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<article id="content">
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<header>
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<h1 class="title">Module <code>miplearn.problems.stab</code></h1>
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</header>
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<section id="section-intro">
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<details class="source">
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<summary>
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<span>Expand source code</span>
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</summary>
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<pre><code class="python"># MIPLearn: Extensible Framework for Learning-Enhanced Mixed-Integer Optimization
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# Copyright (C) 2020, UChicago Argonne, LLC. All rights reserved.
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# Released under the modified BSD license. See COPYING.md for more details.
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import networkx as nx
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import numpy as np
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import pyomo.environ as pe
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from scipy.stats import uniform, randint
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from scipy.stats.distributions import rv_frozen
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from miplearn.instance import Instance
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class ChallengeA:
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def __init__(
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self,
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seed=42,
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n_training_instances=500,
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n_test_instances=50,
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):
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np.random.seed(seed)
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self.generator = MaxWeightStableSetGenerator(
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w=uniform(loc=100.0, scale=50.0),
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n=randint(low=200, high=201),
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p=uniform(loc=0.05, scale=0.0),
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fix_graph=True,
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)
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np.random.seed(seed + 1)
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self.training_instances = self.generator.generate(n_training_instances)
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np.random.seed(seed + 2)
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self.test_instances = self.generator.generate(n_test_instances)
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class MaxWeightStableSetGenerator:
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"""Random instance generator for the Maximum-Weight Stable Set Problem.
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The generator has two modes of operation. When `fix_graph=True` is provided, one random
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Erdős-Rényi graph $G_{n,p}$ is generated in the constructor, where $n$ and $p$ are sampled
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from user-provided probability distributions `n` and `p`. To generate each instance, the
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generator independently samples each $w_v$ from the user-provided probability distribution `w`.
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When `fix_graph=False`, a new random graph is generated for each instance; the remaining
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parameters are sampled in the same way.
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"""
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def __init__(
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self,
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w=uniform(loc=10.0, scale=1.0),
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n=randint(low=250, high=251),
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p=uniform(loc=0.05, scale=0.0),
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fix_graph=True,
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):
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"""Initialize the problem generator.
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Parameters
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----------
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w: rv_continuous
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Probability distribution for vertex weights.
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n: rv_discrete
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Probability distribution for parameter $n$ in Erdős-Rényi model.
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p: rv_continuous
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Probability distribution for parameter $p$ in Erdős-Rényi model.
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"""
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assert isinstance(w, rv_frozen), "w should be a SciPy probability distribution"
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assert isinstance(n, rv_frozen), "n should be a SciPy probability distribution"
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assert isinstance(p, rv_frozen), "p should be a SciPy probability distribution"
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self.w = w
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self.n = n
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self.p = p
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self.fix_graph = fix_graph
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self.graph = None
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if fix_graph:
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self.graph = self._generate_graph()
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def generate(self, n_samples):
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def _sample():
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if self.graph is not None:
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graph = self.graph
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else:
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graph = self._generate_graph()
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weights = self.w.rvs(graph.number_of_nodes())
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return MaxWeightStableSetInstance(graph, weights)
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return [_sample() for _ in range(n_samples)]
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def _generate_graph(self):
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return nx.generators.random_graphs.binomial_graph(self.n.rvs(), self.p.rvs())
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class MaxWeightStableSetInstance(Instance):
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"""An instance of the Maximum-Weight Stable Set Problem.
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Given a graph G=(V,E) and a weight w_v for each vertex v, the problem asks for a stable
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set S of G maximizing sum(w_v for v in S). A stable set (also called independent set) is
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a subset of vertices, no two of which are adjacent.
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This is one of Karp's 21 NP-complete problems.
