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 ProceedingsConference paper (refereed)Researchpeer-review


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 languageEnglish
Title of host publicationEvolutionary Multi-Criterion Optimization - 10th International Conference, EMO 2019, Proceedings
EditorsCarlos A. Coello Coello, Sanaz Mostaghim, Kalyanmoy Deb, Erik Goodman, Kathrin Klamroth, Patrick Reed, Kaisa Miettinen
PublisherSpringer-Verlag GmbH and Co. KG
Number of pages12
ISBN (Print)9783030125974
Publication statusPublished - Feb 2019
Externally publishedYes
Event10th International Conference on Evolutionary Multi-Criterion Optimization - East Lansing, United States
Duration: 10 Mar 201913 Mar 2019

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume11411 LNCS
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349


Conference10th International Conference on Evolutionary Multi-Criterion Optimization
Abbreviated titleEMO 2019
Country/TerritoryUnited States
CityEast Lansing

Bibliographical note

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

Publisher Copyright:
© Springer Nature Switzerland AG 2019.


  • Differential evolution
  • Multiobjective optimization
  • Nonlinear equation systems


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