Approximate Kernel Learning Uncertainty Set for Robust Combinatorial Optimization

Benoît Loger (), Alexandre Dolgui (), Fabien Lehuédé () and Guillaume Massonnet ()
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Benoît Loger: IMT Atlantique, LS2N, 44300 Nantes, France
Alexandre Dolgui: IMT Atlantique, LS2N, 44300 Nantes, France
Fabien Lehuédé: IMT Atlantique, LS2N, 44300 Nantes, France
Guillaume Massonnet: IMT Atlantique, LS2N, 44300 Nantes, France

INFORMS Journal on Computing, 2024, vol. 36, issue 3, 900-917

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.

Keywords: data-driven; robust optimization; machine learning; mixed-integer linear programming (search for similar items in EconPapers)
Date: 2024
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Persistent link: https://EconPapers.repec.org/RePEc:inm:orijoc:v:36:y:2024:i:3:p:900-917

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