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Alinson S. Xavier
2020-02-24 10:31:29 -06:00
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docs/problems/index.html
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@@ -145,11 +145,12 @@
<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>
<div class="col-md-9" role="main">
@@ -173,8 +174,7 @@
<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 0–1 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>