Inverse-Optimization-Based Uncertainty Set for Robust Linear Optimization

Ayaka Ueta (), Mirai Tanaka, Ken Kobayashi and Kazuhide Nakata
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Ayaka Ueta: Tokyo Institute of Technology
Mirai Tanaka: The Institute of Statistical Mathematics
Ken Kobayashi: Tokyo Institute of Technology
Kazuhide Nakata: Tokyo Institute of Technology

Chapter Chapter 67 in Operations Research Proceedings 2023, 2025, pp 527-533 from Springer

Abstract: Abstract We consider solving linear optimization (LO) problems with uncertain objective coefficients. For such problems, we often employ robust optimization (RO) approaches by introducing an uncertainty set for the unknown coefficients. Typical RO approaches require observations or prior knowledge of the unknown coefficient to define an appropriate uncertainty set. However, such information may not always be available in practice. In this study, we propose a novel uncertainty set for robust linear optimization (RLO) problems without prior knowledge of the unknown coefficients. Instead, we assume to have data of known constraint parameters and corresponding optimal solutions. Specifically, we derive an explicit form of the uncertainty set as a polytope by applying techniques of inverse optimization (IO). We prove that the RLO problem with the proposed uncertainty set can be equivalently reformulated as an LO problem. Numerical experiments show that the RO approach with the proposed uncertainty set outperforms classical IO in terms of performance stability.

Keywords: Robust optimization; Inverse optimization; Uncertainty set (search for similar items in EconPapers)
Date: 2025
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Persistent link: https://EconPapers.repec.org/RePEc:spr:lnopch:978-3-031-58405-3_67

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DOI: 10.1007/978-3-031-58405-3_67

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