Learning efficient branch-and-bound for solving Mixed Integer Linear Programs

Abstract

Mixed Integer Linear Programs (MILPs) are widely used to model various real-world optimization problems, traditionally solved using the branch-and-bound (B&B) algorithm framework. Recent advances in Machine Learning (ML) have inspired enhancements in B&B by enabling data-driven decision-making. Two critical decisions in B&B are node selection and variable selection, which directly influence computational efficiency. While prior studies have applied ML to enhance these decisions, they have predominantly focused on either node selection or variable selection, addressing the decision individually and overlooking the significant interdependence between the two. This paper introduces a novel ML-based approach that integrates both decisions within the B&B framework using a unified neural network architecture. By leveraging a bipartite graph representation of MILPs and employing Graph Neural Networks, the model learns adaptive strategies tailored to different problem types through imitation of expert-designed policies. Experiments on various benchmarks show that the integrated policy adapts better to different problem classes than models targeting individual decisions, delivering strong performance in solving time, search tree size, and optimization dynamics across various configurations. It also surpasses competitive baselines, including the state-of-the-art open-source solver SCIP and a recent reinforcement learning-based approach, demonstrating its potential for broader application in MILP solving.