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arXiv · 2409.06559

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

Arnaud Deza·Elias B. Khalil·Zhenan Fan·Zirui Zhou·Yong Zhang
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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.

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Arnaud Deza, Elias B. Khalil, Zhenan Fan, Zirui Zhou, Yong Zhang. 2024-09-10. Learn2Aggregate: Supervised Generation of Chv\'atal-Gomory Cuts Using Graph Neural Networks. https://arxiv.org/abs/2409.06559

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