New results on the Windy Postman Problem

[EN] In this paper, we study the Windy Postman Problem (WPP). This is a well-known Arc Routing Problem that contains the Mixed Chinese Postman Problem (MCPP) as a special case. We extend to arbitrary dimension some new inequalities that complete the description of the polyhedron associated with the...

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Autores: Corberán, Angel, Oswald, Marcus, Plana, Isaac, Reinelt, Gerhard, Sanchís Llopis, José María|||0000-0002-0039-8122
Formato: artículo
Fecha de publicación:2012
País:España
Recursos:Universitat Politècnica de València (UPV)
Repositorio:RiuNet. Repositorio Institucional de la Universitat Politécnica de Valéncia
Idioma:inglés
OAI Identifier:oai:riunet.upv.es:10251/150344
Acesso em linha:https://riunet.upv.es/handle/10251/150344
Access Level:acceso abierto
Palavra-chave:Arc routing
Facets
Mixed Chinese Postman Problem
Polyhedral combinatorics
Windy Postman Problem
Chinese postman problem
Postman problems
Heuristic methods
Algorithms
MATEMATICA APLICADA
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spelling New results on the Windy Postman ProblemCorberán, AngelOswald, MarcusPlana, IsaacReinelt, GerhardSanchís Llopis, José María|||0000-0002-0039-8122Arc routingFacetsMixed Chinese Postman ProblemPolyhedral combinatoricsWindy Postman ProblemChinese postman problemPostman problemsHeuristic methodsAlgorithmsMATEMATICA APLICADA[EN] In this paper, we study the Windy Postman Problem (WPP). This is a well-known Arc Routing Problem that contains the Mixed Chinese Postman Problem (MCPP) as a special case. We extend to arbitrary dimension some new inequalities that complete the description of the polyhedron associated with the Windy Postman Problem over graphs with up to four vertices and ten edges. We introduce two new families of facet-inducing inequalities and prove that these inequalities, along with the already known odd zigzag inequalities, are Chvátal-Gomory inequalities of rank at most 2. Moreover, a branch-and-cut algorithm that incorporates two new separation algorithms for all the previously mentioned inequalities and a new heuristic procedure to obtain upper bounds are presented. Finally, the performance of a branch-and-cut algorithm over several sets of large WPP and MCPP instances, with up to 3,000 nodes and 9,000 edges (and arcs in the MCPP case), shows that, to our knowledge, this is the best algorithm to date for the exact resolution of the WPP and the MCPP. © 2010 Springer and Mathematical Optimization Society.The authors want to thank the three referees for their careful reading of the manuscript and for their many comments and suggestions that have contributed to improve the paper content and readability. In particular, several remarks regarding the discussion of C-G and mod-k inequalities were pointed out by one of the referees. A. Corberan, I. Plana and J.M. Sanchis wish to thank the Ministerio de Educacion y Ciencia of Spain (projects MTM2006-14961-C05-02 and MTM2009-14039-C06-02) for its support.Springer-VerlagDepartamento de Matemática AplicadaInstituto Universitario de Matemática Pura y AplicadaEscuela Técnica Superior de Ingeniería IndustrialMinisterio de Educación y CienciaMinisterio de Ciencia e InnovaciónRepositorio Institucional de la Universitat Politècnica de València Riunet20122012-04-01journal articlehttp://purl.org/coar/resource_type/c_6501VoRhttp://purl.org/coar/version/c_970fb48d4fbd8a85info:eu-repo/semantics/articleapplication/pdfapplication/pdfhttps://riunet.upv.es/handle/10251/150344reponame:RiuNet. Repositorio Institucional de la Universitat Politécnica de Valénciainstname:Universitat Politècnica de València (UPV)InglésengMinisterio de Ciencia e Innovación http://dx.doi.org/10.13039/501100004837 MTM2009-14039-C06-02 Modelos Y Metodos De Programacion Matematica Y Sus Aplicaciones (Optimos2)Ministerio de Educación y Ciencia https://doi.org/10.13039/501100008743 MTM2006-14961-C05-02 OPTIMOS: OPTIMIZACION PARA LA MOVILIDAD SOSTENIBLEopen accesshttp://purl.org/coar/access_right/c_abf2Reserva de todos los derechoshttp://rightsstatements.org/vocab/InC/1.0/info:eu-repo/semantics/openAccessoai:riunet.upv.es:10251/1503442026-06-13T07:49:27Z
dc.title.none.fl_str_mv New results on the Windy Postman Problem
title New results on the Windy Postman Problem
spellingShingle New results on the Windy Postman Problem
Corberán, Angel
Arc routing
Facets
Mixed Chinese Postman Problem
Polyhedral combinatorics
Windy Postman Problem
Chinese postman problem
