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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| Published in: | Optimization Vol. 73; no. 6; pp. 1897 - 1931 |
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| Format: | Journal Article |
| Language: | English |
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Taylor & Francis
02.06.2024
Taylor & Francis LLC |
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| ISSN: | 0233-1934, 1029-4945 |
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| 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. |
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| AbstractList | 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. |
| Author | Krüger, Corinna Schöbel, Anita Fritzen, Lena Wiecek, Margaret M. |
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| StartPage | 1897 |
| SubjectTerms | efficient solution minmax optimization Multi-criteria programming Multiple objective analysis Pareto optimization pareto outcome robust optimization Robustness Upper bounds |
| Title | The point-based robustness gap for uncertain multiobjective optimization |
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