Adaptive Penalty and Barrier function based on Fuzzy Logic

Detalhes bibliográficos
Autor(a) principal: Matias, João
Data de Publicação: 2015
Outros Autores: Correia, Aldina, Mestre, Pedro, Serodio, Carlos, Couto, Pedro, Teixeira, Christophe, Melo-Pinto, Pedro
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.
id RCAP_a6d546c0174c83d65395775353698fa9
oai_identifier_str oai:recipp.ipp.pt:10400.22/7589
network_acronym_str RCAP
network_name_str Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)
repository_id_str 7160
spelling 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
instname_str Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informação
instacron_str RCAAP
institution RCAAP
reponame_str Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)
collection Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)
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
repository.mail.fl_str_mv
_version_ 1799131376422748160