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Docs: Add TSP

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Alinson S. Xavier
2020-02-24 22:02:16 -06:00
parent 7a01d9cbcf
commit 68e972c635
12 changed files with 107 additions and 86 deletions
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32
docs-src/problems.md
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@@ -20,6 +20,8 @@ To illustrate the performance of `LearningSolver`, and to set a baseline for new
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
@@ -45,6 +47,8 @@ MaxWeightStableSetGenerator(w=uniform(loc=100., scale=50.),
![alt](figures/benchmark_stab_a.png)
## Multidimensional 0-1 Knapsack Problem
### Problem definition
@@ -115,3 +119,31 @@ MultiKnapsackGenerator(n=randint(low=250, high=251),
```
![alt](figures/benchmark_knapsack_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.

16
docs/404.html
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@@ -14,16 +14,14 @@
<title>MIPLearn</title>
<link rel="stylesheet" href="https://use.fontawesome.com/releases/v5.12.0/css/all.css">
<link rel="stylesheet" href="https://use.fontawesome.com/releases/v5.12.0/css/v4-shims.css">
<link rel="stylesheet" href="//use.fontawesome.com/releases/v5.5.0/css/all.css" integrity="sha384-B4dIYHKNBt8Bc12p+WXckhzcICo0wtJAoU8YZTY5qE0Id1GSseTk6S+L3BlXeVIU" crossorigin="anonymous">
<link rel="stylesheet" href="//cdn.jsdelivr.net/npm/hack-font@3.3.0/build/web/hack.min.css">
<link href='//rsms.me/inter/inter.css' rel='stylesheet' type='text/css'>
<link href='//fonts.googleapis.com/css?family=PT+Sans:400,400italic,700,700italic&subset=latin-ext,latin' rel='stylesheet' type='text/css'>
<link href='//fonts.googleapis.com/css?family=Open+Sans:300italic,400italic,700italic,400,300,600,700&subset=latin-ext,latin' rel='stylesheet' type='text/css'>
<link href="/css/bootstrap-custom.min.css" rel="stylesheet">
<link href="/css/base.min.css" rel="stylesheet">
<link href="/css/cinder.min.css" rel="stylesheet">
<link href="/css/highlight.min.css" rel="stylesheet">
<link href="/css/custom.css" rel="stylesheet">
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@@ -151,7 +149,8 @@
</footer>
<script src="//ajax.googleapis.com/ajax/libs/jquery/1.12.4/jquery.min.js"></script>
<script src="/js/bootstrap-3.0.3.min.js"></script>
<script src="/js/highlight.pack.js"></script>
<script>hljs.initHighlightingOnLoad();</script>
<script>var base_url = "/"</script>
<script src="/js/base.js"></script>
@@ -163,11 +162,8 @@
<div class="modal-dialog modal-lg">
<div class="modal-content">
<div class="modal-header">
<button type="button" class="close" data-dismiss="modal">
<span aria-hidden="true">&times;</span>
<span class="sr-only">Close</span>
</button>
<h4 class="modal-title" id="searchModalLabel">Search</h4>
<button type="button" class="close" data-dismiss="modal"><span aria-hidden="true">&times;</span><span class="sr-only">Close</span></button>
</div>
<div class="modal-body">
<p>

16
docs/about/index.html
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@@ -14,16 +14,14 @@
<title>About - MIPLearn</title>
<link rel="stylesheet" href="https://use.fontawesome.com/releases/v5.12.0/css/all.css">
<link rel="stylesheet" href="https://use.fontawesome.com/releases/v5.12.0/css/v4-shims.css">
<link rel="stylesheet" href="//use.fontawesome.com/releases/v5.5.0/css/all.css" integrity="sha384-B4dIYHKNBt8Bc12p+WXckhzcICo0wtJAoU8YZTY5qE0Id1GSseTk6S+L3BlXeVIU" crossorigin="anonymous">
<link rel="stylesheet" href="//cdn.jsdelivr.net/npm/hack-font@3.3.0/build/web/hack.min.css">
<link href='//rsms.me/inter/inter.css' rel='stylesheet' type='text/css'>
<link href='//fonts.googleapis.com/css?family=PT+Sans:400,400italic,700,700italic&subset=latin-ext,latin' rel='stylesheet' type='text/css'>
<link href='//fonts.googleapis.com/css?family=Open+Sans:300italic,400italic,700italic,400,300,600,700&subset=latin-ext,latin' rel='stylesheet' type='text/css'>
<link href="../css/bootstrap-custom.min.css" rel="stylesheet">
<link href="../css/base.min.css" rel="stylesheet">
<link href="../css/cinder.min.css" rel="stylesheet">
<link href="../css/highlight.min.css" rel="stylesheet">
<link href="../css/custom.css" rel="stylesheet">
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@@ -209,7 +207,8 @@ POSSIBILITY OF SUCH DAMAGE.
