Learning to Select Cutting Planes in Mixed Integer Linear Programming Solving

TL;DR

This paper introduces a novel graph-based learning model for selecting cutting planes in MILP problems, outperforming existing heuristics and learning methods by capturing problem structure and handling input order variability.

Contribution

The paper proposes HGTSM, a heterogeneous graph neural network combined with a tailored sequence model, to improve cut selection in MILP solving by leveraging problem structure and input order robustness.

Findings

Outperforms heuristic and baseline methods on multiple datasets.

Demonstrates stability and generalization across different MILP problem types.

Effectively captures problem structure using heterogeneous tripartite graphs.

Abstract

Cutting planes (cuts) are crucial for solving Mixed Integer Linear Programming (MILP) problems. Advanced MILP solvers typically rely on manually designed heuristic algorithms for cut selection, which require much expert experience and cannot be generalized for different scales of MILP problems. Therefore, learning-based methods for cut selection are considered a promising direction. State-of-the-art learning-based methods formulate cut selection as a sequence-to-sequence problem, easily handled by sequence models. However, the existing sequence models need help with the following issues: (1) the model only captures cut information while neglecting the Linear Programming (LP) relaxation; (2) the sequence model utilizes positional information of the input sequence, which may influence cut selection. To address these challenges, we design a novel learning model HGTSM for better select cuts. We encode MILP problem state as a heterogeneous tripartite graph, utilizing heterogeneous graph networks to fully capture the underlying structure of MILP problems. Simultaneously, we propose a novel sequence model whose architecture is tailored to handle inputs in different orders. Experimental results demonstrate that our model outperforms heuristic methods and learning-based baselines on multiple challenging MILP datasets. Additionally, the model exhibits stability and the ability to generalize to different types of problems.