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```{sectnum}
---
start: 2
depth: 2
suffix: .
---
```
# Benchmarks
MIPLearn provides a selection of benchmark problems and random instance generators, covering applications from different fields, that can be used to evaluate new learning-enhanced MIP techniques in a measurable and reproducible way. In this page, we describe these problems, the included instance generators, and we present some benchmark results for `LearningSolver` with default parameters.
## Preliminaries
### Benchmark challenges
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.
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.
### Baseline results
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](about.md#references). We compare three solvers:
* **baseline:** Gurobi 9.0 with default settings (a conventional state-of-the-art MIP solver)
* **ml-exact:** `LearningSolver` with default settings, using Gurobi 9.0 as internal MIP solver
* **ml-heuristic:** Same as above, but with `mode="heuristic"`
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.
## Maximum Weight Stable Set Problem
### Problem definition
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.
### Random instance generator
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.
### Challenge A
* Fixed random Erdős-Rényi graph $G_{n,p}$ with $n=200$ and $p=5\%$
* Random vertex weights $w_v \sim U(100, 150)$
* 500 training instances, 50 test instances
```python
MaxWeightStableSetGenerator(w=uniform(loc=100., scale=50.),
n=randint(low=200, high=201),
p=uniform(loc=0.05, scale=0.0),
fix_graph=True)
```
![alt](figures/benchmark_stab_a.png)
## Traveling Salesman Problem
### Problem definition
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.
### Random problem generator
The class `TravelingSalesmanGenerator` can be used to generate random instances of this
problem. Initially, the generator creates $n$ cities $(x_1,y_1),\ldots,(x_n,y_n) \in \mathbb{R}^2$,
where $n, x_i$ and $y_i$ are sampled independently from the provided probability distributions `n`,
`x` and `y`. For each pair of cities $(i,j)$, the distance $d_{i,j}$ between them is set to:
$$
d_{i,j} = \gamma_{i,j} \sqrt{(x_i-x_j)^2 + (y_i - y_j)^2}
$$
where $\gamma_{i,j}$ is sampled from the distribution `gamma`.
If `fix_cities=True` is provided, the list of cities is kept the same for all generated instances.
The $gamma$ values, and therefore also the distances, are still different.
By default, all distances $d_{i,j}$ are rounded to the nearest integer. If `round=False`
is provided, this rounding will be disabled.
### Challenge A
* Fixed list of 350 cities in the $[0, 1000]^2$ square
* $\gamma_{i,j} \sim U(0.95, 1.05)$
* 500 training instances, 50 test instances
```python
TravelingSalesmanGenerator(x=uniform(loc=0.0, scale=1000.0),
y=uniform(loc=0.0, scale=1000.0),
n=randint(low=350, high=351),
gamma=uniform(loc=0.95, scale=0.1),
fix_cities=True,
round=True,
)
```
![alt](figures/benchmark_tsp_a.png)
## Multidimensional 0-1 Knapsack Problem
### Problem definition
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:
$$
\begin{align*}
\text{maximize}
& \sum_{j=1}^n p_j x_j
\\
\text{subject to}
& \sum_{j=1}^n w_{ij} x_j \leq b_i
& \forall i=1,\ldots,m \\
& x_j \in \{0,1\}
& \forall j=1,\ldots,n
\end{align*}
$$
### Random instance generator
The class `MultiKnapsackGenerator` can be used to generate random instances of this problem. The number of items $n$ and knapsacks $m$ are sampled from the user-provided probability distributions `n` and `m`. The weights $w_{ij}$ are sampled independently from the provided distribution `w`. The capacity of knapsack $i$ is set to
$$
b_i = \alpha_i \sum_{j=1}^n w_{ij}
$$
where $\alpha_i$, the tightness ratio, is sampled from the provided probability
distribution `alpha`. To make the instances more challenging, the costs of the items
are linearly correlated to their average weights. More specifically, the price of each
item $j$ is set to:
$$
p_j = \sum_{i=1}^m \frac{w_{ij}}{m} + K u_j,
$$
where $K$, the correlation coefficient, and $u_j$, the correlation multiplier, are sampled
from the provided probability distributions `K` and `u`.
If `fix_w=True` is provided, then $w_{ij}$ are kept the same in all generated instances. This also implies that $n$ and $m$ are kept fixed. Although the prices and capacities are derived from $w_{ij}$, as long as `u` and `K` are not constants, the generated instances will still not be completely identical.
If a probability distribution `w_jitter` is provided, then item weights will be set to $w_{ij} \gamma_{ij}$ where $\gamma_{ij}$ is sampled from `w_jitter`. When combined with `fix_w=True`, this argument may be used to generate instances where the weight of each item is roughly the same, but not exactly identical, across all instances. The prices of the items and the capacities of the knapsacks will be calculated as above, but using these perturbed weights instead.
By default, all generated prices, weights and capacities are rounded to the nearest integer number. If `round=False` is provided, this rounding will be disabled.
!!! note "References"
* Freville, Arnaud, and Gérard Plateau. *An efficient preprocessing procedure for the multidimensional 01 knapsack problem.* Discrete applied mathematics 49.1-3 (1994): 189-212.
* Fréville, Arnaud. *The multidimensional 01 knapsack problem: An overview.* European Journal of Operational Research 155.1 (2004): 1-21.
### Challenge A
* 250 variables, 10 constraints, fixed weights
* $w \sim U(0, 1000), \gamma \sim U(0.95, 1.05)$
* $K = 500, u \sim U(0, 1), \alpha = 0.25$
* 500 training instances, 50 test instances
```python
MultiKnapsackGenerator(n=randint(low=250, high=251),
m=randint(low=10, high=11),
w=uniform(loc=0.0, scale=1000.0),
K=uniform(loc=500.0, scale=0.0),
u=uniform(loc=0.0, scale=1.0),
alpha=uniform(loc=0.25, scale=0.0),
fix_w=True,
w_jitter=uniform(loc=0.95, scale=0.1),
)
```
![alt](figures/benchmark_knapsack_a.png)

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```{sectnum}
---
start: 3
depth: 2
suffix: .
---
```
# Customization
## Customizing solver parameters
### Selecting the internal MIP solver
By default, `LearningSolver` uses [Gurobi](https://www.gurobi.com/) as its internal MIP solver, and expects models to be provided using the Pyomo modeling language. Supported solvers and modeling languages include:
* `GurobiPyomoSolver`: Gurobi with Pyomo (default).
* `CplexPyomoSolver`: [IBM ILOG CPLEX](https://www.ibm.com/products/ilog-cplex-optimization-studio) with Pyomo.
* `XpressPyomoSolver`: [FICO XPRESS Solver](https://www.fico.com/en/products/fico-xpress-solver) with Pyomo.
* `GurobiSolver`: Gurobi without any modeling language.
To switch between solvers, provide the desired class using the `solver` argument:
```python
from miplearn import LearningSolver, CplexPyomoSolver
solver = LearningSolver(solver=CplexPyomoSolver)
```
To configure a particular solver, use the `params` constructor argument, as shown below.
```python
from miplearn import LearningSolver, GurobiPyomoSolver
solver = LearningSolver(
solver=lambda: GurobiPyomoSolver(
params={
"TimeLimit": 900,
"MIPGap": 1e-3,
"NodeLimit": 1000,
}
),
)
```
## Customizing solver components
`LearningSolver` is composed by a number of individual machine-learning components, each targeting a different part of the solution process. Each component can be individually enabled, disabled or customized. The following components are enabled by default:
* `LazyConstraintComponent`: Predicts which lazy constraint to initially enforce.
* `ObjectiveValueComponent`: Predicts the optimal value of the optimization problem, given the optimal solution to the LP relaxation.
* `PrimalSolutionComponent`: Predicts optimal values for binary decision variables. In heuristic mode, this component fixes the variables to their predicted values. In exact mode, the predicted values are provided to the solver as a (partial) MIP start.
The following components are also available, but not enabled by default:
* `BranchPriorityComponent`: Predicts good branch priorities for decision variables.
### Selecting components
To create a `LearningSolver` with a specific set of components, the `components` constructor argument may be used, as the next example shows:
```python
# Create a solver without any components
solver1 = LearningSolver(components=[])
# Create a solver with only two components
solver2 = LearningSolver(components=[
LazyConstraintComponent(...),
PrimalSolutionComponent(...),
])
```
### Adjusting component aggressiveness
The aggressiveness of classification components, such as `PrimalSolutionComponent` and `LazyConstraintComponent`, can be adjusted through the `threshold` constructor argument. Internally, these components ask the machine learning models how confident are they on each prediction they make, then automatically discard all predictions that have low confidence. The `threshold` argument specifies how confident should the ML models be for a prediction to be considered trustworthy. Lowering a component's threshold increases its aggressiveness, while raising a component's threshold makes it more conservative.
For example, if the ML model predicts that a certain binary variable will assume value `1.0` in the optimal solution with 75% confidence, and if the `PrimalSolutionComponent` is configured to discard all predictions with less than 90% confidence, then this variable will not be included in the predicted MIP start.
MIPLearn currently provides two types of thresholds:
* `MinProbabilityThreshold(p: List[float])` A threshold which indicates that a prediction is trustworthy if its probability of being correct, as computed by the machine learning model, is above a fixed value.
* `MinPrecisionThreshold(p: List[float])` A dynamic threshold which automatically adjusts itself during training to ensure that the component achieves at least a given precision on the training data set. Note that increasing a component's precision may reduce its recall.
The example below shows how to build a `PrimalSolutionComponent` which fixes variables to zero with at least 80% precision, and to one with at least 95% precision. Other components are configured similarly.
```python
from miplearn import PrimalSolutionComponent, MinPrecisionThreshold
PrimalSolutionComponent(
mode="heuristic",
threshold=MinPrecisionThreshold([0.80, 0.95]),
)
```
### Evaluating component performance
MIPLearn allows solver components to be modified, trained and evaluated in isolation. In the following example, we build and
fit `PrimalSolutionComponent` outside the solver, then evaluate its performance.
```python
from miplearn import PrimalSolutionComponent
# User-provided set of previously-solved instances
train_instances = [...]
# Construct and fit component on a subset of training instances
comp = PrimalSolutionComponent()
comp.fit(train_instances[:100])
# Evaluate performance on an additional set of training instances
ev = comp.evaluate(train_instances[100:150])
```
The method `evaluate` returns a dictionary with performance evaluation statistics for each training instance provided,
and for each type of prediction the component makes. To obtain a summary across all instances, pandas may be used, as below:
```python
import pandas as pd
pd.DataFrame(ev["Fix one"]).mean(axis=1)
```
```text
Predicted positive 3.120000
Predicted negative 196.880000
Condition positive 62.500000
Condition negative 137.500000
True positive 3.060000
True negative 137.440000
False positive 0.060000
False negative 59.440000
Accuracy 0.702500
F1 score 0.093050
Recall 0.048921
Precision 0.981667
Predicted positive (%) 1.560000
Predicted negative (%) 98.440000
Condition positive (%) 31.250000
Condition negative (%) 68.750000
True positive (%) 1.530000
True negative (%) 68.720000
False positive (%) 0.030000
False negative (%) 29.720000
dtype: float64
```
Regression components (such as `ObjectiveValueComponent`) can also be trained and evaluated similarly,
as the next example shows:
```python
from miplearn import ObjectiveValueComponent
comp = ObjectiveValueComponent()
comp.fit(train_instances[:100])
ev = comp.evaluate(train_instances[100:150])
import pandas as pd
pd.DataFrame(ev).mean(axis=1)
```
```text
Mean squared error 7001.977827
Explained variance 0.519790
Max error 242.375804
Mean absolute error 65.843924
R2 0.517612
Median absolute error 65.843924
dtype: float64
```
### Using customized ML classifiers and regressors
By default, given a training set of instantes, MIPLearn trains a fixed set of ML classifiers and regressors, then selects the best one based on cross-validation performance. Alternatively, the user may specify which ML model a component should use through the `classifier` or `regressor` contructor parameters. Scikit-learn classifiers and regressors are currently supported. A future version of the package will add compatibility with Keras models.
The example below shows how to construct a `PrimalSolutionComponent` which internally uses scikit-learn's `KNeighborsClassifiers`. Any other scikit-learn classifier or pipeline can be used. It needs to be wrapped in `ScikitLearnClassifier` to ensure that all the proper data transformations are applied.
```python
from miplearn import PrimalSolutionComponent, ScikitLearnClassifier
from sklearn.neighbors import KNeighborsClassifier
comp = PrimalSolutionComponent(
classifier=ScikitLearnClassifier(
KNeighborsClassifier(n_neighbors=5),
),
)
comp.fit(train_instances)
```

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```{sectnum}
---
start: 2
depth: 2
suffix: .
---
```
Data Format
===========
Input Data Format
-----------------
Instances are specified by JSON files containing the following main sections:
* Parameters
* Buses
* Generators
* Price-sensitive loads
* Transmission lines
* Reserves
* Contingencies
Each section is described in detail below. For a complete example, see [case14](https://github.com/ANL-CEEESA/UnitCommitment.jl/tree/dev/instances/matpower/case14).
### Parameters
This section describes system-wide parameters, such as power balance penalties, optimization parameters, such as the length of the planning horizon and the time.
| Key | Description | Default | Time series?
| :----------------------------- | :------------------------------------------------ | :------: | :------------:
| `Time horizon (h)` | Length of the planning horizon (in hours). | Required | N
| `Time step (min)` | Length of each time step (in minutes). Must be a divisor of 60 (e.g. 60, 30, 20, 15, etc). | `60` | N
| `Power balance penalty ($/MW)` | Penalty for system-wide shortage or surplus in production (in $/MW). This is charged per time step. For example, if there is a shortage of 1 MW for three time steps, three times this amount will be charged. | `1000.0` | Y
#### Example
```json
{
"Parameters": {
"Time horizon (h)": 4,
"Power balance penalty ($/MW)": 1000.0
}
}
```
### Buses
This section describes the characteristics of each bus in the system.
| Key | Description | Default | Time series?
| :----------------- | :------------------------------------------------------------ | ------- | :-------------:
| `Load (MW)` | Fixed load connected to the bus (in MW). | Required | Y
#### Example
```json
{
"Buses": {
"b1": {
"Load (MW)": 0.0
},
"b2": {
"Load (MW)": [
26.01527,
24.46212,
23.29725,
22.90897
]
}
}
}
```
### Generators
This section describes all generators in the system, including thermal units, renewable units and virtual units.
| Key | Description | Default | Time series?
| :------------------------ | :------------------------------------------------| ------- | :-----------:
| `Bus` | Identifier of the bus where this generator is located (string). | Required | N
| `Production cost curve (MW)` and `Production cost curve ($)` | Parameters describing the piecewise-linear production costs. See below for more details. | Required | Y
| `Startup costs ($)` and `Startup delays (h)` | Parameters describing how much it costs to start the generator after it has been shut down for a certain amount of time. If `Startup costs ($)` and `Startup delays (h)` are set to `[300.0, 400.0]` and `[1, 4]`, for example, and the generator is shut down at time `00:00` (h:min), then it costs \$300 to start up the generator at any time between `01:00` and `03:59`, and \$400 to start the generator at time `04:00` or any time after that. The number of startup cost points is unlimited, and may be different for each generator. Startup delays must be strictly increasing and the first entry must equal `Minimum downtime (h)`. | `[0.0]` and `[1]` | N
| `Minimum uptime (h)` | Minimum amount of time the generator must stay operational after starting up (in hours). For example, if the generator starts up at time `00:00` (h:min) and `Minimum uptime (h)` is set to 4, then the generator can only shut down at time `04:00`. | `1` | N
| `Minimum downtime (h)` | Minimum amount of time the generator must stay offline after shutting down (in hours). For example, if the generator shuts down at time `00:00` (h:min) and `Minimum downtime (h)` is set to 4, then the generator can only start producing power again at time `04:00`. | `1` | N
| `Ramp up limit (MW)` | Maximum increase in production from one time step to the next (in MW). For example, if the generator is producing 100 MW at time step 1 and if this parameter is set to 40 MW, then the generator will produce at most 140 MW at time step 2. | `+inf` | N
| `Ramp down limit (MW)` | Maximum decrease in production from one time step to the next (in MW). For example, if the generator is producing 100 MW at time step 1 and this parameter is set to 40 MW, then the generator will produce at least 60 MW at time step 2. | `+inf` | N
| `Startup limit (MW)` | Maximum amount of power a generator can produce immediately after starting up (in MW). For example, if `Startup limit (MW)` is set to 100 MW and the unit is off at time step 1, then it may produce at most 100 MW at time step 2.| `+inf` | N
| `Shutdown limit (MW)` | Maximum amount of power a generator can produce immediately before shutting down (in MW). Specifically, the generator can only shut down at time step `t+1` if its production at time step `t` is below this limit. | `+inf` | N
| `Initial status (h)` | If set to a positive number, indicates the amount of time (in hours) the generator has been on at the beginning of the simulation, and if set to a negative number, the amount of time the generator has been off. For example, if `Initial status (h)` is `-2`, this means that the generator was off since `-02:00` (h:min). The simulation starts at time `00:00`. If `Initial status (h)` is `3`, this means that the generator was on since `-03:00`. A value of zero is not acceptable. | Required | N
| `Initial power (MW)` | Amount of power the generator at time step `-1`, immediately before the planning horizon starts. | Required | N
| `Must run?` | If `true`, the generator should be committed, even if that is not economical (Boolean). | `false` | Y
| `Provides spinning reserves?` | If `true`, this generator may provide spinning reserves (Boolean). | `true` | Y
#### Production costs and limits
Production costs are represented as piecewise-linear curves. Figure 1 shows an example cost curve with three segments, where it costs \$1400, \$1600, \$2200 and \$2400 to generate, respectively, 100, 110, 130 and 135 MW of power. To model this generator, `Production cost curve (MW)` should be set to `[100, 110, 130, 135]`, and `Production cost curve ($)` should be set to `[1400, 1600, 2200, 2400]`.
