Solving nonlinear equation systems using multiobjective differential evolution

Jing-Yu JI; Wei-Jie YU; Jun ZHANG

doi:10.1007/978-3-030-12598-1_12

Solving nonlinear equation systems using multiobjective differential evolution

Jing-Yu JI, Wei-Jie YU^*, Jun ZHANG

^*Corresponding author for this work

Research output: Book Chapters | Papers in Conference Proceedings › Conference paper (refereed) › Research › peer-review

Abstract

Nonlinear equation systems (NESs) usually have more than one optimal solution. However, locating all the optimal solutions in a single run, is one of the most challenging issues for evolutionary optimization. In this paper, we address this issue by transforming all the optimal solutions of an NES to the nondominated solutions of a constructed multiobjective optimization problem (MOP). In the general case, we prove that the proposed transformation fully matches the requirement of multiobjective optimization. That is, the multiple objectives always conflict with each other. In this way, multiobjective optimization techniques can be used to locate these multiple optimal solutions simultaneously as they locate the nondominated solutions of the MOPs. Our proposed approach is evaluated on 22 NESs with different features, such as linear and nonlinear equations, different numbers of optimal solutions, and infinite optimal solutions. Experimental results reveal that the proposed approach is highly competitive with some other state-of-the-art algorithms for NES.

Original language	English
Title of host publication	Evolutionary Multi-Criterion Optimization - 10th International Conference, EMO 2019, Proceedings
Editors	Carlos A. Coello Coello, Sanaz Mostaghim, Kalyanmoy Deb, Erik Goodman, Kathrin Klamroth, Patrick Reed, Kaisa Miettinen
Publisher	Springer-Verlag GmbH and Co. KG
Pages	139-150
Number of pages	12
ISBN (Print)	9783030125974
DOIs	https://doi.org/10.1007/978-3-030-12598-1_12
Publication status	Published - Feb 2019
Externally published	Yes
Event	10th International Conference on Evolutionary Multi-Criterion Optimization - 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
Abbreviated title	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.

Funding

This work was supported by the Science and Technology Planning Project of Guangdong Province, China (Grant No. 2014B050504005).

Keywords

Differential evolution
Multiobjective optimization
Nonlinear equation systems

Access to Document

10.1007/978-3-030-12598-1_12

Cite this

JI, J.-Y., YU, W.-J., & ZHANG, J. (2019). Solving nonlinear equation systems using multiobjective differential evolution. In C. A. Coello Coello, S. Mostaghim, K. Deb, E. Goodman, K. Klamroth, P. Reed, & K. Miettinen (Eds.), Evolutionary Multi-Criterion Optimization - 10th International Conference, EMO 2019, Proceedings (pp. 139-150). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 11411 LNCS). Springer-Verlag GmbH and Co. KG. https://doi.org/10.1007/978-3-030-12598-1_12

JI, Jing-Yu ; YU, Wei-Jie ; ZHANG, Jun. / Solving nonlinear equation systems using multiobjective differential evolution. Evolutionary Multi-Criterion Optimization - 10th International Conference, EMO 2019, Proceedings. editor / Carlos A. Coello Coello ; Sanaz Mostaghim ; Kalyanmoy Deb ; Erik Goodman ; Kathrin Klamroth ; Patrick Reed ; Kaisa Miettinen. Springer-Verlag GmbH and Co. KG, 2019. pp. 139-150 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)).

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title = "Solving nonlinear equation systems using multiobjective differential evolution",

abstract = "Nonlinear equation systems (NESs) usually have more than one optimal solution. However, locating all the optimal solutions in a single run, is one of the most challenging issues for evolutionary optimization. In this paper, we address this issue by transforming all the optimal solutions of an NES to the nondominated solutions of a constructed multiobjective optimization problem (MOP). In the general case, we prove that the proposed transformation fully matches the requirement of multiobjective optimization. That is, the multiple objectives always conflict with each other. In this way, multiobjective optimization techniques can be used to locate these multiple optimal solutions simultaneously as they locate the nondominated solutions of the MOPs. Our proposed approach is evaluated on 22 NESs with different features, such as linear and nonlinear equations, different numbers of optimal solutions, and infinite optimal solutions. Experimental results reveal that the proposed approach is highly competitive with some other state-of-the-art algorithms for NES.",

keywords = "Differential evolution, Multiobjective optimization, Nonlinear equation systems",

author = "Jing-Yu JI and Wei-Jie YU and Jun ZHANG",

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",

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doi = "10.1007/978-3-030-12598-1_12",