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"""
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def __init__(self, graph, weights):
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super().__init__()
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self.graph = graph
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self.weights = weights
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def to_model(self):
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nodes = list(self.graph.nodes)
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model = pe.ConcreteModel()
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model.x = pe.Var(nodes, domain=pe.Binary)
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model.OBJ = pe.Objective(
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expr=sum(model.x[v] * self.weights[v] for v in nodes), sense=pe.maximize
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)
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model.clique_eqs = pe.ConstraintList()
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for clique in nx.find_cliques(self.graph):
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model.clique_eqs.add(sum(model.x[i] for i in clique) <= 1)
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return model
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def get_instance_features(self):
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return np.ones(0)
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def get_variable_features(self, var, index):
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neighbor_weights = [0] * 15
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neighbor_degrees = [100] * 15
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for n in self.graph.neighbors(index):
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neighbor_weights += [self.weights[n] / self.weights[index]]
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neighbor_degrees += [self.graph.degree(n) / self.graph.degree(index)]
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neighbor_weights.sort(reverse=True)
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neighbor_degrees.sort()
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features = []
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features += neighbor_weights[:5]
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features += neighbor_degrees[:5]
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features += [self.graph.degree(index)]
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return np.array(features)
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def get_variable_category(self, var, index):
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return "default"</code></pre>
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</details>
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</section>
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<section>
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</section>
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<section>
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</section>
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<section>
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</section>
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<section>
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<h2 class="section-title" id="header-classes">Classes</h2>
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<dl>
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<dt id="miplearn.problems.stab.ChallengeA"><code class="flex name class">
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<span>class <span class="ident">ChallengeA</span></span>
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<span>(</span><span>seed=42, n_training_instances=500, n_test_instances=50)</span>
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</code></dt>
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<dd>
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<section class="desc"></section>
|
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<details class="source">
|
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<summary>
|
|
<span>Expand source code</span>
|
|
</summary>
|
|
<pre><code class="python">class ChallengeA:
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def __init__(
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self,
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seed=42,
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n_training_instances=500,
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n_test_instances=50,
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):
|
|
|
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np.random.seed(seed)
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self.generator = MaxWeightStableSetGenerator(
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w=uniform(loc=100.0, scale=50.0),
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n=randint(low=200, high=201),
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p=uniform(loc=0.05, scale=0.0),
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fix_graph=True,
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)
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np.random.seed(seed + 1)
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self.training_instances = self.generator.generate(n_training_instances)
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np.random.seed(seed + 2)
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self.test_instances = self.generator.generate(n_test_instances)</code></pre>
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</details>
|
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</dd>
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<dt id="miplearn.problems.stab.MaxWeightStableSetGenerator"><code class="flex name class">
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<span>class <span class="ident">MaxWeightStableSetGenerator</span></span>
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<span>(</span><span>w=<scipy.stats._distn_infrastructure.rv_frozen object>, n=<scipy.stats._distn_infrastructure.rv_frozen object>, p=<scipy.stats._distn_infrastructure.rv_frozen object>, fix_graph=True)</span>
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</code></dt>
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<dd>
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<section class="desc"><p>Random instance generator for the Maximum-Weight Stable Set Problem.</p>
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<p>The generator has two modes of operation. When <code>fix_graph=True</code> is provided, one random
|
|
Erdős-Rényi graph $G_{n,p}$ is generated in the constructor, where $n$ and $p$ are sampled
|
|
from user-provided probability distributions <code>n</code> and <code>p</code>. To generate each instance, the
|
|
generator independently samples each $w_v$ from the user-provided probability distribution <code>w</code>.</p>
|
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<p>When <code>fix_graph=False</code>, a new random graph is generated for each instance; the remaining
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parameters are sampled in the same way.</p>
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<p>Initialize the problem generator.</p>
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<h2 id="parameters">Parameters</h2>
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<dl>
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<dt><strong><code>w</code></strong> : <code>rv_continuous</code></dt>
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<dd>Probability distribution for vertex weights.</dd>
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<dt><strong><code>n</code></strong> : <code>rv_discrete</code></dt>
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<dd>Probability distribution for parameter $n$ in Erdős-Rényi model.</dd>
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<dt><strong><code>p</code></strong> : <code>rv_continuous</code></dt>
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<dd>Probability distribution for parameter $p$ in Erdős-Rényi model.</dd>
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</dl></section>
|
|
<details class="source">
|
|
<summary>
|
|
<span>Expand source code</span>
|
|
</summary>
|
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<pre><code class="python">class MaxWeightStableSetGenerator:
|
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"""Random instance generator for the Maximum-Weight Stable Set Problem.
