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<div class="col-md-9" role="main">
<h1 id="miplearn">MIPLearn</h1>
<p><strong>MIPLearn</strong> is an extensible framework for <em>Learning-Enhanced Mixed-Integer Optimization</em>, an approach targeted at discrete optimization problems that need to be repeatedly solved with only minor changes to input data. The package uses Machine Learning (ML) to automatically identify patterns in previously solved instances of the problem, or in the solution process itself, and produces hints that can guide a conventional MIP solver towards the optimal solution faster. For particular classes of problems, this approach has been shown to provide significant performance benefits (see <a href="benchmark/#benchmark-results">benchmark results</a> and <a href="about/#references">references</a> for more details).</p>
<p><strong>MIPLearn</strong> is an extensible framework for <strong>Learning-Enhanced Mixed-Integer Optimization</strong>, an approach targeted at discrete optimization problems that need to be repeatedly solved with only minor changes to input data.</p>
<p>The package uses Machine Learning (ML) to automatically identify patterns in previously solved instances of the problem, or in the solution process itself, and produces hints that can guide a conventional MIP solver towards the optimal solution faster. For particular classes of problems, this approach has been shown to provide significant performance benefits (see <a href="problems/">benchmark results</a> and <a href="about/#references">references</a> for more details).</p>
<h3 id="features">Features</h3>
<ul>
<li>
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</ul>
<h3 id="souce-code">Souce Code</h3>
<ul>
<li><a href="https://github.com/iSoron/miplearn">https://github.com/iSoron/miplearn</a></li>
<li><a href="https://github.com/ANL-CEEESA/MIPLearn">https://github.com/ANL-CEEESA/MIPLearn</a></li>
</ul></div>
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<li class="third-level"><a href="#problem-definition">Problem definition</a></li>
<li class="third-level"><a href="#random-instance-generator">Random instance generator</a></li>
<li class="third-level"><a href="#benchmark-challenges_1">Benchmark challenges</a></li>
<li class="third-level"><a href="#challenge-a">Challenge A</a></li>
<li class="second-level"><a href="#multidimensional-0-1-knapsack-problem">Multidimensional 0-1 Knapsack Problem</a></li>
<li class="third-level"><a href="#problem-definition_1">Problem definition</a></li>
<li class="third-level"><a href="#random-instance-generator_1">Random instance generator</a></li>
<li class="third-level"><a href="#challenge-a_1">Challenge A</a></li>
</ul>
</div></div>
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<p>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 <em>stable set</em> if no two vertices of $S$ are adjacent. This is one of Karp's 21 NP-complete problems.</p>
<h3 id="random-instance-generator">Random instance generator</h3>
<p>The class <code>MaxWeightStableSetGenerator</code> can be used to generate random instances of this problem, with user-specified probability distributions. When the constructor parameter <code>fix_graph=True</code> 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 <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>. When <code>fix_graph=False</code>, a new random graph is generated for each instance, while the remaining parameters are sampled in the same way.</p>
<h3 id="benchmark-challenges_1">Benchmark challenges</h3>
<h4 id="challenge-a">Challenge A</h4>
<h3 id="challenge-a">Challenge A</h3>
<ul>
<li>Fixed random Erdős-Rényi graph $G_{n,p}$ with $n=200$ and $p=5\%$</li>
<li>Random vertex weights $w_v \sim U(100, 150)$</li>
@@ -230,7 +230,7 @@ from the provided probability distributions <code>K</code> and <code>u</code>.</
<li>Fréville, Arnaud. <em>The multidimensional 01 knapsack problem: An overview.</em> European Journal of Operational Research 155.1 (2004): 1-21.</li>
</ul>
</div>
<h4 id="challenge-a_1">Challenge A</h4>
<h3 id="challenge-a_1">Challenge A</h3>
<ul>
<li>250 variables, 10 constraints, fixed weights</li>
<li>$w \sim U(0, 1000), \gamma \sim U(0.95, 1.05)$</li>

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