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On Generalized Dominance Structures for Multi-Objective Optimization

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On Generalized Dominance Structures for Multi-Objective Optimization. / Deb, Kalyanmoy; Ehrgott, Matthias.
In: Mathematical and Computational Applications, Vol. 28, No. 5, 100, 07.10.2023.

Research output: Contribution to Journal/Magazine › Journal article › peer-review

Harvard

Deb, K & Ehrgott, M 2023, 'On Generalized Dominance Structures for Multi-Objective Optimization', Mathematical and Computational Applications, vol. 28, no. 5, 100. https://doi.org/10.3390/mca28050100

APA

Deb, K., & Ehrgott, M. (2023). On Generalized Dominance Structures for Multi-Objective Optimization. Mathematical and Computational Applications, 28(5), Article 100. https://doi.org/10.3390/mca28050100

Vancouver

Deb K, Ehrgott M. On Generalized Dominance Structures for Multi-Objective Optimization. Mathematical and Computational Applications. 2023 Oct 7;28(5):100. doi: 10.3390/mca28050100

Author

Deb, Kalyanmoy ; Ehrgott, Matthias. / On Generalized Dominance Structures for Multi-Objective Optimization. In: Mathematical and Computational Applications. 2023 ; Vol. 28, No. 5.

Bibtex

@article{77c4aadc69554f7a841387ff5dc13033,
title = "On Generalized Dominance Structures for Multi-Objective Optimization",
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.",
keywords = "Applied Mathematics, Computational Mathematics, General Engineering",
author = "Kalyanmoy Deb and Matthias Ehrgott",
year = "2023",
month = oct,
day = "7",
doi = "10.3390/mca28050100",
language = "English",
volume = "28",
journal = "Mathematical and Computational Applications",
issn = "2297-8747",
publisher = "MDPI AG",
number = "5",

}

RIS

TY - JOUR

T1 - On Generalized Dominance Structures for Multi-Objective Optimization

AU - Deb, Kalyanmoy

AU - Ehrgott, Matthias

PY - 2023/10/7

Y1 - 2023/10/7

N2 - 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.

AB - 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.

KW - Applied Mathematics

KW - Computational Mathematics

KW - General Engineering

U2 - 10.3390/mca28050100

DO - 10.3390/mca28050100

M3 - Journal article

VL - 28

JO - Mathematical and Computational Applications

JF - Mathematical and Computational Applications

SN - 2297-8747

IS - 5

M1 - 100

ER -