Note that this curve also specifies the production limits. Specifically, the first point identifies the minimum power output when the unit is operational, while the last point identifies the maximum power output.
<center>
<img src="../_static/cost_curve.png" style="max-width: 500px"/>
<div><b>Figure 1.</b> Piecewise-linear production cost curve.</div>
<br/>
</center>
#### Additional remarks:
* For time-dependent production limits or time-dependent production costs, the usage of nested arrays is allowed. For example, if `Production cost curve (MW)` is set to `[5.0, [10.0, 12.0, 15.0, 20.0]]`, then the unit may generate at most 10, 12, 15 and 20 MW of power during time steps 1, 2, 3 and 4, respectively. The minimum output for all time periods is fixed to at 5 MW.
* There is no limit to the number of piecewise-linear segments, and different generators may have a different number of segments.
* If `Production cost curve (MW)` and `Production cost curve ($)` both contain a single element, then the generator must produce exactly that amount of power when operational. To specify that the generator may produce any amount of power up to a certain limit `P`, the parameter `Production cost curve (MW)` should be set to `[0, P]`.
* Production cost curves must be convex.
#### Example
```json
{
"Generators": {
"gen1": {
"Bus": "b1",
"Production cost curve (MW)": [100.0, 110.0, 130.0, 135.0],
"Production cost curve ($)": [1400.0, 1600.0, 2200.0, 2400.0],
"Startup costs ($)": [300.0, 400.0],
"Startup delays (h)": [1, 4],
"Ramp up limit (MW)": 232.68,
"Ramp down limit (MW)": 232.68,
"Startup limit (MW)": 232.68,
"Shutdown limit (MW)": 232.68,
"Minimum downtime (h)": 4,
"Minimum uptime (h)": 4,
"Initial status (h)": 12,
"Must run?": false,
"Provides spinning reserves?": true,
},
"gen2": {
"Bus": "b5",
"Production cost curve (MW)": [0.0, [10.0, 8.0, 0.0, 3.0]],
"Production cost curve ($)": [0.0, 0.0],
"Provides spinning reserves?": true,
}
}
}
```
### Price-sensitive loads
This section describes components in the system which may increase or reduce their energy consumption according to the energy prices. Fixed loads (as described in the `buses` section) are always served, regardless of the price, unless there is significant congestion in the system or insufficient production capacity. Price-sensitive loads, on the other hand, are only served if it is economical to do so.
| Key | Description | Default | Time series?
| :---------------- | :------------------------------------------------ | :------: | :------------:
| `Bus` | Bus where the load is located. Multiple price-sensitive loads may be placed at the same bus. | Required | N
| `Revenue ($/MW)` | Revenue obtained for serving each MW of power to this load. | Required | Y
| `Demand (MW)` | Maximum amount of power required by this load. Any amount lower than this may be served. | Required | Y
#### Example
```json
{
"Price-sensitive loads": {
"p1": {
"Bus": "b3",
"Revenue ($/MW)": 23.0,
"Demand (MW)": 50.0
}
}
}
```
### Transmission Lines
This section describes the characteristics of transmission system, such as its topology and the susceptance of each transmission line.
| Key | Description | Default | Time series?
| :--------------------- | :----------------------------------------------- | ------- | :------------:
| `Source bus` | Identifier of the bus where the transmission line originates. | Required | N
| `Target bus` | Identifier of the bus where the transmission line reaches. | Required | N
| `Reactance (ohms)` | Reactance of the transmission line (in ohms). | Required | N
| `Susceptance (S)` | Susceptance of the transmission line (in siemens). | Required | N
| `Normal flow limit (MW)` | Maximum amount of power (in MW) allowed to flow through the line when the system is in its regular, fully-operational state. | `+inf` | Y
| `Emergency flow limit (MW)` | Maximum amount of power (in MW) allowed to flow through the line when the system is in degraded state (for example, after the failure of another transmission line). | `+inf` | Y
| `Flow limit penalty ($/MW)` | Penalty for violating the flow limits of the transmission line (in $/MW). This is charged per time step. For example, if there is a thermal violation of 1 MW for three time steps, then three times this amount will be charged. | `5000.0` | Y
#### Example
```json
{
"Transmission lines": {
"l1": {
"Source bus": "b1",
"Target bus": "b2",
"Reactance (ohms)": 0.05917,
"Susceptance (S)": 29.49686,
"Normal flow limit (MW)": 15000.0,
"Emergency flow limit (MW)": 20000.0,
"Flow limit penalty ($/MW)": 5000.0
}
}
}
```
### Reserves
This section describes the hourly amount of operating reserves required.
| Key | Description | Default | Time series?
| :-------------------- | :------------------------------------------------- | --------- | :----:
| `Spinning (MW)` | Minimum amount of system-wide spinning reserves (in MW). Only generators which are online may provide this reserve. | `0.0` | Y
#### Example
```json
{
"Reserves": {
"Spinning (MW)": [
57.30552,
53.88429,
51.31838,
50.46307
]
}
}
```
### Contingencies
This section describes credible contingency scenarios in the optimization, such as the loss of a transmission line or generator.
| Key | Description | Default
| :-------------------- | :----------------------------------------------- | ----------
| `Affected generators` | List of generators affected by this contingency. May be omitted if no generators are affected. | `[]`
| `Affected lines` | List of transmission lines affected by this contingency. May be omitted if no lines are affected. | `[]`
#### Example
```json
{
"Contingencies": {
"c1": {
"Affected lines": ["l1", "l2", "l3"],
"Affected generators": ["g1"]
},
"c2": {
"Affected lines": ["l4"]
},
}
}
```
### Additional remarks
#### Time series parameters
Many numerical properties in the JSON file can be specified either as a single floating point number if they are time-independent, or as an array containing exactly `T` elements, if they are time-dependent, where `T` is the number of time steps in the planning horizon. For example, both formats below are valid when `T=3`:
```json
{
"Load (MW)": 800.0,
"Load (MW)": [800.0, 850.0, 730.0]
}
```
The value `T` depends on both `Time horizon (h)` and `Time step (min)`, as the table below illustrates.
Time horizon (h) | Time step (min) | T
:---------------:|:---------------:|:----:
24 | 60 | 24
24 | 15 | 96
24 | 5 | 288
36 | 60 | 36
36 | 15 | 144
36 | 5 | 432
Output Data Format
------------------
The output data format is also JSON-based, but it is not currently documented since we expect it to change significantly in a future version of the package.
Current limitations
-------------------
* All reserves are system-wide. Zonal reserves are not currently supported.
* Network topology remains the same for all time periods
* Only N-1 transmission contingencies are supported. Generator contingencies are not currently supported.
* Time-varying minimum production amounts are not currently compatible with ramp/startup/shutdown limits.

@ -0,0 +1,72 @@
# UnitCommitment.jl
**UnitCommitment.jl** (UC.jl) is a Julia/JuMP optimization package for the Security-Constrained Unit Commitment Problem (SCUC), a fundamental optimization problem in power systems used, for example, to clear the day-ahead electricity markets. The package provides benchmark instances for the problem and Julia/JuMP implementations of state-of-the-art mixed-integer programming formulations.
### Package Components
* **Data Format:** The package proposes an extensible and fully-documented JSON-based data specification format for SCUC, developed in collaboration with Independent System Operators (ISOs), which describes the most important aspects of the problem. The format supports all the most common generator characteristics (including ramping, piecewise-linear production cost curves and time-dependent startup costs), as well as operating reserves, price-sensitive loads, transmission networks and contingencies.
* **Benchmark Instances:** The package provides a diverse collection of large-scale benchmark instances collected from the literature and extended to make them more challenging and realistic.
* **Model Implementation**: The package provides a Julia/JuMP implementation of state-of-the-art formulations and solution methods for SCUC. Our goal is to keep this implementation up-to-date, as new methods are proposed in the literature.
* **Benchmark Tools:** The package provides automated benchmark scripts to accurately evaluate the performance impact of proposed code changes.
### Authors
* **Alinson Santos Xavier** (Argonne National Laboratory)
* **Feng Qiu** (Argonne National Laboratory)
### Acknowledgments
* We would like to thank **Aleksandr M. Kazachkov** (University of Florida), **Yonghong Chen** (Midcontinent Independent System Operator), **Feng Pan** (Pacific Northwest National Laboratory) for valuable feedback on early versions of this package.
* 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
* Based upon work supported by the **U.S. Department of Energy Advanced Grid Modeling Program** under Grant DE-OE0000875.
### Citing
If you use UnitCommitment.jl in your research (that is, if you use either the provided instances files, the mathematical models, or the algorithms), we kindly request that you cite the package as follows:
* **Alinson S. Xavier, Feng Qiu**, "UnitCommitment.jl: A Julia/JuMP Optimization Package for Security-Constrained Unit Commitment". Zenodo (2020). [DOI: 10.5281/zenodo.4269874](https://doi.org/10.5281/zenodo.4269874).
If you use the instances, we additionally request that you cite the original sources, as described in the [instances page](instances.md).
### License
```text
UnitCommitment.jl: A Julia/JuMP Optimization Package for Security-Constrained Unit Commitment
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.
```
## Site contents
```{toctree}
---
maxdepth: 2
---
usage.md
format.md
instances.md
about.md
```

@ -0,0 +1,343 @@
```{sectnum}
---
start: 3
depth: 2
suffix: .
---
```
Instances
=========
UnitCommitment.jl provides a large collection of benchmark instances collected
from the literature and converted to a [common data format](format.md). In some cases, as indicated below, the original instances have been extended, with realistic parameters, using data-driven methods.
If you use these instances in your research, we request that you cite UnitCommitment.jl [UCJL], as well as the original sources.
Raw instances files are [available at our GitHub repository](https://github.com/ANL-CEEESA/UnitCommitment.jl/tree/dev/instances). Benchmark instances can also be loaded with
`UnitCommitment.read_benchmark(name)`, as explained in the [usage section](usage.md).
MATPOWER
--------
[MATPOWER](https://github.com/MATPOWER/matpower) is an open-source package for solving power flow problems in MATLAB and Octave. It contains a number of power flow test cases, which have been widely used in the power systems literature.
Because most MATPOWER test cases were originally designed for power flow studies, they lack a number of important unit commitment parameters, such as time-varying loads, production cost curves, ramp limits, reserves and initial conditions. The test cases included in UnitCommitment.jl are extended versions of the original MATPOWER test cases, modified as following:
* **Production cost** curves were generated using a data-driven approach, based on publicly available data. More specifically, machine learning models were trained to predict typical production cost curves, for each day of the year, based on a generator's maximum and minimum power output.
* **Load profiles** were generated using a similar data-driven approach.
* **Ramp-up, ramp-down, startup and shutdown rates** were set to a fixed proportion of the generator's maximum output.
* **Minimum reserves** were set to a fixed proportion of the total demand.
* **Contingencies** were set to include all N-1 transmission line contingencies that do not generate islands or isolated buses. More specifically, there is one contingency for each transmission line, as long as that transmission line is not a bridge in the network graph.
For each MATPOWER test case, UC.jl provides two variations (`2017-02-01` and `2017-08-01`) corresponding respectively to a winter and to a summer test case.
### MATPOWER/UW-PSTCA
A variety of smaller IEEE test cases, [compiled by University of Washington](http://labs.ece.uw.edu/pstca/), corresponding mostly to small portions of the American Electric Power System in the 1960s.
| Name | Buses | Generators | Lines | Contingencies | References |
|------|-------|------------|-------|---------------|--------|
| `matpower/case14/2017-02-01` | 14 | 5 | 20 | 19 | [MTPWR, PSTCA]
| `matpower/case14/2017-08-01` | 14 | 5 | 20 | 19 | [MTPWR, PSTCA]
| `matpower/case30/2017-02-01` | 30 | 6 | 41 | 38 | [MTPWR, PSTCA]
| `matpower/case30/2017-08-01` | 30 | 6 | 41 | 38 | [MTPWR, PSTCA]
| `matpower/case57/2017-02-01` | 57 | 7 | 80 | 79 | [MTPWR, PSTCA]
| `matpower/case57/2017-08-01` | 57 | 7 | 80 | 79 | [MTPWR, PSTCA]
| `matpower/case118/2017-02-01` | 118 | 54 | 186 | 177 | [MTPWR, PSTCA]
| `matpower/case118/2017-08-01` | 118 | 54 | 186 | 177 | [MTPWR, PSTCA]
| `matpower/case300/2017-02-01` | 300 | 69 | 411 | 320 | [MTPWR, PSTCA]
| `matpower/case300/2017-08-01` | 300 | 69 | 411 | 320 | [MTPWR, PSTCA]
### MATPOWER/Polish
Test cases based on the Polish 400, 220 and 110 kV networks, originally provided by **Roman Korab** (Politechnika Śląska) and corrected by the MATPOWER team.
| Name | Buses | Generators | Lines | Contingencies | References |
|------|-------|------------|-------|---------------|--------|
| `matpower/case2383wp/2017-02-01` | 2383 | 323 | 2896 | 2240 | [MTPWR]
| `matpower/case2383wp/2017-08-01` | 2383 | 323 | 2896 | 2240 | [MTPWR]
| `matpower/case2736sp/2017-02-01` | 2736 | 289 | 3504 | 3159 | [MTPWR]
| `matpower/case2736sp/2017-08-01` | 2736 | 289 | 3504 | 3159 | [MTPWR]
| `matpower/case2737sop/2017-02-01` | 2737 | 267 | 3506 | 3161 | [MTPWR]
| `matpower/case2737sop/2017-08-01` | 2737 | 267 | 3506 | 3161 | [MTPWR]
| `matpower/case2746wop/2017-02-01` | 2746 | 443 | 3514 | 3155 | [MTPWR]
| `matpower/case2746wop/2017-08-01` | 2746 | 443 | 3514 | 3155 | [MTPWR]
| `matpower/case2746wp/2017-02-01` | 2746 | 457 | 3514 | 3156 | [MTPWR]
| `matpower/case2746wp/2017-08-01` | 2746 | 457 | 3514 | 3156 | [MTPWR]
| `matpower/case3012wp/2017-02-01` | 3012 | 496 | 3572 | 2854 | [MTPWR]
| `matpower/case3012wp/2017-08-01` | 3012 | 496 | 3572 | 2854 | [MTPWR]
| `matpower/case3120sp/2017-02-01` | 3120 | 483 | 3693 | 2950 | [MTPWR]
| `matpower/case3120sp/2017-08-01` | 3120 | 483 | 3693 | 2950 | [MTPWR]
| `matpower/case3375wp/2017-02-01` | 3374 | 590 | 4161 | 3245 | [MTPWR]
| `matpower/case3375wp/2017-08-01` | 3374 | 590 | 4161 | 3245 | [MTPWR]
### MATPOWER/PEGASE
Test cases from the [Pan European Grid Advanced Simulation and State Estimation (PEGASE) project](https://cordis.europa.eu/project/id/211407), describing part of the European high voltage transmission network.
