A Prescriptive Machine Learning Approach to Mixed-Integer Convex Optimization

Dimitris Bertsimas () and Cheol Woo Kim ()
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Dimitris Bertsimas: Sloan School of Management, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139
Cheol Woo Kim: Operations Research Center, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139

INFORMS Journal on Computing, 2023, vol. 35, issue 6, 1225-1241

Abstract: We introduce a prescriptive machine learning approach to speed up the process of solving mixed-integer convex optimization (MICO) problems. We solve multiple optimization instances and train a machine learning model in advance, which we use to solve new instances. Previous works have shown that the predictions of classification algorithms enable us to solve optimization problems much faster than commercial solvers. What distinguishes this paper from the previous work is that we use a prescriptive algorithm, Optimal Policy Trees (OPT), instead of classification algorithms. Whereas classification algorithms aim to predict the correct label and consider all other labels equally undesirable, a prescriptive approach takes into account all the available decision options and their counterfactuals. We first introduce an algorithm that is purely based on OPT and also its extension. We compare their performance with Optimal Classification Trees (OCT) on various MICO problems. Test problems include transportation optimization, portfolio optimization, facility location, and hybrid vehicle control. We also experiment on real-world instances taken from the Mixed Integer Programming Library. OPT-based methods have a significant edge on finding feasible solutions, whereas OCT-based methods have a slight edge on the degree of suboptimality. The proposed extension of the pure OPT algorithm improves on the suboptimality of the solutions the algorithm produces.

Keywords: mixed-integer optimization; prescriptive analytics; artificial intelligence; decision trees; computational methods (search for similar items in EconPapers)
Date: 2023
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Citations: View citations in EconPapers (2)

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