
&& activeElementType !== 'BUTTON' && !event.altKey && !event.ctrlKey && !event.metaKey
&& !event.shiftKey) {
switch (event.keyCode) {
case 37: // left
var prevHref = $('link[rel="prev"]').prop('href');
if (prevHref) {
window.location.href = prevHref;
return false;
}
case 39: // right
var nextHref = $('link[rel="next"]').prop('href');
if (nextHref) {
window.location.href = nextHref;
return false;
}
}
}
});
}
};
// quick alias for translations
_ = Documentation.gettext;
$(document).ready(function() {
Documentation.init();
});

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var DOCUMENTATION_OPTIONS = {
URL_ROOT: document.getElementById("documentation_options").getAttribute('data-url_root'),
VERSION: '0.2.0',
LANGUAGE: 'None',
COLLAPSE_INDEX: false,
BUILDER: 'dirhtml',
FILE_SUFFIX: '.html',
LINK_SUFFIX: '.html',
HAS_SOURCE: true,
SOURCELINK_SUFFIX: '.txt',
NAVIGATION_WITH_KEYS: true
};

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0.2/_static/images/logo_binder.svg
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<?xml version="1.0" encoding="utf-8"?>
<!-- Generator: Adobe Illustrator 23.0.1, SVG Export Plug-In . SVG Version: 6.00 Build 0) -->
<svg version="1.1" id="Layer_1" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink" x="0px" y="0px"
viewBox="0 0 44.4 44.4" style="enable-background:new 0 0 44.4 44.4;" xml:space="preserve">
<style type="text/css">
.st0{fill:none;stroke:#F5A252;stroke-width:5;stroke-miterlimit:10;}
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.st2{fill:none;stroke:#E66581;stroke-width:5;stroke-miterlimit:10;}
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<title>logo</title>
<g>
<path class="st0" d="M33.9,6.4c3.6,3.9,3.4,9.9-0.5,13.5s-9.9,3.4-13.5-0.5s-3.4-9.9,0.5-13.5l0,0C24.2,2.4,30.2,2.6,33.9,6.4z"/>
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</g>
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/*
* language_data.js
* ~~~~~~~~~~~~~~~~
*
* This script contains the language-specific data used by searchtools.js,
* namely the list of stopwords, stemmer, scorer and splitter.
*
* :copyright: Copyright 2007-2021 by the Sphinx team, see AUTHORS.
* :license: BSD, see LICENSE for details.
*
*/
var stopwords = ["a","and","are","as","at","be","but","by","for","if","in","into","is","it","near","no","not","of","on","or","such","that","the","their","then","there","these","they","this","to","was","will","with"];
/* Non-minified version is copied as a separate JS file, is available */
/**
* Porter Stemmer
*/
var Stemmer = function() {
var step2list = {
ational: 'ate',
tional: 'tion',
enci: 'ence',
anci: 'ance',
izer: 'ize',
bli: 'ble',
alli: 'al',
entli: 'ent',
eli: 'e',
ousli: 'ous',
ization: 'ize',
ation: 'ate',
ator: 'ate',
alism: 'al',
iveness: 'ive',
fulness: 'ful',
ousness: 'ous',
aliti: 'al',
iviti: 'ive',
biliti: 'ble',
logi: 'log'
};
var step3list = {
icate: 'ic',
ative: '',
alize: 'al',
iciti: 'ic',
ical: 'ic',
ful: '',
ness: ''
};
var c = "[^aeiou]"; // consonant
var v = "[aeiouy]"; // vowel
var C = c + "[^aeiouy]*"; // consonant sequence
var V = v + "[aeiou]*"; // vowel sequence
var mgr0 = "^(" + C + ")?" + V + C; // [C]VC... is m>0
var meq1 = "^(" + C + ")?" + V + C + "(" + V + ")?$"; // [C]VC[V] is m=1
var mgr1 = "^(" + C + ")?" + V + C + V + C; // [C]VCVC... is m>1
var s_v = "^(" + C + ")?" + v; // vowel in stem
this.stemWord = function (w) {
var stem;
var suffix;
var firstch;
var origword = w;
if (w.length < 3)
return w;
var re;
var re2;
var re3;
var re4;
firstch = w.substr(0,1);
if (firstch == "y")
w = firstch.toUpperCase() + w.substr(1);
// Step 1a
re = /^(.+?)(ss|i)es$/;
re2 = /^(.+?)([^s])s$/;
if (re.test(w))
w = w.replace(re,"$1$2");
else if (re2.test(w))
w = w.replace(re2,"$1$2");
// Step 1b
re = /^(.+?)eed$/;
re2 = /^(.+?)(ed|ing)$/;
if (re.test(w)) {
var fp = re.exec(w);
re = new RegExp(mgr0);
if (re.test(fp[1])) {
re = /.$/;
w = w.replace(re,"");
}
}
else if (re2.test(w)) {
var fp = re2.exec(w);
stem = fp[1];
re2 = new RegExp(s_v);
if (re2.test(stem)) {
w = stem;
re2 = /(at|bl|iz)$/;
re3 = new RegExp("([^aeiouylsz])\\1$");
re4 = new RegExp("^" + C + v + "[^aeiouwxy]$");
if (re2.test(w))
w = w + "e";
else if (re3.test(w)) {
re = /.$/;
w = w.replace(re,"");
}
else if (re4.test(w))
w = w + "e";
}
}
// Step 1c
re = /^(.+?)y$/;
if (re.test(w)) {
var fp = re.exec(w);
stem = fp[1];
re = new RegExp(s_v);
if (re.test(stem))
w = stem + "i";
}
// Step 2
re = /^(.+?)(ational|tional|enci|anci|izer|bli|alli|entli|eli|ousli|ization|ation|ator|alism|iveness|fulness|ousness|aliti|iviti|biliti|logi)$/;
if (re.test(w)) {
var fp = re.exec(w);
stem = fp[1];
suffix = fp[2];
re = new RegExp(mgr0);
if (re.test(stem))
w = stem + step2list[suffix];
}
// Step 3
re = /^(.+?)(icate|ative|alize|iciti|ical|ful|ness)$/;
if (re.test(w)) {
var fp = re.exec(w);
stem = fp[1];
suffix = fp[2];
re = new RegExp(mgr0);
if (re.test(stem))
w = stem + step3list[suffix];
}
// Step 4
re = /^(.+?)(al|ance|ence|er|ic|able|ible|ant|ement|ment|ent|ou|ism|ate|iti|ous|ive|ize)$/;
re2 = /^(.+?)(s|t)(ion)$/;
if (re.test(w)) {
var fp = re.exec(w);
stem = fp[1];
re = new RegExp(mgr1);
if (re.test(stem))
w = stem;
}
else if (re2.test(w)) {
var fp = re2.exec(w);
stem = fp[1] + fp[2];
re2 = new RegExp(mgr1);
if (re2.test(stem))
w = stem;
}
// Step 5
re = /^(.+?)e$/;
if (re.test(w)) {
var fp = re.exec(w);
stem = fp[1];
re = new RegExp(mgr1);
re2 = new RegExp(meq1);
re3 = new RegExp("^" + C + v + "[^aeiouwxy]$");
if (re.test(stem) || (re2.test(stem) && !(re3.test(stem))))
w = stem;
}
re = /ll$/;
re2 = new RegExp(mgr1);
if (re.test(w) && re2.test(w)) {
re = /.$/;
w = w.replace(re,"");
}
// and turn initial Y back to y
if (firstch == "y")
w = firstch.toLowerCase() + w.substr(1);
return w;
}
}
var splitChars = (function() {
var result = {};
var singles = [96, 180, 187, 191, 215, 247, 749, 885, 903, 907, 909, 930, 1014, 1648,
1748, 1809, 2416, 2473, 2481, 2526, 2601, 2609, 2612, 2615, 2653, 2702,
2706, 2729, 2737, 2740, 2857, 2865, 2868, 2910, 2928, 2948, 2961, 2971,
2973, 3085, 3089, 3113, 3124, 3213, 3217, 3241, 3252, 3295, 3341, 3345,
3369, 3506, 3516, 3633, 3715, 3721, 3736, 3744, 3748, 3750, 3756, 3761,
3781, 3912, 4239, 4347, 4681, 4695, 4697, 4745, 4785, 4799, 4801, 4823,
4881, 5760, 5901, 5997, 6313, 7405, 8024, 8026, 8028, 8030, 8117, 8125,
8133, 8181, 8468, 8485, 8487, 8489, 8494, 8527, 11311, 11359, 11687, 11695,
11703, 11711, 11719, 11727, 11735, 12448, 12539, 43010, 43014, 43019, 43587,
43696, 43713, 64286, 64297, 64311, 64317, 64319, 64322, 64325, 65141];
var i, j, start, end;
for (i = 0; i < singles.length; i++) {
result[singles[i]] = true;
}
var ranges = [[0, 47], [58, 64], [91, 94], [123, 169], [171, 177], [182, 184], [706, 709],
[722, 735], [741, 747], [751, 879], [888, 889], [894, 901], [1154, 1161],
[1318, 1328], [1367, 1368], [1370, 1376], [1416, 1487], [1515, 1519], [1523, 1568],
[1611, 1631], [1642, 1645], [1750, 1764], [1767, 1773], [1789, 1790], [1792, 1807],
[1840, 1868], [1958, 1968], [1970, 1983], [2027, 2035], [2038, 2041], [2043, 2047],
[2070, 2073], [2075, 2083], [2085, 2087], [2089, 2307], [2362, 2364], [2366, 2383],
[2385, 2391], [2402, 2405], [2419, 2424], [2432, 2436], [2445, 2446], [2449, 2450],
[2483, 2485], [2490, 2492], [2494, 2509], [2511, 2523], [2530, 2533], [2546, 2547],
[2554, 2564], [2571, 2574], [2577, 2578], [2618, 2648], [2655, 2661], [2672, 2673],
[2677, 2692], [2746, 2748], [2750, 2767], [2769, 2783], [2786, 2789], [2800, 2820],
[2829, 2830], [2833, 2834], [2874, 2876], [2878, 2907], [2914, 2917], [2930, 2946],
[2955, 2957], [2966, 2968], [2976, 2978], [2981, 2983], [2987, 2989], [3002, 3023],
[3025, 3045], [3059, 3076], [3130, 3132], [3134, 3159], [3162, 3167], [3170, 3173],
[3184, 3191], [3199, 3204], [3258, 3260], [3262, 3293], [3298, 3301], [3312, 3332],
[3386, 3388], [3390, 3423], [3426, 3429], [3446, 3449], [3456, 3460], [3479, 3481],
[3518, 3519], [3527, 3584], [3636, 3647], [3655, 3663], [3674, 3712], [3717, 3718],
[3723, 3724], [3726, 3731], [3752, 3753], [3764, 3772], [3774, 3775], [3783, 3791],
[3802, 3803], [3806, 3839], [3841, 3871], [3892, 3903], [3949, 3975], [3980, 4095],
[4139, 4158], [4170, 4175], [4182, 4185], [4190, 4192], [4194, 4196], [4199, 4205],
[4209, 4212], [4226, 4237], [4250, 4255], [4294, 4303], [4349, 4351], [4686, 4687],
[4702, 4703], [4750, 4751], [4790, 4791], [4806, 4807], [4886, 4887], [4955, 4968],
[4989, 4991], [5008, 5023], [5109, 5120], [5741, 5742], [5787, 5791], [5867, 5869],
[5873, 5887], [5906, 5919], [5938, 5951], [5970, 5983], [6001, 6015], [6068, 6102],
[6104, 6107], [6109, 6111], [6122, 6127], [6138, 6159], [6170, 6175], [6264, 6271],
[6315, 6319], [6390, 6399], [6429, 6469], [6510, 6511], [6517, 6527], [6572, 6592],
[6600, 6607], [6619, 6655], [6679, 6687], [6741, 6783], [6794, 6799], [6810, 6822],
[6824, 6916], [6964, 6980], [6988, 6991], [7002, 7042], [7073, 7085], [7098, 7167],
[7204, 7231], [7242, 7244], [7294, 7400], [7410, 7423], [7616, 7679], [7958, 7959],
[7966, 7967], [8006, 8007], [8014, 8015], [8062, 8063], [8127, 8129], [8141, 8143],
[8148, 8149], [8156, 8159], [8173, 8177], [8189, 8303], [8306, 8307], [8314, 8318],
[8330, 8335], [8341, 8449], [8451, 8454], [8456, 8457], [8470, 8472], [8478, 8483],
[8506, 8507], [8512, 8516], [8522, 8525], [8586, 9311], [9372, 9449], [9472, 10101],
[10132, 11263], [11493, 11498], [11503, 11516], [11518, 11519], [11558, 11567],
[11622, 11630], [11632, 11647], [11671, 11679], [11743, 11822], [11824, 12292],
[12296, 12320], [12330, 12336], [12342, 12343], [12349, 12352], [12439, 12444],
[12544, 12548], [12590, 12592], [12687, 12689], [12694, 12703], [12728, 12783],
[12800, 12831], [12842, 12880], [12896, 12927], [12938, 12976], [12992, 13311],
[19894, 19967], [40908, 40959], [42125, 42191], [42238, 42239], [42509, 42511],
[42540, 42559], [42592, 42593], [42607, 42622], [42648, 42655], [42736, 42774],
[42784, 42785], [42889, 42890], [42893, 43002], [43043, 43055], [43062, 43071],
[43124, 43137], [43188, 43215], [43226, 43249], [43256, 43258], [43260, 43263],
[43302, 43311], [43335, 43359], [43389, 43395], [43443, 43470], [43482, 43519],
[43561, 43583], [43596, 43599], [43610, 43615], [43639, 43641], [43643, 43647],
[43698, 43700], [43703, 43704], [43710, 43711], [43715, 43738], [43742, 43967],
[44003, 44015], [44026, 44031], [55204, 55215], [55239, 55242], [55292, 55295],
[57344, 63743], [64046, 64047], [64110, 64111], [64218, 64255], [64263, 64274],
[64280, 64284], [64434, 64466], [64830, 64847], [64912, 64913], [64968, 65007],
[65020, 65135], [65277, 65295], [65306, 65312], [65339, 65344], [65371, 65381],
[65471, 65473], [65480, 65481], [65488, 65489], [65496, 65497]];
for (i = 0; i < ranges.length; i++) {
start = ranges[i][0];
end = ranges[i][1];
for (j = start; j <= end; j++) {
result[j] = true;
}
}
return result;
})();
function splitQuery(query) {
var result = [];
var start = -1;
for (var i = 0; i < query.length; i++) {
if (splitChars[query.charCodeAt(i)]) {
if (start !== -1) {
result.push(query.slice(start, i));
start = -1;
}
} else if (start === -1) {
start = i;
}
}
if (start !== -1) {
result.push(query.slice(start));
}
return result;
}

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pre { line-height: 125%; }
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span.linenos.special { color: #000000; background-color: #ffffc0; padding-left: 5px; padding-right: 5px; }
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/*
* searchtools.js
* ~~~~~~~~~~~~~~~~
*
* Sphinx JavaScript utilities for the full-text search.
