Exact Combinatorial Optimization with Graph Convolutional Neural Networks

Part of Advances in Neural Information Processing Systems 32 (NeurIPS 2019)

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Authors

Maxime Gasse, Didier Chetelat, Nicola Ferroni, Laurent Charlin, Andrea Lodi

Abstract

<p>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.</p>