Data-driven Mixed Integer Optimization through Probabilistic Multi-variable Branching

Yanguang Chen, Wenzhi Gao, Wanyu Zhang, Dongdong Ge, Huikang Liu, Yinyu Ye
Proceedings of the 43rd International Conference on Machine Learning, PMLR 306:14324-14345, 2026.

Abstract

This paper introduces Probabilistic Multi-Variable Branching (PMVB), a simple and effective technique for accelerating mixed-integer optimization using data-driven machine learning models. At its core, PMVB employs a multi-variable branching procedure that partitions the feasible region via data-driven hyperplanes and requires only two lines of code to implement. Moreover, PMVB is model-agnostic and compatible with a wide range of machine learning models. Leveraging tools from statistical learning theory, we develop interpretable hyperparameter selection strategies and propose several extensions to further enhance performance. We evaluate PMVB by integrating it into state-of-the-art MIP solvers and conducting experiments on both classical benchmark datasets and real-world instances. The results demonstrate the effectiveness of PMVB in improving MIP-solving efficiency.

Cite this Paper

BibTeX
@InProceedings{pmlr-v306-chen26ah, title = {Data-driven Mixed Integer Optimization through Probabilistic Multi-variable Branching}, author = {Chen, Yanguang and Gao, Wenzhi and Zhang, Wanyu and Ge, Dongdong and Liu, Huikang and Ye, Yinyu}, booktitle = {Proceedings of the 43rd International Conference on Machine Learning}, pages = {14324--14345}, year = {2026}, editor = {Zhang, Tong and Dudik, Miroslav and Jaggi, Martin and Agarwal, Alekh and Li, Sharon and Schuurmans, Dale and Zhu, Jerry and Berkenkamp, Felix and Dong, Hanze and Bietti, Alberto}, volume = {306}, series = {Proceedings of Machine Learning Research}, month = {06--11 Jul}, publisher = {PMLR}, pdf = {https://raw.githubusercontent.com/mlresearch/v306/main/assets/chen26ah/chen26ah.pdf}, url = {https://proceedings.mlr.press/v306/chen26ah.html}, abstract = {This paper introduces Probabilistic Multi-Variable Branching (PMVB), a simple and effective technique for accelerating mixed-integer optimization using data-driven machine learning models. At its core, PMVB employs a multi-variable branching procedure that partitions the feasible region via data-driven hyperplanes and requires only two lines of code to implement. Moreover, PMVB is model-agnostic and compatible with a wide range of machine learning models. Leveraging tools from statistical learning theory, we develop interpretable hyperparameter selection strategies and propose several extensions to further enhance performance. We evaluate PMVB by integrating it into state-of-the-art MIP solvers and conducting experiments on both classical benchmark datasets and real-world instances. The results demonstrate the effectiveness of PMVB in improving MIP-solving efficiency.} }
Endnote
%0 Conference Paper %T Data-driven Mixed Integer Optimization through Probabilistic Multi-variable Branching %A Yanguang Chen %A Wenzhi Gao %A Wanyu Zhang %A Dongdong Ge %A Huikang Liu %A Yinyu Ye %B Proceedings of the 43rd International Conference on Machine Learning %C Proceedings of Machine Learning Research %D 2026 %E Tong Zhang %E Miroslav Dudik %E Martin Jaggi %E Alekh Agarwal %E Sharon Li %E Dale Schuurmans %E Jerry Zhu %E Felix Berkenkamp %E Hanze Dong %E Alberto Bietti %F pmlr-v306-chen26ah %I PMLR %P 14324--14345 %U https://proceedings.mlr.press/v306/chen26ah.html %V 306 %X This paper introduces Probabilistic Multi-Variable Branching (PMVB), a simple and effective technique for accelerating mixed-integer optimization using data-driven machine learning models. At its core, PMVB employs a multi-variable branching procedure that partitions the feasible region via data-driven hyperplanes and requires only two lines of code to implement. Moreover, PMVB is model-agnostic and compatible with a wide range of machine learning models. Leveraging tools from statistical learning theory, we develop interpretable hyperparameter selection strategies and propose several extensions to further enhance performance. We evaluate PMVB by integrating it into state-of-the-art MIP solvers and conducting experiments on both classical benchmark datasets and real-world instances. The results demonstrate the effectiveness of PMVB in improving MIP-solving efficiency.
APA
Chen, Y., Gao, W., Zhang, W., Ge, D., Liu, H. & Ye, Y.. (2026). Data-driven Mixed Integer Optimization through Probabilistic Multi-variable Branching. Proceedings of the 43rd International Conference on Machine Learning, in Proceedings of Machine Learning Research 306:14324-14345 Available from https://proceedings.mlr.press/v306/chen26ah.html.

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