The point-based robustness gap for uncertain multiobjective optimization

In robust single-objective optimization, the robustness gap is a measure of the distance between the robust optimal objective value and the optimal objective values of the scenarios. While robust multiobjective optimization is a growing field of study, no notion of a robustness gap has been proposed...

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Bibliographic Details
Published in:Optimization Vol. 73; no. 6; pp. 1897 - 1931
Main Authors: Krüger, Corinna, Schöbel, Anita, Fritzen, Lena, Wiecek, Margaret M.
Format: Journal Article
Language:English
Published: Philadelphia Taylor & Francis 02.06.2024
Taylor & Francis LLC
Subjects:
efficient solution
minmax optimization
Multi-criteria programming
Multiple objective analysis
Pareto optimization
pareto outcome
robust optimization
Robustness
Upper bounds
ISSN:0233-1934, 1029-4945
Online Access:Get full text
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Summary:In robust single-objective optimization, the robustness gap is a measure of the distance between the robust optimal objective value and the optimal objective values of the scenarios. While robust multiobjective optimization is a growing field of study, no notion of a robustness gap has been proposed. A concept of a point-based robustness gap for uncertain multiobjective optimization problems is introduced. The gap is defined as the minimal distance between the robust Pareto set and the Pareto sets of the scenarios. It is shown that the gap is zero whenever the uncertainty is constraint-wise and objective-wise, supplementing a major result about the single-objective robustness gap. Because the distance between Pareto sets is hard to compute, lower and upper bounds on the gap are constructed for convex problems. Specific results about the zero gap and the bounds are presented for linear problems. Numerical examples are included.
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ISSN:0233-1934
1029-4945
DOI:10.1080/02331934.2023.2181080