*
* :copyright: Copyright 2007-2021 by the Sphinx team, see AUTHORS.
* :license: BSD, see LICENSE for details.
*
*/
if (!Scorer) {
/**
* Simple result scoring code.
*/
var Scorer = {
// Implement the following function to further tweak the score for each result
// The function takes a result array [filename, title, anchor, descr, score]
// and returns the new score.
/*
score: function(result) {
return result[4];
},
*/
// query matches the full name of an object
objNameMatch: 11,
// or matches in the last dotted part of the object name
objPartialMatch: 6,
// Additive scores depending on the priority of the object
objPrio: {0: 15, // used to be importantResults
1: 5, // used to be objectResults
2: -5}, // used to be unimportantResults
// Used when the priority is not in the mapping.
objPrioDefault: 0,
// query found in title
title: 15,
partialTitle: 7,
// query found in terms
term: 5,
partialTerm: 2
};
}
if (!splitQuery) {
function splitQuery(query) {
return query.split(/\s+/);
}
}
/**
* Search Module
*/
var Search = {
_index : null,
_queued_query : null,
_pulse_status : -1,
htmlToText : function(htmlString) {
var virtualDocument = document.implementation.createHTMLDocument('virtual');
var htmlElement = $(htmlString, virtualDocument);
htmlElement.find('.headerlink').remove();
docContent = htmlElement.find('[role=main]')[0];
if(docContent === undefined) {
console.warn("Content block not found. Sphinx search tries to obtain it " +
"via '[role=main]'. Could you check your theme or template.");
return "";
}
return docContent.textContent || docContent.innerText;
},
init : function() {
var params = $.getQueryParameters();
if (params.q) {
var query = params.q[0];
$('input[name="q"]')[0].value = query;
this.performSearch(query);
}
},
loadIndex : function(url) {
$.ajax({type: "GET", url: url, data: null,
dataType: "script", cache: true,
complete: function(jqxhr, textstatus) {
if (textstatus != "success") {
document.getElementById("searchindexloader").src = url;
}
}});
},
setIndex : function(index) {
var q;
this._index = index;
if ((q = this._queued_query) !== null) {
this._queued_query = null;
Search.query(q);
}
},
hasIndex : function() {
return this._index !== null;
},
deferQuery : function(query) {
this._queued_query = query;
},
stopPulse : function() {
this._pulse_status = 0;
},
startPulse : function() {
if (this._pulse_status >= 0)
return;
function pulse() {
var i;
Search._pulse_status = (Search._pulse_status + 1) % 4;
var dotString = '';
for (i = 0; i < Search._pulse_status; i++)
dotString += '.';
Search.dots.text(dotString);
if (Search._pulse_status > -1)
window.setTimeout(pulse, 500);
}
pulse();
},
/**
* perform a search for something (or wait until index is loaded)
*/
performSearch : function(query) {
// create the required interface elements
this.out = $('#search-results');
this.title = $('<h2>' + _('Searching') + '</h2>').appendTo(this.out);
this.dots = $('<span></span>').appendTo(this.title);
this.status = $('<p class="search-summary">&nbsp;</p>').appendTo(this.out);
this.output = $('<ul class="search"/>').appendTo(this.out);
$('#search-progress').text(_('Preparing search...'));
this.startPulse();
// index already loaded, the browser was quick!
if (this.hasIndex())
this.query(query);
else
this.deferQuery(query);
},
/**
* execute search (requires search index to be loaded)
*/
query : function(query) {
var i;
// stem the searchterms and add them to the correct list
var stemmer = new Stemmer();
var searchterms = [];
var excluded = [];
var hlterms = [];
var tmp = splitQuery(query);
var objectterms = [];
for (i = 0; i < tmp.length; i++) {
if (tmp[i] !== "") {
objectterms.push(tmp[i].toLowerCase());
}
if ($u.indexOf(stopwords, tmp[i].toLowerCase()) != -1 || tmp[i] === "") {
// skip this "word"
continue;
}
// stem the word
var word = stemmer.stemWord(tmp[i].toLowerCase());
// prevent stemmer from cutting word smaller than two chars
if(word.length < 3 && tmp[i].length >= 3) {
word = tmp[i];
}
var toAppend;
// select the correct list
if (word[0] == '-') {
toAppend = excluded;
word = word.substr(1);
}
else {
toAppend = searchterms;
hlterms.push(tmp[i].toLowerCase());
}
// only add if not already in the list
if (!$u.contains(toAppend, word))
toAppend.push(word);
}
var highlightstring = '?highlight=' + $.urlencode(hlterms.join(" "));
// console.debug('SEARCH: searching for:');
// console.info('required: ', searchterms);
// console.info('excluded: ', excluded);
// prepare search
var terms = this._index.terms;
var titleterms = this._index.titleterms;
// array of [filename, title, anchor, descr, score]
var results = [];
$('#search-progress').empty();
// lookup as object
for (i = 0; i < objectterms.length; i++) {
var others = [].concat(objectterms.slice(0, i),
objectterms.slice(i+1, objectterms.length));
results = results.concat(this.performObjectSearch(objectterms[i], others));
}
// lookup as search terms in fulltext
results = results.concat(this.performTermsSearch(searchterms, excluded, terms, titleterms));
// let the scorer override scores with a custom scoring function
if (Scorer.score) {
for (i = 0; i < results.length; i++)
results[i][4] = Scorer.score(results[i]);
}
// now sort the results by score (in opposite order of appearance, since the
// display function below uses pop() to retrieve items) and then
// alphabetically
results.sort(function(a, b) {
var left = a[4];
var right = b[4];
if (left > right) {
return 1;
} else if (left < right) {
return -1;
} else {
// same score: sort alphabetically
left = a[1].toLowerCase();
right = b[1].toLowerCase();
return (left > right) ? -1 : ((left < right) ? 1 : 0);
}
});
// for debugging
//Search.lastresults = results.slice(); // a copy
//console.info('search results:', Search.lastresults);
// print the results
var resultCount = results.length;
function displayNextItem() {
// results left, load the summary and display it
if (results.length) {
var item = results.pop();
var listItem = $('<li></li>');
var requestUrl = "";
var linkUrl = "";
if (DOCUMENTATION_OPTIONS.BUILDER === 'dirhtml') {
// dirhtml builder
var dirname = item[0] + '/';
if (dirname.match(/\/index\/$/)) {
dirname = dirname.substring(0, dirname.length-6);
} else if (dirname == 'index/') {
dirname = '';
}
requestUrl = DOCUMENTATION_OPTIONS.URL_ROOT + dirname;
linkUrl = requestUrl;
} else {
// normal html builders
requestUrl = DOCUMENTATION_OPTIONS.URL_ROOT + item[0] + DOCUMENTATION_OPTIONS.FILE_SUFFIX;
linkUrl = item[0] + DOCUMENTATION_OPTIONS.LINK_SUFFIX;
}
listItem.append($('<a/>').attr('href',
linkUrl +
highlightstring + item[2]).html(item[1]));
if (item[3]) {
listItem.append($('<span> (' + item[3] + ')</span>'));
Search.output.append(listItem);
setTimeout(function() {
displayNextItem();
}, 5);
} else if (DOCUMENTATION_OPTIONS.HAS_SOURCE) {
$.ajax({url: requestUrl,
dataType: "text",
complete: function(jqxhr, textstatus) {
var data = jqxhr.responseText;
if (data !== '' && data !== undefined) {
listItem.append(Search.makeSearchSummary(data, searchterms, hlterms));
}
Search.output.append(listItem);
setTimeout(function() {
displayNextItem();
}, 5);
}});
} else {
// no source available, just display title
Search.output.append(listItem);
setTimeout(function() {
displayNextItem();
}, 5);
}
}
// search finished, update title and status message
else {
Search.stopPulse();
Search.title.text(_('Search Results'));
if (!resultCount)
Search.status.text(_('Your search did not match any documents. Please make sure that all words are spelled correctly and that you\'ve selected enough categories.'));
else
Search.status.text(_('Search finished, found %s page(s) matching the search query.').replace('%s', resultCount));
Search.status.fadeIn(500);
}
}
displayNextItem();
},
/**
* search for object names
*/
performObjectSearch : function(object, otherterms) {
var filenames = this._index.filenames;
var docnames = this._index.docnames;
var objects = this._index.objects;
var objnames = this._index.objnames;
var titles = this._index.titles;
var i;
var results = [];
for (var prefix in objects) {
for (var name in objects[prefix]) {
var fullname = (prefix ? prefix + '.' : '') + name;
var fullnameLower = fullname.toLowerCase()
if (fullnameLower.indexOf(object) > -1) {
var score = 0;
var parts = fullnameLower.split('.');
// check for different match types: exact matches of full name or
// "last name" (i.e. last dotted part)
if (fullnameLower == object || parts[parts.length - 1] == object) {
score += Scorer.objNameMatch;
// matches in last name
} else if (parts[parts.length - 1].indexOf(object) > -1) {
score += Scorer.objPartialMatch;
}
var match = objects[prefix][name];
var objname = objnames[match[1]][2];
var title = titles[match[0]];
// If more than one term searched for, we require other words to be
// found in the name/title/description
if (otherterms.length > 0) {
var haystack = (prefix + ' ' + name + ' ' +
objname + ' ' + title).toLowerCase();
var allfound = true;
for (i = 0; i < otherterms.length; i++) {
if (haystack.indexOf(otherterms[i]) == -1) {
allfound = false;
break;
}
}
if (!allfound) {
continue;
}
}
var descr = objname + _(', in ') + title;
var anchor = match[3];
if (anchor === '')
anchor = fullname;
else if (anchor == '-')
anchor = objnames[match[1]][1] + '-' + fullname;
// add custom score for some objects according to scorer
if (Scorer.objPrio.hasOwnProperty(match[2])) {
score += Scorer.objPrio[match[2]];
} else {
score += Scorer.objPrioDefault;
}
results.push([docnames[match[0]], fullname, '#'+anchor, descr, score, filenames[match[0]]]);
}
}
}
return results;
},
/**
* See https://developer.mozilla.org/en-US/docs/Web/JavaScript/Guide/Regular_Expressions
*/
escapeRegExp : function(string) {
return string.replace(/[.*+\-?^${}()|[\]\\]/g, '\\$&'); // $& means the whole matched string
},
/**
* search for full-text terms in the index
*/
performTermsSearch : function(searchterms, excluded, terms, titleterms) {
var docnames = this._index.docnames;
var filenames = this._index.filenames;
var titles = this._index.titles;
var i, j, file;
var fileMap = {};
var scoreMap = {};
var results = [];
// perform the search on the required terms
for (i = 0; i < searchterms.length; i++) {
var word = searchterms[i];
var files = [];
var _o = [
{files: terms[word], score: Scorer.term},
{files: titleterms[word], score: Scorer.title}
];
// add support for partial matches
if (word.length > 2) {
var word_regex = this.escapeRegExp(word);
for (var w in terms) {
if (w.match(word_regex) && !terms[word]) {
_o.push({files: terms[w], score: Scorer.partialTerm})
}
}
for (var w in titleterms) {
if (w.match(word_regex) && !titleterms[word]) {
_o.push({files: titleterms[w], score: Scorer.partialTitle})
}
}
}
// no match but word was a required one
if ($u.every(_o, function(o){return o.files === undefined;})) {
break;
}
// found search word in contents
$u.each(_o, function(o) {
var _files = o.files;
if (_files === undefined)
return
if (_files.length === undefined)
_files = [_files];
files = files.concat(_files);
// set score for the word in each file to Scorer.term
for (j = 0; j < _files.length; j++) {
file = _files[j];
if (!(file in scoreMap))
scoreMap[file] = {};
scoreMap[file][word] = o.score;
}
});
// create the mapping
for (j = 0; j < files.length; j++) {
file = files[j];
if (file in fileMap && fileMap[file].indexOf(word) === -1)
fileMap[file].push(word);
else
fileMap[file] = [word];
}
}
// now check if the files don't contain excluded terms
for (file in fileMap) {
var valid = true;
// check if all requirements are matched
var filteredTermCount = // as search terms with length < 3 are discarded: ignore
searchterms.filter(function(term){return term.length > 2}).length
if (
fileMap[file].length != searchterms.length &&
fileMap[file].length != filteredTermCount
) continue;
// ensure that none of the excluded terms is in the search result
for (i = 0; i < excluded.length; i++) {
