Exact Combinatorial Optimization with Graph Convolutional Neural Networks

TL;DR

This paper introduces a graph convolutional neural network model that learns effective variable selection policies for branch-and-bound algorithms in combinatorial optimization, outperforming existing machine learning methods and traditional expert rules.

Contribution

It presents a novel GCN-based approach trained via imitation learning to improve variable selection in mixed-integer linear programming, demonstrating superior performance and generalization.

Findings

Outperforms state-of-the-art ML methods in branching.

Generalizes well to larger problem instances.

Surpasses expert-designed rules on large problems.

Abstract

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.