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JI, J-Y, YU, W-J & ZHANG, J 2019, Solving nonlinear equation systems using multiobjective differential evolution. in CA Coello Coello, S Mostaghim, K Deb, E Goodman, K Klamroth, P Reed & 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 GmbH and Co. KG, pp. 139-150, 10th International Conference on Evolutionary Multi-Criterion Optimization, East Lansing, Michigan, United States, 10/03/19. https://doi.org/10.1007/978-3-030-12598-1_12

Solving nonlinear equation systems using multiobjective differential evolution. / JI, Jing-Yu; YU, Wei-Jie; ZHANG, Jun.
Evolutionary Multi-Criterion Optimization - 10th International Conference, EMO 2019, Proceedings. ed. / Carlos A. Coello Coello; Sanaz Mostaghim; Kalyanmoy Deb; Erik Goodman; Kathrin Klamroth; Patrick Reed; Kaisa Miettinen. Springer-Verlag GmbH and Co. KG, 2019. p. 139-150 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 11411 LNCS).

Research output: Book Chapters | Papers in Conference Proceedings › Conference paper (refereed) › Research › peer-review

TY - GEN

T1 - Solving nonlinear equation systems using multiobjective differential evolution

AU - JI, Jing-Yu

AU - YU, Wei-Jie

AU - ZHANG, Jun

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

PY - 2019/2

Y1 - 2019/2

N2 - Nonlinear equation systems (NESs) usually have more than one optimal solution. However, locating all the optimal solutions in a single run, is one of the most challenging issues for evolutionary optimization. In this paper, we address this issue by transforming all the optimal solutions of an NES to the nondominated solutions of a constructed multiobjective optimization problem (MOP). In the general case, we prove that the proposed transformation fully matches the requirement of multiobjective optimization. That is, the multiple objectives always conflict with each other. In this way, multiobjective optimization techniques can be used to locate these multiple optimal solutions simultaneously as they locate the nondominated solutions of the MOPs. Our proposed approach is evaluated on 22 NESs with different features, such as linear and nonlinear equations, different numbers of optimal solutions, and infinite optimal solutions. Experimental results reveal that the proposed approach is highly competitive with some other state-of-the-art algorithms for NES.

AB - Nonlinear equation systems (NESs) usually have more than one optimal solution. However, locating all the optimal solutions in a single run, is one of the most challenging issues for evolutionary optimization. In this paper, we address this issue by transforming all the optimal solutions of an NES to the nondominated solutions of a constructed multiobjective optimization problem (MOP). In the general case, we prove that the proposed transformation fully matches the requirement of multiobjective optimization. That is, the multiple objectives always conflict with each other. In this way, multiobjective optimization techniques can be used to locate these multiple optimal solutions simultaneously as they locate the nondominated solutions of the MOPs. Our proposed approach is evaluated on 22 NESs with different features, such as linear and nonlinear equations, different numbers of optimal solutions, and infinite optimal solutions. Experimental results reveal that the proposed approach is highly competitive with some other state-of-the-art algorithms for NES.

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

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

A2 - Coello Coello, Carlos A.

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JI JY, YU WJ, ZHANG J. Solving nonlinear equation systems using multiobjective differential evolution. In Coello Coello CA, Mostaghim S, Deb K, Goodman E, Klamroth K, Reed P, Miettinen K, editors, Evolutionary Multi-Criterion Optimization - 10th International Conference, EMO 2019, Proceedings. Springer-Verlag GmbH and Co. KG. 2019. p. 139-150. (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)). Epub 2019 Feb 3. doi: 10.1007/978-3-030-12598-1_12

Solving nonlinear equation systems using multiobjective differential evolution

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