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Journal Articles INFORMS Journal on Computing Year : 2024

Approximate Kernel Learning Uncertainty Set for Robust Combinatorial Optimization

Abstract

Support vector clustering (SVC) has been proposed in the literature as a data-driven approach to build uncertainty sets in robust optimization. Unfortunately, the resulting SVC-based uncertainty sets induces a large number of additional variables and constraints in the robust counterpart of mathematical formulations. We propose a two-phase method to approximate the resulting uncertainty sets and overcome these tractability issues. This method is controlled by a parameter defining a trade-off between the quality of the approximation and the complexity of the robust models formulated. We evaluate the approximation method on three distinct, well-known optimization problems. Experimental results show that the approximated uncertainty set leads to solutions that are comparable to those obtained with the classic SVC-based uncertainty set with a significant reduction of the computation time. History: Accepted by Andrea Lodi, Area Editor for Design and Analysis of Algorithms—Discrete. Funding: This work was supported by the German-French Academy for the Industry of the Future [Data-driven collaboration in Industrial Supply Chains project].
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hal-04556151 , version 1 (23-04-2024)

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Benoît Loger, Alexandre Dolgui, Fabien Lehuédé, Guillaume Massonnet. Approximate Kernel Learning Uncertainty Set for Robust Combinatorial Optimization. INFORMS Journal on Computing, 2024, ⟨10.1287/ijoc.2022.0330⟩. ⟨hal-04556151⟩
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