An optimality theory based proximity measure for evolutionary multi-objective and many-objective optimization

Kalyanmoy Deb; Mohamed Abouhawwash; Joydeep Dutta

doi:10.1007/978-3-319-15892-1_2

An optimality theory based proximity measure for evolutionary multi-objective and many-objective optimization

Kalyanmoy Deb^*, Mohamed Abouhawwash, Joydeep Dutta

^*Corresponding author for this work

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

19 Scopus citations

Abstract

Evolutionarymulti- andmany-objective optimization (EMO) methods attempt to find a set of Pareto-optimal solutions, instead of a single optimal solution. To evaluate these algorithms, performancemetrics either require the knowledge of the true Pareto-optimal solutions or, are ad-hoc and heuristic based. In this paper, we suggest a KKT proximity measure (KKTPM) that can provide an estimate of the proximity of a set of trade-off solutions from the true Pareto-optimal solutions. Besides theoretical results, the proposed KKT proximity measure is computed for iteration-wise trade-off solutions obtained from specific EMO algorithms on two, three, five and 10-objective optimization problems. Results amply indicate the usefulness of the proposed KKTPM as a termination criterion for an EMO algorithm.

Original language	English
Title of host publication	Evolutionary Multi-Criterion Optimization - 8th International Conference, EMO 2015, Proceedings
Editors	António Gaspar-Cunha, Carlos Henggeler Antunes, Carlos A. Coello Coello
Publisher	Springer Verlag
Pages	18-33
Number of pages	16
ISBN (Electronic)	9783319158914
DOIs	https://doi.org/10.1007/978-3-319-15892-1_2
State	Published - 2015
Externally published	Yes
Event	8th International Conference on Evolutionary Multi-Criterion Optimization, EMO 2015 - Guimarães, Portugal Duration: 29 Mar 2015 → 1 Apr 2015

Publication series

Name	Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume	9019
ISSN (Print)	0302-9743
ISSN (Electronic)	1611-3349

Conference

Conference	8th International Conference on Evolutionary Multi-Criterion Optimization, EMO 2015
Country/Territory	Portugal
City	Guimarães
Period	29/03/15 → 1/04/15

Bibliographical note

Publisher Copyright:
© Springer International Publishing Switzerland 2015.

Keywords

Evolutionary optimization
KkT optimality conditions
Multi-objective optimization
Termination criterion

ASJC Scopus subject areas

Theoretical Computer Science
General Computer Science

Access to Document

10.1007/978-3-319-15892-1_2

Cite this

Deb, K., Abouhawwash, M., & Dutta, J. (2015). An optimality theory based proximity measure for evolutionary multi-objective and many-objective optimization. In A. Gaspar-Cunha, C. H. Antunes, & C. A. C. Coello (Eds.), Evolutionary Multi-Criterion Optimization - 8th International Conference, EMO 2015, Proceedings (pp. 18-33). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 9019). Springer Verlag. https://doi.org/10.1007/978-3-319-15892-1_2

Deb, Kalyanmoy ; Abouhawwash, Mohamed ; Dutta, Joydeep. / An optimality theory based proximity measure for evolutionary multi-objective and many-objective optimization. Evolutionary Multi-Criterion Optimization - 8th International Conference, EMO 2015, Proceedings. editor / António Gaspar-Cunha ; Carlos Henggeler Antunes ; Carlos A. Coello Coello. Springer Verlag, 2015. pp. 18-33 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)).

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title = "An optimality theory based proximity measure for evolutionary multi-objective and many-objective optimization",

abstract = "Evolutionarymulti- andmany-objective optimization (EMO) methods attempt to find a set of Pareto-optimal solutions, instead of a single optimal solution. To evaluate these algorithms, performancemetrics either require the knowledge of the true Pareto-optimal solutions or, are ad-hoc and heuristic based. In this paper, we suggest a KKT proximity measure (KKTPM) that can provide an estimate of the proximity of a set of trade-off solutions from the true Pareto-optimal solutions. Besides theoretical results, the proposed KKT proximity measure is computed for iteration-wise trade-off solutions obtained from specific EMO algorithms on two, three, five and 10-objective optimization problems. Results amply indicate the usefulness of the proposed KKTPM as a termination criterion for an EMO algorithm.",

