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arXiv · 2604.23053

ML-Guided Primal Heuristics for Mixed Binary Quadratic Programs

Weimin Huang·Natalie M. Isenberg·Ján Drgoňa·Draguna L Vrabie·Bistra Dilkina
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Abstract

Mixed Binary Quadratic Programs (MBQPs) are an important and complex set of 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 introduce a new neural network architecture for MBQP solution prediction and a new training data collection procedure. Moreover, we extend existing loss functions in solution prediction and propose to combine contrastive and weighted cross-entropy losses. We evaluate the methods on standard and real-world MBQP benchmarks and show that the developed ML-guided methods significantly outperform existing primal heuristics and state-of-the-art solvers. Furthermore, models trained with our proposed extension with combined losses outperform other ML-based methods adapted from MILPs and improve generalization in cross-regional inference on a real-world wind farm layout optimization problem.

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Weimin Huang, Natalie M. Isenberg, Ján Drgoňa, Draguna L Vrabie, Bistra Dilkina. 2026-07-04. ML-Guided Primal Heuristics for Mixed Binary Quadratic Programs. https://arxiv.org/abs/2604.23053

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