Optimality-based bound contraction with multiparametric disaggregation for the global optimization of mixed-integer bilinear problems

Detalhes bibliográficos
Autor(a) principal: Castro, Pedro
Data de Publicação: 2014
Outros Autores: Grossmann, Ignacio E.
Tipo de documento: Artigo
Idioma: eng
Título da fonte: Repositórios Científicos de Acesso Aberto de Portugal (RCAAP)
Texto Completo: http://hdl.handle.net/10400.9/2649
Resumo: We address nonconvex mixed-integer bilinear problems where the main challenge is the computation of a tight upper bound for the objective function to be maximized. This can be obtained by using the recently developed concept of multiparametric disaggregation following the solution of a mixed-integer linear relaxation of the bilinear problem. Besides showing that it can provide tighter bounds than a commercial global optimization solver within a given computational time, we propose to also take advantage of the relaxed formulation for contracting the variables domain and further reduce the optimality gap. Through the solution of a real-life case study from a hydroelectric power system, we show that this can be an efficient approach depending on the problem size. The relaxed formulation from multiparametric formulation is provided for a generic numeric representation system featuring a base between 2 (binary) and 10 (decimal).
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spelling Optimality-based bound contraction with multiparametric disaggregation for the global optimization of mixed-integer bilinear problemsGlobal optimizationMixed-integer nonlinear programmingMixed-integer linear programmingSchedulingHydroelectric systemWe address nonconvex mixed-integer bilinear problems where the main challenge is the computation of a tight upper bound for the objective function to be maximized. This can be obtained by using the recently developed concept of multiparametric disaggregation following the solution of a mixed-integer linear relaxation of the bilinear problem. Besides showing that it can provide tighter bounds than a commercial global optimization solver within a given computational time, we propose to also take advantage of the relaxed formulation for contracting the variables domain and further reduce the optimality gap. Through the solution of a real-life case study from a hydroelectric power system, we show that this can be an efficient approach depending on the problem size. The relaxed formulation from multiparametric formulation is provided for a generic numeric representation system featuring a base between 2 (binary) and 10 (decimal).SpringerRepositório do LNEGCastro, PedroGrossmann, Ignacio E.2015-03-17T16:54:13Z20142014-01-01T00:00:00Zinfo:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/articleapplication/pdfhttp://hdl.handle.net/10400.9/2649eng0925-5001info:eu-repo/semantics/openAccessreponame:Repositórios Científicos de Acesso Aberto de Portugal (RCAAP)instname:FCCN, serviços digitais da FCT – Fundação para a Ciência e a Tecnologiainstacron:RCAAP2025-03-10T11:32:23Zoai:null:10400.9/2649Portal AgregadorONGhttps://www.rcaap.pt/oai/openaireinfo@rcaap.ptopendoar:https://opendoar.ac.uk/repository/71602025-05-29T01:14:25.472846Repositórios Científicos de Acesso Aberto de Portugal (RCAAP) - FCCN, serviços digitais da FCT – Fundação para a Ciência e a Tecnologiafalse
dc.title.none.fl_str_mv Optimality-based bound contraction with multiparametric disaggregation for the global optimization of mixed-integer bilinear problems
title Optimality-based bound contraction with multiparametric disaggregation for the global optimization of mixed-integer bilinear problems
spellingShingle Optimality-based bound contraction with multiparametric disaggregation for the global optimization of mixed-integer bilinear problems
Castro, Pedro
Global optimization
Mixed-integer nonlinear programming
Mixed-integer linear programming
Scheduling
Hydroelectric system
title_short Optimality-based bound contraction with multiparametric disaggregation for the global optimization of mixed-integer bilinear problems
title_full Optimality-based bound contraction with multiparametric disaggregation for the global optimization of mixed-integer bilinear problems
title_fullStr Optimality-based bound contraction with multiparametric disaggregation for the global optimization of mixed-integer bilinear problems
title_full_unstemmed Optimality-based bound contraction with multiparametric disaggregation for the global optimization of mixed-integer bilinear problems
title_sort Optimality-based bound contraction with multiparametric disaggregation for the global optimization of mixed-integer bilinear problems
author Castro, Pedro
author_facet Castro, Pedro
Grossmann, Ignacio E.
author_role author
author2 Grossmann, Ignacio E.
author2_role author
dc.contributor.none.fl_str_mv Repositório do LNEG
dc.contributor.author.fl_str_mv Castro, Pedro
Grossmann, Ignacio E.
dc.subject.por.fl_str_mv Global optimization
Mixed-integer nonlinear programming
Mixed-integer linear programming
Scheduling
Hydroelectric system
topic Global optimization
Mixed-integer nonlinear programming
Mixed-integer linear programming
Scheduling
Hydroelectric system
description We address nonconvex mixed-integer bilinear problems where the main challenge is the computation of a tight upper bound for the objective function to be maximized. This can be obtained by using the recently developed concept of multiparametric disaggregation following the solution of a mixed-integer linear relaxation of the bilinear problem. Besides showing that it can provide tighter bounds than a commercial global optimization solver within a given computational time, we propose to also take advantage of the relaxed formulation for contracting the variables domain and further reduce the optimality gap. Through the solution of a real-life case study from a hydroelectric power system, we show that this can be an efficient approach depending on the problem size. The relaxed formulation from multiparametric formulation is provided for a generic numeric representation system featuring a base between 2 (binary) and 10 (decimal).
publishDate 2014
dc.date.none.fl_str_mv 2014
2014-01-01T00:00:00Z
2015-03-17T16:54:13Z
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/10400.9/2649
url http://hdl.handle.net/10400.9/2649
dc.language.iso.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv 0925-5001
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:Repositórios Científicos de Acesso Aberto de Portugal (RCAAP)
instname:FCCN, serviços digitais da FCT – Fundação para a Ciência e a Tecnologia
instacron:RCAAP
instname_str FCCN, serviços digitais da FCT – Fundação para a Ciência e a Tecnologia
instacron_str RCAAP
institution RCAAP
reponame_str Repositórios Científicos de Acesso Aberto de Portugal (RCAAP)
collection Repositórios Científicos de Acesso Aberto de Portugal (RCAAP)
repository.name.fl_str_mv Repositórios Científicos de Acesso Aberto de Portugal (RCAAP) - FCCN, serviços digitais da FCT – Fundação para a Ciência e a Tecnologia
repository.mail.fl_str_mv info@rcaap.pt
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