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Workshop: OPT 2023: Optimization for Machine Learning

Contrastive Predict-and-Search for Mixed Integer Linear Programs

Taoan Huang · Aaron Ferber · Arman Zharmagambetov · Yuandong Tian · Bistra Dilkina


Mixed integer linear programs (MILP) are flexible and powerful tool for modeling and solving many difficult real-world combinatorial optimization problems. In this paper, we propose a novel machine learning-based framework ConPaS that learns to predict solutions to MILPs with contrastive learning. For training, we collect high-quality solutions as positive samples and low-quality or infeasible solutions as negative samples. We then learn to make discriminative predictions by contrasting the positive and negative samples. During test time, we predict assignments for a subset of integer variables of a MILP and then solve the resulting reduced MILP to construct high-quality solutions. Empirically, we show that ConPaS achieves state-of-the-art results compared to other ML-based approaches in terms of the quality of and the speed at which the solutions are found.

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