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<div id="content" class="content">
<h1 class="title">On Statistical Learning of Branch and Bound for Vehicle Routing Optimization <img SRC="imgs/vrp.png" ALIGN="right" HSPACE="50" VSPACE="50" width="150pt"></h1>
<div id="table-of-contents" role="doc-toc">
<h2>Table of Contents</h2>
<div id="text-table-of-contents" role="doc-toc">
<ul>
<li><a href="#orged6fca3">1. Vehicle Routing Problem</a>
<ul>
<li><a href="#orgc0a1ac6">1.1. Integer Program</a></li>
</ul>
</li>
<li><a href="#org22e277e">2. Bin Packing Problem</a>
<ul>
<li><a href="#orgbccd27c">2.1. Integer Program</a></li>
</ul>
</li>
<li><a href="#org143049b">3. Installation</a>
<ul>
<li><a href="#org49de77a">3.1. Optimization Problems Instances</a></li>
</ul>
</li>
<li><a href="#orgd5a05e2">4. Usage Instructions</a>
<ul>
<li><a href="#org7d728b6">4.1. Sampling</a>
<ul>
<li><a href="#org207655d">4.1.1. Research sampled datasets</a></li>
</ul>
</li>
<li><a href="#orgf99123b">4.2. Training</a></li>
<li><a href="#org9a4fc69">4.3. Evaluation</a>
<ul>
<li><a href="#orgd5968fb">4.3.1. Pre-trained Models</a></li>
</ul>
</li>
</ul>
</li>
</ul>
</div>
</div>
<p>
<a href="https://github.com/isotlaboratory/ml4vrp">This repository</a> contains the code for reproducing the experiments performed in the <a href="https://arxiv.org/abs/2310.09986">"On Statistical Learning of Branch and Bound for Vehicle Routing Optimization"</a> research paper.
</p>
<div id="outline-container-orged6fca3" class="outline-2">
<h2 id="orged6fca3"><span class="section-number-2">1.</span> Vehicle Routing Problem</h2>
<div class="outline-text-2" id="text-1">
<p>
The violet lines represent integer but not feasible solutions, once a feasible
solution has been found, the paths are distinguished by colors. The light blue
lines fumbling around represent the LP-relaxed problem.
</p>
<div class="org-center">
nil</div>
<div class="org-center">
<table border="2" cellspacing="0" cellpadding="6" rules="groups" frame="hsides">
<caption class="t-above"><span class="table-number">Table 1:</span> Solving topologically different VRP instances using modified versions of <a href="https://arxiv.org/abs/1906.01629">GCNN</a>, <a href="https://arxiv.org/abs/1706.02216">GraphSAGE</a>, and <a href="https://arxiv.org/abs/1710.10903">GAT</a>.</caption>
<colgroup>
<col class="org-left" />
<col class="org-left" />
<col class="org-left" />
</colgroup>
<thead>
<tr>
<th scope="col" class="org-left">GCNN</th>
<th scope="col" class="org-left">GraphSAGE</th>
<th scope="col" class="org-left">GAT</th>
</tr>
</thead>
<tbody>
<tr>
<td class="org-left"><img src="./gifs/P-n55-k10_GCNN.gif" alt="P-n55-k10_GCNN.gif" /></td>
<td class="org-left"><img src="./gifs/P-n55-k10_GraphSAGE.gif" alt="P-n55-k10_GraphSAGE.gif" /></td>
<td class="org-left"><img src="./gifs/P-n55-k10_GAT.gif" alt="P-n55-k10_GAT.gif" /></td>
</tr>
<tr>
<td class="org-left"><img src="./gifs/B-n66-k9_GAT.gif" alt="B-n66-k9_GAT.gif" /></td>
<td class="org-left"><img src="./gifs/B-n66-k9_GraphSAGE.gif" alt="B-n66-k9_GraphSAGE.gif" /></td>
<td class="org-left"><img src="./gifs/B-n66-k9_GAT.gif" alt="B-n66-k9_GAT.gif" /></td>
</tr>
<tr>
<td class="org-left"><img src="./gifs/E-n76-k8_GCNN.gif" alt="E-n76-k8_GCNN.gif" /></td>
<td class="org-left"><img src="./gifs/E-n76-k8_GraphSAGE.gif" alt="E-n76-k8_GraphSAGE.gif" /></td>
<td class="org-left"><img src="./gifs/E-n76-k8_GAT.gif" alt="E-n76-k8_GAT.gif" /></td>
</tr>
<tr>
<td class="org-left"><img src="./gifs/P-n55-k15.gif" alt="P-n55-k15.gif" /></td>
<td class="org-left"><img src="./gifs/P-n55-k15_GraphSAGE.gif" alt="P-n55-k15_GraphSAGE.gif" /></td>