| Name | Buses | Generators | Lines | Contingencies | References |
|------|-------|------------|-------|---------------|--------|
| `matpower/case89pegase/2017-02-01` | 89 | 12 | 210 | 192 | [JoFlMa16, FlPaCa13, MTPWR]
| `matpower/case89pegase/2017-08-01` | 89 | 12 | 210 | 192 | [JoFlMa16, FlPaCa13, MTPWR]
| `matpower/case1354pegase/2017-02-01` | 1354 | 260 | 1991 | 1288 | [JoFlMa16, FlPaCa13, MTPWR]
| `matpower/case1354pegase/2017-08-01` | 1354 | 260 | 1991 | 1288 | [JoFlMa16, FlPaCa13, MTPWR]
| `matpower/case2869pegase/2017-02-01` | 2869 | 510 | 4582 | 3579 | [JoFlMa16, FlPaCa13, MTPWR]
| `matpower/case2869pegase/2017-08-01` | 2869 | 510 | 4582 | 3579 | [JoFlMa16, FlPaCa13, MTPWR]
| `matpower/case9241pegase/2017-02-01` | 9241 | 1445 | 16049 | 13932 | [JoFlMa16, FlPaCa13, MTPWR]
| `matpower/case9241pegase/2017-08-01` | 9241 | 1445 | 16049 | 13932 | [JoFlMa16, FlPaCa13, MTPWR]
| `matpower/case13659pegase/2017-02-01` | 13659 | 4092 | 20467 | 13932 | [JoFlMa16, FlPaCa13, MTPWR]
| `matpower/case13659pegase/2017-08-01` | 13659 | 4092 | 20467 | 13932 | [JoFlMa16, FlPaCa13, MTPWR]
### MATPOWER/RTE
Test cases from the R&D Division at [Reseau de Transport d'Electricite](https://www.rte-france.com) representing the size and complexity of the French very high voltage transmission network.
| Name | Buses | Generators | Lines | Contingencies | References |
|------|-------|------------|-------|---------------|--------|
| `matpower/case1888rte/2017-02-01` | 1888 | 296 | 2531 | 1484 | [MTPWR, JoFlMa16]
| `matpower/case1888rte/2017-08-01` | 1888 | 296 | 2531 | 1484 | [MTPWR, JoFlMa16]
| `matpower/case1951rte/2017-02-01` | 1951 | 390 | 2596 | 1497 | [MTPWR, JoFlMa16]
| `matpower/case1951rte/2017-08-01` | 1951 | 390 | 2596 | 1497 | [MTPWR, JoFlMa16]
| `matpower/case2848rte/2017-02-01` | 2848 | 544 | 3776 | 2242 | [MTPWR, JoFlMa16]
| `matpower/case2848rte/2017-08-01` | 2848 | 544 | 3776 | 2242 | [MTPWR, JoFlMa16]
| `matpower/case2868rte/2017-02-01` | 2868 | 596 | 3808 | 2260 | [MTPWR, JoFlMa16]
| `matpower/case2868rte/2017-08-01` | 2868 | 596 | 3808 | 2260 | [MTPWR, JoFlMa16]
| `matpower/case6468rte/2017-02-01` | 6468 | 1262 | 9000 | 6094 | [MTPWR, JoFlMa16]
| `matpower/case6468rte/2017-08-01` | 6468 | 1262 | 9000 | 6094 | [MTPWR, JoFlMa16]
| `matpower/case6470rte/2017-02-01` | 6470 | 1306 | 9005 | 6085 | [MTPWR, JoFlMa16]
| `matpower/case6470rte/2017-08-01` | 6470 | 1306 | 9005 | 6085 | [MTPWR, JoFlMa16]
| `matpower/case6495rte/2017-02-01` | 6495 | 1352 | 9019 | 6060 | [MTPWR, JoFlMa16]
| `matpower/case6495rte/2017-08-01` | 6495 | 1352 | 9019 | 6060 | [MTPWR, JoFlMa16]
| `matpower/case6515rte/2017-02-01` | 6515 | 1368 | 9037 | 6063 | [MTPWR, JoFlMa16]
| `matpower/case6515rte/2017-08-01` | 6515 | 1368 | 9037 | 6063 | [MTPWR, JoFlMa16]
PGLIB-UC Instances
------------------
[PGLIB-UC](https://github.com/power-grid-lib/pglib-uc) is a benchmark library curated and maintained by the [IEEE PES Task Force on Benchmarks for Validation of Emerging Power System Algorithms](https://power-grid-lib.github.io/). These test cases have been used in [KnOsWa20].
### PGLIB-UC/California
Test cases based on publicly available data from the California ISO. For more details, see [PGLIB-UC case file overview](https://github.com/power-grid-lib/pglib-uc).
| Name | Buses | Generators | Lines | Contingencies | References |
|------|-------|------------|-------|---------------|--------|
| `pglib-uc/ca/2014-09-01_reserves_0` | 1 | 610 | 0 | 0 | [KnOsWa20]
| `pglib-uc/ca/2014-09-01_reserves_1` | 1 | 610 | 0 | 0 | [KnOsWa20]
| `pglib-uc/ca/2014-09-01_reserves_3` | 1 | 610 | 0 | 0 | [KnOsWa20]
| `pglib-uc/ca/2014-09-01_reserves_5` | 1 | 610 | 0 | 0 | [KnOsWa20]
| `pglib-uc/ca/2014-12-01_reserves_0` | 1 | 610 | 0 | 0 | [KnOsWa20]
| `pglib-uc/ca/2014-12-01_reserves_1` | 1 | 610 | 0 | 0 | [KnOsWa20]
| `pglib-uc/ca/2014-12-01_reserves_3` | 1 | 610 | 0 | 0 | [KnOsWa20]
| `pglib-uc/ca/2014-12-01_reserves_5` | 1 | 610 | 0 | 0 | [KnOsWa20]
| `pglib-uc/ca/2015-03-01_reserves_0` | 1 | 610 | 0 | 0 | [KnOsWa20]
| `pglib-uc/ca/2015-03-01_reserves_1` | 1 | 610 | 0 | 0 | [KnOsWa20]
| `pglib-uc/ca/2015-03-01_reserves_3` | 1 | 610 | 0 | 0 | [KnOsWa20]
| `pglib-uc/ca/2015-03-01_reserves_5` | 1 | 610 | 0 | 0 | [KnOsWa20]
| `pglib-uc/ca/2015-06-01_reserves_0` | 1 | 610 | 0 | 0 | [KnOsWa20]
| `pglib-uc/ca/2015-06-01_reserves_1` | 1 | 610 | 0 | 0 | [KnOsWa20]
| `pglib-uc/ca/2015-06-01_reserves_3` | 1 | 610 | 0 | 0 | [KnOsWa20]
| `pglib-uc/ca/2015-06-01_reserves_5` | 1 | 610 | 0 | 0 | [KnOsWa20]
| `pglib-uc/ca/Scenario400_reserves_0` | 1 | 611 | 0 | 0 | [KnOsWa20]
| `pglib-uc/ca/Scenario400_reserves_1` | 1 | 611 | 0 | 0 | [KnOsWa20]
| `pglib-uc/ca/Scenario400_reserves_3` | 1 | 611 | 0 | 0 | [KnOsWa20]
| `pglib-uc/ca/Scenario400_reserves_5` | 1 | 611 | 0 | 0 | [KnOsWa20]
### PGLIB-UC/FERC
Test cases based on a publicly available [unit commitment test case produced by the Federal Energy Regulatory Commission](https://www.ferc.gov/industries-data/electric/power-sales-and-markets/increasing-efficiency-through-improved-software-1). For more details, see [PGLIB-UC case file overview](https://github.com/power-grid-lib/pglib-uc).
| Name | Buses | Generators | Lines | Contingencies | References |
|------|-------|------------|-------|---------------|--------|
| `pglib-uc/ferc/2015-01-01_hw` | 1 | 935 | 0 | 0 | [KnOsWa20, KrHiOn12]
| `pglib-uc/ferc/2015-01-01_lw` | 1 | 935 | 0 | 0 | [KnOsWa20, KrHiOn12]
| `pglib-uc/ferc/2015-02-01_hw` | 1 | 935 | 0 | 0 | [KnOsWa20, KrHiOn12]
| `pglib-uc/ferc/2015-02-01_lw` | 1 | 935 | 0 | 0 | [KnOsWa20, KrHiOn12]
| `pglib-uc/ferc/2015-03-01_hw` | 1 | 935 | 0 | 0 | [KnOsWa20, KrHiOn12]
| `pglib-uc/ferc/2015-03-01_lw` | 1 | 935 | 0 | 0 | [KnOsWa20, KrHiOn12]
| `pglib-uc/ferc/2015-04-01_hw` | 1 | 979 | 0 | 0 | [KnOsWa20, KrHiOn12]
| `pglib-uc/ferc/2015-04-01_lw` | 1 | 979 | 0 | 0 | [KnOsWa20, KrHiOn12]
| `pglib-uc/ferc/2015-05-01_hw` | 1 | 979 | 0 | 0 | [KnOsWa20, KrHiOn12]
| `pglib-uc/ferc/2015-05-01_lw` | 1 | 979 | 0 | 0 | [KnOsWa20, KrHiOn12]
| `pglib-uc/ferc/2015-06-01_hw` | 1 | 979 | 0 | 0 | [KnOsWa20, KrHiOn12]
| `pglib-uc/ferc/2015-06-01_lw` | 1 | 979 | 0 | 0 | [KnOsWa20, KrHiOn12]
| `pglib-uc/ferc/2015-07-01_hw` | 1 | 979 | 0 | 0 | [KnOsWa20, KrHiOn12]
| `pglib-uc/ferc/2015-07-01_lw` | 1 | 979 | 0 | 0 | [KnOsWa20, KrHiOn12]
| `pglib-uc/ferc/2015-08-01_hw` | 1 | 979 | 0 | 0 | [KnOsWa20, KrHiOn12]
| `pglib-uc/ferc/2015-08-01_lw` | 1 | 979 | 0 | 0 | [KnOsWa20, KrHiOn12]
| `pglib-uc/ferc/2015-09-01_hw` | 1 | 979 | 0 | 0 | [KnOsWa20, KrHiOn12]
| `pglib-uc/ferc/2015-09-01_lw` | 1 | 979 | 0 | 0 | [KnOsWa20, KrHiOn12]
| `pglib-uc/ferc/2015-10-01_hw` | 1 | 935 | 0 | 0 | [KnOsWa20, KrHiOn12]
| `pglib-uc/ferc/2015-10-01_lw` | 1 | 935 | 0 | 0 | [KnOsWa20, KrHiOn12]
| `pglib-uc/ferc/2015-11-02_hw` | 1 | 935 | 0 | 0 | [KnOsWa20, KrHiOn12]
| `pglib-uc/ferc/2015-11-02_lw` | 1 | 935 | 0 | 0 | [KnOsWa20, KrHiOn12]
| `pglib-uc/ferc/2015-12-01_hw` | 1 | 935 | 0 | 0 | [KnOsWa20, KrHiOn12]
| `pglib-uc/ferc/2015-12-01_lw` | 1 | 935 | 0 | 0 | [KnOsWa20, KrHiOn12]
### PGLIB-UC/RTS-GMLC
[RTS-GMLC](https://github.com/GridMod/RTS-GMLC) is an updated version of the RTS-96 test system produced by the United States Department of Energy's [Grid Modernization Laboratory Consortium](https://gmlc.doe.gov/). The PGLIB-UC/RTS-GMLC instances are modified versions of the original RTS-GMLC instances, with modified ramp-rates and without a transmission network. For more details, see [PGLIB-UC case file overview](https://github.com/power-grid-lib/pglib-uc).
| Name | Buses | Generators | Lines | Contingencies | References |
|------|-------|------------|-------|---------------|--------|
| `pglib-uc/rts_gmlc/2020-01-27` | 1 | 154 | 0 | 0 | [BaBlEh19]
| `pglib-uc/rts_gmlc/2020-02-09` | 1 | 154 | 0 | 0 | [BaBlEh19]
| `pglib-uc/rts_gmlc/2020-03-05` | 1 | 154 | 0 | 0 | [BaBlEh19]
| `pglib-uc/rts_gmlc/2020-04-03` | 1 | 154 | 0 | 0 | [BaBlEh19]
| `pglib-uc/rts_gmlc/2020-05-05` | 1 | 154 | 0 | 0 | [BaBlEh19]
| `pglib-uc/rts_gmlc/2020-06-09` | 1 | 154 | 0 | 0 | [BaBlEh19]
| `pglib-uc/rts_gmlc/2020-07-06` | 1 | 154 | 0 | 0 | [BaBlEh19]
| `pglib-uc/rts_gmlc/2020-08-12` | 1 | 154 | 0 | 0 | [BaBlEh19]
| `pglib-uc/rts_gmlc/2020-09-20` | 1 | 154 | 0 | 0 | [BaBlEh19]
| `pglib-uc/rts_gmlc/2020-10-27` | 1 | 154 | 0 | 0 | [BaBlEh19]
| `pglib-uc/rts_gmlc/2020-11-25` | 1 | 154 | 0 | 0 | [BaBlEh19]
| `pglib-uc/rts_gmlc/2020-12-23` | 1 | 154 | 0 | 0 | [BaBlEh19]
OR-LIB/UC
---------
[OR-LIB](http://people.brunel.ac.uk/~mastjjb/jeb/info.html) is a collection of test data sets for a variety of operations research problems, including unit commitment. The UC instances in OR-LIB are synthetic instances generated by a [random problem generator](http://groups.di.unipi.it/optimize/Data/UC.html) developed by the [Operations Research Group at University of Pisa](http://groups.di.unipi.it/optimize/). These test cases have been used in [FrGe06] and many other publications.
| Name | Hours | Buses | Generators | Lines | Contingencies | References |
|------|-------|-------|------------|-------|---------------|------------|
| `or-lib/10_0_1_w` | 24 | 1 | 10 | 0 | 0 | [ORLIB, FrGe06]
| `or-lib/10_0_2_w` | 24 | 1 | 10 | 0 | 0 | [ORLIB, FrGe06]
| `or-lib/10_0_3_w` | 24 | 1 | 10 | 0 | 0 | [ORLIB, FrGe06]
| `or-lib/10_0_4_w` | 24 | 1 | 10 | 0 | 0 | [ORLIB, FrGe06]
| `or-lib/10_0_5_w` | 24 | 1 | 10 | 0 | 0 | [ORLIB, FrGe06]
| `or-lib/20_0_1_w` | 24 | 1 | 20 | 0 | 0 | [ORLIB, FrGe06]
| `or-lib/20_0_2_w` | 24 | 1 | 20 | 0 | 0 | [ORLIB, FrGe06]
| `or-lib/20_0_3_w` | 24 | 1 | 20 | 0 | 0 | [ORLIB, FrGe06]
| `or-lib/20_0_4_w` | 24 | 1 | 20 | 0 | 0 | [ORLIB, FrGe06]
| `or-lib/20_0_5_w` | 24 | 1 | 20 | 0 | 0 | [ORLIB, FrGe06]
| `or-lib/50_0_1_w` | 24 | 1 | 50 | 0 | 0 | [ORLIB, FrGe06]
| `or-lib/50_0_2_w` | 24 | 1 | 50 | 0 | 0 | [ORLIB, FrGe06]
| `or-lib/50_0_3_w` | 24 | 1 | 50 | 0 | 0 | [ORLIB, FrGe06]
| `or-lib/50_0_4_w` | 24 | 1 | 50 | 0 | 0 | [ORLIB, FrGe06]
| `or-lib/50_0_5_w` | 24 | 1 | 50 | 0 | 0 | [ORLIB, FrGe06]
| `or-lib/75_0_1_w` | 24 | 1 | 75 | 0 | 0 | [ORLIB, FrGe06]
| `or-lib/75_0_2_w` | 24 | 1 | 75 | 0 | 0 | [ORLIB, FrGe06]
| `or-lib/75_0_3_w` | 24 | 1 | 75 | 0 | 0 | [ORLIB, FrGe06]
| `or-lib/75_0_4_w` | 24 | 1 | 75 | 0 | 0 | [ORLIB, FrGe06]
| `or-lib/75_0_5_w` | 24 | 1 | 75 | 0 | 0 | [ORLIB, FrGe06]
| `or-lib/100_0_1_w` | 24 | 1 | 100 | 0 | 0 | [ORLIB, FrGe06]
| `or-lib/100_0_2_w` | 24 | 1 | 100 | 0 | 0 | [ORLIB, FrGe06]
| `or-lib/100_0_3_w` | 24 | 1 | 100 | 0 | 0 | [ORLIB, FrGe06]
| `or-lib/100_0_4_w` | 24 | 1 | 100 | 0 | 0 | [ORLIB, FrGe06]
| `or-lib/100_0_5_w` | 24 | 1 | 100 | 0 | 0 | [ORLIB, FrGe06]
| `or-lib/150_0_1_w` | 24 | 1 | 150 | 0 | 0 | [ORLIB, FrGe06]
| `or-lib/150_0_2_w` | 24 | 1 | 150 | 0 | 0 | [ORLIB, FrGe06]
| `or-lib/150_0_3_w` | 24 | 1 | 150 | 0 | 0 | [ORLIB, FrGe06]
| `or-lib/150_0_4_w` | 24 | 1 | 150 | 0 | 0 | [ORLIB, FrGe06]
| `or-lib/150_0_5_w` | 24 | 1 | 150 | 0 | 0 | [ORLIB, FrGe06]
| `or-lib/200_0_10_w` | 24 | 1 | 200 | 0 | 0 | [ORLIB, FrGe06]
| `or-lib/200_0_11_w` | 24 | 1 | 200 | 0 | 0 | [ORLIB, FrGe06]
| `or-lib/200_0_12_w` | 24 | 1 | 200 | 0 | 0 | [ORLIB, FrGe06]
| `or-lib/200_0_1_w` | 24 | 1 | 200 | 0 | 0 | [ORLIB, FrGe06]
| `or-lib/200_0_2_w` | 24 | 1 | 200 | 0 | 0 | [ORLIB, FrGe06]
| `or-lib/200_0_3_w` | 24 | 1 | 200 | 0 | 0 | [ORLIB, FrGe06]
| `or-lib/200_0_4_w` | 24 | 1 | 200 | 0 | 0 | [ORLIB, FrGe06]
| `or-lib/200_0_5_w` | 24 | 1 | 200 | 0 | 0 | [ORLIB, FrGe06]
| `or-lib/200_0_6_w` | 24 | 1 | 200 | 0 | 0 | [ORLIB, FrGe06]
| `or-lib/200_0_7_w` | 24 | 1 | 200 | 0 | 0 | [ORLIB, FrGe06]
| `or-lib/200_0_8_w` | 24 | 1 | 200 | 0 | 0 | [ORLIB, FrGe06]
| `or-lib/200_0_9_w` | 24 | 1 | 200 | 0 | 0 | [ORLIB, FrGe06]
Tejada19
--------
Test cases used in [TeLuSa19]. These instances are similar to OR-LIB/UC, in the sense that they use the same random problem generator, but are much larger.
