Evolutionary multi-objective optimization using benson’s karush-kuhn-tucker proximity measure

Mohamed Abouhawwash; Mohamed A. Jameel

doi:10.1007/978-3-030-12598-1_3

Evolutionary multi-objective optimization using benson’s karush-kuhn-tucker proximity measure

Mohamed Abouhawwash^*
, Mohamed A. Jameel

^*Corresponding author for this work

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

15 Scopus citations

Abstract

Many Evolutionary Algorithms (EAs) have been proposed over the last decade aiming at solving multi- and many-objective optimization problems. Although EA literature is rich in performance metrics designed specifically to evaluate the convergence ability of these algorithms, most of these metrics require the knowledge of the true Pareto Optimal (PO) front. In this paper, we suggest a novel Karush-Kuhn-Tucker (KKT) based proximity measure using Benson’s method (we call it B-KKTPM). B-KKTPM can determine the relative closeness of any point from the true PO front, without prior knowledge of this front. Finally, we integrate the proposed metric with two recent algorithms and apply it on several multi and many-objective optimization problems. Results show that B-KKTPM can be used as a termination condition for an Evolutionary Multi-objective Optimization (EMO) approach.

Original language	English
Title of host publication	Evolutionary Multi-Criterion Optimization - 10th International Conference, EMO 2019, Proceedings
Editors	Sanaz Mostaghim, Patrick Reed, Kalyanmoy Deb, Erik Goodman, Carlos A. Coello Coello, Kathrin Klamroth, Kaisa Miettinen
Publisher	Springer Verlag
Pages	27-38
Number of pages	12
ISBN (Print)	9783030125974
DOIs	https://doi.org/10.1007/978-3-030-12598-1_3
State	Published - 2019
Externally published	Yes
Event	10th International Conference on Evolutionary Multi-Criterion Optimization, EMO 2019 - East Lansing, United States Duration: 10 Mar 2019 → 13 Mar 2019

Publication series

Name	Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume	11411 LNCS
ISSN (Print)	0302-9743
ISSN (Electronic)	1611-3349

Conference

Conference	10th International Conference on Evolutionary Multi-Criterion Optimization, EMO 2019
Country/Territory	United States
City	East Lansing
Period	10/03/19 → 13/03/19

Bibliographical note

Publisher Copyright:
© Springer Nature Switzerland AG 2019.

Keywords

Benson’s method
Evolutionary optimization
Karush-Kuhn-Tucker conditions
Multi-objective optimization
Termination criterion

ASJC Scopus subject areas

Theoretical Computer Science
General Computer Science

Access to Document

10.1007/978-3-030-12598-1_3

Cite this

Abouhawwash, M., & Jameel, M. A. (2019). Evolutionary multi-objective optimization using benson’s karush-kuhn-tucker proximity measure. In S. Mostaghim, P. Reed, K. Deb, E. Goodman, C. A. Coello Coello, K. Klamroth, & K. Miettinen (Eds.), Evolutionary Multi-Criterion Optimization - 10th International Conference, EMO 2019, Proceedings (pp. 27-38). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 11411 LNCS). Springer Verlag. https://doi.org/10.1007/978-3-030-12598-1_3

Abouhawwash, Mohamed ; Jameel, Mohamed A. / Evolutionary multi-objective optimization using benson’s karush-kuhn-tucker proximity measure. Evolutionary Multi-Criterion Optimization - 10th International Conference, EMO 2019, Proceedings. editor / Sanaz Mostaghim ; Patrick Reed ; Kalyanmoy Deb ; Erik Goodman ; Carlos A. Coello Coello ; Kathrin Klamroth ; Kaisa Miettinen. Springer Verlag, 2019. pp. 27-38 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)).

@inproceedings{c3471ecb9ea946c9bd93f8729abf3fb8,

title = "Evolutionary multi-objective optimization using benson{\textquoteright}s karush-kuhn-tucker proximity measure",

abstract = "Many Evolutionary Algorithms (EAs) have been proposed over the last decade aiming at solving multi- and many-objective optimization problems. Although EA literature is rich in performance metrics designed specifically to evaluate the convergence ability of these algorithms, most of these metrics require the knowledge of the true Pareto Optimal (PO) front. In this paper, we suggest a novel Karush-Kuhn-Tucker (KKT) based proximity measure using Benson{\textquoteright}s method (we call it B-KKTPM). B-KKTPM can determine the relative closeness of any point from the true PO front, without prior knowledge of this front. Finally, we integrate the proposed metric with two recent algorithms and apply it on several multi and many-objective optimization problems. Results show that B-KKTPM can be used as a termination condition for an Evolutionary Multi-objective Optimization (EMO) approach.",

keywords = "Benson{\textquoteright}s method, Evolutionary optimization, Karush-Kuhn-Tucker conditions, Multi-objective optimization, Termination criterion",

author = "Mohamed Abouhawwash and Jameel, \{Mohamed A.\}",

note = "Publisher Copyright: {\textcopyright} Springer Nature Switzerland AG 2019.; 10th International Conference on Evolutionary Multi-Criterion Optimization, EMO 2019 ; Conference date: 10-03-2019 Through 13-03-2019",

