On Generalized Dominance Structures for Multi-Objective Optimization

Deb, Kalyanmoy and Ehrgott, Matthias (2023) On Generalized Dominance Structures for Multi-Objective Optimization. Mathematical and Computational Applications, 28 (5): 100. ISSN 2297-8747

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Abstract

Various dominance structures have been proposed in the multi-objective optimization literature. However, a systematic procedure to understand their effect in determining the resulting optimal set for generic domination principles, besides the standard Pareto-dominance principle, is lacking. In this paper, we analyze and lay out properties of generalized dominance structures which help provide insights for resulting optimal solutions. We introduce the concept of the anti-dominance structure, derived from the chosen dominance structure, to explain how the resulting non-dominated or optimal set can be identified easily compared to using the dominance structure directly. The concept allows a unified explanation of optimal solutions for both single- and multi-objective optimization problems. The anti-dominance structure is applied to analyze respective optimal solutions for most popularly used static and spatially changing dominance structures. The theoretical and deductive results of this study can be utilized to create more meaningful dominance structures for practical problems, understand and identify resulting optimal solutions, and help develop better test problems and algorithms for multi-objective optimization.

Item Type:
Journal Article
Journal or Publication Title:
Mathematical and Computational Applications
Subjects:
?? applied mathematicscomputational mathematicsgeneral engineering ??
ID Code:
207693
Deposited By:
Deposited On:
19 Oct 2023 10:30
Refereed?:
Yes
Published?:
Published
Last Modified:
16 Jul 2024 00:24