| Name | Hours | Buses | Generators | Lines | Contingencies | References |
|------|-------|-------|------------|-------|---------------|------------|
| `tejada19/UC_24h_214g` | 24 | 1 | 214 | 0 | 0 | [TeLuSa19]
| `tejada19/UC_24h_250g` | 24 | 1 | 250 | 0 | 0 | [TeLuSa19]
| `tejada19/UC_24h_290g` | 24 | 1 | 290 | 0 | 0 | [TeLuSa19]
| `tejada19/UC_24h_480g` | 24 | 1 | 480 | 0 | 0 | [TeLuSa19]
| `tejada19/UC_24h_505g` | 24 | 1 | 505 | 0 | 0 | [TeLuSa19]
| `tejada19/UC_24h_623g` | 24 | 1 | 623 | 0 | 0 | [TeLuSa19]
| `tejada19/UC_24h_647g` | 24 | 1 | 647 | 0 | 0 | [TeLuSa19]
| `tejada19/UC_24h_836g` | 24 | 1 | 836 | 0 | 0 | [TeLuSa19]
| `tejada19/UC_24h_850g` | 24 | 1 | 850 | 0 | 0 | [TeLuSa19]
| `tejada19/UC_24h_918g` | 24 | 1 | 918 | 0 | 0 | [TeLuSa19]
| `tejada19/UC_24h_931g` | 24 | 1 | 931 | 0 | 0 | [TeLuSa19]
| `tejada19/UC_24h_940g` | 24 | 1 | 940 | 0 | 0 | [TeLuSa19]
| `tejada19/UC_24h_957g` | 24 | 1 | 957 | 0 | 0 | [TeLuSa19]
| `tejada19/UC_24h_959g` | 24 | 1 | 959 | 0 | 0 | [TeLuSa19]
| `tejada19/UC_24h_1069g` | 24 | 1 | 1069 | 0 | 0 | [TeLuSa19]
| `tejada19/UC_24h_1130g` | 24 | 1 | 1130 | 0 | 0 | [TeLuSa19]
| `tejada19/UC_24h_1376g` | 24 | 1 | 1376 | 0 | 0 | [TeLuSa19]
| `tejada19/UC_24h_1393g` | 24 | 1 | 1393 | 0 | 0 | [TeLuSa19]
| `tejada19/UC_24h_1577g` | 24 | 1 | 1577 | 0 | 0 | [TeLuSa19]
| `tejada19/UC_24h_1615g` | 24 | 1 | 1615 | 0 | 0 | [TeLuSa19]
| `tejada19/UC_24h_1632g` | 24 | 1 | 1632 | 0 | 0 | [TeLuSa19]
| `tejada19/UC_24h_1768g` | 24 | 1 | 1768 | 0 | 0 | [TeLuSa19]
| `tejada19/UC_24h_1804g` | 24 | 1 | 1804 | 0 | 0 | [TeLuSa19]
| `tejada19/UC_24h_1820g` | 24 | 1 | 1820 | 0 | 0 | [TeLuSa19]
| `tejada19/UC_24h_1823g` | 24 | 1 | 1823 | 0 | 0 | [TeLuSa19]
| `tejada19/UC_24h_1888g` | 24 | 1 | 1888 | 0 | 0 | [TeLuSa19]
| `tejada19/UC_168h_36g` | 168 | 1 | 36 | 0 | 0 | [TeLuSa19]
| `tejada19/UC_168h_38g` | 168 | 1 | 38 | 0 | 0 | [TeLuSa19]
| `tejada19/UC_168h_40g` | 168 | 1 | 40 | 0 | 0 | [TeLuSa19]
| `tejada19/UC_168h_53g` | 168 | 1 | 53 | 0 | 0 | [TeLuSa19]
| `tejada19/UC_168h_58g` | 168 | 1 | 58 | 0 | 0 | [TeLuSa19]
| `tejada19/UC_168h_59g` | 168 | 1 | 59 | 0 | 0 | [TeLuSa19]
| `tejada19/UC_168h_72g` | 168 | 1 | 72 | 0 | 0 | [TeLuSa19]
| `tejada19/UC_168h_84g` | 168 | 1 | 84 | 0 | 0 | [TeLuSa19]
| `tejada19/UC_168h_86g` | 168 | 1 | 86 | 0 | 0 | [TeLuSa19]
| `tejada19/UC_168h_88g` | 168 | 1 | 88 | 0 | 0 | [TeLuSa19]
| `tejada19/UC_168h_93g` | 168 | 1 | 93 | 0 | 0 | [TeLuSa19]
| `tejada19/UC_168h_105g` | 168 | 1 | 105 | 0 | 0 | [TeLuSa19]
| `tejada19/UC_168h_110g` | 168 | 1 | 110 | 0 | 0 | [TeLuSa19]
| `tejada19/UC_168h_125g` | 168 | 1 | 125 | 0 | 0 | [TeLuSa19]
| `tejada19/UC_168h_130g` | 168 | 1 | 130 | 0 | 0 | [TeLuSa19]
| `tejada19/UC_168h_131g` | 168 | 1 | 131 | 0 | 0 | [TeLuSa19]
| `tejada19/UC_168h_140g` | 168 | 1 | 140 | 0 | 0 | [TeLuSa19]
| `tejada19/UC_168h_165g` | 168 | 1 | 165 | 0 | 0 | [TeLuSa19]
| `tejada19/UC_168h_175g` | 168 | 1 | 175 | 0 | 0 | [TeLuSa19]
| `tejada19/UC_168h_179g` | 168 | 1 | 179 | 0 | 0 | [TeLuSa19]
| `tejada19/UC_168h_188g` | 168 | 1 | 188 | 0 | 0 | [TeLuSa19]
| `tejada19/UC_168h_192g` | 168 | 1 | 192 | 0 | 0 | [TeLuSa19]
| `tejada19/UC_168h_199g` | 168 | 1 | 199 | 0 | 0 | [TeLuSa19]
References
----------
* [UCJL] **Alinson S. Xavier, Feng Qiu.** "UnitCommitment.jl: A Julia/JuMP Optimization Package for Security-Constrained Unit Commitment". Zenodo (2020). [DOI: 10.5281/zenodo.4269874](https://doi.org/10.5281/zenodo.4269874)
* [KnOsWa20] **Bernard Knueven, James Ostrowski and Jean-Paul Watson.** "On Mixed-Integer Programming Formulations for the Unit Commitment Problem". INFORMS Journal on Computing (2020). [DOI: 10.1287/ijoc.2019.0944](https://doi.org/10.1287/ijoc.2019.0944)
* [KrHiOn12] **Eric Krall, Michael Higgins and Richard P. ONeill.** "RTO unit commitment test system." Federal Energy Regulatory Commission. Available at: <https://www.ferc.gov/industries-data/electric/power-sales-and-markets/increasing-efficiency-through-improved-software-1> (Accessed: Nov 14, 2020)
* [BaBlEh19] **Clayton Barrows, Aaron Bloom, Ali Ehlen, Jussi Ikaheimo, Jennie Jorgenson, Dheepak Krishnamurthy, Jessica Lau et al.** "The IEEE Reliability Test System: A Proposed 2019 Update." IEEE Transactions on Power Systems (2019). [DOI: 10.1109/TPWRS.2019.2925557](https://doi.org/10.1109/TPWRS.2019.2925557)
* [JoFlMa16] **C. Josz, S. Fliscounakis, J. Maeght, and P. Panciatici.** "AC Power Flow
Data in MATPOWER and QCQP Format: iTesla, RTE Snapshots, and PEGASE". [ArXiv (2016)](https://arxiv.org/abs/1603.01533).
* [FlPaCa13] **S. Fliscounakis, P. Panciatici, F. Capitanescu, and L. Wehenkel.**
"Contingency ranking with respect to overloads in very large power
systems taking into account uncertainty, preventive and corrective
actions", Power Systems, IEEE Trans. on, (28)4:4909-4917, 2013.
[DOI: 10.1109/TPWRS.2013.2251015](https://doi.org/10.1109/TPWRS.2013.2251015)
* [MTPWR] **D. Zimmerman, C. E. Murillo-Sandnchez and R. J. Thomas.** "Matpower: Steady-state operations, planning, and analysis tools forpower systems research and education", IEEE Transactions on PowerSystems, vol. 26, no. 1, pp. 12 19, Feb. 2011. [DOI: 10.1109/TPWRS.2010.2051168](https://doi.org/10.1109/TPWRS.2010.2051168)
* [PSTCA] **University of Washington, Dept. of Electrical Engineering.** "Power Systems Test Case Archive". Available at: <http://www.ee.washington.edu/research/pstca/> (Accessed: Nov 14, 2020)
* [ORLIB] **J.E.Beasley.** "OR-Library: distributing test problems by electronic mail", Journal of the Operational Research Society 41(11) (1990). [DOI: 10.2307/2582903](https://doi.org/10.2307/2582903)
* [FrGe06] **A. Frangioni, C. Gentile.** "Solving nonlinear single-unit commitment problems with ramping constraints" Operations Research 54(4), p. 767 - 775, 2006. [DOI: 10.1287/opre.1060.0309](https://doi.org/10.1287/opre.1060.0309)
* [TeLuSa19] **D. A. Tejada-Arango, S. Lumbreras, P. Sanchez-Martin and A. Ramos.** "Which Unit-Commitment Formulation is Best? A Systematic Comparison," in IEEE Transactions on Power Systems. [DOI: 10.1109/TPWRS.2019.2962024](https://ieeexplore.ieee.org/document/8941313/).

@ -0,0 +1,120 @@
```{sectnum}
---
start: 1
depth: 2
suffix: .
---
```
Usage
=====
Installation
------------
UnitCommitment.jl was tested and developed with [Julia 1.6](https://julialang.org/). To install Julia, please follow the [installation guide on the official Julia website](https://julialang.org/downloads/platform.html). To install UnitCommitment.jl, run the Julia interpreter, type `]` to open the package manager, then type:
```text
pkg> add UnitCommitment@0.2
```
To test that the package has been correctly installed, run:
```text
pkg> test UnitCommitment
```
If all tests pass, the package should now be ready to be used by any Julia script on the machine.
To solve the optimization models, a mixed-integer linear programming (MILP) solver is also required. Please see the [JuMP installation guide](https://jump.dev/JuMP.jl/stable/installation/) for more instructions on installing a solver. Typical open-source choices are [Cbc](https://github.com/JuliaOpt/Cbc.jl) and [GLPK](https://github.com/JuliaOpt/GLPK.jl). In the instructions below, Cbc will be used, but any other MILP solver listed in JuMP installation guide should also be compatible.
Typical Usage
-------------
### Solving user-provided instances
The first step to use UC.jl is to construct a JSON file describing your unit commitment instance. See the [data format page]() for a complete description of the data format UC.jl expects. The next steps, as shown below, are to read the instance from file, construct the optimization model, run the optimization and extract the optimal solution.
```julia
using Cbc
using JSON
using UnitCommitment
# Read instance
instance = UnitCommitment.read("/path/to/input.json")
# Construct optimization model
model = UnitCommitment.build_model(
instance=instance,
optimizer=Cbc.Optimizer,
)
# Solve model
UnitCommitment.optimize!(model)
# Extract solution and write it to a file
solution = UnitCommitment.get_solution(model)
open("/path/to/output.json", "w") do file
JSON.print(file, solution, 2)
end
```
### Solving benchmark instances
As described in the [Instances page](instances.md), UnitCommitment.jl contains a number of benchmark instances collected from the literature. To solve one of these instances individually, instead of constructing your own, the function `read_benchmark` can be used:
```julia
using UnitCommitment
instance = UnitCommitment.read_benchmark("matpower/case3375wp/2017-02-01")
```
Advanced usage
--------------
### Modifying the formulation
For the time being, the recommended way of modifying the MILP formulation used by UC.jl is to create a local copy of our git repository and directly modify the source code of the package. In a future version, it will be possible to switch between multiple formulations, or to simply add/remove constraints after the model has been generated.
### Generating initial conditions
When creating random unit commitment instances for benchmark purposes, it is often hard to compute, in advance, sensible initial conditions for all generators. Setting initial conditions naively (for example, making all generators initially off and producing no power) can easily cause the instance to become infeasible due to excessive ramping. Initial conditions can also make it hard to modify existing instances. For example, increasing the system load without carefully modifying the initial conditions may make the problem infeasible or unrealistically challenging to solve.
To help with this issue, UC.jl provides a utility function which can generate feasible initial conditions by solving a single-period optimization problem, as shown below:
```julia
using Cbc
using UnitCommitment
# Read original instance
instance = UnitCommitment.read("instance.json")
# Generate initial conditions (in-place)
UnitCommitment.generate_initial_conditions!(instance, Cbc.Optimizer)
# Construct and solve optimization model
model = UnitCommitment.build_model(instance, Cbc.Optimizer)
UnitCommitment.optimize!(model)
```
```{warning}
The function `generate_initial_conditions!` may return different initial conditions after each call, even if the same instance and the same optimizer is provided. The particular algorithm may also change in a future version of UC.jl. For these reasons, it is recommended that you generate initial conditions exactly once for each instance and store them for later use.
```
### Verifying solutions
When developing new formulations, it is very easy to introduce subtle errors in the model that result in incorrect solutions. To help with this, UC.jl includes a utility function that verifies if a given solution is feasible, and, if not, prints all the validation errors it found. The implementation of this function is completely independent from the implementation of the optimization model, and therefore can be used to validate it. The function can also be used to verify solutions produced by other optimization packages, as long as they follow the [UC.jl data format](format.md).