keywords = "Evolutionary optimization, KkT optimality conditions, Multi-objective optimization, Termination criterion",

author = "Kalyanmoy Deb and Mohamed Abouhawwash and Joydeep Dutta",

note = "Publisher Copyright: {\textcopyright} Springer International Publishing Switzerland 2015.; 8th International Conference on Evolutionary Multi-Criterion Optimization, EMO 2015 ; Conference date: 29-03-2015 Through 01-04-2015",

year = "2015",

doi = "10.1007/978-3-319-15892-1\_2",

language = "English",

series = "Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)",

publisher = "Springer Verlag",

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editor = "Ant{\'o}nio Gaspar-Cunha and Antunes, \{Carlos Henggeler\} and Coello, \{Carlos A. Coello\}",

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Deb, K, Abouhawwash, M & Dutta, J 2015, An optimality theory based proximity measure for evolutionary multi-objective and many-objective optimization. in A Gaspar-Cunha, CH Antunes & CAC Coello (eds), Evolutionary Multi-Criterion Optimization - 8th International Conference, EMO 2015, Proceedings. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 9019, Springer Verlag, pp. 18-33, 8th International Conference on Evolutionary Multi-Criterion Optimization, EMO 2015, Guimarães, Portugal, 29/03/15. https://doi.org/10.1007/978-3-319-15892-1_2

An optimality theory based proximity measure for evolutionary multi-objective and many-objective optimization. / Deb, Kalyanmoy; Abouhawwash, Mohamed; Dutta, Joydeep.
Evolutionary Multi-Criterion Optimization - 8th International Conference, EMO 2015, Proceedings. ed. / António Gaspar-Cunha; Carlos Henggeler Antunes; Carlos A. Coello Coello. Springer Verlag, 2015. p. 18-33 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 9019).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

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AU - Deb, Kalyanmoy

AU - Abouhawwash, Mohamed

AU - Dutta, Joydeep

N1 - Publisher Copyright: © Springer International Publishing Switzerland 2015.

PY - 2015

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N2 - Evolutionarymulti- andmany-objective optimization (EMO) methods attempt to find a set of Pareto-optimal solutions, instead of a single optimal solution. To evaluate these algorithms, performancemetrics either require the knowledge of the true Pareto-optimal solutions or, are ad-hoc and heuristic based. In this paper, we suggest a KKT proximity measure (KKTPM) that can provide an estimate of the proximity of a set of trade-off solutions from the true Pareto-optimal solutions. Besides theoretical results, the proposed KKT proximity measure is computed for iteration-wise trade-off solutions obtained from specific EMO algorithms on two, three, five and 10-objective optimization problems. Results amply indicate the usefulness of the proposed KKTPM as a termination criterion for an EMO algorithm.

AB - Evolutionarymulti- andmany-objective optimization (EMO) methods attempt to find a set of Pareto-optimal solutions, instead of a single optimal solution. To evaluate these algorithms, performancemetrics either require the knowledge of the true Pareto-optimal solutions or, are ad-hoc and heuristic based. In this paper, we suggest a KKT proximity measure (KKTPM) that can provide an estimate of the proximity of a set of trade-off solutions from the true Pareto-optimal solutions. Besides theoretical results, the proposed KKT proximity measure is computed for iteration-wise trade-off solutions obtained from specific EMO algorithms on two, three, five and 10-objective optimization problems. Results amply indicate the usefulness of the proposed KKTPM as a termination criterion for an EMO algorithm.

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ER -

Deb K, Abouhawwash M, Dutta J. An optimality theory based proximity measure for evolutionary multi-objective and many-objective optimization. In Gaspar-Cunha A, Antunes CH, Coello CAC, editors, Evolutionary Multi-Criterion Optimization - 8th International Conference, EMO 2015, Proceedings. Springer Verlag. 2015. p. 18-33. (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)). doi: 10.1007/978-3-319-15892-1_2

An optimality theory based proximity measure for evolutionary multi-objective and many-objective optimization

Abstract

Publication series

Conference

Bibliographical note

Keywords

ASJC Scopus subject areas

Access to Document

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Cite this