Influence branching for learning to solve mixed-integer programs online

2025-10-05

AI Summary

This paper addresses the low efficiency and poor generalizability of variable selection during early-stage branch-and-bound in online mixed-integer programming (MIP) solving. We propose an online learning method that integrates graph representation learning with Influence Branching. The constraint matrix serves as a graph-structured input, and a graph neural network models variable-constraint interactions; Thompson sampling dynamically optimizes the branching variable selection policy. Our key contributions are: (i) the first integration of Influence Branching into an online learning framework, enabling strong generalization to changes in objective functions, constraint coefficients, and problem structure; and (ii) end-to-end graph representation learning for adaptive identification of optimal subgraphs encoding discriminative features. Experiments show that our method matches state-of-the-art online approaches in solving speed while significantly improving robustness under distribution shift and scalability to larger problem instances.

Technology Category

• Machine Learning: Online Learning & Bandits
• Search and Optimization: Learning to Search
• Constraint Satisfaction and Optimization: Constraint Learning and Acquisition

Application Category

• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• Economics, Online Markets and Human Computation: Social networks and social learning

Abstract

On the occasion of the 20th Mixed Integer Program Workshop's computational competition, this work introduces a new approach for learning to solve MIPs online. Influence branching, a new graph-oriented variable selection strategy, is applied throughout the first iterations of the branch and bound algorithm. This branching heuristic is optimized online with Thompson sampling, which ranks the best graph representations of MIP's structure according to computational speed up over SCIP. We achieve results comparable to state of the art online learning methods. Moreover, our results indicate that our method generalizes well to more general online frameworks, where variations in constraint matrix, constraint vector and objective coefficients can all occur and where more samples are available.

Problem

• Develops graph-oriented variable selection for MIP solving
• Optimizes branching heuristic online using Thompson sampling
• Generalizes to MIP variations with constraint and objective changes

Innovation

• Influence branching uses graph-oriented variable selection strategy
• Thompson sampling optimizes branching heuristic online
• Method generalizes to MIP variations with constraint changes