```julia
using JSON
using UnitCommitment
# Read instance
instance = UnitCommitment.read("instance.json")
# Read solution (potentially produced by other packages)
solution = JSON.parsefile("solution.json")
# Validate solution and print validation errors
UnitCommitment.validate(instance, solution)
```

@ -0,0 +1,861 @@
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margin-bottom: 0;
list-style-type: none;
}
table.indextable > tbody > tr > td > ul {
padding-left: 0em;
}
table.indextable tr.pcap {
height: 10px;
}
table.indextable tr.cap {
margin-top: 10px;
background-color: #f2f2f2;
}
img.toggler {
margin-right: 3px;
margin-top: 3px;
cursor: pointer;
}
div.modindex-jumpbox {
border-top: 1px solid #ddd;
border-bottom: 1px solid #ddd;
margin: 1em 0 1em 0;
padding: 0.4em;
}
div.genindex-jumpbox {
border-top: 1px solid #ddd;
border-bottom: 1px solid #ddd;
margin: 1em 0 1em 0;
padding: 0.4em;
}
/* -- domain module index --------------------------------------------------- */
table.modindextable td {
padding: 2px;
border-collapse: collapse;
}
/* -- general body styles --------------------------------------------------- */
div.body {
min-width: 450px;
max-width: 800px;
}
div.body p, div.body dd, div.body li, div.body blockquote {
-moz-hyphens: auto;
-ms-hyphens: auto;
-webkit-hyphens: auto;
hyphens: auto;
}
a.headerlink {
visibility: hidden;
}
a.brackets:before,
span.brackets > a:before{
content: "[";
}
a.brackets:after,
span.brackets > a:after {
content: "]";
}
h1:hover > a.headerlink,
h2:hover > a.headerlink,
h3:hover > a.headerlink,
h4:hover > a.headerlink,
h5:hover > a.headerlink,
h6:hover > a.headerlink,
dt:hover > a.headerlink,
caption:hover > a.headerlink,
p.caption:hover > a.headerlink,
div.code-block-caption:hover > a.headerlink {
visibility: visible;
}
div.body p.caption {
text-align: inherit;
}
div.body td {
text-align: left;
}
.first {
margin-top: 0 !important;
}
p.rubric {
margin-top: 30px;
font-weight: bold;
}
img.align-left, figure.align-left, .figure.align-left, object.align-left {
clear: left;
float: left;
margin-right: 1em;
}
img.align-right, figure.align-right, .figure.align-right, object.align-right {
clear: right;
float: right;
margin-left: 1em;
}
img.align-center, figure.align-center, .figure.align-center, object.align-center {
display: block;
margin-left: auto;
margin-right: auto;
}
img.align-default, figure.align-default, .figure.align-default {
display: block;
margin-left: auto;
margin-right: auto;
}
.align-left {
text-align: left;
}
.align-center {
text-align: center;
}
.align-default {
text-align: center;
}
.align-right {
text-align: right;
}
/* -- sidebars -------------------------------------------------------------- */
div.sidebar,
aside.sidebar {
margin: 0 0 0.5em 1em;
border: 1px solid #ddb;
padding: 7px;
background-color: #ffe;
width: 40%;
float: right;
clear: right;
overflow-x: auto;
}
p.sidebar-title {
font-weight: bold;
}
div.admonition, div.topic, blockquote {
clear: left;
}
/* -- topics ---------------------------------------------------------------- */
div.topic {
border: 1px solid #ccc;
padding: 7px;
margin: 10px 0 10px 0;
}
p.topic-title {
font-size: 1.1em;
font-weight: bold;
margin-top: 10px;
}
/* -- admonitions ----------------------------------------------------------- */
div.admonition {
margin-top: 10px;
margin-bottom: 10px;
padding: 7px;
}
div.admonition dt {
font-weight: bold;
}
p.admonition-title {
margin: 0px 10px 5px 0px;
font-weight: bold;
}
div.body p.centered {
text-align: center;
margin-top: 25px;
}
/* -- content of sidebars/topics/admonitions -------------------------------- */
div.sidebar > :last-child,
aside.sidebar > :last-child,
div.topic > :last-child,
div.admonition > :last-child {
margin-bottom: 0;
}
div.sidebar::after,
aside.sidebar::after,
div.topic::after,
div.admonition::after,
blockquote::after {
display: block;
content: '';
clear: both;
}
/* -- tables ---------------------------------------------------------------- */
table.docutils {
margin-top: 10px;
margin-bottom: 10px;
border: 0;
border-collapse: collapse;
}
table.align-center {
margin-left: auto;
margin-right: auto;
}
table.align-default {
margin-left: auto;
margin-right: auto;
}
table caption span.caption-number {
font-style: italic;
}
table caption span.caption-text {
}
table.docutils td, table.docutils th {
padding: 1px 8px 1px 5px;
border-top: 0;
border-left: 0;
border-right: 0;
border-bottom: 1px solid #aaa;
}
table.footnote td, table.footnote th {
border: 0 !important;
}
th {
text-align: left;
padding-right: 5px;
}
table.citation {
border-left: solid 1px gray;
margin-left: 1px;
}
table.citation td {
border-bottom: none;
}
th > :first-child,
td > :first-child {
margin-top: 0px;
}
th > :last-child,
td > :last-child {
margin-bottom: 0px;
}
/* -- figures --------------------------------------------------------------- */
div.figure, figure {
margin: 0.5em;
padding: 0.5em;
}
div.figure p.caption, figcaption {
padding: 0.3em;
}
div.figure p.caption span.caption-number,
figcaption span.caption-number {
font-style: italic;
}
div.figure p.caption span.caption-text,
figcaption span.caption-text {
}
/* -- field list styles ----------------------------------------------------- */
table.field-list td, table.field-list th {
border: 0 !important;
}
.field-list ul {
margin: 0;
padding-left: 1em;
}
.field-list p {
margin: 0;
}
.field-name {
-moz-hyphens: manual;
-ms-hyphens: manual;
-webkit-hyphens: manual;
hyphens: manual;
}
/* -- hlist styles ---------------------------------------------------------- */
table.hlist {
margin: 1em 0;
}
table.hlist td {
vertical-align: top;
}
/* -- other body styles ----------------------------------------------------- */
ol.arabic {
list-style: decimal;
}
ol.loweralpha {
list-style: lower-alpha;
}
ol.upperalpha {
list-style: upper-alpha;
}
ol.lowerroman {
list-style: lower-roman;
}
ol.upperroman {
list-style: upper-roman;
}
:not(li) > ol > li:first-child > :first-child,
:not(li) > ul > li:first-child > :first-child {
margin-top: 0px;
}
:not(li) > ol > li:last-child > :last-child,
:not(li) > ul > li:last-child > :last-child {
margin-bottom: 0px;
}
ol.simple ol p,
ol.simple ul p,
ul.simple ol p,
ul.simple ul p {
margin-top: 0;
}
ol.simple > li:not(:first-child) > p,
ul.simple > li:not(:first-child) > p {
margin-top: 0;
}
ol.simple p,
ul.simple p {
margin-bottom: 0;
}
dl.footnote > dt,
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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@ -0,0 +1,117 @@
:root {
/*****************************************************************************
* Theme config
**/
--pst-header-height: 60px;
/*****************************************************************************
* Font size
**/
--pst-font-size-base: 15px; /* base font size - applied at body / html level */
/* heading font sizes */
--pst-font-size-h1: 36px;
--pst-font-size-h2: 32px;
--pst-font-size-h3: 26px;
--pst-font-size-h4: 21px;
--pst-font-size-h5: 18px;
--pst-font-size-h6: 16px;
/* smaller then heading font sizes*/
--pst-font-size-milli: 12px;
--pst-sidebar-font-size: .9em;
--pst-sidebar-caption-font-size: .9em;
/*****************************************************************************
* Font family
**/
/* These are adapted from https://systemfontstack.com/ */
--pst-font-family-base-system: -apple-system, BlinkMacSystemFont, Segoe UI, "Helvetica Neue",
Arial, sans-serif, Apple Color Emoji, Segoe UI Emoji, Segoe UI Symbol;
--pst-font-family-monospace-system: "SFMono-Regular", Menlo, Consolas, Monaco,
Liberation Mono, Lucida Console, monospace;
--pst-font-family-base: var(--pst-font-family-base-system);
--pst-font-family-heading: var(--pst-font-family-base);
--pst-font-family-monospace: var(--pst-font-family-monospace-system);
/*****************************************************************************
* Color
*
* Colors are defined in rgb string way, "red, green, blue"
**/
--pst-color-primary: 19, 6, 84;
--pst-color-success: 40, 167, 69;
--pst-color-info: 0, 123, 255; /*23, 162, 184;*/
--pst-color-warning: 255, 193, 7;
--pst-color-danger: 220, 53, 69;
--pst-color-text-base: 51, 51, 51;
--pst-color-h1: var(--pst-color-primary);
--pst-color-h2: var(--pst-color-primary);
--pst-color-h3: var(--pst-color-text-base);
--pst-color-h4: var(--pst-color-text-base);
--pst-color-h5: var(--pst-color-text-base);
--pst-color-h6: var(--pst-color-text-base);
--pst-color-paragraph: var(--pst-color-text-base);
--pst-color-link: 0, 91, 129;
--pst-color-link-hover: 227, 46, 0;
--pst-color-headerlink: 198, 15, 15;
--pst-color-headerlink-hover: 255, 255, 255;
--pst-color-preformatted-text: 34, 34, 34;
--pst-color-preformatted-background: 250, 250, 250;
--pst-color-inline-code: 232, 62, 140;
--pst-color-active-navigation: 19, 6, 84;
--pst-color-navbar-link: 77, 77, 77;
--pst-color-navbar-link-hover: var(--pst-color-active-navigation);
--pst-color-navbar-link-active: var(--pst-color-active-navigation);
--pst-color-sidebar-link: 77, 77, 77;
--pst-color-sidebar-link-hover: var(--pst-color-active-navigation);
--pst-color-sidebar-link-active: var(--pst-color-active-navigation);
--pst-color-sidebar-expander-background-hover: 244, 244, 244;
--pst-color-sidebar-caption: 77, 77, 77;
--pst-color-toc-link: 119, 117, 122;
--pst-color-toc-link-hover: var(--pst-color-active-navigation);
--pst-color-toc-link-active: var(--pst-color-active-navigation);
/*****************************************************************************
* Icon
**/
/* font awesome icons*/
--pst-icon-check-circle: '\f058';
--pst-icon-info-circle: '\f05a';
--pst-icon-exclamation-triangle: '\f071';
--pst-icon-exclamation-circle: '\f06a';
--pst-icon-times-circle: '\f057';
--pst-icon-lightbulb: '\f0eb';
/*****************************************************************************
* Admonitions
**/
--pst-color-admonition-default: var(--pst-color-info);
--pst-color-admonition-note: var(--pst-color-info);
--pst-color-admonition-attention: var(--pst-color-warning);
--pst-color-admonition-caution: var(--pst-color-warning);
--pst-color-admonition-warning: var(--pst-color-warning);
--pst-color-admonition-danger: var(--pst-color-danger);
--pst-color-admonition-error: var(--pst-color-danger);
--pst-color-admonition-hint: var(--pst-color-success);
--pst-color-admonition-tip: var(--pst-color-success);
--pst-color-admonition-important: var(--pst-color-success);
--pst-icon-admonition-default: var(--pst-icon-info-circle);
--pst-icon-admonition-note: var(--pst-icon-info-circle);
--pst-icon-admonition-attention: var(--pst-icon-exclamation-circle);
--pst-icon-admonition-caution: var(--pst-icon-exclamation-triangle);
--pst-icon-admonition-warning: var(--pst-icon-exclamation-triangle);
--pst-icon-admonition-danger: var(--pst-icon-exclamation-triangle);
--pst-icon-admonition-error: var(--pst-icon-times-circle);
--pst-icon-admonition-hint: var(--pst-icon-lightbulb);
--pst-icon-admonition-tip: var(--pst-icon-lightbulb);
--pst-icon-admonition-important: var(--pst-icon-exclamation-circle);
}

@ -0,0 +1,49 @@
h1.site-logo {
font-size: 30px !important;
}
h1.site-logo small {
font-size: 20px !important;
}
h1.site-logo {
font-size: 30px !important;
}
h1.site-logo small {
font-size: 20px !important;
}
tbody, thead, pre {
border: 1px solid rgba(0, 0, 0, 0.25);
}
table td, th {
padding: 8px;
}
table p {
margin-bottom: 0;
}
table td code {
white-space: nowrap;
}
table tr,
table th {
border-bottom: 1px solid rgba(0, 0, 0, 0.1);
}
table tr:last-child {
border-bottom: 0;
}
pre {
box-shadow: inherit !important;
background-color: #fff;
}
.text-align\:center {
text-align: center;
}

@ -0,0 +1,321 @@
/*
* doctools.js
* ~~~~~~~~~~~
*
* Sphinx JavaScript utilities for all documentation.
*
* :copyright: Copyright 2007-2021 by the Sphinx team, see AUTHORS.
* :license: BSD, see LICENSE for details.
*
*/
/**
* select a different prefix for underscore
*/
$u = _.noConflict();
/**
* make the code below compatible with browsers without
* an installed firebug like debugger
if (!window.console || !console.firebug) {
var names = ["log", "debug", "info", "warn", "error", "assert", "dir",
"dirxml", "group", "groupEnd", "time", "timeEnd", "count", "trace",
"profile", "profileEnd"];
window.console = {};
for (var i = 0; i < names.length; ++i)
window.console[names[i]] = function() {};
}
*/
/**
* small helper function to urldecode strings
*
* See https://developer.mozilla.org/en-US/docs/Web/JavaScript/Reference/Global_Objects/decodeURIComponent#Decoding_query_parameters_from_a_URL
*/
jQuery.urldecode = function(x) {
if (!x) {
return x
}
return decodeURIComponent(x.replace(/\+/g, ' '));
};
/**
* small helper function to urlencode strings
*/
jQuery.urlencode = encodeURIComponent;
/**
* This function returns the parsed url parameters of the
* current request. Multiple values per key are supported,
* it will always return arrays of strings for the value parts.
*/
jQuery.getQueryParameters = function(s) {
if (typeof s === 'undefined')
s = document.location.search;
var parts = s.substr(s.indexOf('?') + 1).split('&');
var result = {};
for (var i = 0; i < parts.length; i++) {
var tmp = parts[i].split('=', 2);
var key = jQuery.urldecode(tmp[0]);
var value = jQuery.urldecode(tmp[1]);
if (key in result)
result[key].push(value);
else
result[key] = [value];
}
return result;
};
/**
* highlight a given string on a jquery object by wrapping it in
* span elements with the given class name.
*/
jQuery.fn.highlightText = function(text, className) {
function highlight(node, addItems) {
if (node.nodeType === 3) {
var val = node.nodeValue;
var pos = val.toLowerCase().indexOf(text);
if (pos >= 0 &&
!jQuery(node.parentNode).hasClass(className) &&
!jQuery(node.parentNode).hasClass("nohighlight")) {
var span;
var isInSVG = jQuery(node).closest("body, svg, foreignObject").is("svg");
if (isInSVG) {
span = document.createElementNS("http://www.w3.org/2000/svg", "tspan");
} else {
span = document.createElement("span");
span.className = className;
}
span.appendChild(document.createTextNode(val.substr(pos, text.length)));
node.parentNode.insertBefore(span, node.parentNode.insertBefore(
document.createTextNode(val.substr(pos + text.length)),
node.nextSibling));
node.nodeValue = val.substr(0, pos);
if (isInSVG) {
var rect = document.createElementNS("http://www.w3.org/2000/svg", "rect");
var bbox = node.parentElement.getBBox();
rect.x.baseVal.value = bbox.x;
rect.y.baseVal.value = bbox.y;
rect.width.baseVal.value = bbox.width;
rect.height.baseVal.value = bbox.height;
rect.setAttribute('class', className);
addItems.push({
"parent": node.parentNode,
"target": rect});
}
}
}
else if (!jQuery(node).is("button, select, textarea")) {
jQuery.each(node.childNodes, function() {
highlight(this, addItems);
});
}
}
var addItems = [];
var result = this.each(function() {
highlight(this, addItems);
});
for (var i = 0; i < addItems.length; ++i) {
jQuery(addItems[i].parent).before(addItems[i].target);
}
return result;
};
/*
* backward compatibility for jQuery.browser
* This will be supported until firefox bug is fixed.