<td class="org-left"><img src="./gifs/P-n55-k15_GAT.gif" alt="P-n55-k15_GAT.gif" /></td>
</tr>
<tr>
<td class="org-left"><img src="./imgs/gcnn.png" alt="gcnn.png" /></td>
<td class="org-left"><img src="./imgs/graph_sage.png" alt="graph_sage.png" /></td>
<td class="org-left"><img src="./imgs/gat.png" alt="gat.png" /></td>
</tr>
</tbody>
</table>
</div>
</div>
<div id="outline-container-orgc0a1ac6" class="outline-3">
<h3 id="orgc0a1ac6"><span class="section-number-3">1.1.</span> Integer Program</h3>
<div class="outline-text-3" id="text-1-1">
<div id="org8c0a4d7" class="figure">
<p><img src="./imgs/cvrp_ip.png" alt="cvrp_ip.png" width="300pt" />
</p>
</div>
</div>
</div>
</div>
<div id="outline-container-org22e277e" class="outline-2">
<h2 id="org22e277e"><span class="section-number-2">2.</span> Bin Packing Problem</h2>
<div class="outline-text-2" id="text-2">
<p>
Although BPP classifiers can be used/trained independently, the original motive
for this research was to provide a means to calculating the minimum number of
required vehicles for solving a VRP instance. The blue boxes, filling the right
side of the bin, analogously, represent the LP-relaxed problem (which are
cruising out of the bins since they have less constraints :).
</p>
<div class="org-center">
<div id="org7c06387" class="figure">
<p><img src="./gifs/u80_00_GCNN.gif" alt="u80_00_GCNN.gif" width="90%" />
</p>
<p><span class="figure-number">Figure 1: </span>Distributing 80 weighted items across 48 bins using GraphSAGE</p>
</div>
</div>
</div>
<div id="outline-container-orgbccd27c" class="outline-3">
<h3 id="orgbccd27c"><span class="section-number-3">2.1.</span> Integer Program</h3>
<div class="outline-text-3" id="text-2-1">
<div id="org4a9965b" class="figure">
<p><img src="./imgs/bpp_ip.png" alt="bpp_ip.png" width="300pt" />
</p>
</div>
</div>
</div>
</div>
<div id="outline-container-org143049b" class="outline-2">
<h2 id="org143049b"><span class="section-number-2">3.</span> Installation</h2>
<div class="outline-text-2" id="text-3">
<p>
Cloning the repository:
</p>
<pre class="example">
git clone git@github.com:isotlaboratory/ml4vrp.git
</pre>
<p>
Then our fork of <a href="https://github.com/ds4dm/ecole">École</a>:
</p>
<pre class="example">
git clone git@github.com:ndrwnaguib/ecole.git
</pre>
<p>
or, equivalently, cloning the original source code of École and patching it using:
</p>
<pre class="example">
git clone git@github.com:ds4dm/ecole.git
cd ecole
patch -p1 < ../ecole.patch
</pre>
<p>
And eventually, SCIP, which is the underlying mathematical solver where we
replace the branching strategies with trained classifiers, <a href="https://scipopt.org/index.php#download">from here</a>. Once the
precomplied version have been extracted, install école using:
</p>
<pre class="example">
cd [PATH]/[TO]/ecole
CMAKE_ARGS="-DSCIP_DIR=[PATH]/[TO]/scipoptsuite/src/build/scip -DCMAKE_INSTALL_RPATH_USE_LINK_PATH=ON" python -m pip install .
</pre>
<p>
Moreover, the following packages are necessary for the sampling, training, and evaluation steps:
</p>
<pre class="example">
export SCIPOPTDIR=[PATH]/[TO]/scipoptsuite/usr
python -m pip install pyscipopt
#
python -m pip install pytorch-lightning
python -m pip install fairscale
python -m pip install randomname
</pre>
</div>
<div id="outline-container-org49de77a" class="outline-3">
<h3 id="org49de77a"><span class="section-number-3">3.1.</span> Optimization Problems Instances</h3>
<div class="outline-text-3" id="text-3-1">
<p>
The instances used in our experiments for BPP are already included in the
repository given their light size. However, to download the VRP instances,
please run the <a href="./instances/vrp/download.sh">./instances/vrp/download.sh</a> bash script.
