Nonlinear Equations Solving with Intelligent Optimization Algorithms: A Survey

Nonlinear Equations (NEs), which may usually have multiple roots, are ubiquitous in diverse fields. One of the main purposes of solving NEs is to locate as many roots as possible simultaneously in a single run, however, it is a difficult and challenging task in numerical computation. In recent years...

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Bibliographic Details
Published in:	Complex System Modeling and Simulation Vol. 1; no. 1; pp. 15 - 32
Main Authors:	Gong, Wenyin, Liao, Zuowen, Mi, Xianyan, Wang, Ling, Guo, Yuanyuan
Format:	Journal Article
Language:	English
Published:	Tsinghua University Press 01.03.2021
Subjects:	diversity preservation intelligent optimization algorithms (ioa) multiple roots location nonlinear equations (nes) transformation techniques
ISSN:	2096-9929, 2096-9929
Online Access:	Get full text
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Summary:	Nonlinear Equations (NEs), which may usually have multiple roots, are ubiquitous in diverse fields. One of the main purposes of solving NEs is to locate as many roots as possible simultaneously in a single run, however, it is a difficult and challenging task in numerical computation. In recent years, Intelligent Optimization Algorithms (IOAs) have shown to be particularly effective in solving NEs. This paper provides a comprehensive survey on IOAs that have been exploited to locate multiple roots of NEs. This paper first revisits the fundamental definition of NEs and reviews the most recent development of the transformation techniques. Then, solving NEs with IOAs is reviewed, followed by the benchmark functions and the performance comparison of several state-of-the-art algorithms. Finally, this paper points out the challenges and some possible open issues for solving NEs.
ISSN:	2096-9929 2096-9929
DOI:	10.23919/CSMS.2021.0002