Postman problems
Heuristic methods
Algorithms
MATEMATICA APLICADA
title_short New results on the Windy Postman Problem
title_full New results on the Windy Postman Problem
title_fullStr New results on the Windy Postman Problem
title_full_unstemmed New results on the Windy Postman Problem
title_sort New results on the Windy Postman Problem
dc.creator.none.fl_str_mv Corberán, Angel
Oswald, Marcus
Plana, Isaac
Reinelt, Gerhard
Sanchís Llopis, José María|||0000-0002-0039-8122
author Corberán, Angel
author_facet Corberán, Angel
Oswald, Marcus
Plana, Isaac
Reinelt, Gerhard
Sanchís Llopis, José María|||0000-0002-0039-8122
author_role author
author2 Oswald, Marcus
Plana, Isaac
Reinelt, Gerhard
Sanchís Llopis, José María|||0000-0002-0039-8122
author2_role author
author
author
author
dc.contributor.none.fl_str_mv Departamento de Matemática Aplicada
Instituto Universitario de Matemática Pura y Aplicada
Escuela Técnica Superior de Ingeniería Industrial
Ministerio de Educación y Ciencia
Ministerio de Ciencia e Innovación
Repositorio Institucional de la Universitat Politècnica de València Riunet
dc.subject.none.fl_str_mv Arc routing
Facets
Mixed Chinese Postman Problem
Polyhedral combinatorics
Windy Postman Problem
Chinese postman problem
Postman problems
Heuristic methods
Algorithms
MATEMATICA APLICADA
topic Arc routing
Facets
Mixed Chinese Postman Problem
Polyhedral combinatorics
Windy Postman Problem
Chinese postman problem
Postman problems
Heuristic methods
Algorithms
MATEMATICA APLICADA
description [EN] In this paper, we study the Windy Postman Problem (WPP). This is a well-known Arc Routing Problem that contains the Mixed Chinese Postman Problem (MCPP) as a special case. We extend to arbitrary dimension some new inequalities that complete the description of the polyhedron associated with the Windy Postman Problem over graphs with up to four vertices and ten edges. We introduce two new families of facet-inducing inequalities and prove that these inequalities, along with the already known odd zigzag inequalities, are Chvátal-Gomory inequalities of rank at most 2. Moreover, a branch-and-cut algorithm that incorporates two new separation algorithms for all the previously mentioned inequalities and a new heuristic procedure to obtain upper bounds are presented. Finally, the performance of a branch-and-cut algorithm over several sets of large WPP and MCPP instances, with up to 3,000 nodes and 9,000 edges (and arcs in the MCPP case), shows that, to our knowledge, this is the best algorithm to date for the exact resolution of the WPP and the MCPP. © 2010 Springer and Mathematical Optimization Society.
publishDate 2012
dc.date.none.fl_str_mv 2012
2012-04-01
dc.type.none.fl_str_mv journal article
http://purl.org/coar/resource_type/c_6501
VoR
http://purl.org/coar/version/c_970fb48d4fbd8a85
dc.type.openaire.fl_str_mv info:eu-repo/semantics/article
format article
dc.identifier.none.fl_str_mv https://riunet.upv.es/handle/10251/150344
url https://riunet.upv.es/handle/10251/150344
dc.language.none.fl_str_mv Inglés
eng
language_invalid_str_mv Inglés
language eng
dc.relation.none.fl_str_mv Ministerio de Ciencia e Innovación http://dx.doi.org/10.13039/501100004837 MTM2009-14039-C06-02 Modelos Y Metodos De Programacion Matematica Y Sus Aplicaciones (Optimos2)
Ministerio de Educación y Ciencia https://doi.org/10.13039/501100008743 MTM2006-14961-C05-02 OPTIMOS: OPTIMIZACION PARA LA MOVILIDAD SOSTENIBLE
dc.rights.none.fl_str_mv open access
http://purl.org/coar/access_right/c_abf2
Reserva de todos los derechos
http://rightsstatements.org/vocab/InC/1.0/
dc.rights.openaire.fl_str_mv info:eu-repo/semantics/openAccess
rights_invalid_str_mv open access
http://purl.org/coar/access_right/c_abf2
Reserva de todos los derechos
http://rightsstatements.org/vocab/InC/1.0/
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv application/pdf
application/pdf
dc.publisher.none.fl_str_mv Springer-Verlag
publisher.none.fl_str_mv Springer-Verlag
dc.source.none.fl_str_mv reponame:RiuNet. Repositorio Institucional de la Universitat Politécnica de Valéncia
instname:Universitat Politècnica de València (UPV)
instname_str Universitat Politècnica de València (UPV)
reponame_str RiuNet. Repositorio Institucional de la Universitat Politécnica de Valéncia
collection RiuNet. Repositorio Institucional de la Universitat Politécnica de Valéncia
repository.name.fl_str_mv
repository.mail.fl_str_mv
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score 15,300719

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