if (terms[excluded[i]] == file ||
titleterms[excluded[i]] == file ||
$u.contains(terms[excluded[i]] || [], file) ||
$u.contains(titleterms[excluded[i]] || [], file)) {
valid = false;
break;
}
}
// if we have still a valid result we can add it to the result list
if (valid) {
// select one (max) score for the file.
// for better ranking, we should calculate ranking by using words statistics like basic tf-idf...
var score = $u.max($u.map(fileMap[file], function(w){return scoreMap[file][w]}));
results.push([docnames[file], titles[file], '', null, score, filenames[file]]);
}
}
return results;
},
/**
* helper function to return a node containing the
* search summary for a given text. keywords is a list
* of stemmed words, hlwords is the list of normal, unstemmed
* words. the first one is used to find the occurrence, the
* latter for highlighting it.
*/
makeSearchSummary : function(htmlText, keywords, hlwords) {
var text = Search.htmlToText(htmlText);
var textLower = text.toLowerCase();
var start = 0;
$.each(keywords, function() {
var i = textLower.indexOf(this.toLowerCase());
if (i > -1)
start = i;
});
start = Math.max(start - 120, 0);
var excerpt = ((start > 0) ? '...' : '') +
$.trim(text.substr(start, 240)) +
((start + 240 - text.length) ? '...' : '');
var rv = $('<div class="context"></div>').text(excerpt);
$.each(hlwords, function() {
rv = rv.highlightText(this, 'highlighted');
});
return rv;
}
};
$(document).ready(function() {
Search.init();
});

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var active_pages=navbar.querySelectorAll(".active")
var active_page=active_pages[active_pages.length-1]
if(active_page!==undefined&&active_page.offsetTop>($(window).height()*.5)){navbar.scrollTop=active_page.offsetTop-($(window).height()*.2)}}
var sbRunWhenDOMLoaded=cb=>{if(document.readyState!='loading'){cb()}else if(document.addEventListener){document.addEventListener('DOMContentLoaded',cb)}else{document.attachEvent('onreadystatechange',function(){if(document.readyState=='complete')cb()})}}
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Font Awesome Free License
-------------------------
Font Awesome Free is free, open source, and GPL friendly. You can use it for
commercial projects, open source projects, or really almost whatever you want.
Full Font Awesome Free license: https://fontawesome.com/license/free.
# Icons: CC BY 4.0 License (https://creativecommons.org/licenses/by/4.0/)
In the Font Awesome Free download, the CC BY 4.0 license applies to all icons
packaged as SVG and JS file types.
# Fonts: SIL OFL 1.1 License (https://scripts.sil.org/OFL)
In the Font Awesome Free download, the SIL OFL license applies to all icons
packaged as web and desktop font files.
# Code: MIT License (https://opensource.org/licenses/MIT)
In the Font Awesome Free download, the MIT license applies to all non-font and
non-icon files.
# Attribution
Attribution is required by MIT, SIL OFL, and CC BY licenses. Downloaded Font
Awesome Free files already contain embedded comments with sufficient
attribution, so you shouldn't need to do anything additional when using these
files normally.
We've kept attribution comments terse, so we ask that you do not actively work
to remove them from files, especially code. They're a great way for folks to
learn about Font Awesome.
# Brand Icons
All brand icons are trademarks of their respective owners. The use of these
trademarks does not indicate endorsement of the trademark holder by Font
Awesome, nor vice versa. **Please do not use brand logos for any purpose except
to represent the company, product, or service to which they refer.**

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<?xml version="1.0" standalone="no"?>
<!--
Font Awesome Free 5.13.0 by @fontawesome - https://fontawesome.com
License - https://fontawesome.com/license/free (Icons: CC BY 4.0, Fonts: SIL OFL 1.1, Code: MIT License)
-->
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Created by FontForge 20190801 at Mon Mar 23 10:45:51 2020
By Robert Madole
Copyright (c) Font Awesome
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"# Multidimensional Knapsack\n",
"\n",
"### Problem definition\n",
"\n",
"Given a set of $n$ items and $m$ types of resources (also called *knapsacks*), the problem is to find a subset of items that maximizes profit without consuming more resources than it is available. More precisely, the problem is:\n",
"\n",
"$$\n",
"\\begin{align*}\n",
" \\text{maximize}\n",
" & \\sum_{j=1}^n p_j x_j\n",
" \\\\\n",
" \\text{subject to}\n",
" & \\sum_{j=1}^n w_{ij} x_j \\leq b_i\n",
" & \\forall i=1,\\ldots,m \\\\\n",
" & x_j \\in \\{0,1\\}\n",
" & \\forall j=1,\\ldots,n\n",
"\\end{align*}\n",
"$$\n",
"\n",
"### Random instance generator\n",
"\n",
"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\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.\n",
"\n",
"\n",
"<div class=\"alert alert-info\">\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",
"</div>\n",
" \n",
"### Challenge A\n",
"\n",
"* 250 variables, 10 constraints, fixed weights\n",
"* $w \\sim U(0, 1000), \\gamma \\sim U(0.95, 1.05)$\n",
"* $K = 500, u \\sim U(0, 1), \\alpha = 0.25$\n",
"* 500 training instances, 50 test instances\n"
]
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" n=randint(low=250, high=251),\n",
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" w=uniform(loc=0.0, scale=1000.0),\n",
" K=uniform(loc=500.0, scale=0.0),\n",
" u=uniform(loc=0.0, scale=1.0),\n",
" alpha=uniform(loc=0.25, scale=0.0),\n",
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<div class="section" id="Multidimensional-Knapsack">
<h1><span class="section-number">3. </span>Multidimensional Knapsack<a class="headerlink" href="#Multidimensional-Knapsack" title="Permalink to this headline"></a></h1>
<div class="section" id="Problem-definition">
<h2><span class="section-number">3.1. </span>Problem definition<a class="headerlink" href="#Problem-definition" title="Permalink to this headline"></a></h2>
<p>Given a set of <span class="math notranslate nohighlight">\(n\)</span> items and <span class="math notranslate nohighlight">\(m\)</span> types of resources (also called <em>knapsacks</em>), the problem is to find a subset of items that maximizes profit without consuming more resources than it is available. More precisely, the problem is:</p>
<div class="math notranslate nohighlight">
\[\begin{split}\begin{align*}
\text{maximize}
&amp; \sum_{j=1}^n p_j x_j
\\
\text{subject to}
&amp; \sum_{j=1}^n w_{ij} x_j \leq b_i
&amp; \forall i=1,\ldots,m \\
&amp; x_j \in \{0,1\}
&amp; \forall j=1,\ldots,n
\end{align*}\end{split}\]</div>
</div>
<div class="section" id="Random-instance-generator">
<h2><span class="section-number">3.2. </span>Random instance generator<a class="headerlink" href="#Random-instance-generator" title="Permalink to this headline"></a></h2>
<p>The class <code class="docutils literal notranslate"><span class="pre">MultiKnapsackGenerator</span></code> can be used to generate random instances of this problem. The number of items <span class="math notranslate nohighlight">\(n\)</span> and knapsacks <span class="math notranslate nohighlight">\(m\)</span> are sampled from the user-provided probability distributions <code class="docutils literal notranslate"><span class="pre">n</span></code> and <code class="docutils literal notranslate"><span class="pre">m</span></code>. The weights <span class="math notranslate nohighlight">\(w_{ij}\)</span> are sampled independently from the provided distribution <code class="docutils literal notranslate"><span class="pre">w</span></code>. The capacity of knapsack <span class="math notranslate nohighlight">\(i\)</span> is set to</p>
<div class="math notranslate nohighlight">
\[b_i = \alpha_i \sum_{j=1}^n w_{ij}\]</div>
<p>where <span class="math notranslate nohighlight">\(\alpha_i\)</span>, the tightness ratio, is sampled from the provided probability distribution <code class="docutils literal notranslate"><span class="pre">alpha</span></code>. 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 <span class="math notranslate nohighlight">\(j\)</span> is set to:</p>
<div class="math notranslate nohighlight">
\[p_j = \sum_{i=1}^m \frac{w_{ij}}{m} + K u_j,\]</div>
<p>where <span class="math notranslate nohighlight">\(K\)</span>, the correlation coefficient, and <span class="math notranslate nohighlight">\(u_j\)</span>, the correlation multiplier, are sampled from the provided probability distributions <code class="docutils literal notranslate"><span class="pre">K</span></code> and <code class="docutils literal notranslate"><span class="pre">u</span></code>.</p>
<p>If <code class="docutils literal notranslate"><span class="pre">fix_w=True</span></code> is provided, then <span class="math notranslate nohighlight">\(w_{ij}\)</span> are kept the same in all generated instances. This also implies that <span class="math notranslate nohighlight">\(n\)</span> and <span class="math notranslate nohighlight">\(m\)</span> are kept fixed. Although the prices and capacities are derived from <span class="math notranslate nohighlight">\(w_{ij}\)</span>, as long as <code class="docutils literal notranslate"><span class="pre">u</span></code> and <code class="docutils literal notranslate"><span class="pre">K</span></code> are not constants, the generated instances will still not be completely identical.</p>
<p>If a probability distribution <code class="docutils literal notranslate"><span class="pre">w_jitter</span></code> is provided, then item weights will be set to <span class="math notranslate nohighlight">\(w_{ij} \gamma_{ij}\)</span> where <span class="math notranslate nohighlight">\(\gamma_{ij}\)</span> is sampled from <code class="docutils literal notranslate"><span class="pre">w_jitter</span></code>. When combined with <code class="docutils literal notranslate"><span class="pre">fix_w=True</span></code>, 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.</p>
<p>By default, all generated prices, weights and capacities are rounded to the nearest integer number. If <code class="docutils literal notranslate"><span class="pre">round=False</span></code> is provided, this rounding will be disabled.</p>
<div class="admonition note">
<p class="admonition-title">References</p>
<ul class="simple">
<li><p><strong>Freville, Arnaud, and Gérard Plateau.</strong> <em>An efficient preprocessing procedure for the multidimensional 0–1 knapsack problem.</em> Discrete applied mathematics 49.1-3 (1994): 189-212.</p></li>
<li><p><strong>Fréville, Arnaud.</strong> <em>The multidimensional 0–1 knapsack problem: An overview.</em> European Journal of Operational Research 155.1 (2004): 1-21.</p></li>
</ul>
</div>
</div>
<div class="section" id="Challenge-A">
<h2><span class="section-number">3.3. </span>Challenge A<a class="headerlink" href="#Challenge-A" title="Permalink to this headline"></a></h2>
<ul class="simple">
<li><p>250 variables, 10 constraints, fixed weights</p></li>
<li><p><span class="math notranslate nohighlight">\(w \sim U(0, 1000), \gamma \sim U(0.95, 1.05)\)</span></p></li>
<li><p><span class="math notranslate nohighlight">\(K = 500, u \sim U(0, 1), \alpha = 0.25\)</span></p></li>
<li><p>500 training instances, 50 test instances</p></li>
</ul>
<div class="nbinput nblast docutils container">
<div class="prompt highlight-none notranslate"><div class="highlight"><pre><span></span>[ ]:
</pre></div>
</div>
<div class="input_area highlight-ipython3 notranslate"><div class="highlight"><pre>
<span></span><span class="n">MultiKnapsackGenerator</span><span class="p">(</span>
<span class="n">n</span><span class="o">=</span><span class="n">randint</span><span class="p">(</span><span class="n">low</span><span class="o">=</span><span class="mi">250</span><span class="p">,</span> <span class="n">high</span><span class="o">=</span><span class="mi">251</span><span class="p">),</span>
