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Set-based robust optimization of uncertain multiobjective problems via epigraphical reformulations

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  • Eichfelder, Gabriele
  • Quintana, Ernest

Abstract

In this paper, we study a method for finding robust solutions to multiobjective optimization problems under uncertainty. We follow the set-based minmax approach for handling the uncertainties which leads to a certain set optimization problem with the strict upper type set relation. We introduce, under some assumptions, a reformulation using instead the strict lower type set relation without sacrificing the compactness property of the image sets. This allows to apply vectorization results to characterize the optimal solutions of these set optimization problems as optimal solutions of a multiobjective optimization problem. We end up with multiobjective semi-infinite problems which can then be studied with classical techniques from the literature.

Suggested Citation

  • Eichfelder, Gabriele & Quintana, Ernest, 2024. "Set-based robust optimization of uncertain multiobjective problems via epigraphical reformulations," European Journal of Operational Research, Elsevier, vol. 313(3), pages 871-882.
    • Handle: RePEc:eee:ejores:v:313:y:2024:i:3:p:871-882
    DOI: 10.1016/j.ejor.2023.09.017
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    References listed on IDEAS

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    1. Jiang, Ling & Cao, Jinde & Xiong, Lianglin, 2019. "Generalized multiobjective robustness and relations to set-valued optimization," Applied Mathematics and Computation, Elsevier, vol. 361(C), pages 599-608.
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    4. Truong Quang Bao & Christiane Tammer, 2019. "Scalarization Functionals with Uniform Level Sets in Set Optimization," Journal of Optimization Theory and Applications, Springer, vol. 182(1), pages 310-335, July.
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    6. Jonas Ide & Elisabeth Köbis, 2014. "Concepts of efficiency for uncertain multi-objective optimization problems based on set order relations," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 80(1), pages 99-127, August.
    7. Jonas Ide & Anita Schöbel, 2016. "Robustness for uncertain multi-objective optimization: a survey and analysis of different concepts," OR Spectrum: Quantitative Approaches in Management, Springer;Gesellschaft für Operations Research e.V., vol. 38(1), pages 235-271, January.
    8. Schöbel, Anita & Zhou-Kangas, Yue, 2021. "The price of multiobjective robustness: Analyzing solution sets to uncertain multiobjective problems," European Journal of Operational Research, Elsevier, vol. 291(2), pages 782-793.
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