Set-based Robust Optimization of Uncertain Multiobjective Problems via Epigraphical Reformulations

2022/12/28 by Gabriele Eichfelder, Eichfelder, Gabriele, Ernest Quintana +1
Decision Sciences · Engineering · #90C29 #90C31 #90C34 #90C47 #FOS: Mathematics #Multi-Criteria Decision Making #Optimization and Control (math.OC) #Process Optimization and Integration #Water resources management and optimization

paper · pdf · doi:10.48550/arxiv.2212.14018

openalex publication_date 2022/12/28 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

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