On a smoothed penalty-based algorithm for global optimization
Autor(a) principal: | |
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Data de Publicação: | 2017 |
Outros Autores: | , |
Tipo de documento: | Artigo |
Idioma: | eng |
Título da fonte: | Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) |
Texto Completo: | http://hdl.handle.net/1822/49539 |
Resumo: | This paper presents a coercive smoothed penalty framework for nonsmooth and nonconvex constrained global optimization problems. The properties of the smoothed penalty function are derived. Convergence to an ε -global minimizer is proved. At each iteration k, the framework requires the ε(k) -global minimizer of a subproblem, where ε(k)→ε . We show that the subproblem may be solved by well-known stochastic metaheuristics, as well as by the artificial fish swarm (AFS) algorithm. In the limit, the AFS algorithm convergence to an ε(k) -global minimum of the real-valued smoothed penalty function is guaranteed with probability one, using the limiting behavior of Markov chains. In this context, we show that the transition probability of the Markov chain produced by the AFS algorithm, when generating a population where the best fitness is in the ε(k)-neighborhood of the global minimum, is one when this property holds in the current population, and is strictly bounded from zero when the property does not hold. Preliminary numerical experiments show that the presented penalty algorithm based on the coercive smoothed penalty gives very competitive results when compared with other penalty-based methods. |
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On a smoothed penalty-based algorithm for global optimizationGlobal optimizationPenalty functionArtificial fish swarmMarkov chainsEngenharia e Tecnologia::Outras Engenharias e TecnologiasScience & TechnologyThis paper presents a coercive smoothed penalty framework for nonsmooth and nonconvex constrained global optimization problems. The properties of the smoothed penalty function are derived. Convergence to an ε -global minimizer is proved. At each iteration k, the framework requires the ε(k) -global minimizer of a subproblem, where ε(k)→ε . We show that the subproblem may be solved by well-known stochastic metaheuristics, as well as by the artificial fish swarm (AFS) algorithm. In the limit, the AFS algorithm convergence to an ε(k) -global minimum of the real-valued smoothed penalty function is guaranteed with probability one, using the limiting behavior of Markov chains. In this context, we show that the transition probability of the Markov chain produced by the AFS algorithm, when generating a population where the best fitness is in the ε(k)-neighborhood of the global minimum, is one when this property holds in the current population, and is strictly bounded from zero when the property does not hold. Preliminary numerical experiments show that the presented penalty algorithm based on the coercive smoothed penalty gives very competitive results when compared with other penalty-based methods.The authors would like to thank two anonymous referees for their valuable comments and suggestions to improve the paper. This work has been supported by COMPETE: POCI-01-0145-FEDER-007043 and FCT - Fundac¸ao para a Ci ˜ encia e Tecnologia within the projects UID/CEC/00319/2013 and ˆ UID/MAT/00013/2013.info:eu-repo/semantics/publishedVersionSpringerUniversidade do MinhoRocha, Ana Maria A. C.Costa, M. Fernanda P.Fernandes, Edite Manuela da G. P.20172017-01-01T00:00:00Zinfo:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/articleapplication/pdfhttp://hdl.handle.net/1822/49539engRocha, A.M.A.C., Costa, M.F.P. & Fernandes, E.M.G.P. J Glob Optim (2017) 69: 561. https://doi.org/10.1007/s10898-017-0504-20925-500110.1007/s10898-017-0504-2www.springerlink.cominfo: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:RCAAP2023-07-21T12:12:36ZPortal AgregadorONG |
dc.title.none.fl_str_mv |
On a smoothed penalty-based algorithm for global optimization |
title |
On a smoothed penalty-based algorithm for global optimization |
spellingShingle |
On a smoothed penalty-based algorithm for global optimization Rocha, Ana Maria A. C. Global optimization Penalty function Artificial fish swarm Markov chains Engenharia e Tecnologia::Outras Engenharias e Tecnologias Science & Technology |
title_short |
On a smoothed penalty-based algorithm for global optimization |
title_full |
On a smoothed penalty-based algorithm for global optimization |
title_fullStr |
On a smoothed penalty-based algorithm for global optimization |
title_full_unstemmed |
On a smoothed penalty-based algorithm for global optimization |
title_sort |
On a smoothed penalty-based algorithm for global optimization |
author |
Rocha, Ana Maria A. C. |
author_facet |
Rocha, Ana Maria A. C. Costa, M. Fernanda P. Fernandes, Edite Manuela da G. P. |
author_role |
author |
author2 |
Costa, M. Fernanda P. Fernandes, Edite Manuela da G. P. |
author2_role |
author author |
dc.contributor.none.fl_str_mv |
Universidade do Minho |
dc.contributor.author.fl_str_mv |
Rocha, Ana Maria A. C. Costa, M. Fernanda P. Fernandes, Edite Manuela da G. P. |
dc.subject.por.fl_str_mv |
Global optimization Penalty function Artificial fish swarm Markov chains Engenharia e Tecnologia::Outras Engenharias e Tecnologias Science & Technology |
topic |
Global optimization Penalty function Artificial fish swarm Markov chains Engenharia e Tecnologia::Outras Engenharias e Tecnologias Science & Technology |
description |
This paper presents a coercive smoothed penalty framework for nonsmooth and nonconvex constrained global optimization problems. The properties of the smoothed penalty function are derived. Convergence to an ε -global minimizer is proved. At each iteration k, the framework requires the ε(k) -global minimizer of a subproblem, where ε(k)→ε . We show that the subproblem may be solved by well-known stochastic metaheuristics, as well as by the artificial fish swarm (AFS) algorithm. In the limit, the AFS algorithm convergence to an ε(k) -global minimum of the real-valued smoothed penalty function is guaranteed with probability one, using the limiting behavior of Markov chains. In this context, we show that the transition probability of the Markov chain produced by the AFS algorithm, when generating a population where the best fitness is in the ε(k)-neighborhood of the global minimum, is one when this property holds in the current population, and is strictly bounded from zero when the property does not hold. Preliminary numerical experiments show that the presented penalty algorithm based on the coercive smoothed penalty gives very competitive results when compared with other penalty-based methods. |
publishDate |
2017 |
dc.date.none.fl_str_mv |
2017 2017-01-01T00:00:00Z |
dc.type.status.fl_str_mv |
info:eu-repo/semantics/publishedVersion |
dc.type.driver.fl_str_mv |
info:eu-repo/semantics/article |
format |
article |
status_str |
publishedVersion |
dc.identifier.uri.fl_str_mv |
http://hdl.handle.net/1822/49539 |
url |
http://hdl.handle.net/1822/49539 |
dc.language.iso.fl_str_mv |
eng |
language |
eng |
dc.relation.none.fl_str_mv |
Rocha, A.M.A.C., Costa, M.F.P. & Fernandes, E.M.G.P. J Glob Optim (2017) 69: 561. https://doi.org/10.1007/s10898-017-0504-2 0925-5001 10.1007/s10898-017-0504-2 www.springerlink.com |
dc.rights.driver.fl_str_mv |
info:eu-repo/semantics/openAccess |
eu_rights_str_mv |
openAccess |
dc.format.none.fl_str_mv |
application/pdf |
dc.publisher.none.fl_str_mv |
Springer |
publisher.none.fl_str_mv |
Springer |
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 instacron:RCAAP |
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Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informação |
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RCAAP |
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RCAAP |
reponame_str |
Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) |
collection |
Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) |
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1777303705765281792 |