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

Shuli Zeng, Sijia Zhang, Shaoang Li, Feng Wu, Xiang-Yang Li

TL;DR

The paper tackles the inefficiency of local, node-centric cut selection in MIP solvers by introducing Global Cut Selection (GCS), which represents the entire Branch-and-Cut search tree as a bipartite graph and learns cut strategies across all nodes. It combines graph neural networks to aggregate tree-wide information with a Transformer to capture interactions among cuts, and models the decision process as a reinforcement learning problem trained with PPO. Key contributions include a global graph-based representation of the search tree, an RL framework for cross-node cut selection, and extensive empirical evidence showing speedups and node reductions on synthetic and real-world MIPs. This approach enhances solver efficiency and scalability, offering a pathway to more robust, generalizable MIP solving in practice.

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.

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

TL;DR

The paper tackles the inefficiency of local, node-centric cut selection in MIP solvers by introducing Global Cut Selection (GCS), which represents the entire Branch-and-Cut search tree as a bipartite graph and learns cut strategies across all nodes. It combines graph neural networks to aggregate tree-wide information with a Transformer to capture interactions among cuts, and models the decision process as a reinforcement learning problem trained with PPO. Key contributions include a global graph-based representation of the search tree, an RL framework for cross-node cut selection, and extensive empirical evidence showing speedups and node reductions on synthetic and real-world MIPs. This approach enhances solver efficiency and scalability, offering a pathway to more robust, generalizable MIP solving in practice.

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.

Paper Structure

This paper contains 24 sections, 14 equations, 2 figures, 9 tables, 1 algorithm.

Table of Contents

  1. Introduction
  2. Background
  3. Motivation
  4. Global Cut Selection
  5. Constructing Graph from the B&C Tree and Generated Cuts
  6. Reinforcement Learning Formulation
  7. Policy Network Architecture
  8. Training
  9. Discussion on Advantages of GCS
  10. Experiments
  11. Experimental Setup
  12. Experiment Results
  13. Conclusion
  14. Related Work
  15. List of Symbols
  16. ...and 9 more sections

Figures (2)

  • Figure 1: Bipartite graph based on B&C tree and generated cuts. (a) Using all leaf nodes to represent the search tree.(b) Using a bipartite graph to represent all leaf nodes.
  • Figure 2: Procedures for adding cutting planes to the current node. (a) Bipartite graph representation. This panel illustrates the encoding of the B&C tree as a bipartite graph. (b) Neural architecture. This panel outlines the architecture of the neural network.