Global optimization: a machine learning approach
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10898_2024_Article_1434.pdf
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2.1 MB
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6e8aafa861178c66516935a40ac15343
Author(s)
Bertsimas, Dimitris
Margaritis, Georgios
Date Issued
October 7, 2024
Journal
Journal of Global Optimization
Publisher
Springer US
Citation
Bertsimas, D., Margaritis, G. Global optimization: a machine learning approach. J Glob Optim (2024).
Version
Final published version
Abstract
Many approaches for addressing global optimization problems typically rely on relaxations of nonlinear constraints over specific mathematical primitives. This is restricting in applications with constraints that are implicit or consist of more general primitives. Trying to address such limitations, Bertsimas and Ozturk (2023) proposed OCTHaGOn as a way of solving very general global optimization problems by approximating the nonlinear constraints using hyperplane-based decision-trees and then using those trees to construct a unified MIO approximation of the original problem. We provide extensions to this approach, by (i) approximating the original problem using other MIO-representable ML models besides decision trees, such as gradient boosted trees, multi layer perceptrons and suport vector machines (ii) proposing adaptive sampling procedures for more accurate ML-based constraint approximations, (iii) utilizing robust optimization to account for the uncertainty of the sample-dependent training of the ML models, (iv) leveraging a family of relaxations to address the infeasibilities of the final MIO approximation. We then test the enhanced framework in 81 global optimization instances. We show improvements in solution feasibility and optimality in the majority of instances. We also compare against BARON, showing improved optimality gaps and solution times in more than 9 instances.
MIT Department
Sloan School of Management
Massachusetts Institute of Technology. Operations Research Center
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Creative Commons Attribution
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DOI of Published Version
https://doi.org/10.1007/s10898-024-01434-9
