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On Statistical Learning of Branch and Bound for Vehicle Routing Optimization

This repository contains the code for reproducing the experiments performed in the “On Statistical Learning of Branch and Bound for Vehicle Routing Optimization” research paper.

Vehicle Routing Problem

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.

GCNN	GraphSAGE	GAT

Integer Program

Bin Packing Problem

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 :).

Integer Program

Installation

Cloning the repository:

git clone git@github.com:isotlaboratory/ml4vrp.git

Then our fork of École:

git clone git@github.com:ndrwnaguib/ecole.git

or, equivalently, cloning the original source code of École and patching it using:

git clone git@github.com:ds4dm/ecole.git
cd ecole
patch -p1 < ../ecole.patch

And eventually, SCIP, which is the underlying mathematical solver where we replace the branching strategies with trained classifiers, from here. Once the precomplied version have been extracted, install école using:

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 .

Moreover, the following packages are necessary for the sampling, training, and evaluation steps:

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

Optimization Problems Instances

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 ./instances/vrp/download.sh bash script.

Usage Instructions

Sampling

To sample B&B decisions when solving a VRP instance, please use the following command:

python sample.py --problem "VRP" --instance [VRP_FILE_FORMAT_FILE_PATH] --num-train-samples [DECISION SAMPLES SIZE]

For example, to sample a dataset of 1000 decision samples for the A-n32-k5 instance, the command is:

python sample.py --problem "VRP" --instance datasets/vrp/A/A-n32-k5.vrp --num-train-samples 1000

The same command can be used with src_sh[:exports_code]{–problem BPP} to do the sample B&B decisions for the BPP; however, along with changing the input instance accordingly.

Research sampled datasets

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.

Training

python train.py --samples-path samples/A-n32-k5 --gpus 1 --cpus 6 --name [EXP_NAME] --model-name GCNN --log-dir logs --epochs 1

Evaluation

The trained models can be evaluated using:

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

Additionally, there is a src_sh[:exports code]{–live} for both problems which plots the process of solving both the relaxed problem and printing the feasible solutions.

A small warning 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.

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.

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-trained Models

The trained models weights are available under ./weights. For example, one can load the src_sh[:exports_code]{GraphSAGE} architecture weights when trained on src_sh[:exports_code]{A-n32-k5} as follows:

python evaluate.py --checkpoint weights/[PROBLEM]/A-n32-k5_GraphSAGE

where PROBLEM ${\tiny ∈}$ {CVRP, BPP}.