</footer>
<script src="//ajax.googleapis.com/ajax/libs/jquery/1.12.4/jquery.min.js"></script>
<script src="../js/bootstrap-3.0.3.min.js"></script>
<script src="../js/highlight.pack.js"></script>
<script>hljs.initHighlightingOnLoad();</script>
<script>var base_url = ".."</script>
<script src="../js/base.js"></script>
@@ -221,11 +220,8 @@ POSSIBILITY OF SUCH DAMAGE.
<div class="modal-dialog modal-lg">
<div class="modal-content">
<div class="modal-header">
<button type="button" class="close" data-dismiss="modal">
<span aria-hidden="true">&times;</span>
<span class="sr-only">Close</span>
</button>
<h4 class="modal-title" id="searchModalLabel">Search</h4>
<button type="button" class="close" data-dismiss="modal"><span aria-hidden="true">&times;</span><span class="sr-only">Close</span></button>
</div>
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16
docs/benchmark/index.html
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@@ -14,16 +14,14 @@
<title>Benchmark - MIPLearn</title>
<link rel="stylesheet" href="https://use.fontawesome.com/releases/v5.12.0/css/all.css">
<link rel="stylesheet" href="https://use.fontawesome.com/releases/v5.12.0/css/v4-shims.css">
<link rel="stylesheet" href="//use.fontawesome.com/releases/v5.5.0/css/all.css" integrity="sha384-B4dIYHKNBt8Bc12p+WXckhzcICo0wtJAoU8YZTY5qE0Id1GSseTk6S+L3BlXeVIU" crossorigin="anonymous">
<link rel="stylesheet" href="//cdn.jsdelivr.net/npm/hack-font@3.3.0/build/web/hack.min.css">
<link href='//rsms.me/inter/inter.css' rel='stylesheet' type='text/css'>
<link href='//fonts.googleapis.com/css?family=PT+Sans:400,400italic,700,700italic&subset=latin-ext,latin' rel='stylesheet' type='text/css'>
<link href='//fonts.googleapis.com/css?family=Open+Sans:300italic,400italic,700italic,400,300,600,700&subset=latin-ext,latin' rel='stylesheet' type='text/css'>
<link href="../css/bootstrap-custom.min.css" rel="stylesheet">
<link href="../css/base.min.css" rel="stylesheet">
<link href="../css/cinder.min.css" rel="stylesheet">
<link href="../css/highlight.min.css" rel="stylesheet">
<link href="../css/custom.css" rel="stylesheet">
<!-- HTML5 shim and Respond.js IE8 support of HTML5 elements and media queries -->
@@ -218,7 +216,8 @@ benchmark.parallel_solve(test_instances)
</footer>
<script src="//ajax.googleapis.com/ajax/libs/jquery/1.12.4/jquery.min.js"></script>
<script src="../js/bootstrap-3.0.3.min.js"></script>
<script src="../js/highlight.pack.js"></script>
<script>hljs.initHighlightingOnLoad();</script>
<script>var base_url = ".."</script>
<script src="../js/base.js"></script>
@@ -230,11 +229,8 @@ benchmark.parallel_solve(test_instances)
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18
docs/css/cinder.css
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@@ -10,28 +10,23 @@ body {
color: #343838;
}
h1, h2, h3, h4, h5, h6 {
font-family:'Inter', 'Helvetica Neue', Helvetica, Arial, sans-serif;
font-family:'PT Sans', 'Helvetica Neue', Helvetica, Arial, sans-serif;
color: #222;
}
h1 small, h2 small, h3 small, h4 small, h5 small, h6 small, .h1 small, .h2 small, .h3 small, .h4 small, .h5 small, .h6 small, h1 .small, h2 .small, h3 .small, h4 .small, h5 .small, h6 .small, .h1 .small, .h2 .small, .h3 .small, .h4 .small, .h5 .small, .h6 .small {
color: #B1B7B9;
}
h2 {
margin-top: 35px;
}
h1, h2 {
font-weight: 700;
}
h4 {
