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

Fuente: arXiv
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Main Authors: Deza, Arnaud, Khalil, Elias B., Fan, Zhenan, Zhou, Zirui, Zhang, Yong
Format: Preprint
Published: 2024
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author Deza, Arnaud
Khalil, Elias B.
Fan, Zhenan
Zhou, Zirui
Zhang, Yong
author_facet Deza, Arnaud
Khalil, Elias B.
Fan, Zhenan
Zhou, Zirui
Zhang, Yong
contents We present $\textit{Learn2Aggregate}$, 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 $\textit{twice}$ 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.
format Preprint
id arxiv_https___arxiv_org_abs_2409_06559
institution arXiv
publishDate 2024
record_format arxiv
spellingShingle Learn2Aggregate: Supervised Generation of Chvátal-Gomory Cuts Using Graph Neural Networks
Deza, Arnaud
Khalil, Elias B.
Fan, Zhenan
Zhou, Zirui
Zhang, Yong
Machine Learning
Optimization and Control
We present $\textit{Learn2Aggregate}$, 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 $\textit{twice}$ 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.
title Learn2Aggregate: Supervised Generation of Chvátal-Gomory Cuts Using Graph Neural Networks
topic Machine Learning
Optimization and Control
url https://arxiv.org/abs/2409.06559