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Finish TSP implementation; improve performance of Extractors

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Alinson S. Xavier
2020-02-25 22:31:03 -06:00
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<title>Problems - MIPLearn</title>
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@@ -147,15 +140,16 @@
<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="#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>
<li class="second-level"><a href="#traveling-salesman-problem">Traveling Salesman Problem</a></li>
<li class="third-level"><a href="#problem-definition_2">Problem definition</a></li>
<li class="third-level"><a href="#problem-definition_1">Problem definition</a></li>
<li class="third-level"><a href="#random-problem-generator">Random problem generator</a></li>
<li class="third-level"><a href="#challenge-a_1">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_2">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_2">Challenge A</a></li>
</ul>
</div></div>
<div class="col-md-9" role="main">
@@ -192,8 +186,43 @@
</code></pre>
<p><img alt="alt" src="../figures/benchmark_stab_a.png" /></p>
<h2 id="multidimensional-0-1-knapsack-problem">Multidimensional 0-1 Knapsack Problem</h2>
<h2 id="traveling-salesman-problem">Traveling Salesman Problem</h2>
<h3 id="problem-definition_1">Problem definition</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 Karp's
21 NP-complete problems.</p>
<h3 id="random-problem-generator">Random problem generator</h3>
<p>The class <code>TravelingSalesmanGenerator</code> 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 <code>n</code>,
<code>x</code> and <code>y</code>. For each pair of cities $(i,j)$, the distance $d_{i,j}$ between them is set to:
<script type="math/tex; mode=display">
d_{i,j} = \gamma_{i,j} \sqrt{(x_i-x_j)^2 + (y_i - y_j)^2}
</script>
where $\gamma_{i,j}$ is sampled from the distribution <code>gamma</code>.</p>
<p>If <code>fix_cities=True</code> 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.</p>
<p>By default, all distances $d_{i,j}$ are rounded to the nearest integer. If <code>round=False</code>
is provided, this rounding will be disabled.</p>
<h3 id="challenge-a_1">Challenge A</h3>
<ul>
<li>Fixed list of 350 cities in the $[0, 1000]^2$ square</li>
<li>$\gamma_{i,j} \sim U(0.95, 1.05)$</li>
<li>500 training instances, 50 test instances</li>
</ul>
<pre><code class="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,
)
</code></pre>
<p><img alt="alt" src="../figures/benchmark_tsp_a.png" /></p>
<h2 id="multidimensional-0-1-knapsack-problem">Multidimensional 0-1 Knapsack Problem</h2>
<h3 id="problem-definition_2">Problem definition</h3>
<p>Given a set of $n$ items and $m$ 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>
<p>
<script type="math/tex; mode=display">\begin{align*}
@@ -235,7 +264,7 @@ 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>
<h3 id="challenge-a_1">Challenge A</h3>
<h3 id="challenge-a_2">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>
@@ -253,26 +282,7 @@ from the provided probability distributions <code>K</code> and <code>u</code>.</
)
</code></pre>
<p><img alt="alt" src="../figures/benchmark_knapsack_a.png" /></p>
<h2 id="traveling-salesman-problem">Traveling Salesman Problem</h2>
<h3 id="problem-definition_2">Problem definition</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 Karp's
21 NP-complete problems.</p>
<h3 id="random-problem-generator">Random problem generator</h3>
<p>The class <code>TravelingSalesmanGenerator</code> 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 <code>n</code>,
<code>x</code> and <code>y</code>. For each pair of cities $(i,j)$, the distance $d_{i,j}$ between them is set to:
<script type="math/tex; mode=display">
d_{i,j} = \gamma_{i,j} \sqrt{(x_i-x_j)^2 + (y_i - y_j)^2}
</script>
where $\gamma_{i,j}$ is sampled from the distribution <code>gamma</code>.</p>
<p>If <code>fix_cities=True</code> 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.</p>
<p>By default, all distances $d_{i,j}$ are rounded to the nearest integer. If <code>round=False</code>
is provided, this rounding will be disabled.</p></div>
<p><img alt="alt" src="../figures/benchmark_knapsack_a.png" /></p></div>
</div>
@@ -281,17 +291,17 @@ is provided, this rounding will be disabled.</p></div>
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