Learn2Aggregate: Supervised Generation of Chv\'atal-Gomory Cuts Using Graph Neural Networks

TL;DR

Learn2Aggregate employs graph neural networks to intelligently select constraints for Chvatal-Gomory cuts in MILP, significantly improving solution quality and speed by focusing on impactful constraints.

Contribution

This paper introduces a novel ML framework that uses GNNs for constraint classification, enhancing CG cut generation efficiency and effectiveness in MILP solving.

Findings

Closes twice as much integrality gap as standard methods.

Runs 40% faster than traditional CG cut generation.

Eliminates 75% of constraints before aggregation.

Abstract

We present $\textit{Learn2Aggregate}$, a machine learning (ML) framework for optimizing the generation of Chv\'atal-Gomory (CG) cuts in mixed integer linear programming (MILP). The framework trains a graph neural network to classify useful constraints for aggregation in CG cut generation. The ML-driven CG separator selectively focuses on a small set of impactful constraints, improving runtimes without compromising the strength of the generated cuts. Key to our approach is the formulation of a constraint classification task which favours sparse aggregation of constraints, consistent with empirical findings. This, in conjunction with a careful constraint labeling scheme and a hybrid of deep learning and feature engineering, results in enhanced CG cut generation across five diverse MILP benchmarks. On the largest test sets, our method closes roughly $\textit{twice}$ as much of the integrality gap as the standard CG method while running 40$% faster. This performance improvement is due to our method eliminating 75% of the constraints prior to aggregation.