font-family: 'Inter', 'Helvetica Neue', Helvetica, Arial, sans-serif;
font-family: 'Open Sans', 'Helvetica Neue', Helvetica, Arial, sans-serif;
font-weight: 300;
margin-top: 20px;
font-style: italic;
}
h5 {
font-family: 'Inter', 'Helvetica Neue', Helvetica, Arial, sans-serif;
font-family: 'Open Sans', 'Helvetica Neue', Helvetica, Arial, sans-serif;
font-weight: 300;
font-variant: small-caps;
}
@@ -46,7 +41,7 @@ pre {
margin-bottom: 25px;
}
.lead {
font-family:"Inter", "Helvetica Neue", Helvetica, Arial, sans-serif;
font-family:"Open Sans", "Helvetica Neue", Helvetica, Arial, sans-serif;
font-weight: 400;
line-height: 1.4;
letter-spacing: 0.0312em;
@@ -59,8 +54,7 @@ pre {
.bs-sidenav {
background-image: url("../img/grid11.png");
background-repeat: repeat;
font-family: Inter,"Helvetica Neue",Helvetica,Arial,sans-serif;
font-size: 13px;
font-size: 12px;
}
.well {
background-color: #FCFDFF;
@@ -77,7 +71,7 @@ pre {
box-shadow: none;
}
#mkdocs-search-query {
font-family:"Inter", "Helvetica Neue", Helvetica, Arial, sans-serif;
font-family:"Open Sans", "Helvetica Neue", Helvetica, Arial, sans-serif;
font-size: 20px;
font-weight: 700;
color: #343838;

2
docs/css/cinder.min.css vendored
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@@ -1 +1 @@
body{font-family:"Open Sans","Helvetica Neue",Helvetica,Arial,sans-serif;font-size:16px;line-height:1.7;background-color:#FFF;color:#343838}h1,h2,h3,h4,h5,h6{font-family:'Inter','Helvetica Neue',Helvetica,Arial,sans-serif;color:#222}h1 small,h2 small,h3 small,h4 small,h5 small,h6 small,.h1 small,.h2 small,.h3 small,.h4 small,.h5 small,.h6 small,h1 .small,h2 .small,h3 .small,h4 .small,h5 .small,h6 .small,.h1 .small,.h2 .small,.h3 .small,.h4 .small,.h5 .small,.h6 .small{color:#b1b7b9}h2{margin-top:35px}h1,h2{font-weight:700}h4{font-family:'Inter','Helvetica Neue',Helvetica,Arial,sans-serif;font-weight:300;margin-top:20px;font-style:italic}h5{font-family:'Inter','Helvetica Neue',Helvetica,Arial,sans-serif;font-weight:300;font-variant:small-caps}pre,code{background-color:#fcfdff}pre>code{font-size:13px}pre{margin-top:25px;margin-bottom:25px}.lead{font-family:"Inter","Helvetica Neue",Helvetica,Arial,sans-serif;font-weight:400;line-height:1.4;letter-spacing:.0312em;color:#b1b7b9}.navbar-default{background-color:#343838;border-bottom:8px #ebf2f2 solid}.bs-sidenav{background-image:url("../img/grid11.png");background-repeat:repeat;font-family:Inter,"Helvetica Neue",Helvetica,Arial,sans-serif;font-size:13px}.well{background-color:#fcfdff}.btn-default{background-color:#fcfdff}.table-striped>tbody>tr:nth-child(2n+1)>td,.table-striped>tbody>tr:nth-child(2n+1)>th{background-color:#fcfdff}#mkdocs-search-query:focus{outline:0;-webkit-box-shadow:none;box-shadow:none}#mkdocs-search-query{font-family:"Inter","Helvetica Neue",Helvetica,Arial,sans-serif;font-size:20px;font-weight:700;color:#343838;height:45px}footer>hr{width:35%}
