Parametric global optimisation for bilevel programming
Autor(a) principal: | |
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Data de Publicação: | 2007 |
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/10316/7672 https://doi.org/10.1007/s10898-006-9100-6 |
Resumo: | Abstract We propose a global optimisation approach for the solution of various classes of bilevel programming problems (BLPP) based on recently developed parametric programming algorithms. We first describe how we can recast and solve the inner (follower’s) problem of the bilevel formulation as a multi-parametric programming problem, with parameters being the (unknown) variables of the outer (leader’s) problem. By inserting the obtained rational reaction sets in the upper level problem the overall problem is transformed into a set of independent quadratic, linear or mixed integer linear programming problems, which can be solved to global optimality. In particular, we solve bilevel quadratic and bilevel mixed integer linear problems, with or without right-hand-side uncertainty. A number of examples are presented to illustrate the steps and details of the proposed global optimisation strategy. |
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Parametric global optimisation for bilevel programmingAbstract We propose a global optimisation approach for the solution of various classes of bilevel programming problems (BLPP) based on recently developed parametric programming algorithms. We first describe how we can recast and solve the inner (follower’s) problem of the bilevel formulation as a multi-parametric programming problem, with parameters being the (unknown) variables of the outer (leader’s) problem. By inserting the obtained rational reaction sets in the upper level problem the overall problem is transformed into a set of independent quadratic, linear or mixed integer linear programming problems, which can be solved to global optimality. In particular, we solve bilevel quadratic and bilevel mixed integer linear problems, with or without right-hand-side uncertainty. A number of examples are presented to illustrate the steps and details of the proposed global optimisation strategy.2007info:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/articlehttp://hdl.handle.net/10316/7672http://hdl.handle.net/10316/7672https://doi.org/10.1007/s10898-006-9100-6engJournal of Global Optimization. 38:4 (2007) 609-623Faísca, NunoDua, VivekRustem, BerçSaraiva, PedroPistikopoulos, Efstratiosinfo: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:RCAAP2020-05-25T06:31:18Zoai:estudogeral.uc.pt:10316/7672Portal AgregadorONGhttps://www.rcaap.pt/oai/openaireopendoar:71602024-03-19T20:59:18.473893Repositório 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 |
Parametric global optimisation for bilevel programming |
title |
Parametric global optimisation for bilevel programming |
spellingShingle |
Parametric global optimisation for bilevel programming Faísca, Nuno |
title_short |
Parametric global optimisation for bilevel programming |
title_full |
Parametric global optimisation for bilevel programming |
title_fullStr |
Parametric global optimisation for bilevel programming |
title_full_unstemmed |
Parametric global optimisation for bilevel programming |
title_sort |
Parametric global optimisation for bilevel programming |
author |
Faísca, Nuno |
author_facet |
Faísca, Nuno Dua, Vivek Rustem, Berç Saraiva, Pedro Pistikopoulos, Efstratios |
author_role |
author |
author2 |
Dua, Vivek Rustem, Berç Saraiva, Pedro Pistikopoulos, Efstratios |
author2_role |
author author author author |
dc.contributor.author.fl_str_mv |
Faísca, Nuno Dua, Vivek Rustem, Berç Saraiva, Pedro Pistikopoulos, Efstratios |
description |
Abstract We propose a global optimisation approach for the solution of various classes of bilevel programming problems (BLPP) based on recently developed parametric programming algorithms. We first describe how we can recast and solve the inner (follower’s) problem of the bilevel formulation as a multi-parametric programming problem, with parameters being the (unknown) variables of the outer (leader’s) problem. By inserting the obtained rational reaction sets in the upper level problem the overall problem is transformed into a set of independent quadratic, linear or mixed integer linear programming problems, which can be solved to global optimality. In particular, we solve bilevel quadratic and bilevel mixed integer linear problems, with or without right-hand-side uncertainty. A number of examples are presented to illustrate the steps and details of the proposed global optimisation strategy. |
publishDate |
2007 |
dc.date.none.fl_str_mv |
2007 |
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/10316/7672 http://hdl.handle.net/10316/7672 https://doi.org/10.1007/s10898-006-9100-6 |
url |
http://hdl.handle.net/10316/7672 https://doi.org/10.1007/s10898-006-9100-6 |
dc.language.iso.fl_str_mv |
eng |
language |
eng |
dc.relation.none.fl_str_mv |
Journal of Global Optimization. 38:4 (2007) 609-623 |
dc.rights.driver.fl_str_mv |
info:eu-repo/semantics/openAccess |
eu_rights_str_mv |
openAccess |
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 |
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 |
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