ML-Guided Primal Heuristics for Mixed Binary Quadratic Programs

Weimin Huang, Natalie M. Isenberg, Jan Drgona, Draguna L Vrabie, Bistra Dilkina

Keywords: Machine learning, primal heuristics, mixed-binary quadratic programs, combinatorial optimization

Abstract: Mixed Binary Quadratic Programs (MBQPs) are classic problems in combinatorial optimization. As solving large-scale combinatorial optimization problems is challenging, primal heuristics have been developed to quickly identify high-quality solutions within a short amount of time. Recently, a growing body of research has also used machine learning to accelerate solution methods for challenging combinatorial optimization problems. Despite the increasing popularity of these ML-guided methods, a large body of work has focused on Mixed-Integer Linear Programs (MILPs). MBQPs are challenging to solve due to the combinatorial complexity coupled with nonlinearities. This work proposes ML-guided primal heuristics for Mixed Binary Quadratic Programs (MBQPs) by adapting and extending existing work on ML-guided MILP solution prediction to MBQPs. We propose a new neural network architecture for MBQP solution prediction and a new data collection procedure for training. Moreover, we propose to combine Binary Cross-Entropy loss and Contrastive Loss in solution prediction. We compare the methods on standard and real-world MBQP benchmarks and show that our proposed methods significantly outperform state-of-the-art solvers and existing primal heuristics.

Submission Number: 28