<span class="n">m</span><span class="o">=</span><span class="n">randint</span><span class="p">(</span><span class="n">low</span><span class="o">=</span><span class="mi">10</span><span class="p">,</span> <span class="n">high</span><span class="o">=</span><span class="mi">11</span><span class="p">),</span>
<span class="n">w</span><span class="o">=</span><span class="n">uniform</span><span class="p">(</span><span class="n">loc</span><span class="o">=</span><span class="mf">0.0</span><span class="p">,</span> <span class="n">scale</span><span class="o">=</span><span class="mf">1000.0</span><span class="p">),</span>
<span class="n">K</span><span class="o">=</span><span class="n">uniform</span><span class="p">(</span><span class="n">loc</span><span class="o">=</span><span class="mf">500.0</span><span class="p">,</span> <span class="n">scale</span><span class="o">=</span><span class="mf">0.0</span><span class="p">),</span>
<span class="n">u</span><span class="o">=</span><span class="n">uniform</span><span class="p">(</span><span class="n">loc</span><span class="o">=</span><span class="mf">0.0</span><span class="p">,</span> <span class="n">scale</span><span class="o">=</span><span class="mf">1.0</span><span class="p">),</span>
<span class="n">alpha</span><span class="o">=</span><span class="n">uniform</span><span class="p">(</span><span class="n">loc</span><span class="o">=</span><span class="mf">0.25</span><span class="p">,</span> <span class="n">scale</span><span class="o">=</span><span class="mf">0.0</span><span class="p">),</span>
<span class="n">fix_w</span><span class="o">=</span><span class="kc">True</span><span class="p">,</span>
<span class="n">w_jitter</span><span class="o">=</span><span class="n">uniform</span><span class="p">(</span><span class="n">loc</span><span class="o">=</span><span class="mf">0.95</span><span class="p">,</span> <span class="n">scale</span><span class="o">=</span><span class="mf">0.1</span><span class="p">),</span>
<span class="p">)</span>
</pre></div>
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{
"cells": [
{
"cell_type": "markdown",
"id": "423ee254",
"metadata": {},
"source": [
"# Preliminaries\n",
"\n",
"## Benchmark challenges\n",
"\n",
"When evaluating the performance of a conventional MIP solver, *benchmark sets*, such as MIPLIB and TSPLIB, are typically used. The performance of newly proposed solvers or solution techniques are typically measured as the average (or total) running time the solver takes to solve the entire benchmark set. For Learning-Enhanced MIP solvers, it is also necessary to specify what instances should the solver be trained on (the *training instances*) before solving the actual set of instances we are interested in (the *test instances*). If the training instances are very similar to the test instances, we would expect a Learning-Enhanced Solver to present stronger perfomance benefits.\n",
"\n",
"In MIPLearn, each optimization problem comes with a set of **benchmark challenges**, which specify how should the training and test instances be generated. The first challenges are typically easier, in the sense that training and test instances are very similar. Later challenges gradually make the sets more distinct, and therefore harder to learn from.\n",
"\n",
"## Baseline results\n",
"\n",
"To illustrate the performance of `LearningSolver`, and to set a baseline for newly proposed techniques, we present in this page, for each benchmark challenge, a small set of computational results measuring the solution speed of the solver and the solution quality with default parameters. For more detailed computational studies, see [references](index.md#references). We compare three solvers:\n",
"\n",
"* **baseline:** Gurobi 9.1 with default settings (a conventional state-of-the-art MIP solver)\n",
"* **ml-exact:** `LearningSolver` with default settings, using Gurobi 9.0 as internal MIP solver\n",
"* **ml-heuristic:** Same as above, but with `mode=\"heuristic\"`\n",
"\n",
"All experiments presented here were performed on a Linux server (Ubuntu Linux 18.04 LTS) with Intel Xeon Gold 6230s (2 processors, 40 cores, 80 threads) and 256 GB RAM (DDR4, 2933 MHz). All solvers were restricted to use 4 threads, with no time limits, and 10 instances were solved simultaneously at a time."
]
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"display_name": "Julia 1.6.0",
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<div class="section" id="Preliminaries">
<h1><span class="section-number">1. </span>Preliminaries<a class="headerlink" href="#Preliminaries" title="Permalink to this headline"></a></h1>
<div class="section" id="Benchmark-challenges">
<h2><span class="section-number">1.1. </span>Benchmark challenges<a class="headerlink" href="#Benchmark-challenges" title="Permalink to this headline"></a></h2>
<p>When evaluating the performance of a conventional MIP solver, <em>benchmark sets</em>, such as MIPLIB and TSPLIB, are typically used. The performance of newly proposed solvers or solution techniques are typically measured as the average (or total) running time the solver takes to solve the entire benchmark set. For Learning-Enhanced MIP solvers, it is also necessary to specify what instances should the solver be trained on (the <em>training instances</em>) before solving the actual set of instances we are
interested in (the <em>test instances</em>). If the training instances are very similar to the test instances, we would expect a Learning-Enhanced Solver to present stronger perfomance benefits.</p>
<p>In MIPLearn, each optimization problem comes with a set of <strong>benchmark challenges</strong>, which specify how should the training and test instances be generated. The first challenges are typically easier, in the sense that training and test instances are very similar. Later challenges gradually make the sets more distinct, and therefore harder to learn from.</p>
</div>
<div class="section" id="Baseline-results">
<h2><span class="section-number">1.2. </span>Baseline results<a class="headerlink" href="#Baseline-results" title="Permalink to this headline"></a></h2>
<p>To illustrate the performance of <code class="docutils literal notranslate"><span class="pre">LearningSolver</span></code>, and to set a baseline for newly proposed techniques, we present in this page, for each benchmark challenge, a small set of computational results measuring the solution speed of the solver and the solution quality with default parameters. For more detailed computational studies, see <a class="reference external" href="index.md#references">references</a>. We compare three solvers:</p>
<ul class="simple">
<li><p><strong>baseline:</strong> Gurobi 9.1 with default settings (a conventional state-of-the-art MIP solver)</p></li>
<li><p><strong>ml-exact:</strong> <code class="docutils literal notranslate"><span class="pre">LearningSolver</span></code> with default settings, using Gurobi 9.0 as internal MIP solver</p></li>
<li><p><strong>ml-heuristic:</strong> Same as above, but with <code class="docutils literal notranslate"><span class="pre">mode=&quot;heuristic&quot;</span></code></p></li>
</ul>
<p>All experiments presented here were performed on a Linux server (Ubuntu Linux 18.04 LTS) with Intel Xeon Gold 6230s (2 processors, 40 cores, 80 threads) and 256 GB RAM (DDR4, 2933 MHz). All solvers were restricted to use 4 threads, with no time limits, and 10 instances were solved simultaneously at a time.</p>
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{
"cells": [
{
"cell_type": "markdown",
"id": "23083bd9",
"metadata": {},
"source": [
"# Maximum Weight Stable Set\n",
"\n",
"## Problem definition\n",
"\n",
"Given a simple undirected graph $G=(V,E)$ and weights $w \\in \\mathbb{R}^V$, the problem is to find a stable set $S \\subseteq V$ that maximizes $ \\sum_{v \\in V} w_v$. We recall that a subset $S \\subseteq V$ is a *stable set* if no two vertices of $S$ are adjacent. This is one of Karp's 21 NP-complete problems.\n",
"\n",
"## Random instance generator\n",
"\n",
"The class `MaxWeightStableSetGenerator` can be used to generate random instances of this problem, with user-specified probability distributions. When the constructor parameter `fix_graph=True` is provided, one random Erdős-Rényi graph $G_{n,p}$ is generated during 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, while the remaining parameters are sampled in the same way.\n",
"\n",
"## Challenge A\n",
"\n",
"* Fixed random Erdős-Rényi graph $G_{n,p}$ with $n=200$ and $p=5\\%$\n",
"* Random vertex weights $w_v \\sim U(100, 150)$\n",
"* 500 training instances, 50 test instances"
]
},
{
"cell_type": "code",
"execution_count": null,
"id": "207c7846",
"metadata": {},
"outputs": [],
"source": [
"MaxWeightStableSetGenerator(\n",
" w=uniform(loc=100., scale=50.),\n",
" n=randint(low=200, high=201),\n",
" p=uniform(loc=0.05, scale=0.0),\n",
" fix_graph=True,\n",
")"
]
}
],
"metadata": {
"kernelspec": {
"display_name": "miplearn",
"language": "python",
"name": "miplearn"
},
"language_info": {
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"version": 3
},
"file_extension": ".py",
"mimetype": "text/x-python",
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<div class="section" id="Maximum-Weight-Stable-Set">
<h1><span class="section-number">2. </span>Maximum Weight Stable Set<a class="headerlink" href="#Maximum-Weight-Stable-Set" title="Permalink to this headline"></a></h1>
<div class="section" id="Problem-definition">
<h2><span class="section-number">2.1. </span>Problem definition<a class="headerlink" href="#Problem-definition" title="Permalink to this headline"></a></h2>
<p>Given a simple undirected graph <span class="math notranslate nohighlight">\(G=(V,E)\)</span> and weights <span class="math notranslate nohighlight">\(w \in \mathbb{R}^V\)</span>, the problem is to find a stable set <span class="math notranslate nohighlight">\(S \subseteq V\)</span> that maximizes $ <span class="math">\sum</span>_{v <span class="math">\in `V} w_v$. We recall that a subset :math:`S \subseteq V</span> is a <em>stable set</em> if no two vertices of <span class="math notranslate nohighlight">\(S\)</span> are adjacent. This is one of Karp’s 21 NP-complete problems.</p>
</div>
<div class="section" id="Random-instance-generator">
<h2><span class="section-number">2.2. </span>Random instance generator<a class="headerlink" href="#Random-instance-generator" title="Permalink to this headline"></a></h2>
<p>The class <code class="docutils literal notranslate"><span class="pre">MaxWeightStableSetGenerator</span></code> can be used to generate random instances of this problem, with user-specified probability distributions. When the constructor parameter <code class="docutils literal notranslate"><span class="pre">fix_graph=True</span></code> is provided, one random Erdős-Rényi graph <span class="math notranslate nohighlight">\(G_{n,p}\)</span> is generated during the constructor, where <span class="math notranslate nohighlight">\(n\)</span> and <span class="math notranslate nohighlight">\(p\)</span> are sampled from user-provided probability distributions <code class="docutils literal notranslate"><span class="pre">n</span></code> and <code class="docutils literal notranslate"><span class="pre">p</span></code>. To generate each instance, the generator independently samples each <span class="math notranslate nohighlight">\(w_v\)</span> from the user-provided
probability distribution <code class="docutils literal notranslate"><span class="pre">w</span></code>. When <code class="docutils literal notranslate"><span class="pre">fix_graph=False</span></code>, a new random graph is generated for each instance, while the remaining parameters are sampled in the same way.</p>
</div>
<div class="section" id="Challenge-A">
