Tightening piecewise McCormick relaxations for bilinear problems

Detalhes bibliográficos
Autor(a) principal: Castro, Pedro
Data de Publicação: 2015
Tipo de documento: Artigo
Idioma: eng
Título da fonte: Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)
Texto Completo: http://hdl.handle.net/10400.9/2947
Resumo: We address nonconvex bilinear problems where the main objective is the computation of a tight lowerbound for the objective function to be minimized. This can be obtained through a mixed-integer linearprogramming formulation relying on the concept of piecewise McCormick relaxation. It works by dividingthe domain of one of the variables in each bilinear term into a given number of partitions, while consid-ering global bounds for the other. We now propose using partition-dependent bounds for the latter so asto further improve the quality of the relaxation. While it involves solving hundreds or even thousands oflinear bound contracting problems in a pre-processing step, the benefit from having a tighter formula-tion more than compensates the additional computational time. Results for a set of water network designproblems show that the new algorithm can lead to orders of magnitude reduction in the optimality gapcompared to commercial solvers.
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spelling Tightening piecewise McCormick relaxations for bilinear problemsWater minimizationNonlinear programmingMathematical modellingOptimizationWe address nonconvex bilinear problems where the main objective is the computation of a tight lowerbound for the objective function to be minimized. This can be obtained through a mixed-integer linearprogramming formulation relying on the concept of piecewise McCormick relaxation. It works by dividingthe domain of one of the variables in each bilinear term into a given number of partitions, while consid-ering global bounds for the other. We now propose using partition-dependent bounds for the latter so asto further improve the quality of the relaxation. While it involves solving hundreds or even thousands oflinear bound contracting problems in a pre-processing step, the benefit from having a tighter formula-tion more than compensates the additional computational time. Results for a set of water network designproblems show that the new algorithm can lead to orders of magnitude reduction in the optimality gapcompared to commercial solvers.ElsevierRepositório do LNEGCastro, Pedro2016-04-26T13:55:32Z2015-01-01T00:00:00Z2015-01-01T00:00:00Zinfo:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/articleapplication/pdfhttp://hdl.handle.net/10400.9/2947engCastro, P.M. - Tightening piecewise McCormick relaxations for bilinear problems. In: Computers and Chemical Engineering, 2015, Vol. 72, p. 300-3110098-135410.1016/j.compchemeng.2014.03.025info: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:RCAAP2022-09-06T12:28:14Zoai:repositorio.lneg.pt:10400.9/2947Portal AgregadorONGhttps://www.rcaap.pt/oai/openaireopendoar:71602024-03-19T15:36:06.769362Repositório 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 Tightening piecewise McCormick relaxations for bilinear problems
title Tightening piecewise McCormick relaxations for bilinear problems
spellingShingle Tightening piecewise McCormick relaxations for bilinear problems
Castro, Pedro
Water minimization
Nonlinear programming
Mathematical modelling
Optimization
title_short Tightening piecewise McCormick relaxations for bilinear problems
title_full Tightening piecewise McCormick relaxations for bilinear problems
title_fullStr Tightening piecewise McCormick relaxations for bilinear problems
title_full_unstemmed Tightening piecewise McCormick relaxations for bilinear problems
title_sort Tightening piecewise McCormick relaxations for bilinear problems
author Castro, Pedro
author_facet Castro, Pedro
author_role author
dc.contributor.none.fl_str_mv Repositório do LNEG
dc.contributor.author.fl_str_mv Castro, Pedro
dc.subject.por.fl_str_mv Water minimization
Nonlinear programming
Mathematical modelling
Optimization
topic Water minimization
Nonlinear programming
Mathematical modelling
Optimization
description We address nonconvex bilinear problems where the main objective is the computation of a tight lowerbound for the objective function to be minimized. This can be obtained through a mixed-integer linearprogramming formulation relying on the concept of piecewise McCormick relaxation. It works by dividingthe domain of one of the variables in each bilinear term into a given number of partitions, while consid-ering global bounds for the other. We now propose using partition-dependent bounds for the latter so asto further improve the quality of the relaxation. While it involves solving hundreds or even thousands oflinear bound contracting problems in a pre-processing step, the benefit from having a tighter formula-tion more than compensates the additional computational time. Results for a set of water network designproblems show that the new algorithm can lead to orders of magnitude reduction in the optimality gapcompared to commercial solvers.
publishDate 2015
dc.date.none.fl_str_mv 2015-01-01T00:00:00Z
2015-01-01T00:00:00Z
2016-04-26T13:55:32Z
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/10400.9/2947
url http://hdl.handle.net/10400.9/2947
dc.language.iso.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv Castro, P.M. - Tightening piecewise McCormick relaxations for bilinear problems. In: Computers and Chemical Engineering, 2015, Vol. 72, p. 300-311
0098-1354
10.1016/j.compchemeng.2014.03.025
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
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