Valid inequalities for a single constrained 0-1 MIP set intersected with a conflict graph
Autor(a) principal: | |
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Data de Publicação: | 2016 |
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/10773/16477 |
Resumo: | In this paper a mixed integer set resulting from the intersection of a single constrained mixed 0–1 set with the vertex packing set is investigated. This set arises as a subproblem of more general mixed integer problems such as inventory routing and facility location problems. Families of strong valid inequalities that take into account the structure of the simple mixed integer set and that of the vertex packing set simultaneously are introduced. In particular, the well-known mixed integer rounding inequality is generalized to the case where incompatibilities between binary variables are present. Exact and heuristic algorithms are designed to solve the separation problems associated to the proposed valid inequalities. Preliminary computational experiments show that these inequalities can be useful to reduce the integrality gaps and to solve integer programming problems. |
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Valid inequalities for a single constrained 0-1 MIP set intersected with a conflict graphMixed integer programmingValid inequalitySeparationVertex packing setConflict graphIndependent setIn this paper a mixed integer set resulting from the intersection of a single constrained mixed 0–1 set with the vertex packing set is investigated. This set arises as a subproblem of more general mixed integer problems such as inventory routing and facility location problems. Families of strong valid inequalities that take into account the structure of the simple mixed integer set and that of the vertex packing set simultaneously are introduced. In particular, the well-known mixed integer rounding inequality is generalized to the case where incompatibilities between binary variables are present. Exact and heuristic algorithms are designed to solve the separation problems associated to the proposed valid inequalities. Preliminary computational experiments show that these inequalities can be useful to reduce the integrality gaps and to solve integer programming problems.Elsevier2018-07-20T14:00:57Z2016-08-01T00:00:00Z2016-082017-08-01T11:00:00Zinfo:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/articleapplication/pdfhttp://hdl.handle.net/10773/16477eng1572-528610.1016/j.disopt.2016.05.005Agra, AgostinhoDoostmohammadi, MahdiSouza, Cid C. deinfo: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:RCAAP2024-02-22T11:30:47Zoai:ria.ua.pt:10773/16477Portal AgregadorONGhttps://www.rcaap.pt/oai/openaireopendoar:71602024-03-20T02:51:37.539532Repositório 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 |
Valid inequalities for a single constrained 0-1 MIP set intersected with a conflict graph |
title |
Valid inequalities for a single constrained 0-1 MIP set intersected with a conflict graph |
spellingShingle |
Valid inequalities for a single constrained 0-1 MIP set intersected with a conflict graph Agra, Agostinho Mixed integer programming Valid inequality Separation Vertex packing set Conflict graph Independent set |
title_short |
Valid inequalities for a single constrained 0-1 MIP set intersected with a conflict graph |
title_full |
Valid inequalities for a single constrained 0-1 MIP set intersected with a conflict graph |
title_fullStr |
Valid inequalities for a single constrained 0-1 MIP set intersected with a conflict graph |
title_full_unstemmed |
Valid inequalities for a single constrained 0-1 MIP set intersected with a conflict graph |
title_sort |
Valid inequalities for a single constrained 0-1 MIP set intersected with a conflict graph |
author |
Agra, Agostinho |
author_facet |
Agra, Agostinho Doostmohammadi, Mahdi Souza, Cid C. de |
author_role |
author |
author2 |
Doostmohammadi, Mahdi Souza, Cid C. de |
author2_role |
author author |
dc.contributor.author.fl_str_mv |
Agra, Agostinho Doostmohammadi, Mahdi Souza, Cid C. de |
dc.subject.por.fl_str_mv |
Mixed integer programming Valid inequality Separation Vertex packing set Conflict graph Independent set |
topic |
Mixed integer programming Valid inequality Separation Vertex packing set Conflict graph Independent set |
description |
In this paper a mixed integer set resulting from the intersection of a single constrained mixed 0–1 set with the vertex packing set is investigated. This set arises as a subproblem of more general mixed integer problems such as inventory routing and facility location problems. Families of strong valid inequalities that take into account the structure of the simple mixed integer set and that of the vertex packing set simultaneously are introduced. In particular, the well-known mixed integer rounding inequality is generalized to the case where incompatibilities between binary variables are present. Exact and heuristic algorithms are designed to solve the separation problems associated to the proposed valid inequalities. Preliminary computational experiments show that these inequalities can be useful to reduce the integrality gaps and to solve integer programming problems. |
publishDate |
2016 |
dc.date.none.fl_str_mv |
2016-08-01T00:00:00Z 2016-08 2017-08-01T11:00:00Z 2018-07-20T14:00:57Z |
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/10773/16477 |
url |
http://hdl.handle.net/10773/16477 |
dc.language.iso.fl_str_mv |
eng |
language |
eng |
dc.relation.none.fl_str_mv |
1572-5286 10.1016/j.disopt.2016.05.005 |
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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1799137565994909696 |