Contrastive Predict-and-Search for Mixed Integer Linear Programs

Taoan Huang, Aaron M Ferber, Arman Zharmagambetov, Yuandong Tian, Bistra Dilkina
Proceedings of the 41st International Conference on Machine Learning, PMLR 235:19757-19771, 2024.

Abstract

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

Cite this Paper

BibTeX
@InProceedings{pmlr-v235-huang24f, title = {Contrastive Predict-and-Search for Mixed Integer Linear Programs}, author = {Huang, Taoan and Ferber, Aaron M and Zharmagambetov, Arman and Tian, Yuandong and Dilkina, Bistra}, booktitle = {Proceedings of the 41st International Conference on Machine Learning}, pages = {19757--19771}, year = {2024}, editor = {Salakhutdinov, Ruslan and Kolter, Zico and Heller, Katherine and Weller, Adrian and Oliver, Nuria and Scarlett, Jonathan and Berkenkamp, Felix}, volume = {235}, series = {Proceedings of Machine Learning Research}, month = {21--27 Jul}, publisher = {PMLR}, pdf = {https://raw.githubusercontent.com/mlresearch/v235/main/assets/huang24f/huang24f.pdf}, url = {https://proceedings.mlr.press/v235/huang24f.html}, abstract = {Mixed integer linear programs (MILP) are flexible and powerful tools for modeling and solving many difficult real-world combinatorial optimization problems. In this paper, we propose a novel machine learning (ML)-based framework ConPaS that learns to predict solutions to MILPs with contrastive learning. For training, we collect high-quality solutions as positive samples. We also collect low-quality or infeasible solutions as negative samples using novel optimization-based or sampling approaches. We then learn to make discriminative predictions by contrasting the positive and negative samples. During testing, we predict and fix the assignments for a subset of integer variables and then solve the resulting reduced MILP to find high-quality solutions. Empirically, ConPaS achieves state-of-the-art results compared to other ML-based approaches in terms of the quality of and the speed at which solutions are found.} }
Endnote
%0 Conference Paper %T Contrastive Predict-and-Search for Mixed Integer Linear Programs %A Taoan Huang %A Aaron M Ferber %A Arman Zharmagambetov %A Yuandong Tian %A Bistra Dilkina %B Proceedings of the 41st International Conference on Machine Learning %C Proceedings of Machine Learning Research %D 2024 %E Ruslan Salakhutdinov %E Zico Kolter %E Katherine Heller %E Adrian Weller %E Nuria Oliver %E Jonathan Scarlett %E Felix Berkenkamp %F pmlr-v235-huang24f %I PMLR %P 19757--19771 %U https://proceedings.mlr.press/v235/huang24f.html %V 235 %X Mixed integer linear programs (MILP) are flexible and powerful tools for modeling and solving many difficult real-world combinatorial optimization problems. In this paper, we propose a novel machine learning (ML)-based framework ConPaS that learns to predict solutions to MILPs with contrastive learning. For training, we collect high-quality solutions as positive samples. We also collect low-quality or infeasible solutions as negative samples using novel optimization-based or sampling approaches. We then learn to make discriminative predictions by contrasting the positive and negative samples. During testing, we predict and fix the assignments for a subset of integer variables and then solve the resulting reduced MILP to find high-quality solutions. Empirically, ConPaS achieves state-of-the-art results compared to other ML-based approaches in terms of the quality of and the speed at which solutions are found.
APA
Huang, T., Ferber, A.M., Zharmagambetov, A., Tian, Y. & Dilkina, B.. (2024). Contrastive Predict-and-Search for Mixed Integer Linear Programs. Proceedings of the 41st International Conference on Machine Learning, in Proceedings of Machine Learning Research 235:19757-19771 Available from https://proceedings.mlr.press/v235/huang24f.html.

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