Combinatorial optimization problems are typically tackled by the branch-and-bound paradigm. We propose a new graph convolutional neural network model for learning branch-and-bound variable selection policies, which leverages the natural variable-constraint bipartite graph representation of mixed-integer linear programs. We train our model via imitation learning from the strong branching expert rule, and demonstrate on a series of hard problems that our approach produces policies that improve upon state-of-the-art machine-learning methods for branching and generalize to instances significantly larger than seen during training. Moreover, we improve for the first time over expert-designed branching rules implemented in a state-of-the-art solver on large problems. Code for reproducing all the experiments can be found at https://github.com/ds4dm/learn2branch.
@article{arxiv.1906.01629,
title = {Exact Combinatorial Optimization with Graph Convolutional Neural Networks},
author = {Maxime Gasse and Didier Chételat and Nicola Ferroni and Laurent Charlin and Andrea Lodi},
journal= {arXiv preprint arXiv:1906.01629},
year = {2019}
}