Exact Combinatorial Optimization with Graph Convolutional Neural Networks

Understand

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.