Adaptive Penalty and Barrier function based on Fuzzy Logic
Autor(a) principal: | |
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Data de Publicação: | 2015 |
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/10400.22/7589 |
Resumo: | Optimization methods have been used in many areas of knowledge, such as Engineering, Statistics, Chemistry, among others, to solve optimization problems. In many cases it is not possible to use derivative methods, due to the characteristics of the problem to be solved and/or its constraints, for example if the involved functions are non-smooth and/or their derivatives are not know. To solve this type of problems a Java based API has been implemented, which includes only derivative-free optimization methods, and that can be used to solve both constrained and unconstrained problems. For solving constrained problems, the classic Penalty and Barrier functions were included in the API. In this paper a new approach to Penalty and Barrier functions, based on Fuzzy Logic, is proposed. Two penalty functions, that impose a progressive penalization to solutions that violate the constraints, are discussed. The implemented functions impose a low penalization when the violation of the constraints is low and a heavy penalty when the violation is high. Numerical results, obtained using twenty-eight test problems, comparing the proposed Fuzzy Logic based functions to six of the classic Penalty and Barrier functions are presented. Considering the achieved results, it can be concluded that the proposed penalty functions besides being very robust also have a very good performance. |
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Adaptive Penalty and Barrier function based on Fuzzy LogicApplicationsFuzzy mathematical programmingMathematicsDerivative free optimizationDirect search methodsPenalty and Barrier functionsFuzzy LogicOptimization methods have been used in many areas of knowledge, such as Engineering, Statistics, Chemistry, among others, to solve optimization problems. In many cases it is not possible to use derivative methods, due to the characteristics of the problem to be solved and/or its constraints, for example if the involved functions are non-smooth and/or their derivatives are not know. To solve this type of problems a Java based API has been implemented, which includes only derivative-free optimization methods, and that can be used to solve both constrained and unconstrained problems. For solving constrained problems, the classic Penalty and Barrier functions were included in the API. In this paper a new approach to Penalty and Barrier functions, based on Fuzzy Logic, is proposed. Two penalty functions, that impose a progressive penalization to solutions that violate the constraints, are discussed. The implemented functions impose a low penalization when the violation of the constraints is low and a heavy penalty when the violation is high. Numerical results, obtained using twenty-eight test problems, comparing the proposed Fuzzy Logic based functions to six of the classic Penalty and Barrier functions are presented. Considering the achieved results, it can be concluded that the proposed penalty functions besides being very robust also have a very good performance.ElsevierRepositório Científico do Instituto Politécnico do PortoMatias, JoãoCorreia, AldinaMestre, PedroSerodio, CarlosCouto, PedroTeixeira, ChristopheMelo-Pinto, Pedro2016-11-01T01:30:09Z20152015-01-01T00:00:00Zinfo:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/articleapplication/pdfhttp://hdl.handle.net/10400.22/7589eng10.1016/j.eswa.2015.04.070info: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:RCAAP2023-03-13T12:48:14Zoai:recipp.ipp.pt:10400.22/7589Portal AgregadorONGhttps://www.rcaap.pt/oai/openaireopendoar:71602024-03-19T17:28:01.893409Repositório 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 |
Adaptive Penalty and Barrier function based on Fuzzy Logic |
title |
Adaptive Penalty and Barrier function based on Fuzzy Logic |
spellingShingle |
Adaptive Penalty and Barrier function based on Fuzzy Logic Matias, João Applications Fuzzy mathematical programming Mathematics Derivative free optimization Direct search methods Penalty and Barrier functions Fuzzy Logic |
title_short |
Adaptive Penalty and Barrier function based on Fuzzy Logic |
title_full |
Adaptive Penalty and Barrier function based on Fuzzy Logic |
title_fullStr |
Adaptive Penalty and Barrier function based on Fuzzy Logic |
title_full_unstemmed |
Adaptive Penalty and Barrier function based on Fuzzy Logic |
title_sort |
Adaptive Penalty and Barrier function based on Fuzzy Logic |
author |
Matias, João |
author_facet |
Matias, João Correia, Aldina Mestre, Pedro Serodio, Carlos Couto, Pedro Teixeira, Christophe Melo-Pinto, Pedro |
author_role |
author |
author2 |
Correia, Aldina Mestre, Pedro Serodio, Carlos Couto, Pedro Teixeira, Christophe Melo-Pinto, Pedro |
author2_role |
author author author author author author |
dc.contributor.none.fl_str_mv |
Repositório Científico do Instituto Politécnico do Porto |
dc.contributor.author.fl_str_mv |
Matias, João Correia, Aldina Mestre, Pedro Serodio, Carlos Couto, Pedro Teixeira, Christophe Melo-Pinto, Pedro |
dc.subject.por.fl_str_mv |
Applications Fuzzy mathematical programming Mathematics Derivative free optimization Direct search methods Penalty and Barrier functions Fuzzy Logic |
topic |
Applications Fuzzy mathematical programming Mathematics Derivative free optimization Direct search methods Penalty and Barrier functions Fuzzy Logic |
description |
Optimization methods have been used in many areas of knowledge, such as Engineering, Statistics, Chemistry, among others, to solve optimization problems. In many cases it is not possible to use derivative methods, due to the characteristics of the problem to be solved and/or its constraints, for example if the involved functions are non-smooth and/or their derivatives are not know. To solve this type of problems a Java based API has been implemented, which includes only derivative-free optimization methods, and that can be used to solve both constrained and unconstrained problems. For solving constrained problems, the classic Penalty and Barrier functions were included in the API. In this paper a new approach to Penalty and Barrier functions, based on Fuzzy Logic, is proposed. Two penalty functions, that impose a progressive penalization to solutions that violate the constraints, are discussed. The implemented functions impose a low penalization when the violation of the constraints is low and a heavy penalty when the violation is high. Numerical results, obtained using twenty-eight test problems, comparing the proposed Fuzzy Logic based functions to six of the classic Penalty and Barrier functions are presented. Considering the achieved results, it can be concluded that the proposed penalty functions besides being very robust also have a very good performance. |
publishDate |
2015 |
dc.date.none.fl_str_mv |
2015 2015-01-01T00:00:00Z 2016-11-01T01:30:09Z |
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/10400.22/7589 |
url |
http://hdl.handle.net/10400.22/7589 |
dc.language.iso.fl_str_mv |
eng |
language |
eng |
dc.relation.none.fl_str_mv |
10.1016/j.eswa.2015.04.070 |
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 |
Elsevier |
publisher.none.fl_str_mv |
Elsevier |
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) |
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Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) |
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Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) - Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informação |
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1799131376422748160 |