Solving nonlinear equation systems via clustering-based adaptive speciation differential evolution

In numerical computation, locating multiple roots of nonlinear equations (NESs) in a single run is a challenging work. In order to solve the problem of population grouping and parameters settings during the evolutionary, a clustering-based adaptive speciation differential evolution, referred to as C...

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Autores principales:	Qishuo Pang, Xianyan Mi, Jixuan Sun, Huayong Qin
Formato:	article
Lenguaje:	EN
Publicado:	AIMS Press 2021
Materias:	nonlinear equation systems dynamic clustering sizes niche adaptive parameter control re-initialization mechanism differential evolution Biotechnology TP248.13-248.65 Mathematics QA1-939
Acceso en línea:	https://doaj.org/article/4eacf77d8f504f80a86c42dc480c5dcf
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id	oai:doaj.org-article:4eacf77d8f504f80a86c42dc480c5dcf
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spelling	oai:doaj.org-article:4eacf77d8f504f80a86c42dc480c5dcf2021-11-11T00:53:04ZSolving nonlinear equation systems via clustering-based adaptive speciation differential evolution10.3934/mbe.20213021551-0018https://doaj.org/article/4eacf77d8f504f80a86c42dc480c5dcf2021-07-01T00:00:00Zhttps://www.aimspress.com/article/doi/10.3934/mbe.2021302?viewType=HTMLhttps://doaj.org/toc/1551-0018In numerical computation, locating multiple roots of nonlinear equations (NESs) in a single run is a challenging work. In order to solve the problem of population grouping and parameters settings during the evolutionary, a clustering-based adaptive speciation differential evolution, referred to as CASDE, is presented to deal with NESs. CASDE offers three advantages: 1) the clustering with dynamic clustering sizes is used to set clustering sizes for different problems; 2) adaptive parameter control at the niche level is proposed to enhance the search ability and efficiency; 3) re-initialization mechanism motivates the algorithm to search new roots and saves computing resources. To evaluate the performance of CASDE, we select 30 problems with different features as test suite. Experimental results indicate that the speciation clustering with dynamic clustering sizes, niche adaptive parameter control, and re-initialization mechanism when combined together in a synergistic manner can improve the ability to find multiple roots in a single run. Additionally, our method is also compared with other state-of-the-art methods, which is capable of obtaining better results in terms of peak ratio and success rate. Finally, two practical mechanical problems are used to verify the performance of CASDE, and it also demonstrates superior results.Qishuo PangXianyan MiJixuan Sun Huayong QinAIMS Pressarticlenonlinear equation systemsdynamic clustering sizesniche adaptive parameter controlre-initialization mechanismdifferential evolutionBiotechnologyTP248.13-248.65MathematicsQA1-939ENMathematical Biosciences and Engineering, Vol 18, Iss 5, Pp 6034-6065 (2021)
institution	DOAJ
collection	DOAJ
language	EN
topic	nonlinear equation systems dynamic clustering sizes niche adaptive parameter control re-initialization mechanism differential evolution Biotechnology TP248.13-248.65 Mathematics QA1-939
spellingShingle	nonlinear equation systems dynamic clustering sizes niche adaptive parameter control re-initialization mechanism differential evolution Biotechnology TP248.13-248.65 Mathematics QA1-939 Qishuo Pang Xianyan Mi Jixuan Sun Huayong Qin Solving nonlinear equation systems via clustering-based adaptive speciation differential evolution
description	In numerical computation, locating multiple roots of nonlinear equations (NESs) in a single run is a challenging work. In order to solve the problem of population grouping and parameters settings during the evolutionary, a clustering-based adaptive speciation differential evolution, referred to as CASDE, is presented to deal with NESs. CASDE offers three advantages: 1) the clustering with dynamic clustering sizes is used to set clustering sizes for different problems; 2) adaptive parameter control at the niche level is proposed to enhance the search ability and efficiency; 3) re-initialization mechanism motivates the algorithm to search new roots and saves computing resources. To evaluate the performance of CASDE, we select 30 problems with different features as test suite. Experimental results indicate that the speciation clustering with dynamic clustering sizes, niche adaptive parameter control, and re-initialization mechanism when combined together in a synergistic manner can improve the ability to find multiple roots in a single run. Additionally, our method is also compared with other state-of-the-art methods, which is capable of obtaining better results in terms of peak ratio and success rate. Finally, two practical mechanical problems are used to verify the performance of CASDE, and it also demonstrates superior results.
format	article
author	Qishuo Pang Xianyan Mi Jixuan Sun Huayong Qin
author_facet	Qishuo Pang Xianyan Mi Jixuan Sun Huayong Qin
author_sort	Qishuo Pang
title	Solving nonlinear equation systems via clustering-based adaptive speciation differential evolution
title_short	Solving nonlinear equation systems via clustering-based adaptive speciation differential evolution
title_full	Solving nonlinear equation systems via clustering-based adaptive speciation differential evolution
title_fullStr	Solving nonlinear equation systems via clustering-based adaptive speciation differential evolution
title_full_unstemmed	Solving nonlinear equation systems via clustering-based adaptive speciation differential evolution
title_sort	solving nonlinear equation systems via clustering-based adaptive speciation differential evolution
publisher	AIMS Press
publishDate	2021
url	https://doaj.org/article/4eacf77d8f504f80a86c42dc480c5dcf
work_keys_str_mv	AT qishuopang solvingnonlinearequationsystemsviaclusteringbasedadaptivespeciationdifferentialevolution AT xianyanmi solvingnonlinearequationsystemsviaclusteringbasedadaptivespeciationdifferentialevolution AT jixuansun solvingnonlinearequationsystemsviaclusteringbasedadaptivespeciationdifferentialevolution AT huayongqin solvingnonlinearequationsystemsviaclusteringbasedadaptivespeciationdifferentialevolution
_version_	1718439583058755584

Solving nonlinear equation systems via clustering-based adaptive speciation differential evolution

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