<h2><span class="section-number">2.3. </span>Challenge A<a class="headerlink" href="#Challenge-A" title="Permalink to this headline"></a></h2>
<ul class="simple">
<li><p>Fixed random Erdős-Rényi graph <span class="math notranslate nohighlight">\(G_{n,p}\)</span> with <span class="math notranslate nohighlight">\(n=200\)</span> and <span class="math notranslate nohighlight">\(p=5\%\)</span></p></li>
<li><p>Random vertex weights <span class="math notranslate nohighlight">\(w_v \sim U(100, 150)\)</span></p></li>
<li><p>500 training instances, 50 test instances</p></li>
</ul>
<div class="nbinput nblast docutils container">
<div class="prompt highlight-none notranslate"><div class="highlight"><pre><span></span>[ ]:
</pre></div>
</div>
<div class="input_area highlight-ipython3 notranslate"><div class="highlight"><pre>
<span></span><span class="n">MaxWeightStableSetGenerator</span><span class="p">(</span>
<span class="n">w</span><span class="o">=</span><span class="n">uniform</span><span class="p">(</span><span class="n">loc</span><span class="o">=</span><span class="mf">100.</span><span class="p">,</span> <span class="n">scale</span><span class="o">=</span><span class="mf">50.</span><span class="p">),</span>
<span class="n">n</span><span class="o">=</span><span class="n">randint</span><span class="p">(</span><span class="n">low</span><span class="o">=</span><span class="mi">200</span><span class="p">,</span> <span class="n">high</span><span class="o">=</span><span class="mi">201</span><span class="p">),</span>
<span class="n">p</span><span class="o">=</span><span class="n">uniform</span><span class="p">(</span><span class="n">loc</span><span class="o">=</span><span class="mf">0.05</span><span class="p">,</span> <span class="n">scale</span><span class="o">=</span><span class="mf">0.0</span><span class="p">),</span>
<span class="n">fix_graph</span><span class="o">=</span><span class="kc">True</span><span class="p">,</span>
<span class="p">)</span>
</pre></div>
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{
"cells": [
{
"cell_type": "markdown",
"id": "2f39414b",
"metadata": {},
"source": [
"# Traveling Salesman\n",
"\n",
"### Problem definition\n",
"\n",
"Given a list of cities and the distance between each pair of cities, the problem asks for the\n",
"shortest route starting at the first city, visiting each other city exactly once, then returning\n",
"to the first city. This problem is a generalization of the Hamiltonian path problem, one of Karp's\n",
"21 NP-complete problems.\n",
"\n",
"### Random problem generator\n",
"\n",
"The class `TravelingSalesmanGenerator` can be used to generate random instances of this\n",
"problem. Initially, the generator creates $n$ cities $(x_1,y_1),\\ldots,(x_n,y_n) \\in \\mathbb{R}^2$,\n",
"where $n, x_i$ and $y_i$ are sampled independently from the provided probability distributions `n`,\n",
"`x` and `y`. For each pair of cities $(i,j)$, the distance $d_{i,j}$ between them is set to:\n",
"$$\n",
" d_{i,j} = \\gamma_{i,j} \\sqrt{(x_i-x_j)^2 + (y_i - y_j)^2}\n",
"$$\n",
"where $\\gamma_{i,j}$ is sampled from the distribution `gamma`.\n",
"\n",
"If `fix_cities=True` is provided, the list of cities is kept the same for all generated instances.\n",
"The $gamma$ values, and therefore also the distances, are still different.\n",
"\n",
"By default, all distances $d_{i,j}$ are rounded to the nearest integer. If `round=False`\n",
"is provided, this rounding will be disabled.\n",
"\n",
"### Challenge A\n",
"\n",
"* Fixed list of 350 cities in the $[0, 1000]^2$ square\n",
"* $\\gamma_{i,j} \\sim U(0.95, 1.05)$\n",
"* 500 training instances, 50 test instances"
]
},
{
"cell_type": "code",
"execution_count": null,
"id": "6b2c4ff9",
"metadata": {},
"outputs": [],
"source": [
"TravelingSalesmanGenerator(\n",
" x=uniform(loc=0.0, scale=1000.0),\n",
" y=uniform(loc=0.0, scale=1000.0),\n",
" n=randint(low=350, high=351),\n",
" gamma=uniform(loc=0.95, scale=0.1),\n",
" fix_cities=True,\n",
" round=True,\n",
")"
]
},
{
"cell_type": "code",
"execution_count": null,
"id": "cc125860",
"metadata": {},
"outputs": [],
"source": []
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<div class="section" id="Traveling-Salesman">
<h1><span class="section-number">4. </span>Traveling Salesman<a class="headerlink" href="#Traveling-Salesman" title="Permalink to this headline"></a></h1>
<div class="section" id="Problem-definition">
<h2><span class="section-number">4.1. </span>Problem definition<a class="headerlink" href="#Problem-definition" title="Permalink to this headline"></a></h2>
<p>Given a list of cities and the distance between each pair of cities, the 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.</p>
</div>
<div class="section" id="Random-problem-generator">
<h2><span class="section-number">4.2. </span>Random problem generator<a class="headerlink" href="#Random-problem-generator" title="Permalink to this headline"></a></h2>
<p>The class <code class="docutils literal notranslate"><span class="pre">TravelingSalesmanGenerator</span></code> can be used to generate random instances of this problem. Initially, the generator creates <span class="math notranslate nohighlight">\(n\)</span> cities <span class="math notranslate nohighlight">\((x_1,y_1),\ldots,(x_n,y_n) \in \mathbb{R}^2\)</span>, where <span class="math notranslate nohighlight">\(n, x_i\)</span> and <span class="math notranslate nohighlight">\(y_i\)</span> are sampled independently from the provided probability distributions <code class="docutils literal notranslate"><span class="pre">n</span></code>, <code class="docutils literal notranslate"><span class="pre">x</span></code> and <code class="docutils literal notranslate"><span class="pre">y</span></code>. For each pair of cities <span class="math notranslate nohighlight">\((i,j)\)</span>, the distance <span class="math notranslate nohighlight">\(d_{i,j}\)</span> between them is set to:</p>
<div class="math notranslate nohighlight">
\[d_{i,j} = \gamma_{i,j} \sqrt{(x_i-x_j)^2 + (y_i - y_j)^2}\]</div>
<p>where <span class="math notranslate nohighlight">\(\gamma_{i,j}\)</span> is sampled from the distribution <code class="docutils literal notranslate"><span class="pre">gamma</span></code>.</p>
<p>If <code class="docutils literal notranslate"><span class="pre">fix_cities=True</span></code> is provided, the list of cities is kept the same for all generated instances. The <span class="math notranslate nohighlight">\(gamma\)</span> values, and therefore also the distances, are still different.</p>
<p>By default, all distances <span class="math notranslate nohighlight">\(d_{i,j}\)</span> are rounded to the nearest integer. If <code class="docutils literal notranslate"><span class="pre">round=False</span></code> is provided, this rounding will be disabled.</p>
</div>
<div class="section" id="Challenge-A">
<h2><span class="section-number">4.3. </span>Challenge A<a class="headerlink" href="#Challenge-A" title="Permalink to this headline"></a></h2>
<ul class="simple">
<li><p>Fixed list of 350 cities in the <span class="math notranslate nohighlight">\([0, 1000]^2\)</span> square</p></li>
<li><p><span class="math notranslate nohighlight">\(\gamma_{i,j} \sim U(0.95, 1.05)\)</span></p></li>
<li><p>500 training instances, 50 test instances</p></li>
</ul>
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<span></span><span class="n">TravelingSalesmanGenerator</span><span class="p">(</span>
<span class="n">x</span><span class="o">=</span><span class="n">uniform</span><span class="p">(</span><span class="n">loc</span><span class="o">=</span><span class="mf">0.0</span><span class="p">,</span> <span class="n">scale</span><span class="o">=</span><span class="mf">1000.0</span><span class="p">),</span>
<span class="n">y</span><span class="o">=</span><span class="n">uniform</span><span class="p">(</span><span class="n">loc</span><span class="o">=</span><span class="mf">0.0</span><span class="p">,</span> <span class="n">scale</span><span class="o">=</span><span class="mf">1000.0</span><span class="p">),</span>
<span class="n">n</span><span class="o">=</span><span class="n">randint</span><span class="p">(</span><span class="n">low</span><span class="o">=</span><span class="mi">350</span><span class="p">,</span> <span class="n">high</span><span class="o">=</span><span class="mi">351</span><span class="p">),</span>
<span class="n">gamma</span><span class="o">=</span><span class="n">uniform</span><span class="p">(</span><span class="n">loc</span><span class="o">=</span><span class="mf">0.95</span><span class="p">,</span> <span class="n">scale</span><span class="o">=</span><span class="mf">0.1</span><span class="p">),</span>
<span class="n">fix_cities</span><span class="o">=</span><span class="kc">True</span><span class="p">,</span>
<span class="nb">round</span><span class="o">=</span><span class="kc">True</span><span class="p">,</span>
<span class="p">)</span>
</pre></div>
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<h1>MIPLearn<a class="headerlink" href="#miplearn" title="Permalink to this headline"></a></h1>
<p><strong>MIPLearn</strong> is an extensible framework for solving discrete optimization problems using a combination of Mixed-Integer Linear Programming (MIP) and Machine Learning (ML). The framework 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).</p>
<p>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).</p>
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<li><p><strong>Alinson S. Xavier,</strong> Argonne National Laboratory &lt;<a class="reference external" href="mailto:axavier&#37;&#52;&#48;anl&#46;gov">mailto:axavier<span>&#64;</span>anl<span>&#46;</span>gov</a>&gt;</p></li>
<li><p><strong>Feng Qiu,</strong> Argonne National Laboratory &lt;<a class="reference external" href="mailto:fqiu&#37;&#52;&#48;anl&#46;gov">mailto:fqiu<span>&#64;</span>anl<span>&#46;</span>gov</a>&gt;</p></li>
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<li><p>Based upon work supported by <strong>Laboratory Directed Research and Development</strong> (LDRD) funding from Argonne National Laboratory, provided by the Director, Office of Science, of the U.S. Department of Energy under Contract No. DE-AC02-06CH11357, and the <strong>U.S. Department of Energy Advanced Grid Modeling Program</strong> under Grant DE-OE0000875.</p></li>
</ul>
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<div class="section" id="references">
<h2>References<a class="headerlink" href="#references" title="Permalink to this headline"></a></h2>
<p>If you use MIPLearn in your research, or the included problem generators, we kindly request that you cite the package as follows:</p>
<ul class="simple">
<li><p><strong>Alinson S. Xavier, Feng Qiu.</strong> <em>MIPLearn: An Extensible Framework for Learning-Enhanced Optimization</em>. Zenodo (2020). DOI: <a class="reference external" href="https://doi.org/10.5281/zenodo.4287567">10.5281/zenodo.4287567</a></p></li>
</ul>
<p>If you use MIPLearn in the field of power systems optimization, we kindly request that you cite the reference below, in which the main techniques implemented in MIPLearn were first developed:</p>
<ul class="simple">
<li><p><strong>Alinson S. Xavier, Feng Qiu, Shabbir Ahmed.</strong> <em>Learning to Solve Large-Scale Unit Commitment Problems.</em> INFORMS Journal on Computing (2021). DOI: <a class="reference external" href="https://doi.org/10.1287/ijoc.2020.0976">10.1287/ijoc.2020.0976</a></p></li>
</ul>
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<h2>License<a class="headerlink" href="#license" title="Permalink to this headline"></a></h2>
<div class="highlight-text notranslate"><div class="highlight"><pre><span></span>MIPLearn, an extensible framework for Learning-Enhanced Mixed-Integer Optimization
Copyright © 2020, UChicago Argonne, LLC. All Rights Reserved.