body{font-family:"Open Sans","Helvetica Neue",Helvetica,Arial,sans-serif;font-size:16px;line-height:1.7;background-color:#FFF;color:#343838}h1,h2,h3,h4,h5,h6{font-family:'PT Sans','Helvetica Neue',Helvetica,Arial,sans-serif;color:#222}h1 small,h2 small,h3 small,h4 small,h5 small,h6 small,.h1 small,.h2 small,.h3 small,.h4 small,.h5 small,.h6 small,h1 .small,h2 .small,h3 .small,h4 .small,h5 .small,h6 .small,.h1 .small,.h2 .small,.h3 .small,.h4 .small,.h5 .small,.h6 .small{color:#b1b7b9}h1,h2{font-weight:700}h4{font-family:'Open Sans','Helvetica Neue',Helvetica,Arial,sans-serif;font-weight:300;margin-top:20px;font-style:italic}h5{font-family:'Open Sans','Helvetica Neue',Helvetica,Arial,sans-serif;font-weight:300;font-variant:small-caps}pre,code{background-color:#fcfdff}pre>code{font-size:13px}pre{margin-top:25px;margin-bottom:25px}.lead{font-family:"Open Sans","Helvetica Neue",Helvetica,Arial,sans-serif;font-weight:400;line-height:1.4;letter-spacing:.0312em;color:#b1b7b9}.navbar-default{background-color:#343838;border-bottom:8px #ebf2f2 solid}.bs-sidenav{background-image:url("../img/grid11.png");background-repeat:repeat;font-size:12px}.well{background-color:#fcfdff}.btn-default{background-color:#fcfdff}.table-striped>tbody>tr:nth-child(2n+1)>td,.table-striped>tbody>tr:nth-child(2n+1)>th{background-color:#fcfdff}#mkdocs-search-query:focus{outline:0;-webkit-box-shadow:none;box-shadow:none}#mkdocs-search-query{font-family:"Open Sans","Helvetica Neue",Helvetica,Arial,sans-serif;font-size:20px;font-weight:700;color:#343838;height:45px}footer>hr{width:35%}

16
docs/customization/index.html
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@@ -14,16 +14,14 @@
<title>Customization - MIPLearn</title>
<link rel="stylesheet" href="https://use.fontawesome.com/releases/v5.12.0/css/all.css">
<link rel="stylesheet" href="https://use.fontawesome.com/releases/v5.12.0/css/v4-shims.css">
<link rel="stylesheet" href="//use.fontawesome.com/releases/v5.5.0/css/all.css" integrity="sha384-B4dIYHKNBt8Bc12p+WXckhzcICo0wtJAoU8YZTY5qE0Id1GSseTk6S+L3BlXeVIU" crossorigin="anonymous">
<link rel="stylesheet" href="//cdn.jsdelivr.net/npm/hack-font@3.3.0/build/web/hack.min.css">
<link href='//rsms.me/inter/inter.css' rel='stylesheet' type='text/css'>
<link href='//fonts.googleapis.com/css?family=PT+Sans:400,400italic,700,700italic&subset=latin-ext,latin' rel='stylesheet' type='text/css'>
<link href='//fonts.googleapis.com/css?family=Open+Sans:300italic,400italic,700italic,400,300,600,700&subset=latin-ext,latin' rel='stylesheet' type='text/css'>
<link href="../css/bootstrap-custom.min.css" rel="stylesheet">
<link href="../css/base.min.css" rel="stylesheet">
<link href="../css/cinder.min.css" rel="stylesheet">
<link href="../css/highlight.min.css" rel="stylesheet">
<link href="../css/custom.css" rel="stylesheet">
<!-- HTML5 shim and Respond.js IE8 support of HTML5 elements and media queries -->
@@ -171,7 +169,8 @@ solver = LearningSolver(solver=&quot;cplex&quot;,
</footer>
<script src="//ajax.googleapis.com/ajax/libs/jquery/1.12.4/jquery.min.js"></script>
<script src="../js/bootstrap-3.0.3.min.js"></script>
<script src="../js/highlight.pack.js"></script>
<script>hljs.initHighlightingOnLoad();</script>
<script>var base_url = ".."</script>
<script src="../js/base.js"></script>
@@ -183,11 +182,8 @@ solver = LearningSolver(solver=&quot;cplex&quot;,
<div class="modal-dialog modal-lg">
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docs/index.html
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@@ -14,16 +14,14 @@
<title>Home - MIPLearn</title>
<link rel="stylesheet" href="https://use.fontawesome.com/releases/v5.12.0/css/all.css">
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<link rel="stylesheet" href="//cdn.jsdelivr.net/npm/hack-font@3.3.0/build/web/hack.min.css">
