Finding multiple roots of systems of nonlinear equations by a hybrid harmony search-based multistart method

Detalhes bibliográficos
Autor(a) principal: Ramadas, Gisela C. V.
Data de Publicação: 2018
Outros Autores: Fernandes, Edite Manuela da G. P., Rocha, Ana Maria A. C.
Tipo de documento: Artigo
Idioma: eng
Título da fonte: Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)
Texto Completo: http://hdl.handle.net/1822/57918
Resumo: A multistart (MS) clustering technique to compute multiple roots of a system of nonlinear equations through the global optimization of an appropriate merit function is presented. The search procedure that is invoked to converge to a root, starting from a randomly generated point inside the search space, is a new variant of the harmony search (HS) metaheuristic. The HS draws its inspiration from an artistic process, the improvisation process of musicians seeking a wonderful harmony. The new hybrid HS algorithm is based on an improvisation operator that mimics the best harmony and uses the idea of a differential variation, borrowed from the differential evolution algorithm. Computational experiments involving a benchmark set of small and large dimensional problems with multiple roots are presented. The results show that the proposed hybrid HS-based MS algorithm is effective in locating multiple roots and competitive when compared with other metaheuristics.
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spelling Finding multiple roots of systems of nonlinear equations by a hybrid harmony search-based multistart methodDifferential evolutionHarmony searchMultistartNonlinear equationsA multistart (MS) clustering technique to compute multiple roots of a system of nonlinear equations through the global optimization of an appropriate merit function is presented. The search procedure that is invoked to converge to a root, starting from a randomly generated point inside the search space, is a new variant of the harmony search (HS) metaheuristic. The HS draws its inspiration from an artistic process, the improvisation process of musicians seeking a wonderful harmony. The new hybrid HS algorithm is based on an improvisation operator that mimics the best harmony and uses the idea of a differential variation, borrowed from the differential evolution algorithm. Computational experiments involving a benchmark set of small and large dimensional problems with multiple roots are presented. The results show that the proposed hybrid HS-based MS algorithm is effective in locating multiple roots and competitive when compared with other metaheuristics.FCT - Fuel Cell Technologies Program(UID/EMS/0615/2016). The authors are grateful to the anonymous referees for their helpful suggestions to improve the paper. This research has been supported by CIDEM (Centre for Research & Development in Mechanical Engineering, Portugal), by COMPETE POCI-01-0145-FEDER-007043 and FCT (Foundation for Science and Technology, Portugal) within the projects UID/EMS/0615/2016 and UID/CEC/00319/2013.Natural Sciences PublishingUniversidade do MinhoRamadas, Gisela C. V.Fernandes, Edite Manuela da G. P.Rocha, Ana Maria A. C.20182018-01-01T00:00:00Zinfo:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/articleapplication/pdfhttp://hdl.handle.net/1822/57918eng1935-009010.18576/amis/120102info:eu-repo/semantics/openAccessreponame:Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)instname:Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informaçãoinstacron:RCAAP2023-07-21T12:18:50Zoai:repositorium.sdum.uminho.pt:1822/57918Portal AgregadorONGhttps://www.rcaap.pt/oai/openaireopendoar:71602024-03-19T19:11:40.828898Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) - Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informaçãofalse
dc.title.none.fl_str_mv Finding multiple roots of systems of nonlinear equations by a hybrid harmony search-based multistart method
title Finding multiple roots of systems of nonlinear equations by a hybrid harmony search-based multistart method
spellingShingle Finding multiple roots of systems of nonlinear equations by a hybrid harmony search-based multistart method
Ramadas, Gisela C. V.
Differential evolution
Harmony search
Multistart
Nonlinear equations
title_short Finding multiple roots of systems of nonlinear equations by a hybrid harmony search-based multistart method
title_full Finding multiple roots of systems of nonlinear equations by a hybrid harmony search-based multistart method
title_fullStr Finding multiple roots of systems of nonlinear equations by a hybrid harmony search-based multistart method
title_full_unstemmed Finding multiple roots of systems of nonlinear equations by a hybrid harmony search-based multistart method
title_sort Finding multiple roots of systems of nonlinear equations by a hybrid harmony search-based multistart method
author Ramadas, Gisela C. V.
author_facet Ramadas, Gisela C. V.
Fernandes, Edite Manuela da G. P.
Rocha, Ana Maria A. C.
author_role author
author2 Fernandes, Edite Manuela da G. P.
Rocha, Ana Maria A. C.
author2_role author
author
dc.contributor.none.fl_str_mv Universidade do Minho
dc.contributor.author.fl_str_mv Ramadas, Gisela C. V.
Fernandes, Edite Manuela da G. P.
Rocha, Ana Maria A. C.
dc.subject.por.fl_str_mv Differential evolution
Harmony search
Multistart
Nonlinear equations
topic Differential evolution
Harmony search
Multistart
Nonlinear equations
description A multistart (MS) clustering technique to compute multiple roots of a system of nonlinear equations through the global optimization of an appropriate merit function is presented. The search procedure that is invoked to converge to a root, starting from a randomly generated point inside the search space, is a new variant of the harmony search (HS) metaheuristic. The HS draws its inspiration from an artistic process, the improvisation process of musicians seeking a wonderful harmony. The new hybrid HS algorithm is based on an improvisation operator that mimics the best harmony and uses the idea of a differential variation, borrowed from the differential evolution algorithm. Computational experiments involving a benchmark set of small and large dimensional problems with multiple roots are presented. The results show that the proposed hybrid HS-based MS algorithm is effective in locating multiple roots and competitive when compared with other metaheuristics.
publishDate 2018
dc.date.none.fl_str_mv 2018
2018-01-01T00:00:00Z
dc.type.status.fl_str_mv info:eu-repo/semantics/publishedVersion
dc.type.driver.fl_str_mv info:eu-repo/semantics/article
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status_str publishedVersion
dc.identifier.uri.fl_str_mv http://hdl.handle.net/1822/57918
url http://hdl.handle.net/1822/57918
dc.language.iso.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv 1935-0090
10.18576/amis/120102
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dc.publisher.none.fl_str_mv Natural Sciences Publishing
publisher.none.fl_str_mv Natural Sciences Publishing
dc.source.none.fl_str_mv reponame:Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)
instname:Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informação
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repository.name.fl_str_mv Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) - Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informação
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