Redistribution and use in source and binary forms, with or without modification, are permitted
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1. Redistributions of source code must retain the above copyright notice, this list of
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conditions and the following disclaimer in the documentation and/or other materials provided
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CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR
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SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY
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{
"cells": [
{
"cell_type": "markdown",
"id": "546635ee",
"metadata": {},
"source": [
"# Getting started with MIPLearn\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 Julia/JuMP 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 with SCIP to solve new instances\n",
"\n",
"<div class=\"alert alert-info\">\n",
"Note\n",
" \n",
"In this tutorial, we use SCIP because it is more widely available than commercial MIP solvers. However, all the steps below should work for Gurobi, CPLEX or XPRESS, as long as you have a license for these solvers. The performance impact of MIPLearn may also change for different solvers.\n",
"</div>\n",
"\n",
"<div class=\"alert alert-warning\">\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",
"</div>\n"
]
},
{
"cell_type": "markdown",
"id": "8b97258c",
"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 Julia/JuMP version of the package. The first step is to install the Julia programming language in your computer. [See the official instructions for more details](https://julialang.org/downloads/). Note that MIPLearn was developed and tested with Julia 1.6, and may not be compatible with newer versions of the language. After Julia is installed, launch its console and run the following commands to download and install the package:"
]
},
{
"cell_type": "code",
"execution_count": 1,
"id": "2dbeacbc",
"metadata": {},
"outputs": [
{
"name": "stderr",
"output_type": "stream",
"text": [
"\u001b[32m\u001b[1m Updating\u001b[22m\u001b[39m git-repo `https://github.com/ANL-CEEESA/MIPLearn.jl.git`\n",
"\u001b[32m\u001b[1m Updating\u001b[22m\u001b[39m registry at `~/.julia/registries/General`\n",
"\u001b[32m\u001b[1m Updating\u001b[22m\u001b[39m git-repo `https://github.com/JuliaRegistries/General.git`\n",
"\u001b[32m\u001b[1m Resolving\u001b[22m\u001b[39m package versions...\n",
"\u001b[32m\u001b[1m No Changes\u001b[22m\u001b[39m to `~/Packages/MIPLearn/dev/docs/jump-tutorials/Project.toml`\n",
"\u001b[32m\u001b[1m No Changes\u001b[22m\u001b[39m to `~/Packages/MIPLearn/dev/docs/jump-tutorials/Manifest.toml`\n"
]
}
],
"source": [
"using Pkg\n",
"Pkg.add(PackageSpec(url=\"https://github.com/ANL-CEEESA/MIPLearn.jl.git\"))"
]
},
{
"cell_type": "markdown",
"id": "b2f449e7",
"metadata": {},
"source": [
"In addition to MIPLearn itself, we will also install a few other packages that are required for this tutorial:\n",
"\n",
"- [**SCIP**](https://www.scipopt.org/), one of the fastest non-commercial MIP solvers currently available\n",
"- [**JuMP**](https://jump.dev/), an open source modeling language for Julia\n",
"- [**Distributions.jl**](https://github.com/JuliaStats/Distributions.jl), a statistics package that we will use to generate random inputs\n",
"- [**Glob.jl**](https://github.com/vtjnash/Glob.jl), a package that retrieves all files in a directory matching a certain pattern"
]
},
{
"cell_type": "code",
"execution_count": 2,
"id": "68f99568",
"metadata": {},
"outputs": [
{
"name": "stderr",
"output_type": "stream",
"text": [
"\u001b[32m\u001b[1m Resolving\u001b[22m\u001b[39m package versions...\n",
"\u001b[32m\u001b[1m No Changes\u001b[22m\u001b[39m to `~/Packages/MIPLearn/dev/docs/jump-tutorials/Project.toml`\n",
"\u001b[32m\u001b[1m No Changes\u001b[22m\u001b[39m to `~/Packages/MIPLearn/dev/docs/jump-tutorials/Manifest.toml`\n"
]
}
],
"source": [
"using Pkg\n",
"Pkg.add([\n",
" PackageSpec(url=\"https://github.com/scipopt/SCIP.jl.git\", rev=\"7aa79aaa\"),\n",
" PackageSpec(name=\"JuMP\", version=\"0.21\"),\n",
" PackageSpec(name=\"Distributions\", version=\"0.25\"),\n",
" PackageSpec(name=\"Glob\", version=\"1\"),\n",
"])"
]
},
{
"cell_type": "markdown",
"id": "51e09fc9",
"metadata": {},
"source": [
"<div class=\"alert alert-info\">\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 Julia projects.\n",
" \n",
"</div>"
]
},
{
"cell_type": "markdown",
"id": "18c300c4",
"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",
"<div class=\"alert alert-info\">\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",
"</div>\n",
"\n",
"Next, let us convert this abstract mathematical formulation into a concrete optimization model, using Julia and JuMP. We start by defining a data structure that holds all the input data."
]
},
{
"cell_type": "code",
"execution_count": 3,
"id": "b12d6483",
"metadata": {},
"outputs": [],
"source": [
"Base.@kwdef struct UnitCommitmentData\n",
" demand::Float64\n",
" pmin::Vector{Float64}\n",
" pmax::Vector{Float64}\n",
" cfix::Vector{Float64}\n",
" cvar::Vector{Float64}\n",
"end;"
]
},
{
"cell_type": "markdown",
"id": "55cdb64b",
"metadata": {},
"source": [
"Next, we create a function that converts this data structure into a concrete JuMP model. For more details on the JuMP syntax, see [the official JuMP documentation](https://jump.dev/JuMP.jl/stable/)."
]
},
{
"cell_type": "code",
"execution_count": 4,
"id": "1e38a266",
"metadata": {},
"outputs": [],
"source": [
"using JuMP\n",
"\n",
"function build_uc_model(data::UnitCommitmentData)::Model\n",
" model = Model()\n",
" n = length(data.pmin)\n",
" @variable(model, x[1:n], Bin)\n",
" @variable(model, y[1:n] >= 0)\n",
" @objective(\n",
" model,\n",
" Min,\n",
" sum(\n",
" data.cfix[i] * x[i] +\n",
" data.cvar[i] * y[i]\n",
" for i in 1:n\n",
" )\n",
" )\n",
" @constraint(model, eq_max_power[i in 1:n], y[i] <= data.pmax[i] * x[i])\n",
" @constraint(model, eq_min_power[i in 1:n], y[i] >= data.pmin[i] * x[i])\n",
" @constraint(model, eq_demand, sum(y[i] for i in 1:n) == data.demand)\n",
" return model\n",
"end;"
]
},
{
"cell_type": "markdown",
"id": "d28c4d5a",
"metadata": {},
"source": [
"At this point, we can already use JuMP 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, using SCIP:"
]
},
{
"cell_type": "code",
"execution_count": 5,
"id": "9ff9f05c",
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"obj = 1320.0\n",
" x = [0.0, 1.0, 1.0]\n",
" y = [0.0, 60.0, 40.0]\n"
]
}
],
"source": [
"using SCIP\n",
"\n",
"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",
"scip = optimizer_with_attributes(SCIP.Optimizer, \"limits/gap\" => 1e-4)\n",
"set_optimizer(model, scip)\n",
"set_silent(model)\n",
"optimize!(model)\n",
"\n",
"println(\"obj = \", objective_value(model))\n",
"println(\" x = \", round.(value.(model[:x])))\n",
"println(\" y = \", round.(value.(model[:y]), digits=2));"
]
},
{
"cell_type": "markdown",
"id": "345de591",
"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": "eb8904ef",
"metadata": {},
"source": [
"## Generating training data\n",
"\n",
"Although SCIP 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 SCIP, 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 can be used to accelerate SCIP's performance on a particular set of instances. More specifically, MIPLearn will train a model that is able to predict the optimal solution for instances that follow a given probability distribution, then it will provide this predicted solution to SCIP as a warm start.\n",
"\n",
"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": "7298bb0d",
"metadata": {},
"outputs": [],
"source": [
"using Distributions\n",
"using Random\n",
"\n",
"function random_uc_data(; samples::Int, n::Int, seed=42)\n",
" Random.seed!(seed)\n",
" pmin = rand(Uniform(100, 500.0), n)\n",
" pmax = pmin .* rand(Uniform(2.0, 2.5), n)\n",
" cfix = pmin .* rand(Uniform(100.0, 125.0), n)\n",
" cvar = rand(Uniform(1.25, 1.5), n)\n",
" return [\n",
" UnitCommitmentData(;\n",
" pmin,\n",
" pmax,\n",
" cfix,\n",
" cvar,\n",
" demand = sum(pmax) * rand(Uniform(0.5, 0.75)),\n",
" )\n",
" for i in 1:samples\n",
" ]\n",
"end;"
]
},
{
"cell_type": "markdown",
"id": "c1feed43",
"metadata": {},
"source": [
"In this example, for simplicity, only the demands change from one instance to the next. We could also have made the prices and the production limits random. 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 100 instances of this problem, each one with 1,000 generators. We will use the first 90 instances for training, and the remaining 10 instances to evaluate SCIP's performance."
]
},
{
"cell_type": "code",
"execution_count": 7,
"id": "61d43994",
"metadata": {},
"outputs": [],
"source": [
"data = random_uc_data(samples=100, n=1000);\n",
"train_data = data[1:90]\n",
"test_data = data[91:100];"
]
},
{
"cell_type": "markdown",
"id": "3fdeb8cd",
"metadata": {},
"source": [
"Next, we write these data structures to individual files. MIPLearn uses files during the training process because, for large-scale optimization problems, it is often impractical to hold the entire training data, as well as the concrete JuMP models, in memory. 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.\n",
"\n",
"The code below generates the files `uc/train/000001.jld2`, `uc/train/000002.jld2`, etc., which contain the input data in [JLD2 format](https://github.com/JuliaIO/JLD2.jl)."
