Global optimization via optimal decision trees
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10898_2023_Article_1311.pdf
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2.17 MB
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Adobe PDF
Checksum (MD5)
7a1572489d7ca9f721e9487e1a7325c4
Author(s)
Bertsimas, Dimitris
Öztürk, Berk
Date Issued
July 21, 2023
Publisher
Springer US
Citation
Bertsimas, Dimitris and Öztürk, Berk. 2023. "Global optimization via optimal decision trees."
Version
Final published version
Abstract
Abstract
The global optimization literature places large emphasis on reducing intractable optimization problems into more tractable structured optimization forms. In order to achieve this goal, many existing methods are restricted to optimization over explicit constraints and objectives that use a subset of possible mathematical primitives. These are limiting in real-world contexts where more general explicit and black box constraints appear. Leveraging the dramatic speed improvements in mixed-integer optimization (MIO) and recent research in machine learning, we propose a new method to learn MIO-compatible approximations of global optimization problems using optimal decision trees with hyperplanes (OCT-Hs). This constraint learning approach only requires a bounded variable domain, and can address both explicit and inexplicit constraints. We solve the MIO approximation to find a near-optimal, near-feasible solution to the global optimization problem. We further improve the solution using a series of projected gradient descent iterations. We test the method on numerical benchmarks from the literature as well as real-world design problems, demonstrating its promise in finding global optima efficiently.
MIT Department
Sloan School of Management
Massachusetts Institute of Technology. Department of Aeronautics and Astronautics
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Creative Commons Attribution
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DOI of Published Version
https://doi.org/10.1007/s10898-023-01311-x