*/
if (!jQuery.browser) {
jQuery.uaMatch = function(ua) {
ua = ua.toLowerCase();
var match = /(chrome)[ \/]([\w.]+)/.exec(ua) ||
/(webkit)[ \/]([\w.]+)/.exec(ua) ||
/(opera)(?:.*version|)[ \/]([\w.]+)/.exec(ua) ||
/(msie) ([\w.]+)/.exec(ua) ||
ua.indexOf("compatible") < 0 && /(mozilla)(?:.*? rv:([\w.]+)|)/.exec(ua) ||
[];
return {
browser: match[ 1 ] || "",
version: match[ 2 ] || "0"
};
};
jQuery.browser = {};
jQuery.browser[jQuery.uaMatch(navigator.userAgent).browser] = true;
}
/**
* Small JavaScript module for the documentation.
*/
var Documentation = {
init : function() {
this.fixFirefoxAnchorBug();
this.highlightSearchWords();
this.initIndexTable();
if (DOCUMENTATION_OPTIONS.NAVIGATION_WITH_KEYS) {
this.initOnKeyListeners();
}
},
/**
* i18n support
*/
TRANSLATIONS : {},
PLURAL_EXPR : function(n) { return n === 1 ? 0 : 1; },
LOCALE : 'unknown',
// gettext and ngettext don't access this so that the functions
// can safely bound to a different name (_ = Documentation.gettext)
gettext : function(string) {
var translated = Documentation.TRANSLATIONS[string];
if (typeof translated === 'undefined')
return string;
return (typeof translated === 'string') ? translated : translated[0];
},
ngettext : function(singular, plural, n) {
var translated = Documentation.TRANSLATIONS[singular];
if (typeof translated === 'undefined')
return (n == 1) ? singular : plural;
return translated[Documentation.PLURALEXPR(n)];
},
addTranslations : function(catalog) {
for (var key in catalog.messages)
this.TRANSLATIONS[key] = catalog.messages[key];
this.PLURAL_EXPR = new Function('n', 'return +(' + catalog.plural_expr + ')');
this.LOCALE = catalog.locale;
},
/**
* add context elements like header anchor links
*/
addContextElements : function() {
$('div[id] > :header:first').each(function() {
$('<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',
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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<?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;}
.st1{fill:none;stroke:#579ACA;stroke-width:5;stroke-miterlimit:10;}
.st2{fill:none;stroke:#E66581;stroke-width:5;stroke-miterlimit:10;}
</style>
<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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<path class="st1" d="M19.2,26.4c3.1-4.3,9.1-5.2,13.3-2.1c1.1,0.8,2,1.8,2.7,3"/>
<path class="st0" d="M19.9,19.4c-3.6-3.9-3.4-9.9,0.5-13.5s9.9-3.4,13.5,0.5"/>
</g>
</svg>

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<svg id="Layer_1" data-name="Layer 1" xmlns="http://www.w3.org/2000/svg" width="38.73" height="50" viewBox="0 0 38.73 50"><defs><style>.cls-1{fill:#767677;}.cls-2{fill:#f37726;}.cls-3{fill:#9e9e9e;}.cls-4{fill:#616262;}.cls-5{font-size:17.07px;fill:#fff;font-family:Roboto-Regular, Roboto;}</style></defs><title>logo_jupyterhub</title><g id="Canvas"><path id="path7_fill" data-name="path7 fill" class="cls-1" d="M39.51,3.53a3,3,0,0,1-1.7,2.9A3,3,0,0,1,34.48,6a3,3,0,0,1-.82-3.26,3,3,0,0,1,1.05-1.41A3,3,0,0,1,37.52.86a2.88,2.88,0,0,1,1,.6,3,3,0,0,1,.7.93,3.18,3.18,0,0,1,.28,1.14Z" transform="translate(-1.87 -0.69)"/><path id="path8_fill" data-name="path8 fill" class="cls-2" d="M21.91,38.39c-8,0-15.06-2.87-18.7-7.12a19.93,19.93,0,0,0,37.39,0C37,35.52,30,38.39,21.91,38.39Z" transform="translate(-1.87 -0.69)"/><path id="path9_fill" data-name="path9 fill" class="cls-2" d="M21.91,10.78c8,0,15.05,2.87,18.69,7.12a19.93,19.93,0,0,0-37.39,0C6.85,13.64,13.86,10.78,21.91,10.78Z" transform="translate(-1.87 -0.69)"/><path id="path10_fill" data-name="path10 fill" class="cls-3" d="M10.88,46.66a3.86,3.86,0,0,1-.52,2.15,3.81,3.81,0,0,1-1.62,1.51,3.93,3.93,0,0,1-2.19.34,3.79,3.79,0,0,1-2-.94,3.73,3.73,0,0,1-1.14-1.9,3.79,3.79,0,0,1,.1-2.21,3.86,3.86,0,0,1,1.33-1.78,3.92,3.92,0,0,1,3.54-.53,3.85,3.85,0,0,1,2.14,1.93,3.74,3.74,0,0,1,.37,1.43Z" transform="translate(-1.87 -0.69)"/><path id="path11_fill" data-name="path11 fill" class="cls-4" d="M4.12,9.81A2.18,2.18,0,0,1,2.9,9.48a2.23,2.23,0,0,1-.84-1A2.26,2.26,0,0,1,1.9,7.26a2.13,2.13,0,0,1,.56-1.13,2.18,2.18,0,0,1,2.36-.56,2.13,2.13,0,0,1,1,.76,2.18,2.18,0,0,1,.42,1.2A2.22,2.22,0,0,1,4.12,9.81Z" transform="translate(-1.87 -0.69)"/></g><text class="cls-5" transform="translate(5.24 30.01)">Hub</text></svg>

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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%; }
td.linenos .normal { color: inherit; background-color: transparent; padding-left: 5px; padding-right: 5px; }
span.linenos { color: inherit; background-color: transparent; padding-left: 5px; padding-right: 5px; }
td.linenos .special { color: #000000; background-color: #ffffc0; padding-left: 5px; padding-right: 5px; }
span.linenos.special { color: #000000; background-color: #ffffc0; padding-left: 5px; padding-right: 5px; }
.highlight .hll { background-color: #ffffcc }
.highlight { background: #f8f8f8; }
.highlight .c { color: #8f5902; font-style: italic } /* Comment */
.highlight .err { color: #a40000; border: 1px solid #ef2929 } /* Error */
.highlight .g { color: #000000 } /* Generic */
.highlight .k { color: #204a87; font-weight: bold } /* Keyword */
.highlight .l { color: #000000 } /* Literal */
.highlight .n { color: #000000 } /* Name */
.highlight .o { color: #ce5c00; font-weight: bold } /* Operator */
.highlight .x { color: #000000 } /* Other */
.highlight .p { color: #000000; font-weight: bold } /* Punctuation */
.highlight .ch { color: #8f5902; font-style: italic } /* Comment.Hashbang */
.highlight .cm { color: #8f5902; font-style: italic } /* Comment.Multiline */
.highlight .cp { color: #8f5902; font-style: italic } /* Comment.Preproc */
.highlight .cpf { color: #8f5902; font-style: italic } /* Comment.PreprocFile */
.highlight .c1 { color: #8f5902; font-style: italic } /* Comment.Single */
.highlight .cs { color: #8f5902; font-style: italic } /* Comment.Special */
.highlight .gd { color: #a40000 } /* Generic.Deleted */
.highlight .ge { color: #000000; font-style: italic } /* Generic.Emph */
.highlight .gr { color: #ef2929 } /* Generic.Error */
.highlight .gh { color: #000080; font-weight: bold } /* Generic.Heading */
.highlight .gi { color: #00A000 } /* Generic.Inserted */
.highlight .go { color: #000000; font-style: italic } /* Generic.Output */
.highlight .gp { color: #8f5902 } /* Generic.Prompt */
.highlight .gs { color: #000000; font-weight: bold } /* Generic.Strong */
.highlight .gu { color: #800080; font-weight: bold } /* Generic.Subheading */
.highlight .gt { color: #a40000; font-weight: bold } /* Generic.Traceback */
.highlight .kc { color: #204a87; font-weight: bold } /* Keyword.Constant */
.highlight .kd { color: #204a87; font-weight: bold } /* Keyword.Declaration */
.highlight .kn { color: #204a87; font-weight: bold } /* Keyword.Namespace */
.highlight .kp { color: #204a87; font-weight: bold } /* Keyword.Pseudo */
.highlight .kr { color: #204a87; font-weight: bold } /* Keyword.Reserved */
.highlight .kt { color: #204a87; font-weight: bold } /* Keyword.Type */
.highlight .ld { color: #000000 } /* Literal.Date */
.highlight .m { color: #0000cf; font-weight: bold } /* Literal.Number */
.highlight .s { color: #4e9a06 } /* Literal.String */
.highlight .na { color: #c4a000 } /* Name.Attribute */
.highlight .nb { color: #204a87 } /* Name.Builtin */
.highlight .nc { color: #000000 } /* Name.Class */
.highlight .no { color: #000000 } /* Name.Constant */
.highlight .nd { color: #5c35cc; font-weight: bold } /* Name.Decorator */
.highlight .ni { color: #ce5c00 } /* Name.Entity */
.highlight .ne { color: #cc0000; font-weight: bold } /* Name.Exception */
.highlight .nf { color: #000000 } /* Name.Function */
.highlight .nl { color: #f57900 } /* Name.Label */
.highlight .nn { color: #000000 } /* Name.Namespace */
.highlight .nx { color: #000000 } /* Name.Other */
.highlight .py { color: #000000 } /* Name.Property */
.highlight .nt { color: #204a87; font-weight: bold } /* Name.Tag */
.highlight .nv { color: #000000 } /* Name.Variable */
.highlight .ow { color: #204a87; font-weight: bold } /* Operator.Word */
.highlight .w { color: #f8f8f8; text-decoration: underline } /* Text.Whitespace */
.highlight .mb { color: #0000cf; font-weight: bold } /* Literal.Number.Bin */
.highlight .mf { color: #0000cf; font-weight: bold } /* Literal.Number.Float */
.highlight .mh { color: #0000cf; font-weight: bold } /* Literal.Number.Hex */
.highlight .mi { color: #0000cf; font-weight: bold } /* Literal.Number.Integer */
.highlight .mo { color: #0000cf; font-weight: bold } /* Literal.Number.Oct */
.highlight .sa { color: #4e9a06 } /* Literal.String.Affix */
.highlight .sb { color: #4e9a06 } /* Literal.String.Backtick */
.highlight .sc { color: #4e9a06 } /* Literal.String.Char */
.highlight .dl { color: #4e9a06 } /* Literal.String.Delimiter */
.highlight .sd { color: #8f5902; font-style: italic } /* Literal.String.Doc */
.highlight .s2 { color: #4e9a06 } /* Literal.String.Double */
.highlight .se { color: #4e9a06 } /* Literal.String.Escape */
.highlight .sh { color: #4e9a06 } /* Literal.String.Heredoc */
.highlight .si { color: #4e9a06 } /* Literal.String.Interpol */
.highlight .sx { color: #4e9a06 } /* Literal.String.Other */
.highlight .sr { color: #4e9a06 } /* Literal.String.Regex */
.highlight .s1 { color: #4e9a06 } /* Literal.String.Single */
.highlight .ss { color: #4e9a06 } /* Literal.String.Symbol */
.highlight .bp { color: #3465a4 } /* Name.Builtin.Pseudo */
.highlight .fm { color: #000000 } /* Name.Function.Magic */
.highlight .vc { color: #000000 } /* Name.Variable.Class */
.highlight .vg { color: #000000 } /* Name.Variable.Global */
.highlight .vi { color: #000000 } /* Name.Variable.Instance */
.highlight .vm { color: #000000 } /* Name.Variable.Magic */
.highlight .il { color: #0000cf; font-weight: bold } /* Literal.Number.Integer.Long */

@ -0,0 +1,522 @@
/*
* 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();
});

@ -0,0 +1,18 @@
var initTriggerNavBar=()=>{if($(window).width()<768){$("#navbar-toggler").trigger("click")}}
var scrollToActive=()=>{var navbar=document.getElementById('site-navigation')
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()})}}
function toggleFullScreen(){var navToggler=$("#navbar-toggler");if(!document.fullscreenElement){document.documentElement.requestFullscreen();if(!navToggler.hasClass("collapsed")){navToggler.click();}}else{if(document.exitFullscreen){document.exitFullscreen();if(navToggler.hasClass("collapsed")){navToggler.click();}}}}
var initTooltips=()=>{$(document).ready(function(){$('[data-toggle="tooltip"]').tooltip();});}
var initTocHide=()=>{var scrollTimeout;var throttle=200;var tocHeight=$("#bd-toc-nav").outerHeight(true)+$(".bd-toc").outerHeight(true);var hideTocAfter=tocHeight+200;var checkTocScroll=function(){var margin_content=$(".margin, .tag_margin, .full-width, .full_width, .tag_full-width, .tag_full_width, .sidebar, .tag_sidebar, .popout, .tag_popout");margin_content.each((index,item)=>{var topOffset=$(item).offset().top-$(window).scrollTop();var bottomOffset=topOffset+$(item).outerHeight(true);var topOverlaps=((topOffset>=0)&&(topOffset<hideTocAfter));var bottomOverlaps=((bottomOffset>=0)&&(bottomOffset<hideTocAfter));var removeToc=(topOverlaps||bottomOverlaps);if(removeToc&&window.pageYOffset>20){$("div.bd-toc").removeClass("show")
return false}else{$("div.bd-toc").addClass("show")};})};var manageScrolledClassOnBody=function(){if(window.scrollY>0){document.body.classList.add("scrolled");}else{document.body.classList.remove("scrolled");}}
$(window).on('scroll',function(){if(!scrollTimeout){scrollTimeout=setTimeout(function(){checkTocScroll();manageScrolledClassOnBody();scrollTimeout=null;},throttle);}});}
var initThebeSBT=()=>{var title=$("div.section h1")[0]
if(!$(title).next().hasClass("thebe-launch-button")){$("<button class='thebe-launch-button'></button>").insertAfter($(title))}
initThebe();}
sbRunWhenDOMLoaded(initTooltips)
sbRunWhenDOMLoaded(initTriggerNavBar)
sbRunWhenDOMLoaded(scrollToActive)
sbRunWhenDOMLoaded(initTocHide)

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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)
-->
<!DOCTYPE svg PUBLIC "-//W3C//DTD SVG 1.1//EN" "http://www.w3.org/Graphics/SVG/1.1/DTD/svg11.dtd" >
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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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<div class="tocsection onthispage pt-5 pb-3">
<i class="fas fa-list"></i> Contents
</div>
<nav id="bd-toc-nav">
<ul class="visible nav section-nav flex-column">
<li class="toc-h2 nav-item toc-entry">
<a class="reference internal nav-link" href="#preliminaries">
<span class="sectnum">
2.1.
</span>
Preliminaries
</a>
<ul class="nav section-nav flex-column">
<li class="toc-h3 nav-item toc-entry">
<a class="reference internal nav-link" href="#benchmark-challenges">
Benchmark challenges
</a>
</li>
<li class="toc-h3 nav-item toc-entry">
<a class="reference internal nav-link" href="#baseline-results">
Baseline results
</a>
</li>
</ul>
</li>
<li class="toc-h2 nav-item toc-entry">
<a class="reference internal nav-link" href="#maximum-weight-stable-set-problem">
<span class="sectnum">
2.2.
</span>
Maximum Weight Stable Set Problem
</a>
<ul class="nav section-nav flex-column">
<li class="toc-h3 nav-item toc-entry">
<a class="reference internal nav-link" href="#problem-definition">
Problem definition
</a>
</li>
<li class="toc-h3 nav-item toc-entry">
<a class="reference internal nav-link" href="#random-instance-generator">
Random instance generator
</a>
</li>
<li class="toc-h3 nav-item toc-entry">
<a class="reference internal nav-link" href="#challenge-a">
Challenge A
</a>
</li>
</ul>
</li>
<li class="toc-h2 nav-item toc-entry">
<a class="reference internal nav-link" href="#traveling-salesman-problem">
<span class="sectnum">
2.3.
</span>
Traveling Salesman Problem
</a>
<ul class="nav section-nav flex-column">
<li class="toc-h3 nav-item toc-entry">
<a class="reference internal nav-link" href="#id1">
Problem definition
</a>
</li>
<li class="toc-h3 nav-item toc-entry">
<a class="reference internal nav-link" href="#random-problem-generator">
Random problem generator
</a>
</li>
<li class="toc-h3 nav-item toc-entry">
<a class="reference internal nav-link" href="#id2">
Challenge A
</a>
</li>
</ul>
</li>
<li class="toc-h2 nav-item toc-entry">
<a class="reference internal nav-link" href="#multidimensional-0-1-knapsack-problem">
<span class="sectnum">
2.4.
