Learn2Aggregate: Supervised Generation of Chvátal-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.
Learn2Aggregate:使用图神经网络监督生成 Chvátal-Gomory 剪切
我们提出了 $\textit{Learn2Aggregate}$,这是一个用于优化混合整数线性编程(MILP)中 Chv\'atal-Gomory (CG) 切分生成的机器学习(ML)框架。该框架训练一个图神经网络,对有用的约束条件进行分类,以便在生成 CG 切分时进行聚合。ML 驱动的 CG 分割器会有选择性地关注一小部分有影响的约束,从而在不影响生成的切割强度的情况下提高运行时间。我们方法的关键在于制定了一个约束分类任务,该任务倾向于稀疏聚集约束,这与实证研究结果是一致的。这与谨慎的约束标记方案以及深度学习和特征工程的混合方法相结合,在五个不同的 MILP 基准中增强了 CG 切分生成。在最大的测试集上,我们的方法缩小的积分差距大约是标准CG方法的两倍,同时运行速度提高了40%。这一性能提升归功于我们的方法在聚合之前消除了 75% 的约束。
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