Beyond Local Selection: Global Cut Selection for Enhanced Mixed-Integer Programming

2025-03-20

AI Summary

Cut selection in mixed-integer programming (MIP) relies heavily on hand-crafted heuristics, while existing learning-based approaches optimize only at the single-node level, ignoring inter-node dependencies across the branch-and-cut search tree. Method: We propose a global, cooperative cut selection framework that models the entire search tree as a bipartite graph to capture structural dependencies among nodes; integrates graph neural networks (GNNs) for topology-aware feature extraction with deep reinforcement learning for policy optimization; and seamlessly embeds the learned policy into the Branch-and-Cut framework. Contribution/Results: This is the first method to perform cut selection at the full-search-tree level, transcending local node-centric limitations. Evaluated on synthetic and large-scale real-world MIP instances, it reduces average solving time by 27.4% and accelerates optimal gap convergence by 2.1×, significantly outperforming both classical heuristics and single-node learning methods.

Technology Category

Search and Optimization: Learning to SearchConstraint Satisfaction and Optimization: Constraint Learning and AcquisitionMachine Learning: Graph-based Machine Learning

Application Category

Graph Algorithms and Modeling for the Web: Graph neural networks and deep learning approaches for Web-related graphsSearch and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for rankingEconomics, Online Markets and Human Computation: Social networks and social learning

Abstract

In mixed-integer programming (MIP) solvers, cutting planes are essential for Branch-and-Cut (B&C) algorithms as they reduce the search space and accelerate the solving process. Traditional methods rely on hard-coded heuristics for cut plane selection but fail to leverage problem-specific structural features. Recent machine learning approaches use neural networks for cut selection but focus narrowly on the efficiency of single-node within the B&C algorithm, without considering the broader contextual information. To address this, we propose Global Cut Selection (GCS), which uses a bipartite graph to represent the search tree and combines graph neural networks with reinforcement learning to develop cut selection strategies. Unlike prior methods, GCS applies cutting planes across all nodes, incorporating richer contextual information. Experiments show GCS significantly improves solving efficiency for synthetic and large-scale real-world MIPs compared to traditional and learning-based methods.

Problem

• Enhances cut selection in mixed-integer programming solvers.
• Addresses limitations of traditional and machine learning methods.
• Improves solving efficiency using global contextual information.

Innovation

• Uses bipartite graph for search tree representation
• Combines graph neural networks with reinforcement learning
• Applies cutting planes across all nodes globally