</span>
Multidimensional 0-1 Knapsack Problem
</a>
<ul class="nav section-nav flex-column">
<li class="toc-h3 nav-item toc-entry">
<a class="reference internal nav-link" href="#id3">
Problem definition
</a>
</li>
<li class="toc-h3 nav-item toc-entry">
<a class="reference internal nav-link" href="#id4">
Random instance generator
</a>
</li>
<li class="toc-h3 nav-item toc-entry">
<a class="reference internal nav-link" href="#id5">
Challenge A
</a>
</li>
</ul>
</li>
</ul>
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</div>
<div id="main-content" class="row">
<div class="col-12 col-md-9 pl-md-3 pr-md-0">
<div>
<div class="section" id="benchmarks">
<h1><span class="sectnum">2.</span> Benchmarks<a class="headerlink" href="#benchmarks" title="Permalink to this headline"></a></h1>
<p>MIPLearn provides a selection of benchmark problems and random instance generators, covering applications from different fields, that can be used to evaluate new learning-enhanced MIP techniques in a measurable and reproducible way. In this page, we describe these problems, the included instance generators, and we present some benchmark results for <code class="docutils literal notranslate"><span class="pre">LearningSolver</span></code> with default parameters.</p>
<div class="section" id="preliminaries">
<h2><span class="sectnum">2.1.</span> Preliminaries<a class="headerlink" href="#preliminaries" title="Permalink to this headline"></a></h2>
<div class="section" id="benchmark-challenges">
<h3>Benchmark challenges<a class="headerlink" href="#benchmark-challenges" title="Permalink to this headline"></a></h3>
<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">
<h3>Baseline results<a class="headerlink" href="#baseline-results" title="Permalink to this headline"></a></h3>
<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="about.md#references">references</a>. We compare three solvers:</p>
<ul class="simple">
<li><p><strong>baseline:</strong> Gurobi 9.0 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>
</div>
</div>
<div class="section" id="maximum-weight-stable-set-problem">
<h2><span class="sectnum">2.2.</span> Maximum Weight Stable Set Problem<a class="headerlink" href="#maximum-weight-stable-set-problem" title="Permalink to this headline"></a></h2>
<div class="section" id="problem-definition">
<h3>Problem definition<a class="headerlink" href="#problem-definition" title="Permalink to this headline"></a></h3>
<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 notranslate nohighlight">\( \sum_{v \in V} w_v\)</span>. We recall that a subset <span class="math notranslate nohighlight">\(S \subseteq V\)</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 Karps 21 NP-complete problems.</p>
</div>
<div class="section" id="random-instance-generator">
<h3>Random instance generator<a class="headerlink" href="#random-instance-generator" title="Permalink to this headline"></a></h3>
<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">
<h3>Challenge A<a class="headerlink" href="#challenge-a" title="Permalink to this headline"></a></h3>
<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="highlight-python 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>
</pre></div>
</div>
<p><img alt="alt" src="figures/benchmark_stab_a.png" /></p>
</div>
</div>
<div class="section" id="traveling-salesman-problem">
<h2><span class="sectnum">2.3.</span> Traveling Salesman Problem<a class="headerlink" href="#traveling-salesman-problem" title="Permalink to this headline"></a></h2>
<div class="section" id="id1">
<h3>Problem definition<a class="headerlink" href="#id1" title="Permalink to this headline"></a></h3>
<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 Karps
21 NP-complete problems.</p>
</div>
<div class="section" id="random-problem-generator">
<h3>Random problem generator<a class="headerlink" href="#random-problem-generator" title="Permalink to this headline"></a></h3>
<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:
$<span class="math notranslate nohighlight">\(
d_{i,j} = \gamma_{i,j} \sqrt{(x_i-x_j)^2 + (y_i - y_j)^2}
\)</span><span class="math notranslate nohighlight">\(
where \)</span>\gamma_{i,j}$ 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="id2">
<h3>Challenge A<a class="headerlink" href="#id2" title="Permalink to this headline"></a></h3>
<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>
<div class="highlight-python notranslate"><div class="highlight"><pre><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>
</div>
<p><img alt="alt" src="figures/benchmark_tsp_a.png" /></p>
</div>
</div>
<div class="section" id="multidimensional-0-1-knapsack-problem">
<h2><span class="sectnum">2.4.</span> Multidimensional 0-1 Knapsack Problem<a class="headerlink" href="#multidimensional-0-1-knapsack-problem" title="Permalink to this headline"></a></h2>
<div class="section" id="id3">
<h3>Problem definition<a class="headerlink" href="#id3" title="Permalink to this headline"></a></h3>
<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="id4">
<h3>Random instance generator<a class="headerlink" href="#id4" title="Permalink to this headline"></a></h3>
<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>
<p>!!! note “References”
* Freville, Arnaud, and Gérard Plateau. <em>An efficient preprocessing procedure for the multidimensional 01 knapsack problem.</em> Discrete applied mathematics 49.1-3 (1994): 189-212.
* Fréville, Arnaud. <em>The multidimensional 01 knapsack problem: An overview.</em> European Journal of Operational Research 155.1 (2004): 1-21.</p>
</div>
<div class="section" id="id5">
<h3>Challenge A<a class="headerlink" href="#id5" title="Permalink to this headline"></a></h3>
<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="highlight-python 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>
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<span class="p">)</span>
</pre></div>
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<i class="fas fa-list"></i> Contents
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<li class="toc-h2 nav-item toc-entry">
<a class="reference internal nav-link" href="#customizing-solver-parameters">
<span class="sectnum">
3.1.
</span>
Customizing solver parameters
</a>
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<li class="toc-h3 nav-item toc-entry">
<a class="reference internal nav-link" href="#selecting-the-internal-mip-solver">
Selecting the internal MIP solver
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<a class="reference internal nav-link" href="#customizing-solver-components">
<span class="sectnum">
3.2.
</span>
Customizing solver components
</a>
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<li class="toc-h3 nav-item toc-entry">
<a class="reference internal nav-link" href="#selecting-components">
Selecting components
</a>
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<li class="toc-h3 nav-item toc-entry">
<a class="reference internal nav-link" href="#adjusting-component-aggressiveness">
Adjusting component aggressiveness
</a>
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Evaluating component performance
</a>
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<a class="reference internal nav-link" href="#using-customized-ml-classifiers-and-regressors">
Using customized ML classifiers and regressors
</a>
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<div>
<div class="section" id="customization">
<h1><span class="sectnum">3.</span> Customization<a class="headerlink" href="#customization" title="Permalink to this headline"></a></h1>
<div class="section" id="customizing-solver-parameters">
<h2><span class="sectnum">3.1.</span> Customizing solver parameters<a class="headerlink" href="#customizing-solver-parameters" title="Permalink to this headline"></a></h2>
<div class="section" id="selecting-the-internal-mip-solver">
<h3>Selecting the internal MIP solver<a class="headerlink" href="#selecting-the-internal-mip-solver" title="Permalink to this headline"></a></h3>
<p>By default, <code class="docutils literal notranslate"><span class="pre">LearningSolver</span></code> uses <a class="reference external" href="https://www.gurobi.com/">Gurobi</a> as its internal MIP solver, and expects models to be provided using the Pyomo modeling language. Supported solvers and modeling languages include:</p>
<ul class="simple">
<li><p><code class="docutils literal notranslate"><span class="pre">GurobiPyomoSolver</span></code>: Gurobi with Pyomo (default).</p></li>
<li><p><code class="docutils literal notranslate"><span class="pre">CplexPyomoSolver</span></code>: <a class="reference external" href="https://www.ibm.com/products/ilog-cplex-optimization-studio">IBM ILOG CPLEX</a> with Pyomo.</p></li>
<li><p><code class="docutils literal notranslate"><span class="pre">XpressPyomoSolver</span></code>: <a class="reference external" href="https://www.fico.com/en/products/fico-xpress-solver">FICO XPRESS Solver</a> with Pyomo.</p></li>
<li><p><code class="docutils literal notranslate"><span class="pre">GurobiSolver</span></code>: Gurobi without any modeling language.</p></li>
</ul>
<p>To switch between solvers, provide the desired class using the <code class="docutils literal notranslate"><span class="pre">solver</span></code> argument:</p>
<div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="kn">from</span> <span class="nn">miplearn</span> <span class="kn">import</span> <span class="n">LearningSolver</span><span class="p">,</span> <span class="n">CplexPyomoSolver</span>
<span class="n">solver</span> <span class="o">=</span> <span class="n">LearningSolver</span><span class="p">(</span><span class="n">solver</span><span class="o">=</span><span class="n">CplexPyomoSolver</span><span class="p">)</span>
</pre></div>
</div>
<p>To configure a particular solver, use the <code class="docutils literal notranslate"><span class="pre">params</span></code> constructor argument, as shown below.</p>
<div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="kn">from</span> <span class="nn">miplearn</span> <span class="kn">import</span> <span class="n">LearningSolver</span><span class="p">,</span> <span class="n">GurobiPyomoSolver</span>
<span class="n">solver</span> <span class="o">=</span> <span class="n">LearningSolver</span><span class="p">(</span>
<span class="n">solver</span><span class="o">=</span><span class="k">lambda</span><span class="p">:</span> <span class="n">GurobiPyomoSolver</span><span class="p">(</span>
<span class="n">params</span><span class="o">=</span><span class="p">{</span>
<span class="s2">&quot;TimeLimit&quot;</span><span class="p">:</span> <span class="mi">900</span><span class="p">,</span>
<span class="s2">&quot;MIPGap&quot;</span><span class="p">:</span> <span class="mf">1e-3</span><span class="p">,</span>
<span class="s2">&quot;NodeLimit&quot;</span><span class="p">:</span> <span class="mi">1000</span><span class="p">,</span>
<span class="p">}</span>
<span class="p">),</span>
<span class="p">)</span>
</pre></div>
</div>
</div>
</div>
<div class="section" id="customizing-solver-components">
<h2><span class="sectnum">3.2.</span> Customizing solver components<a class="headerlink" href="#customizing-solver-components" title="Permalink to this headline"></a></h2>
<p><code class="docutils literal notranslate"><span class="pre">LearningSolver</span></code> is composed by a number of individual machine-learning components, each targeting a different part of the solution process. Each component can be individually enabled, disabled or customized. The following components are enabled by default:</p>
<ul class="simple">
<li><p><code class="docutils literal notranslate"><span class="pre">LazyConstraintComponent</span></code>: Predicts which lazy constraint to initially enforce.</p></li>
<li><p><code class="docutils literal notranslate"><span class="pre">ObjectiveValueComponent</span></code>: Predicts the optimal value of the optimization problem, given the optimal solution to the LP relaxation.</p></li>
<li><p><code class="docutils literal notranslate"><span class="pre">PrimalSolutionComponent</span></code>: Predicts optimal values for binary decision variables. In heuristic mode, this component fixes the variables to their predicted values. In exact mode, the predicted values are provided to the solver as a (partial) MIP start.</p></li>
</ul>
<p>The following components are also available, but not enabled by default:</p>
<ul class="simple">
<li><p><code class="docutils literal notranslate"><span class="pre">BranchPriorityComponent</span></code>: Predicts good branch priorities for decision variables.</p></li>
</ul>
<div class="section" id="selecting-components">
<h3>Selecting components<a class="headerlink" href="#selecting-components" title="Permalink to this headline"></a></h3>
<p>To create a <code class="docutils literal notranslate"><span class="pre">LearningSolver</span></code> with a specific set of components, the <code class="docutils literal notranslate"><span class="pre">components</span></code> constructor argument may be used, as the next example shows:</p>
<div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="c1"># Create a solver without any components</span>
<span class="n">solver1</span> <span class="o">=</span> <span class="n">LearningSolver</span><span class="p">(</span><span class="n">components</span><span class="o">=</span><span class="p">[])</span>
<span class="c1"># Create a solver with only two components</span>
<span class="n">solver2</span> <span class="o">=</span> <span class="n">LearningSolver</span><span class="p">(</span><span class="n">components</span><span class="o">=</span><span class="p">[</span>
<span class="n">LazyConstraintComponent</span><span class="p">(</span><span class="o">...</span><span class="p">),</span>
<span class="n">PrimalSolutionComponent</span><span class="p">(</span><span class="o">...</span><span class="p">),</span>
<span class="p">])</span>
</pre></div>
</div>
</div>
<div class="section" id="adjusting-component-aggressiveness">
<h3>Adjusting component aggressiveness<a class="headerlink" href="#adjusting-component-aggressiveness" title="Permalink to this headline"></a></h3>
<p>The aggressiveness of classification components, such as <code class="docutils literal notranslate"><span class="pre">PrimalSolutionComponent</span></code> and <code class="docutils literal notranslate"><span class="pre">LazyConstraintComponent</span></code>, can be adjusted through the <code class="docutils literal notranslate"><span class="pre">threshold</span></code> constructor argument. Internally, these components ask the machine learning models how confident are they on each prediction they make, then automatically discard all predictions that have low confidence. The <code class="docutils literal notranslate"><span class="pre">threshold</span></code> argument specifies how confident should the ML models be for a prediction to be considered trustworthy. Lowering a components threshold increases its aggressiveness, while raising a components threshold makes it more conservative.</p>
<p>For example, if the ML model predicts that a certain binary variable will assume value <code class="docutils literal notranslate"><span class="pre">1.0</span></code> in the optimal solution with 75% confidence, and if the <code class="docutils literal notranslate"><span class="pre">PrimalSolutionComponent</span></code> is configured to discard all predictions with less than 90% confidence, then this variable will not be included in the predicted MIP start.</p>
<p>MIPLearn currently provides two types of thresholds:</p>
<ul class="simple">
<li><p><code class="docutils literal notranslate"><span class="pre">MinProbabilityThreshold(p:</span> <span class="pre">List[float])</span></code> A threshold which indicates that a prediction is trustworthy if its probability of being correct, as computed by the machine learning model, is above a fixed value.</p></li>
<li><p><code class="docutils literal notranslate"><span class="pre">MinPrecisionThreshold(p:</span> <span class="pre">List[float])</span></code> A dynamic threshold which automatically adjusts itself during training to ensure that the component achieves at least a given precision on the training data set. Note that increasing a components precision may reduce its recall.</p></li>
</ul>
<p>The example below shows how to build a <code class="docutils literal notranslate"><span class="pre">PrimalSolutionComponent</span></code> which fixes variables to zero with at least 80% precision, and to one with at least 95% precision. Other components are configured similarly.</p>
<div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="kn">from</span> <span class="nn">miplearn</span> <span class="kn">import</span> <span class="n">PrimalSolutionComponent</span><span class="p">,</span> <span class="n">MinPrecisionThreshold</span>
<span class="n">PrimalSolutionComponent</span><span class="p">(</span>
<span class="n">mode</span><span class="o">=</span><span class="s2">&quot;heuristic&quot;</span><span class="p">,</span>
<span class="n">threshold</span><span class="o">=</span><span class="n">MinPrecisionThreshold</span><span class="p">([</span><span class="mf">0.80</span><span class="p">,</span> <span class="mf">0.95</span><span class="p">]),</span>
<span class="p">)</span>
</pre></div>
</div>
</div>
<div class="section" id="evaluating-component-performance">
<h3>Evaluating component performance<a class="headerlink" href="#evaluating-component-performance" title="Permalink to this headline"></a></h3>
<p>MIPLearn allows solver components to be modified, trained and evaluated in isolation. In the following example, we build and
fit <code class="docutils literal notranslate"><span class="pre">PrimalSolutionComponent</span></code> outside the solver, then evaluate its performance.</p>