]
},
{
"cell_type": "code",
"execution_count": 8,
"id": "31b48701",
"metadata": {},
"outputs": [],
"source": [
"using MIPLearn\n",
"MIPLearn.save(data[1:90], \"uc/train/\")\n",
"MIPLearn.save(data[91:100], \"uc/test/\")\n",
"\n",
"using Glob\n",
"train_files = glob(\"uc/train/*.jld2\")\n",
"test_files = glob(\"uc/test/*.jld2\");"
]
},
{
"cell_type": "markdown",
"id": "5cecea59",
"metadata": {},
"source": [
"Finally, we use `MIPLearn.LearningSolver` and `MIPLearn.solve!` to solve all the training instances. `LearningSolver` is the main component provided by MIPLearn, which integrates MIP solvers and ML. The `solve!` function can be used to solve either one or multiple instances, and requires: (i) the list of files containing the training data; and (ii) the function that converts the data structure into a concrete JuMP model:"
]
},
{
"cell_type": "code",
"execution_count": 9,
"id": "60732af0",
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"103.808547 seconds (93.52 M allocations: 3.604 GiB, 1.19% gc time, 0.52% compilation time)\n"
]
},
{
"name": "stderr",
"output_type": "stream",
"text": [
"WARNING: Dual bound 1.98665e+07 is larger than the objective of the primal solution 1.98665e+07. The solution might not be optimal.\n"
]
}
],
"source": [
"using Glob\n",
"solver = LearningSolver(scip)\n",
"@time solve!(solver, train_files, build_uc_model);"
]
},
{
"cell_type": "markdown",
"id": "bbc7ad82",
"metadata": {},
"source": [
"The macro `@time` shows us how long did the code take to run. We can see that SCIP was able to solve all training instances in about 2 minutes. The solutions, and other useful training data, are stored by MIPLearn in `.h5` files, stored side-by-side with the original `.jld2` files."
]
},
{
"cell_type": "markdown",
"id": "73379180",
"metadata": {},
"source": [
"## Solving new instances\n",
"\n",
"With training data in hand, we can now fit the ML models using `MIPLearn.fit!`, then solve the test instances with `MIPLearn.solve!`, as shown below:"
]
},
{
"cell_type": "code",
"execution_count": 10,
"id": "e045d644",
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
" 5.951264 seconds (9.33 M allocations: 334.657 MiB, 1.51% gc time)\n"
]
}
],
"source": [
"solver_ml = LearningSolver(scip)\n",
"fit!(solver_ml, train_files, build_uc_model)\n",
"@time solve!(solver_ml, test_files, build_uc_model);"
]
},
{
"cell_type": "markdown",
"id": "d8de7b26",
"metadata": {},
"source": [
"The trained MIP solver was able to solve all test instances in about 6 seconds. To see that ML is being helpful here, let us repeat the code above, but remove the `fit!` line:"
]
},
{
"cell_type": "code",
"execution_count": 11,
"id": "cf2a989e",
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
" 10.390325 seconds (8.17 M allocations: 278.042 MiB, 0.89% gc time)\n"
]
}
],
"source": [
"solver_baseline = LearningSolver(scip)\n",
"@time solve!(solver_baseline, test_files, build_uc_model);"
]
},
{
"cell_type": "markdown",
"id": "e100b25d",
"metadata": {},
"source": [
"Without the help of the ML models, SCIP took around 10 seconds to solve the same test instances.\n",
"\n",
"<div class=\"alert alert-info\">\n",
"Note\n",
" \n",
"Note that is 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",
"</div>"
]
},
{
"cell_type": "markdown",
"id": "af451e87",
"metadata": {},
"source": [
"## Understanding the acceleration\n",
"\n",
"Let us go a bit deeper and try to understand how exactly did MIPLearn accelerate SCIP's performance. First, we are going to solve one of the test instances again, using the trained solver, but this time using the `tee=true` parameter, so that we can see SCIP's log:"
]
},
{
"cell_type": "code",
"execution_count": 12,
"id": "0c675452",
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"presolving:\n",
"(round 1, fast) 861 del vars, 861 del conss, 0 add conss, 2000 chg bounds, 0 chg sides, 0 chg coeffs, 0 upgd conss, 0 impls, 0 clqs\n",
"(round 2, fast) 861 del vars, 1722 del conss, 0 add conss, 2000 chg bounds, 0 chg sides, 0 chg coeffs, 0 upgd conss, 0 impls, 0 clqs\n",
"(round 3, fast) 862 del vars, 1722 del conss, 0 add conss, 2000 chg bounds, 0 chg sides, 0 chg coeffs, 0 upgd conss, 0 impls, 0 clqs\n",
"presolving (4 rounds: 4 fast, 1 medium, 1 exhaustive):\n",
" 862 deleted vars, 1722 deleted constraints, 0 added constraints, 2000 tightened bounds, 0 added holes, 0 changed sides, 0 changed coefficients\n",
" 0 implications, 0 cliques\n",
"presolved problem has 1138 variables (0 bin, 0 int, 0 impl, 1138 cont) and 279 constraints\n",
" 279 constraints of type <linear>\n",
"Presolving Time: 0.03\n",
"\n",
" time | node | left |LP iter|LP it/n|mem/heur|mdpt |vars |cons |rows |cuts |sepa|confs|strbr| dualbound | primalbound | gap | compl. \n",
"* 0.0s| 1 | 0 | 203 | - | LP | 0 |1138 | 279 | 279 | 0 | 0 | 0 | 0 | 1.705035e+07 | 1.705035e+07 | 0.00%| unknown\n",
" 0.0s| 1 | 0 | 203 | - | 8950k | 0 |1138 | 279 | 279 | 0 | 0 | 0 | 0 | 1.705035e+07 | 1.705035e+07 | 0.00%| unknown\n",
"\n",
"SCIP Status : problem is solved [optimal solution found]\n",
"Solving Time (sec) : 0.04\n",
"Solving Nodes : 1\n",
"Primal Bound : +1.70503465600131e+07 (1 solutions)\n",
"Dual Bound : +1.70503465600131e+07\n",
"Gap : 0.00 %\n",
"\n",
"violation: integrality condition of variable <> = 0.338047247943162\n",
"all 1 solutions given by solution candidate storage are infeasible\n",
"\n",
"feasible solution found by completesol heuristic after 0.1 seconds, objective value 1.705169e+07\n",
"presolving:\n",
"(round 1, fast) 0 del vars, 0 del conss, 0 add conss, 3000 chg bounds, 0 chg sides, 0 chg coeffs, 0 upgd conss, 0 impls, 0 clqs\n",
"(round 2, exhaustive) 0 del vars, 0 del conss, 0 add conss, 3000 chg bounds, 0 chg sides, 0 chg coeffs, 1000 upgd conss, 0 impls, 0 clqs\n",
"(round 3, exhaustive) 0 del vars, 0 del conss, 0 add conss, 3000 chg bounds, 0 chg sides, 0 chg coeffs, 2000 upgd conss, 1000 impls, 0 clqs\n",
" (0.1s) probing: 51/1000 (5.1%) - 0 fixings, 0 aggregations, 0 implications, 0 bound changes\n",
" (0.1s) probing aborted: 50/50 successive totally useless probings\n",
" (0.1s) symmetry computation started: requiring (bin +, int -, cont +), (fixed: bin -, int +, cont -)\n",
" (0.1s) no symmetry present\n",
"presolving (4 rounds: 4 fast, 3 medium, 3 exhaustive):\n",
" 0 deleted vars, 0 deleted constraints, 0 added constraints, 3000 tightened bounds, 0 added holes, 0 changed sides, 0 changed coefficients\n",
" 2000 implications, 0 cliques\n",
"presolved problem has 2000 variables (1000 bin, 0 int, 0 impl, 1000 cont) and 2001 constraints\n",
" 2000 constraints of type <varbound>\n",
" 1 constraints of type <linear>\n",
"Presolving Time: 0.11\n",
"transformed 1/1 original solutions to the transformed problem space\n",
"\n",
" time | node | left |LP iter|LP it/n|mem/heur|mdpt |vars |cons |rows |cuts |sepa|confs|strbr| dualbound | primalbound | gap | compl. \n",
" 0.2s| 1 | 0 | 1201 | - | 20M | 0 |2000 |2001 |2001 | 0 | 0 | 0 | 0 | 1.705035e+07 | 1.705169e+07 | 0.01%| unknown\n",
"\n",
"SCIP Status : solving was interrupted [gap limit reached]\n",
"Solving Time (sec) : 0.21\n",
"Solving Nodes : 1\n",
"Primal Bound : +1.70516871251443e+07 (1 solutions)\n",
"Dual Bound : +1.70503465600130e+07\n",
"Gap : 0.01 %\n",
"\n"
]
}
],
"source": [
"solve!(solver_ml, test_files[1], build_uc_model, tee=true);"
]
},
{
"cell_type": "markdown",
"id": "ff0b6858",
"metadata": {},
"source": [
"The log above is quite complicated if you have never seen it before, but the important line is the one starting with `feasible solution found [...] objective value 1.705169e+07`. This line indicates that MIPLearn was able to construct a warm start with value `1.705169e+07`. Using this warm start, SCIP then used the branch-and-cut method to either prove its optimality or to find an even better solution. Very quickly, however, SCIP proved that the solution produced by MIPLearn was indeed optimal. It was able to do this without generating a single cutting plane or running any other heuristics; it could tell the optimality by the root LP relaxation alone, which was very fast. \n",
"\n",
"Let us now repeat the process, but using the untrained solver this time:"
]
},
{
"cell_type": "code",
"execution_count": 13,
"id": "1aa9230e",
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"presolving:\n",
"(round 1, fast) 861 del vars, 861 del conss, 0 add conss, 2000 chg bounds, 0 chg sides, 0 chg coeffs, 0 upgd conss, 0 impls, 0 clqs\n",
"(round 2, fast) 861 del vars, 1722 del conss, 0 add conss, 2000 chg bounds, 0 chg sides, 0 chg coeffs, 0 upgd conss, 0 impls, 0 clqs\n",
"(round 3, fast) 862 del vars, 1722 del conss, 0 add conss, 2000 chg bounds, 0 chg sides, 0 chg coeffs, 0 upgd conss, 0 impls, 0 clqs\n",
"presolving (4 rounds: 4 fast, 1 medium, 1 exhaustive):\n",
" 862 deleted vars, 1722 deleted constraints, 0 added constraints, 2000 tightened bounds, 0 added holes, 0 changed sides, 0 changed coefficients\n",
" 0 implications, 0 cliques\n",
"presolved problem has 1138 variables (0 bin, 0 int, 0 impl, 1138 cont) and 279 constraints\n",
" 279 constraints of type <linear>\n",
"Presolving Time: 0.03\n",
"\n",
" time | node | left |LP iter|LP it/n|mem/heur|mdpt |vars |cons |rows |cuts |sepa|confs|strbr| dualbound | primalbound | gap | compl. \n",
"* 0.0s| 1 | 0 | 203 | - | LP | 0 |1138 | 279 | 279 | 0 | 0 | 0 | 0 | 1.705035e+07 | 1.705035e+07 | 0.00%| unknown\n",
" 0.0s| 1 | 0 | 203 | - | 8950k | 0 |1138 | 279 | 279 | 0 | 0 | 0 | 0 | 1.705035e+07 | 1.705035e+07 | 0.00%| unknown\n",
"\n",
"SCIP Status : problem is solved [optimal solution found]\n",
"Solving Time (sec) : 0.04\n",
"Solving Nodes : 1\n",
"Primal Bound : +1.70503465600131e+07 (1 solutions)\n",
"Dual Bound : +1.70503465600131e+07\n",
"Gap : 0.00 %\n",
"\n",
"violation: integrality condition of variable <> = 0.338047247943162\n",
"all 1 solutions given by solution candidate storage are infeasible\n",
"\n",
"presolving:\n",