|
|
|
|
The generator has two modes of operation. When `fix_graph=True` is provided, one random
|
|
Erdős-Rényi graph $G_{n,p}$ is generated in the constructor, where $n$ and $p$ are sampled
|
|
from user-provided probability distributions `n` and `p`. To generate each instance, the
|
|
generator independently samples each $w_v$ from the user-provided probability distribution `w`.
|
|
|
|
When `fix_graph=False`, a new random graph is generated for each instance; the remaining
|
|
parameters are sampled in the same way.
|
|
"""
|
|
|
|
def __init__(
|
|
self,
|
|
w=uniform(loc=10.0, scale=1.0),
|
|
n=randint(low=250, high=251),
|
|
p=uniform(loc=0.05, scale=0.0),
|
|
fix_graph=True,
|
|
):
|
|
"""Initialize the problem generator.
|
|
|
|
Parameters
|
|
----------
|
|
w: rv_continuous
|
|
Probability distribution for vertex weights.
|
|
n: rv_discrete
|
|
Probability distribution for parameter $n$ in Erdős-Rényi model.
|
|
p: rv_continuous
|
|
Probability distribution for parameter $p$ in Erdős-Rényi model.
|
|
"""
|
|
assert isinstance(w, rv_frozen), "w should be a SciPy probability distribution"
|
|
assert isinstance(n, rv_frozen), "n should be a SciPy probability distribution"
|
|
assert isinstance(p, rv_frozen), "p should be a SciPy probability distribution"
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self.w = w
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self.n = n
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self.p = p
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self.fix_graph = fix_graph
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self.graph = None
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if fix_graph:
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self.graph = self._generate_graph()
|
|
|
|
def generate(self, n_samples):
|
|
def _sample():
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|
if self.graph is not None:
|
|
graph = self.graph
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|
else:
|
|
graph = self._generate_graph()
|
|
weights = self.w.rvs(graph.number_of_nodes())
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return MaxWeightStableSetInstance(graph, weights)
|
|
|
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return [_sample() for _ in range(n_samples)]
|
|
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def _generate_graph(self):
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return nx.generators.random_graphs.binomial_graph(self.n.rvs(), self.p.rvs())</code></pre>
|
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</details>
|
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<h3>Methods</h3>
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<dl>
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<dt id="miplearn.problems.stab.MaxWeightStableSetGenerator.generate"><code class="name flex">
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<span>def <span class="ident">generate</span></span>(<span>self, n_samples)</span>
|
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</code></dt>
|
|
<dd>
|
|
<section class="desc"></section>
|
|
<details class="source">
|
|
<summary>
|
|
<span>Expand source code</span>
|
|
</summary>
|
|
<pre><code class="python">def generate(self, n_samples):
|
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def _sample():
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if self.graph is not None:
|
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graph = self.graph
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else:
|
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graph = self._generate_graph()
|
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weights = self.w.rvs(graph.number_of_nodes())
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return MaxWeightStableSetInstance(graph, weights)
|
|
|
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return [_sample() for _ in range(n_samples)]</code></pre>
|
|
</details>
|
|
</dd>
|
|
</dl>
|
|
</dd>
|
|
<dt id="miplearn.problems.stab.MaxWeightStableSetInstance"><code class="flex name class">
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<span>class <span class="ident">MaxWeightStableSetInstance</span></span>
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<span>(</span><span>graph, weights)</span>
|
|
</code></dt>
|
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<dd>
|
|
<section class="desc"><p>An instance of the Maximum-Weight Stable Set Problem.</p>
|
|
<p>Given a graph G=(V,E) and a weight w_v for each vertex v, the problem asks for a stable
|
|
set S of G maximizing sum(w_v for v in S). A stable set (also called independent set) is
|
|
a subset of vertices, no two of which are adjacent.</p>
|
|
<p>This is one of Karp's 21 NP-complete problems.</p></section>
|
|
<details class="source">
|
|
<summary>
|
|
<span>Expand source code</span>
|
|
</summary>
|
|
<pre><code class="python">class MaxWeightStableSetInstance(Instance):
|
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"""An instance of the Maximum-Weight Stable Set Problem.
|
|
|
|
Given a graph G=(V,E) and a weight w_v for each vertex v, the problem asks for a stable
|
|
set S of G maximizing sum(w_v for v in S). A stable set (also called independent set) is
|
|
a subset of vertices, no two of which are adjacent.