year = "2019",

doi = "10.1007/978-3-030-12598-1\_3",

language = "English",

isbn = "9783030125974",

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

publisher = "Springer Verlag",

pages = "27--38",

editor = "Sanaz Mostaghim and Patrick Reed and Kalyanmoy Deb and Erik Goodman and \{Coello Coello\}, \{Carlos A.\} and Kathrin Klamroth and Kaisa Miettinen",

booktitle = "Evolutionary Multi-Criterion Optimization - 10th International Conference, EMO 2019, Proceedings",

address = "Germany",

}

Abouhawwash, M & Jameel, MA 2019, Evolutionary multi-objective optimization using benson’s karush-kuhn-tucker proximity measure. in S Mostaghim, P Reed, K Deb, E Goodman, CA Coello Coello, K Klamroth & K Miettinen (eds), Evolutionary Multi-Criterion Optimization - 10th International Conference, EMO 2019, Proceedings. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 11411 LNCS, Springer Verlag, pp. 27-38, 10th International Conference on Evolutionary Multi-Criterion Optimization, EMO 2019, East Lansing, United States, 10/03/19. https://doi.org/10.1007/978-3-030-12598-1_3

Evolutionary multi-objective optimization using benson’s karush-kuhn-tucker proximity measure. / Abouhawwash, Mohamed; Jameel, Mohamed A.
Evolutionary Multi-Criterion Optimization - 10th International Conference, EMO 2019, Proceedings. ed. / Sanaz Mostaghim; Patrick Reed; Kalyanmoy Deb; Erik Goodman; Carlos A. Coello Coello; Kathrin Klamroth; Kaisa Miettinen. Springer Verlag, 2019. p. 27-38 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 11411 LNCS).

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

TY - GEN

T1 - Evolutionary multi-objective optimization using benson’s karush-kuhn-tucker proximity measure

AU - Abouhawwash, Mohamed

AU - Jameel, Mohamed A.

N1 - Publisher Copyright: © Springer Nature Switzerland AG 2019.

PY - 2019

Y1 - 2019

N2 - Many Evolutionary Algorithms (EAs) have been proposed over the last decade aiming at solving multi- and many-objective optimization problems. Although EA literature is rich in performance metrics designed specifically to evaluate the convergence ability of these algorithms, most of these metrics require the knowledge of the true Pareto Optimal (PO) front. In this paper, we suggest a novel Karush-Kuhn-Tucker (KKT) based proximity measure using Benson’s method (we call it B-KKTPM). B-KKTPM can determine the relative closeness of any point from the true PO front, without prior knowledge of this front. Finally, we integrate the proposed metric with two recent algorithms and apply it on several multi and many-objective optimization problems. Results show that B-KKTPM can be used as a termination condition for an Evolutionary Multi-objective Optimization (EMO) approach.

AB - Many Evolutionary Algorithms (EAs) have been proposed over the last decade aiming at solving multi- and many-objective optimization problems. Although EA literature is rich in performance metrics designed specifically to evaluate the convergence ability of these algorithms, most of these metrics require the knowledge of the true Pareto Optimal (PO) front. In this paper, we suggest a novel Karush-Kuhn-Tucker (KKT) based proximity measure using Benson’s method (we call it B-KKTPM). B-KKTPM can determine the relative closeness of any point from the true PO front, without prior knowledge of this front. Finally, we integrate the proposed metric with two recent algorithms and apply it on several multi and many-objective optimization problems. Results show that B-KKTPM can be used as a termination condition for an Evolutionary Multi-objective Optimization (EMO) approach.

KW - Benson’s method

KW - Evolutionary optimization

KW - Karush-Kuhn-Tucker conditions

KW - Multi-objective optimization

KW - Termination criterion

UR - https://www.scopus.com/pages/publications/85063061600

U2 - 10.1007/978-3-030-12598-1_3

DO - 10.1007/978-3-030-12598-1_3

M3 - Conference contribution

AN - SCOPUS:85063061600

SN - 9783030125974

T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

SP - 27

EP - 38

BT - Evolutionary Multi-Criterion Optimization - 10th International Conference, EMO 2019, Proceedings

A2 - Mostaghim, Sanaz

A2 - Reed, Patrick

A2 - Deb, Kalyanmoy

A2 - Goodman, Erik

A2 - Coello Coello, Carlos A.

A2 - Klamroth, Kathrin

A2 - Miettinen, Kaisa

PB - Springer Verlag

T2 - 10th International Conference on Evolutionary Multi-Criterion Optimization, EMO 2019

Y2 - 10 March 2019 through 13 March 2019

ER -

Abouhawwash M, Jameel MA. Evolutionary multi-objective optimization using benson’s karush-kuhn-tucker proximity measure. In Mostaghim S, Reed P, Deb K, Goodman E, Coello Coello CA, Klamroth K, Miettinen K, editors, Evolutionary Multi-Criterion Optimization - 10th International Conference, EMO 2019, Proceedings. Springer Verlag. 2019. p. 27-38. (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)). doi: 10.1007/978-3-030-12598-1_3

Evolutionary multi-objective optimization using benson’s karush-kuhn-tucker proximity measure

Abstract

Publication series

Conference

Bibliographical note

Keywords

ASJC Scopus subject areas

Access to Document

Fingerprint

Cite this