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

TL;DR

This paper presents a novel set-based approach for robust multiobjective optimization under uncertainty, reformulating the problem to enable classical solution techniques and improve solution characterization.

Contribution

It introduces a reformulation using the strict lower set relation, preserving compactness and allowing the application of vectorization results for solution analysis.

Findings

Reformulation simplifies the robust optimization problem.

Characterization of solutions via classical multiobjective techniques.

Applicable to multiobjective semi-infinite problems.

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.