<div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="kn">from</span> <span class="nn">miplearn</span> <span class="kn">import</span> <span class="n">PrimalSolutionComponent</span>
<span class="c1"># User-provided set of previously-solved instances</span>
<span class="n">train_instances</span> <span class="o">=</span> <span class="p">[</span><span class="o">...</span><span class="p">]</span>
<span class="c1"># Construct and fit component on a subset of training instances</span>
<span class="n">comp</span> <span class="o">=</span> <span class="n">PrimalSolutionComponent</span><span class="p">()</span>
<span class="n">comp</span><span class="o">.</span><span class="n">fit</span><span class="p">(</span><span class="n">train_instances</span><span class="p">[:</span><span class="mi">100</span><span class="p">])</span>
<span class="c1"># Evaluate performance on an additional set of training instances</span>
<span class="n">ev</span> <span class="o">=</span> <span class="n">comp</span><span class="o">.</span><span class="n">evaluate</span><span class="p">(</span><span class="n">train_instances</span><span class="p">[</span><span class="mi">100</span><span class="p">:</span><span class="mi">150</span><span class="p">])</span>
</pre></div>
</div>
<p>The method <code class="docutils literal notranslate"><span class="pre">evaluate</span></code> returns a dictionary with performance evaluation statistics for each training instance provided,
and for each type of prediction the component makes. To obtain a summary across all instances, pandas may be used, as below:</p>
<div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="kn">import</span> <span class="nn">pandas</span> <span class="k">as</span> <span class="nn">pd</span>
<span class="n">pd</span><span class="o">.</span><span class="n">DataFrame</span><span class="p">(</span><span class="n">ev</span><span class="p">[</span><span class="s2">&quot;Fix one&quot;</span><span class="p">])</span><span class="o">.</span><span class="n">mean</span><span class="p">(</span><span class="n">axis</span><span class="o">=</span><span class="mi">1</span><span class="p">)</span>
</pre></div>
</div>
<div class="highlight-text notranslate"><div class="highlight"><pre><span></span>Predicted positive 3.120000
Predicted negative 196.880000
Condition positive 62.500000
Condition negative 137.500000
True positive 3.060000
True negative 137.440000
False positive 0.060000
False negative 59.440000
Accuracy 0.702500
F1 score 0.093050
Recall 0.048921
Precision 0.981667
Predicted positive (%) 1.560000
Predicted negative (%) 98.440000
Condition positive (%) 31.250000
Condition negative (%) 68.750000
True positive (%) 1.530000
True negative (%) 68.720000
False positive (%) 0.030000
False negative (%) 29.720000
dtype: float64
</pre></div>
</div>
<p>Regression components (such as <code class="docutils literal notranslate"><span class="pre">ObjectiveValueComponent</span></code>) can also be trained and evaluated similarly,
as the next example shows:</p>
<div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="kn">from</span> <span class="nn">miplearn</span> <span class="kn">import</span> <span class="n">ObjectiveValueComponent</span>
<span class="n">comp</span> <span class="o">=</span> <span class="n">ObjectiveValueComponent</span><span class="p">()</span>
<span class="n">comp</span><span class="o">.</span><span class="n">fit</span><span class="p">(</span><span class="n">train_instances</span><span class="p">[:</span><span class="mi">100</span><span class="p">])</span>
<span class="n">ev</span> <span class="o">=</span> <span class="n">comp</span><span class="o">.</span><span class="n">evaluate</span><span class="p">(</span><span class="n">train_instances</span><span class="p">[</span><span class="mi">100</span><span class="p">:</span><span class="mi">150</span><span class="p">])</span>
<span class="kn">import</span> <span class="nn">pandas</span> <span class="k">as</span> <span class="nn">pd</span>
<span class="n">pd</span><span class="o">.</span><span class="n">DataFrame</span><span class="p">(</span><span class="n">ev</span><span class="p">)</span><span class="o">.</span><span class="n">mean</span><span class="p">(</span><span class="n">axis</span><span class="o">=</span><span class="mi">1</span><span class="p">)</span>
</pre></div>
</div>
<div class="highlight-text notranslate"><div class="highlight"><pre><span></span>Mean squared error 7001.977827
Explained variance 0.519790
Max error 242.375804
Mean absolute error 65.843924
R2 0.517612
Median absolute error 65.843924
dtype: float64
</pre></div>
</div>
</div>
<div class="section" id="using-customized-ml-classifiers-and-regressors">
<h3>Using customized ML classifiers and regressors<a class="headerlink" href="#using-customized-ml-classifiers-and-regressors" title="Permalink to this headline"></a></h3>
<p>By default, given a training set of instantes, MIPLearn trains a fixed set of ML classifiers and regressors, then selects the best one based on cross-validation performance. Alternatively, the user may specify which ML model a component should use through the <code class="docutils literal notranslate"><span class="pre">classifier</span></code> or <code class="docutils literal notranslate"><span class="pre">regressor</span></code> contructor parameters. Scikit-learn classifiers and regressors are currently supported. A future version of the package will add compatibility with Keras models.</p>
<p>The example below shows how to construct a <code class="docutils literal notranslate"><span class="pre">PrimalSolutionComponent</span></code> which internally uses scikit-learns <code class="docutils literal notranslate"><span class="pre">KNeighborsClassifiers</span></code>. Any other scikit-learn classifier or pipeline can be used. It needs to be wrapped in <code class="docutils literal notranslate"><span class="pre">ScikitLearnClassifier</span></code> to ensure that all the proper data transformations are applied.</p>
<div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="kn">from</span> <span class="nn">miplearn</span> <span class="kn">import</span> <span class="n">PrimalSolutionComponent</span><span class="p">,</span> <span class="n">ScikitLearnClassifier</span>
<span class="kn">from</span> <span class="nn">sklearn.neighbors</span> <span class="kn">import</span> <span class="n">KNeighborsClassifier</span>
<span class="n">comp</span> <span class="o">=</span> <span class="n">PrimalSolutionComponent</span><span class="p">(</span>
<span class="n">classifier</span><span class="o">=</span><span class="n">ScikitLearnClassifier</span><span class="p">(</span>
<span class="n">KNeighborsClassifier</span><span class="p">(</span><span class="n">n_neighbors</span><span class="o">=</span><span class="mi">5</span><span class="p">),</span>
<span class="p">),</span>
<span class="p">)</span>
<span class="n">comp</span><span class="o">.</span><span class="n">fit</span><span class="p">(</span><span class="n">train_instances</span><span class="p">)</span>
</pre></div>
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<h1 id="unitcommitmentjl">UnitCommitment.jl</h1>
<p><strong>UnitCommitment.jl</strong> (UC.jl) is a Julia optimization package for the Security-Constrained Unit Commitment Problem (SCUC), a fundamental optimization problem in power systems used, for example, to clear the day-ahead electricity markets. The package provides benchmark instances for the problem and Julia/JuMP implementations of state-of-the-art mixed-integer programming formulations.</p>
<h3 id="package-components">Package Components</h3>
<ul>
<li><strong>Data Format:</strong> The package proposes an extensible and fully-documented JSON-based data specification format for SCUC, developed in collaboration with Independent System Operators (ISOs), which describes the most important aspects of the problem. The format supports all the most common generator characteristics (including ramping, piecewise-linear production cost curves and time-dependent startup costs), as well as operating reserves, price-sensitive loads, transmission networks and contingencies.</li>
<li><strong>Benchmark Instances:</strong> The package provides a diverse collection of large-scale benchmark instances collected from the literature and extended to make them more challenging and realistic.</li>
<li><strong>Model Implementation</strong>: The package provides a Julia/JuMP implementation of state-of-the-art formulations and solution methods for SCUC. Our goal is to keep this implementation up-to-date, as new methods are proposed in the literature.</li>
<li><strong>Benchmark Tools:</strong> The package provides automated benchmark scripts to accurately evaluate the performance impact of proposed code changes.</li>
<div id="main-content" class="row">
<div class="col-12 col-md-9 pl-md-3 pr-md-0">
<div>
<div class="section" id="unitcommitment-jl">
<h1>UnitCommitment.jl<a class="headerlink" href="#unitcommitment-jl" title="Permalink to this headline"></a></h1>
<p><strong>UnitCommitment.jl</strong> (UC.jl) is a Julia/JuMP optimization package for the Security-Constrained Unit Commitment Problem (SCUC), a fundamental optimization problem in power systems used, for example, to clear the day-ahead electricity markets. The package provides benchmark instances for the problem and Julia/JuMP implementations of state-of-the-art mixed-integer programming formulations.</p>
<div class="section" id="package-components">
<h2>Package Components<a class="headerlink" href="#package-components" title="Permalink to this headline"></a></h2>
<ul class="simple">
<li><p><strong>Data Format:</strong> The package proposes an extensible and fully-documented JSON-based data specification format for SCUC, developed in collaboration with Independent System Operators (ISOs), which describes the most important aspects of the problem. The format supports all the most common generator characteristics (including ramping, piecewise-linear production cost curves and time-dependent startup costs), as well as operating reserves, price-sensitive loads, transmission networks and contingencies.</p></li>
<li><p><strong>Benchmark Instances:</strong> The package provides a diverse collection of large-scale benchmark instances collected from the literature and extended to make them more challenging and realistic.</p></li>
<li><p><strong>Model Implementation</strong>: The package provides a Julia/JuMP implementation of state-of-the-art formulations and solution methods for SCUC. Our goal is to keep this implementation up-to-date, as new methods are proposed in the literature.</p></li>
<li><p><strong>Benchmark Tools:</strong> The package provides automated benchmark scripts to accurately evaluate the performance impact of proposed code changes.</p></li>
</ul>
<h3 id="documentation">Documentation</h3>
<ul>
<li><a href="usage/">Usage</a></li>
<li><a href="format/">Data Format</a></li>
<li><a href="instances/">Instances</a></li>
</div>
<div class="section" id="authors">
<h2>Authors<a class="headerlink" href="#authors" title="Permalink to this headline"></a></h2>
<ul class="simple">
<li><p><strong>Alinson Santos Xavier</strong> (Argonne National Laboratory)</p></li>
<li><p><strong>Feng Qiu</strong> (Argonne National Laboratory)</p></li>
</ul>
<h3 id="source-code">Source code</h3>
<ul>
<li><a href="https://github.com/ANL-CEEESA/unitcommitment.jl">https://github.com/ANL-CEEESA/unitcommitment.jl</a></li>
</div>
<div class="section" id="acknowledgments">
<h2>Acknowledgments<a class="headerlink" href="#acknowledgments" title="Permalink to this headline"></a></h2>
<ul class="simple">
<li><p>We would like to thank <strong>Aleksandr M. Kazachkov</strong> (University of Florida), <strong>Yonghong Chen</strong> (Midcontinent Independent System Operator), <strong>Feng Pan</strong> (Pacific Northwest National Laboratory) for valuable feedback on early versions of this package.</p></li>
<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</p></li>
<li><p>Based upon work supported by the <strong>U.S. Department of Energy Advanced Grid Modeling Program</strong> under Grant DE-OE0000875.</p></li>
</ul>
<h3 id="authors">Authors</h3>
<ul>
<li><strong>Alinson Santos Xavier</strong> (Argonne National Laboratory)</li>
<li><strong>Feng Qiu</strong> (Argonne National Laboratory)</li>
</div>
<div class="section" id="citing">
<h2>Citing<a class="headerlink" href="#citing" title="Permalink to this headline"></a></h2>
<p>If you use UnitCommitment.jl in your research (that is, if you use either the provided instances files, the mathematical models, or the algorithms), we kindly request that you cite the package as follows:</p>
<ul class="simple">
<li><p><strong>Alinson S. Xavier, Feng Qiu</strong>, “UnitCommitment.jl: A Julia/JuMP Optimization Package for Security-Constrained Unit Commitment”. Zenodo (2020). <a class="reference external" href="https://doi.org/10.5281/zenodo.4269874">DOI: 10.5281/zenodo.4269874</a>.</p></li>
</ul>
<h3 id="acknowledgments">Acknowledgments</h3>
<p>If you use the instances, we additionally request that you cite the original sources, as described in the <a class="reference internal" href="instances/"><span class="doc std std-doc">instances page</span></a>.</p>
</div>
<div class="section" id="license">
<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>UnitCommitment.jl: A Julia/JuMP Optimization Package for Security-Constrained Unit Commitment
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 &quot;AS IS&quot; 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.
</pre></div>
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<div class="section" id="site-contents">
<h2>Site contents<a class="headerlink" href="#site-contents" title="Permalink to this headline"></a></h2>
<div class="toctree-wrapper compound">
<ul>
<li>
<p>We would like to thank <strong>Aleksandr M. Kazachkov</strong> (University of Florida), <strong>Yonghong Chen</strong> (Midcontinent Independent System Operator), <strong>Feng Pan</strong> (Pacific Northwest National Laboratory) for valuable feedback on early versions of this package.</p>
<li class="toctree-l1"><a class="reference internal" href="usage/"><span class="sectnum">1.</span> Usage</a><ul>
<li class="toctree-l2"><a class="reference internal" href="usage/#installation"><span class="sectnum">1.1.</span> Installation</a></li>
<li class="toctree-l2"><a class="reference internal" href="usage/#typical-usage"><span class="sectnum">1.2.</span> Typical Usage</a></li>
<li class="toctree-l2"><a class="reference internal" href="usage/#advanced-usage"><span class="sectnum">1.3.</span> Advanced usage</a></li>
</ul>
</li>
<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.</p>
<li class="toctree-l1"><a class="reference internal" href="format/"><span class="sectnum">2.</span> Data Format</a><ul>
<li class="toctree-l2"><a class="reference internal" href="format/#input-data-format"><span class="sectnum">2.1.</span> Input Data Format</a></li>
<li class="toctree-l2"><a class="reference internal" href="format/#output-data-format"><span class="sectnum">2.2.</span> Output Data Format</a></li>
<li class="toctree-l2"><a class="reference internal" href="format/#current-limitations"><span class="sectnum">2.3.</span> Current limitations</a></li>
</ul>
</li>
<li class="toctree-l1"><a class="reference internal" href="instances/"><span class="sectnum">3.</span> Instances</a><ul>
<li class="toctree-l2"><a class="reference internal" href="instances/#matpower"><span class="sectnum">3.1.</span> MATPOWER</a></li>
<li class="toctree-l2"><a class="reference internal" href="instances/#pglib-uc-instances"><span class="sectnum">3.2.</span> PGLIB-UC Instances</a></li>
<li class="toctree-l2"><a class="reference internal" href="instances/#or-lib-uc"><span class="sectnum">3.3.</span> OR-LIB/UC</a></li>
<li class="toctree-l2"><a class="reference internal" href="instances/#tejada19"><span class="sectnum">3.4.</span> Tejada19</a></li>
<li class="toctree-l2"><a class="reference internal" href="instances/#references"><span class="sectnum">3.5.</span> References</a></li>
</ul>
<h3 id="citing">Citing</h3>
<p>If you use UnitCommitment.jl in your research, we request that you cite the package as follows:</p>
<ul>
<li>Alinson S. Xavier, Feng Qiu, "UnitCommitment.jl: A Julia/JuMP Optimization Package for Security-Constrained Unit Commitment". Zenodo (2020). <a href="https://doi.org/10.5281/zenodo.4269874">DOI: 10.5281/zenodo.4269874</a>.</li>
</li>
</ul>
<p>If you make use of the provided instances files, we request that you additionally cite the original sources, as described in the <a href="instances/">instances page</a>.</p>
<h3 id="license">License</h3>
<p>Released under the modified BSD license. See <code>LICENSE.md</code> for more details.</p></div>
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53: '5',
54: '6',
55: '7',
56: '8',
57: '9',
65: 'a',
66: 'b',
67: 'c',
68: 'd',
69: 'e',
70: 'f',
71: 'g',
72: 'h',
73: 'i',
74: 'j',
75: 'k',
76: 'l',
77: 'm',
78: 'n',
79: 'o',
80: 'p',
81: 'q',
82: 'r',
83: 's',
84: 't',
85: 'u',
86: 'v',
87: 'w',
88: 'x',
89: 'y',
90: 'z',
91: 'Left Windows Key / Left ⌘',
92: 'Right Windows Key',
93: 'Windows Menu / Right ⌘',
96: 'numpad 0',
97: 'numpad 1',
98: 'numpad 2',
99: 'numpad 3',
100: 'numpad 4',
101: 'numpad 5',
102: 'numpad 6',
103: 'numpad 7',
104: 'numpad 8',
105: 'numpad 9',
106: 'multiply',
107: 'add',
109: 'subtract',
110: 'decimal point',
111: 'divide',
112: 'f1',
113: 'f2',
114: 'f3',
115: 'f4',
116: 'f5',
117: 'f6',
118: 'f7',
119: 'f8',
120: 'f9',
121: 'f10',
122: 'f11',
123: 'f12',
124: 'f13',
125: 'f14',
126: 'f15',
127: 'f16',
128: 'f17',
129: 'f18',
130: 'f19',
131: 'f20',
132: 'f21',
133: 'f22',
134: 'f23',
135: 'f24',
144: 'num lock',
145: 'scroll lock',
186: '&semi;',
187: '&equals;',
188: '&comma;',
189: '&hyphen;',
190: '&period;',
191: '&quest;',
192: '&grave;',
219: '&lsqb;',
220: '&bsol;',
221: '&rsqb;',
222: '&apos;',
};

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