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Complex System Modeling and Simulation 2021, 1(1): 15-32 https://doi.org/10.23919/CSMS.2021.0002
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Nonlinear Equations Solving with Intelligent Optimization Algorithms: A Survey

Show Author's Information Wenyin Gong,  Zuowen Liao*( ),  Xianyan Mi*( ),  Ling Wang,  Yuanyuan Guo
School of Computer Science, China University of Geosciences, Wuhan 430074, China
Beibu Gulf Ocean Development Research Center, Beibu Gulf University, Qinzhou 535000, China
College of Economics and Management, Beibu Gulf University, Qinzhou 535000, China
Department of Automation, Tsinghua University, Beijing 100084, China
Cvent Company, Fredericton, E3B 5H8, Canada
Keywords:
Nonlinear Equations (NEs), Intelligent Optimization Algorithms (IOA), multiple roots location, transformation techniques, diversity preservation
Cite this article:
Gong W, Liao Z, Mi X, et al. Nonlinear Equations Solving with Intelligent Optimization Algorithms: A Survey. Complex System Modeling and Simulation, 2021, 1(1): 15-32. https://doi.org/10.23919/CSMS.2021.0002
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Abstract Full text About this article

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.


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About this article

Nonlinear Equations Solving with Intelligent Optimization Algorithms: A Survey

Show Author's information Wenyin Gong, Zuowen Liao*( ), Xianyan Mi*( ), Ling Wang, Yuanyuan Guo
School of Computer Science, China University of Geosciences, Wuhan 430074, China
Beibu Gulf Ocean Development Research Center, Beibu Gulf University, Qinzhou 535000, China
College of Economics and Management, Beibu Gulf University, Qinzhou 535000, China
Department of Automation, Tsinghua University, Beijing 100084, China
Cvent Company, Fredericton, E3B 5H8, Canada

Abstract

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.

Keywords: Nonlinear Equations (NEs), Intelligent Optimization Algorithms (IOA), multiple roots location, transformation techniques, diversity preservation

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Received: 16 February 2021
Accepted: 25 February 2021
Published: 30 April 2021
Issue date: March 2021

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Acknowledgements

This work was partly supported by the National Natural Science Foundation of China (No. 62076225), the Natural Science Foundation of Guangxi Province (No. 2020JJA170038), and the High-Level Talents Research Project of Beibu Gulf (No. 2020KYQD06).

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