The point-based robustness gap for uncertain multiobjective optimization

Krueger C, Schoebel A, Fritzen L, Wiecek MM (2023)

Publication Type: Journal article

Publication year: 2023

Journal

Optimization Taylor & Francis: STM, Behavioural Science and Public Health Titles / Taylor & Francis

DOI: 10.1080/02331934.2023.2181080

Abstract

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.

Involved external institutions

Clemson University US United States (USA) (US) Georg-August-Universität Göttingen DE Germany (DE)

How to cite

APA:

Krueger, C., Schoebel, A., Fritzen, L., & Wiecek, M.M. (2023). The point-based robustness gap for uncertain multiobjective optimization. Optimization. https://dx.doi.org/10.1080/02331934.2023.2181080

MLA:

Krueger, Corinna, et al. "The point-based robustness gap for uncertain multiobjective optimization." Optimization (2023).

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