"(round 1, fast) 0 del vars, 0 del conss, 0 add conss, 2000 chg bounds, 0 chg sides, 0 chg coeffs, 0 upgd conss, 0 impls, 0 clqs\n",
"(round 2, exhaustive) 0 del vars, 0 del conss, 0 add conss, 2000 chg bounds, 0 chg sides, 0 chg coeffs, 1000 upgd conss, 0 impls, 0 clqs\n",
"(round 3, exhaustive) 0 del vars, 0 del conss, 0 add conss, 2000 chg bounds, 0 chg sides, 0 chg coeffs, 2000 upgd conss, 1000 impls, 0 clqs\n",
" (0.0s) probing: 51/1000 (5.1%) - 0 fixings, 0 aggregations, 0 implications, 0 bound changes\n",
" (0.0s) probing aborted: 50/50 successive totally useless probings\n",
" (0.0s) symmetry computation started: requiring (bin +, int -, cont +), (fixed: bin -, int +, cont -)\n",
" (0.0s) no symmetry present\n",
"presolving (4 rounds: 4 fast, 3 medium, 3 exhaustive):\n",
" 0 deleted vars, 0 deleted constraints, 0 added constraints, 2000 tightened bounds, 0 added holes, 0 changed sides, 0 changed coefficients\n",
" 2000 implications, 0 cliques\n",
"presolved problem has 2000 variables (1000 bin, 0 int, 0 impl, 1000 cont) and 2001 constraints\n",
" 2000 constraints of type <varbound>\n",
" 1 constraints of type <linear>\n",
"Presolving Time: 0.03\n",
"\n",
" time | node | left |LP iter|LP it/n|mem/heur|mdpt |vars |cons |rows |cuts |sepa|confs|strbr| dualbound | primalbound | gap | compl. \n",
"p 0.0s| 1 | 0 | 1 | - | locks| 0 |2000 |2001 |2001 | 0 | 0 | 0 | 0 | 0.000000e+00 | 2.335200e+07 | Inf | unknown\n",
"p 0.0s| 1 | 0 | 2 | - | vbounds| 0 |2000 |2001 |2001 | 0 | 0 | 0 | 0 | 0.000000e+00 | 1.839873e+07 | Inf | unknown\n",
" 0.1s| 1 | 0 | 1204 | - | 20M | 0 |2000 |2001 |2001 | 0 | 0 | 0 | 0 | 1.705035e+07 | 1.839873e+07 | 7.91%| unknown\n",
" 0.1s| 1 | 0 | 1207 | - | 22M | 0 |2000 |2001 |2002 | 1 | 1 | 0 | 0 | 1.705036e+07 | 1.839873e+07 | 7.91%| unknown\n",
"r 0.1s| 1 | 0 | 1207 | - |shifting| 0 |2000 |2001 |2002 | 1 | 1 | 0 | 0 | 1.705036e+07 | 1.711399e+07 | 0.37%| unknown\n",
" 0.1s| 1 | 0 | 1209 | - | 22M | 0 |2000 |2001 |2003 | 2 | 2 | 0 | 0 | 1.705037e+07 | 1.711399e+07 | 0.37%| unknown\n",
"r 0.1s| 1 | 0 | 1209 | - |shifting| 0 |2000 |2001 |2003 | 2 | 2 | 0 | 0 | 1.705037e+07 | 1.706492e+07 | 0.09%| unknown\n",
" 0.1s| 1 | 0 | 1210 | - | 22M | 0 |2000 |2001 |2004 | 3 | 3 | 0 | 0 | 1.705037e+07 | 1.706492e+07 | 0.09%| unknown\n",
" 0.1s| 1 | 0 | 1211 | - | 23M | 0 |2000 |2001 |2005 | 4 | 4 | 0 | 0 | 1.705037e+07 | 1.706492e+07 | 0.09%| unknown\n",
" 0.1s| 1 | 0 | 1212 | - | 23M | 0 |2000 |2001 |2006 | 5 | 5 | 0 | 0 | 1.705037e+07 | 1.706492e+07 | 0.09%| unknown\n",
"r 0.1s| 1 | 0 | 1212 | - |shifting| 0 |2000 |2001 |2006 | 5 | 5 | 0 | 0 | 1.705037e+07 | 1.706228e+07 | 0.07%| unknown\n",
" 0.1s| 1 | 0 | 1214 | - | 24M | 0 |2000 |2001 |2007 | 6 | 7 | 0 | 0 | 1.705037e+07 | 1.706228e+07 | 0.07%| unknown\n",
" 0.2s| 1 | 0 | 1216 | - | 24M | 0 |2000 |2001 |2009 | 8 | 8 | 0 | 0 | 1.705037e+07 | 1.706228e+07 | 0.07%| unknown\n",
" 0.2s| 1 | 0 | 1220 | - | 25M | 0 |2000 |2001 |2011 | 10 | 9 | 0 | 0 | 1.705037e+07 | 1.706228e+07 | 0.07%| unknown\n",
" 0.2s| 1 | 0 | 1223 | - | 25M | 0 |2000 |2001 |2014 | 13 | 10 | 0 | 0 | 1.705037e+07 | 1.706228e+07 | 0.07%| unknown\n",
" time | node | left |LP iter|LP it/n|mem/heur|mdpt |vars |cons |rows |cuts |sepa|confs|strbr| dualbound | primalbound | gap | compl. \n",
" 0.2s| 1 | 0 | 1229 | - | 26M | 0 |2000 |2001 |2015 | 14 | 11 | 0 | 0 | 1.705038e+07 | 1.706228e+07 | 0.07%| unknown\n",
"r 0.2s| 1 | 0 | 1403 | - |intshift| 0 |2000 |2001 |2015 | 14 | 11 | 0 | 0 | 1.705038e+07 | 1.705687e+07 | 0.04%| unknown\n",
"L 0.6s| 1 | 0 | 1707 | - | rens| 0 |2000 |2001 |2015 | 14 | 11 | 0 | 0 | 1.705038e+07 | 1.705332e+07 | 0.02%| unknown\n",
"L 0.7s| 1 | 0 | 1707 | - | alns| 0 |2000 |2001 |2015 | 14 | 11 | 0 | 0 | 1.705038e+07 | 1.705178e+07 | 0.01%| unknown\n",
"\n",
"SCIP Status : solving was interrupted [gap limit reached]\n",
"Solving Time (sec) : 0.68\n",
"Solving Nodes : 1\n",
"Primal Bound : +1.70517823853380e+07 (13 solutions)\n",
"Dual Bound : +1.70503798271962e+07\n",
"Gap : 0.01 %\n",
"\n"
]
}
],
"source": [
"solve!(solver_baseline, test_files[1], build_uc_model, tee=true);"
]
},
{
"cell_type": "markdown",
"id": "9417bb85",
"metadata": {},
"source": [
"In this log file, notice how the previous line about warm starts is missing. Since no warm starts were provided, SCIP had to find an initial solution using its own internal heuristics, which are not specifically tailored for this problem. The initial solution found by SCIP's heuristics has value `2.335200e+07`, which is significantly worse than the one constructed by MIPLearn. SCIP then proceeded to improve this solution, by generating cutting planes and repeatedly running additional primal heuristics. In the end, it was able to find the optimal solution, as expected, but it took longer.\n",
"\n",
"In summary, MIPLearn accelerated the solution process by constructing a high-quality initial solution. In the following tutorials, we will see other strategies that MIPLearn can use to accelerate MIP performance, besides warm starts."
]
},
{
"cell_type": "markdown",
"id": "ab9c1ff4",
"metadata": {},
"source": [
"## Accessing the solution\n",
"\n",
"In the example above, we used `MIPLearn.solve!` together with data files to solve both the training and the test instances. The solutions were saved to a `.h5` files in the train/test folders, and could be retrieved by reading theses files, but that is not very convenient. In this section we will use an easier method.\n",
"\n",
"We can use the function `MIPLearn.load!` to obtain a regular JuMP model:"
]
},
{
"cell_type": "code",
"execution_count": 14,
"id": "79759e87",
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"A JuMP Model\n",
"Minimization problem with:\n",
"Variables: 2000\n",
"Objective function type: AffExpr\n",
"`AffExpr`-in-`MathOptInterface.EqualTo{Float64}`: 1 constraint\n",
"`AffExpr`-in-`MathOptInterface.GreaterThan{Float64}`: 1000 constraints\n",
"`AffExpr`-in-`MathOptInterface.LessThan{Float64}`: 1000 constraints\n",
"`VariableRef`-in-`MathOptInterface.GreaterThan{Float64}`: 1000 constraints\n",
"`VariableRef`-in-`MathOptInterface.ZeroOne`: 1000 constraints\n",
"Model mode: AUTOMATIC\n",
"CachingOptimizer state: NO_OPTIMIZER\n",
"Solver name: No optimizer attached.\n",
"Names registered in the model: eq_demand, eq_max_power, eq_min_power, x, y"
]
},
"execution_count": 14,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"model = MIPLearn.load(\"uc/test/000001.jld2\", build_uc_model)"
]
},
{
"cell_type": "markdown",
"id": "b096dcf9",
"metadata": {},
"source": [
"We can then solve this model as before, with `MIPLearn.solve!`:"
]
},
{
"cell_type": "code",
"execution_count": 15,
"id": "1b668c12",
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"obj = 1.7051217395548128e7\n",
" x = [1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 0.0, 0.0, 0.0, 0.0]\n",
" y = [767.11, 646.61, 230.28, 365.46, 1150.99, 1103.36, 0.0, 0.0, 0.0, 0.0]\n"
]
}
],
"source": [
"solve!(solver_ml, model)\n",
"println(\"obj = \", objective_value(model))\n",
"println(\" x = \", round.(value.(model[:x][1:10])))\n",
"println(\" y = \", round.(value.(model[:y][1:10]), digits=2))"
]
}
],
"metadata": {
"kernelspec": {
"display_name": "Julia 1.6.0",
"language": "julia",
"name": "julia-1.6"
},
"language_info": {
"file_extension": ".jl",
"mimetype": "application/julia",
"name": "julia",
"version": "1.6.0"
}
},
"nbformat": 4,
"nbformat_minor": 5
}

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{
"cells": [
{
"cell_type": "markdown",
"id": "18dd2957",
"metadata": {},
"source": [
"# Modeling lazy constraints\n",
"\n",
"TODO"
]
}
],
"metadata": {
"kernelspec": {
"display_name": "Julia 1.6.0",
"language": "julia",
"name": "julia-1.6"
},
"language_info": {
"file_extension": ".jl",
"mimetype": "application/julia",
"name": "julia",
"version": "1.6.0"
}
},
"nbformat": 4,
"nbformat_minor": 5
}

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"solver.fit(train_data)\n",
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@ -2,14 +2,14 @@ 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).
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 may provide significant performance benefits.
Contents
--------
.. toctree::
:maxdepth: 10
:maxdepth: 1
:caption: Tutorials
:numbered: 2
@ -18,7 +18,7 @@ Contents
tutorials/getting-started-jump
.. toctree::
:maxdepth: 10
:maxdepth: 2
:caption: User Guide
:numbered: 2
@ -29,7 +29,7 @@ Contents
guide/solvers
.. toctree::
:maxdepth: 10
:maxdepth: 1
:caption: Python API Reference
:numbered: 2
@ -38,3 +38,30 @@ Contents
api/components
api/solvers
api/helpers
Authors
-------
- **Alinson S. Xavier** (Argonne National Laboratory)
- **Feng Qiu** (Argonne National Laboratory)
- **Xiaoyi Gu** (Georgia Institute of Technology)
- **Berkay Becu** (Georgia Institute of Technology)
- **Santanu S. Dey** (Georgia Institute of Technology)
Acknowledgments
---------------
* Based upon work supported by **Laboratory Directed Research and Development** (LDRD) funding from Argonne National Laboratory, provided by the Director, Office of Science, of the U.S. Department of Energy.
* Based upon work supported by the **U.S. Department of Energy Advanced Grid Modeling Program**.
Citing MIPLearn
---------------
If you use MIPLearn in your research (either the solver or the included problem generators), we kindly request that you cite the package as follows:
* **Alinson S. Xavier, Feng Qiu, Xiaoyi Gu, Berkay Becu, Santanu S. Dey.** *MIPLearn: An Extensible Framework for Learning-Enhanced Optimization (Version 0.3)*. Zenodo (2023). DOI: https://doi.org/10.5281/zenodo.4287567
If you use MIPLearn in the field of power systems optimization, we kindly request that you cite the reference below, in which the main techniques implemented in MIPLearn were first developed:
* **Alinson S. Xavier, Feng Qiu, Shabbir Ahmed.** *Learning to Solve Large-Scale Unit Commitment Problems.* INFORMS Journal on Computing (2020). DOI: https://doi.org/10.1287/ijoc.2020.0976

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