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

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