Learn2Aggregate: Supervised Generation of Chvátal-Gomory Cuts Using Graph Neural Networks

Arnaud Deza, Elias Boutros Khalil, Yong Zhang, Zirui Zhou, Zhenan Fan

Abstract: We present Learn2Aggregate, a machine learning (ML) framework for optimizing the generation of Chvátal-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 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.