</p>
</div>
</div>
</div>
<div id="outline-container-orgd5a05e2" class="outline-2">
<h2 id="orgd5a05e2"><span class="section-number-2">4.</span> Usage Instructions</h2>
<div class="outline-text-2" id="text-4">
</div>
<div id="outline-container-org7d728b6" class="outline-3">
<h3 id="org7d728b6"><span class="section-number-3">4.1.</span> Sampling</h3>
<div class="outline-text-3" id="text-4-1">
<p>
To sample B&B decisions when solving a VRP instance, please use the
following command:
</p>
<pre class="example">
python sample.py --problem "VRP" --instance [VRP_FILE_FORMAT_FILE_PATH] --num-train-samples [DECISION SAMPLES SIZE]
</pre>
<p>
For example, to sample a dataset of 1000 decision samples for the <a href="http://vrp.galgos.inf.puc-rio.br/index.php/en/plotted-instances?data=A-n32-k5">A-n32-k5</a>
instance, the command is:
</p>
<pre class="example">
python sample.py --problem "VRP" --instance datasets/vrp/A/A-n32-k5.vrp --num-train-samples 1000
</pre>
<p>
The same command can be used with to do the sample B&B decisions for the BPP; however, along with changing
the input instance accordingly.
</p>
</div>
<div id="outline-container-org207655d" class="outline-4">
<h4 id="org207655d"><span class="section-number-4">4.1.1.</span> Research sampled datasets</h4>
<div class="outline-text-4" id="text-4-1-1">
<p>
The datasets we sampled and used to train our models are larger in size, we are
going to share them as soon as we find a suitable dataset repository.
</p>
</div>
</div>
</div>
<div id="outline-container-orgf99123b" class="outline-3">
<h3 id="orgf99123b"><span class="section-number-3">4.2.</span> Training</h3>
<div class="outline-text-3" id="text-4-2">
<pre class="example">
python train.py --samples-path samples/A-n32-k5 --gpus 1 --cpus 6 --name [EXP_NAME] --model-name GCNN --log-dir logs --epochs 1
</pre>
</div>
</div>
<div id="outline-container-org9a4fc69" class="outline-3">
<h3 id="org9a4fc69"><span class="section-number-3">4.3.</span> Evaluation</h3>
<div class="outline-text-3" id="text-4-3">
<p>
The trained models can be evaluated using:
</p>
<pre class="example">
python evaluate.py --checkpoint weights/vrp/GraphSAGE/A-32-k5_GraphSAGE --arch GraphSAGE --results-path . --time-limit 60 --dataset datasets/vrp/A/M-n151-k12.vrp --problem CVRP
</pre>
<p>
Additionally, there is a <code class="src src-sh">--live</code> for both problems which plots the
process of solving both the relaxed problem and printing the feasible solutions.
</p>
<p>
A small <i>warning</i> when using that option for BPP; the plotting uses
multi-threading, and spawns a number of threads equal to the number of
available bins, while this may be improved, at the time, we were only
evaluating simple problems where number of bins ranged from 30-60.
</p>
<p>
Also, one might notice that the transparent blue boxes sometimes, if not
always, break free from the bin borders (in BPP), these are not coding
glitches, in fact, they properly represent the relaxed problem, during which
the constraints to the original problem (the boxes in other colors) are
relaxed, i.e., allowed to be violated. The same concept applies to the
background blue lines in the VRP visualization.
</p>
<pre class="example">
python evaluate.py --checkpoint weights/vrp/GraphSAGE/A-32-k5_GraphSAGE --arch GraphSAGE --results-path . --time-limit 60 --dataset datasets/vrp/A/M-n151-k12.vrp --problem CVRP --live
</pre>
</div>
<div id="outline-container-orgd5968fb" class="outline-4">
<h4 id="orgd5968fb"><span class="section-number-4">4.3.1.</span> Pre-trained Models</h4>
<div class="outline-text-4" id="text-4-3-1">
<p>
The trained models weights are available under <a href="./weights">./weights</a>.
For example, one can load the architecture
weights when trained on as follows:
</p>
<pre class="example">
python evaluate.py --checkpoint weights/[PROBLEM]/A-n32-k5_GraphSAGE
</pre>
<p>
where PROBLEM <img src="ltximg/readme_d7090c1eff0b7e1146dc439909daad17541335b7.svg" alt="${\tiny \in}$" class="org-svg" /> {CVRP, BPP}.
</p>
</div>
</div>
</div>
</div>
</div>
<div id="postamble" class="status">
<p class="author">Author: Andrew Naguib</p>
<p class="date">Created: 2023-10-16 Mon 18:03</p>
<p class="validation"><a href="https://validator.w3.org/check?uri=referer">Validate</a></p>
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