Learning to Branch in Combinatorial Optimization with Graph Pointer Networks

TL;DR

This paper introduces a graph pointer network model that learns variable selection policies for branch-and-bound algorithms in combinatorial optimization, significantly improving efficiency and generalization over existing methods.

Contribution

The paper presents a novel graph neural network with pointer mechanism for learning branching decisions, outperforming traditional and existing ML-based approaches.

Findings

Outperforms classic strong branching rules

Reduces search tree size and solving time

Generalizes well to unseen and larger instances

Abstract

Branch-and-bound is a typical way to solve combinatorial optimization problems. This paper proposes a graph pointer network model for learning the variable selection policy in the branch-and-bound. We extract the graph features, global features and historical features to represent the solver state. The proposed model, which combines the graph neural network and the pointer mechanism, can effectively map from the solver state to the branching variable decisions. The model is trained to imitate the classic strong branching expert rule by a designed top-k Kullback-Leibler divergence loss function. Experiments on a series of benchmark problems demonstrate that the proposed approach significantly outperforms the widely used expert-designed branching rules. Our approach also outperforms the state-of-the-art machine-learning-based branch-and-bound methods in terms of solving speed and search tree size on all the test instances. In addition, the model can generalize to unseen instances and scale to larger instances.