<link href='//rsms.me/inter/inter.css' rel='stylesheet' type='text/css'>
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<link href='//fonts.googleapis.com/css?family=Open+Sans:300italic,400italic,700italic,400,300,600,700&subset=latin-ext,latin' rel='stylesheet' type='text/css'>
<link href="css/bootstrap-custom.min.css" rel="stylesheet">
<link href="css/base.min.css" rel="stylesheet">
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@@ -197,7 +195,8 @@
</footer>
<script src="//ajax.googleapis.com/ajax/libs/jquery/1.12.4/jquery.min.js"></script>
<script src="js/bootstrap-3.0.3.min.js"></script>
<script src="js/highlight.pack.js"></script>
<script>hljs.initHighlightingOnLoad();</script>
<script>var base_url = "."</script>
<script src="js/base.js"></script>
@@ -209,11 +208,8 @@
<div class="modal-dialog modal-lg">
<div class="modal-content">
<div class="modal-header">
<button type="button" class="close" data-dismiss="modal">
<span aria-hidden="true">&times;</span>
<span class="sr-only">Close</span>
</button>
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@@ -277,5 +273,5 @@
<!--
MkDocs version : 1.0.4
Build Date UTC : 2020-02-24 16:57:12
Build Date UTC : 2020-02-25 04:02:08
-->

41
docs/problems/index.html
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@@ -14,16 +14,14 @@
<title>Problems - MIPLearn</title>
<link rel="stylesheet" href="https://use.fontawesome.com/releases/v5.12.0/css/all.css">
<link rel="stylesheet" href="https://use.fontawesome.com/releases/v5.12.0/css/v4-shims.css">
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<link href='//fonts.googleapis.com/css?family=PT+Sans:400,400italic,700,700italic&subset=latin-ext,latin' rel='stylesheet' type='text/css'>
<link href='//fonts.googleapis.com/css?family=Open+Sans:300italic,400italic,700italic,400,300,600,700&subset=latin-ext,latin' rel='stylesheet' type='text/css'>
<link href="../css/bootstrap-custom.min.css" rel="stylesheet">
<link href="../css/base.min.css" rel="stylesheet">
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<link href="../css/custom.css" rel="stylesheet">
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@@ -154,6 +152,10 @@
<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="#random-problem-generator">Random problem generator</a></li>
</ul>
</div></div>
<div class="col-md-9" role="main">
@@ -251,7 +253,26 @@ 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></div>
<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>
</div>
@@ -269,7 +290,8 @@ from the provided probability distributions <code>K</code> and <code>u</code>.</
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@@ -281,11 +303,8 @@ from the provided probability distributions <code>K</code> and <code>u</code>.</
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@@ -14,16 +14,14 @@
<title>Usage - MIPLearn</title>
<link rel="stylesheet" href="https://use.fontawesome.com/releases/v5.12.0/css/all.css">
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@@ -254,7 +252,8 @@ solver.solve(test_instance)
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<script>hljs.initHighlightingOnLoad();</script>
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@@ -266,11 +265,8 @@ solver.solve(test_instance)
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