|
|
|
|
This is one of Karp's 21 NP-complete problems.
|
|
"""
|
|
|
|
def __init__(self, graph, weights):
|
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super().__init__()
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self.graph = graph
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self.weights = weights
|
|
|
|
def to_model(self):
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nodes = list(self.graph.nodes)
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model = pe.ConcreteModel()
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model.x = pe.Var(nodes, domain=pe.Binary)
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model.OBJ = pe.Objective(
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expr=sum(model.x[v] * self.weights[v] for v in nodes), sense=pe.maximize
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)
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model.clique_eqs = pe.ConstraintList()
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for clique in nx.find_cliques(self.graph):
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model.clique_eqs.add(sum(model.x[i] for i in clique) <= 1)
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return model
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def get_instance_features(self):
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return np.ones(0)
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def get_variable_features(self, var, index):
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neighbor_weights = [0] * 15
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neighbor_degrees = [100] * 15
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for n in self.graph.neighbors(index):
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neighbor_weights += [self.weights[n] / self.weights[index]]
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neighbor_degrees += [self.graph.degree(n) / self.graph.degree(index)]
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neighbor_weights.sort(reverse=True)
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neighbor_degrees.sort()
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features = []
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features += neighbor_weights[:5]
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features += neighbor_degrees[:5]
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features += [self.graph.degree(index)]
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return np.array(features)
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|
|
def get_variable_category(self, var, index):
|
|
return "default"</code></pre>
|
|
</details>
|
|
<h3>Ancestors</h3>
|
|
<ul class="hlist">
|
|
<li><a title="miplearn.instance.Instance" href="../instance.html#miplearn.instance.Instance">Instance</a></li>
|
|
<li>abc.ABC</li>
|
|
</ul>
|
|
<h3>Inherited members</h3>
|
|
<ul class="hlist">
|
|
<li><code><b><a title="miplearn.instance.Instance" href="../instance.html#miplearn.instance.Instance">Instance</a></b></code>:
|
|
<ul class="hlist">
|
|
<li><code><a title="miplearn.instance.Instance.build_lazy_constraint" href="../instance.html#miplearn.instance.Instance.build_lazy_constraint">build_lazy_constraint</a></code></li>
|
|
<li><code><a title="miplearn.instance.Instance.find_violated_lazy_constraints" href="../instance.html#miplearn.instance.Instance.find_violated_lazy_constraints">find_violated_lazy_constraints</a></code></li>
|
|
<li><code><a title="miplearn.instance.Instance.get_instance_features" href="../instance.html#miplearn.instance.Instance.get_instance_features">get_instance_features</a></code></li>
|
|
<li><code><a title="miplearn.instance.Instance.get_variable_category" href="../instance.html#miplearn.instance.Instance.get_variable_category">get_variable_category</a></code></li>
|
|
<li><code><a title="miplearn.instance.Instance.get_variable_features" href="../instance.html#miplearn.instance.Instance.get_variable_features">get_variable_features</a></code></li>
|
|
<li><code><a title="miplearn.instance.Instance.to_model" href="../instance.html#miplearn.instance.Instance.to_model">to_model</a></code></li>
|
|
</ul>
|
|
</li>
|
|
</ul>
|
|
</dd>
|
|
</dl>
|
|
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<li><h3>Super-module</h3>
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<h4><code><a title="miplearn.problems.stab.ChallengeA" href="#miplearn.problems.stab.ChallengeA">ChallengeA</a></code></h4>
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</li>
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<li>
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<h4><code><a title="miplearn.problems.stab.MaxWeightStableSetGenerator" href="#miplearn.problems.stab.MaxWeightStableSetGenerator">MaxWeightStableSetGenerator</a></code></h4>
|
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<ul class="">
|
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<li><code><a title="miplearn.problems.stab.MaxWeightStableSetGenerator.generate" href="#miplearn.problems.stab.MaxWeightStableSetGenerator.generate">generate</a></code></li>
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</ul>
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</li>
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<li>
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<h4><code><a title="miplearn.problems.stab.MaxWeightStableSetInstance" href="#miplearn.problems.stab.MaxWeightStableSetInstance">MaxWeightStableSetInstance</a></code></h4>
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