Variable symmetry breaking in numerical constraint problems

Symmetry breaking has been a hot topic of research in the past years, leading to many theoretical developments as well as strong scaling strategies for dealing with hard applications. Most of the research has however focused on discrete, combinatorial, problems, and only few considered also continuo...

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Autores: Goldsztejn, Alexandre, Jermann, Christophe, Ruiz de Angulo García, Vicente|||0000-0002-2067-7399, Torras, Carme|||0000-0002-2933-398X
Tipo de documento: artigo
Data de publicação:2015
País:España
Recursos:Universitat Politècnica de Catalunya (UPC)
Repositório:UPCommons. Portal del coneixement obert de la UPC
Idioma:inglês
OAI Identifier:oai:upcommons.upc.edu:2117/84830
Acesso em linha:https://hdl.handle.net/2117/84830
https://dx.doi.org/10.1016/j.artint.2015.08.006
Access Level:Acceso aberto
Palavra-chave:artificial intelligence
mathematical programming
symmetry
constraint programing
numerical constraint satisfaction problems
constraint satisfaction problems
symmetry breaking
variable symmetry breaking
Classificació INSPEC::Cybernetics::Artificial intelligence
Àrees temàtiques de la UPC::Informàtica::Robòtica
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spelling Variable symmetry breaking in numerical constraint problemsGoldsztejn, AlexandreJermann, ChristopheRuiz de Angulo García, Vicente|||0000-0002-2067-7399Torras, Carme|||0000-0002-2933-398Xartificial intelligencemathematical programmingsymmetryconstraint programingnumerical constraint satisfaction problemsconstraint satisfaction problemssymmetry breakingvariable symmetry breakingClassificació INSPEC::Cybernetics::Artificial intelligenceÀrees temàtiques de la UPC::Informàtica::RobòticaSymmetry breaking has been a hot topic of research in the past years, leading to many theoretical developments as well as strong scaling strategies for dealing with hard applications. Most of the research has however focused on discrete, combinatorial, problems, and only few considered also continuous, numerical, problems. While part of the theory applies in both contexts, numerical problems have specificities that make most of the technical developments inadequate. In this paper, we present the rlex constraints, partial symmetry-breaking inequalities corresponding to a relaxation of the famous lex constraints extensively studied in the discrete case. They allow (partially) breaking any variable symmetry and can be generated in polynomial time. Contrarily to lex constraints that are impractical in general (due to their overwhelming number) and inappropriate in the continuous context (due to their form), rlex constraints can be efficiently handled natively by numerical constraint solvers. Moreover, we demonstrate their pruning power on continuous domains is almost as strong as that of lex constraints, and they subsume several previous work on breaking specific symmetry classes for continuous problems. Their experimental behavior is assessed on a collection of standard numerical problems and the factors influencing their impact are studied. The results confirm rlex constraints are a dependable counterpart to lex constraints for numerical problems.Peer Reviewed20152015-01-0120162016-03-29journal articlehttp://purl.org/coar/resource_type/c_6501AMhttp://purl.org/coar/version/c_ab4af688f83e57aainfo:eu-repo/semantics/articleapplication/pdfhttps://hdl.handle.net/2117/84830https://dx.doi.org/10.1016/j.artint.2015.08.006reponame:UPCommons. Portal del coneixement obert de la UPCinstname:Universitat Politècnica de Catalunya (UPC)Inglésengopen accesshttp://purl.org/coar/access_right/c_abf2http://creativecommons.org/licenses/by-nc-nd/3.0/es/info:eu-repo/semantics/openAccessoai:upcommons.upc.edu:2117/848302026-05-27T15:37:01Z
dc.title.none.fl_str_mv Variable symmetry breaking in numerical constraint problems
title Variable symmetry breaking in numerical constraint problems
spellingShingle Variable symmetry breaking in numerical constraint problems
Goldsztejn, Alexandre
artificial intelligence
mathematical programming
symmetry
constraint programing
numerical constraint satisfaction problems
constraint satisfaction problems
symmetry breaking
variable symmetry breaking
Classificació INSPEC::Cybernetics::Artificial intelligence
Àrees temàtiques de la UPC::Informàtica::Robòtica
title_short Variable symmetry breaking in numerical constraint problems
title_full Variable symmetry breaking in numerical constraint problems
title_fullStr Variable symmetry breaking in numerical constraint problems
title_full_unstemmed Variable symmetry breaking in numerical constraint problems
title_sort Variable symmetry breaking in numerical constraint problems
dc.creator.none.fl_str_mv Goldsztejn, Alexandre
Jermann, Christophe
Ruiz de Angulo García, Vicente|||0000-0002-2067-7399
Torras, Carme|||0000-0002-2933-398X
author Goldsztejn, Alexandre
author_facet Goldsztejn, Alexandre
Jermann, Christophe
Ruiz de Angulo García, Vicente|||0000-0002-2067-7399
Torras, Carme|||0000-0002-2933-398X
author_role author
author2 Jermann, Christophe
Ruiz de Angulo García, Vicente|||0000-0002-2067-7399
Torras, Carme|||0000-0002-2933-398X
author2_role author
author
author
dc.subject.none.fl_str_mv artificial intelligence
mathematical programming
symmetry
constraint programing
numerical constraint satisfaction problems
constraint satisfaction problems
symmetry breaking
variable symmetry breaking
Classificació INSPEC::Cybernetics::Artificial intelligence
Àrees temàtiques de la UPC::Informàtica::Robòtica
topic artificial intelligence
mathematical programming
symmetry
constraint programing
numerical constraint satisfaction problems
constraint satisfaction problems
symmetry breaking
variable symmetry breaking
Classificació INSPEC::Cybernetics::Artificial intelligence
Àrees temàtiques de la UPC::Informàtica::Robòtica
description Symmetry breaking has been a hot topic of research in the past years, leading to many theoretical developments as well as strong scaling strategies for dealing with hard applications. Most of the research has however focused on discrete, combinatorial, problems, and only few considered also continuous, numerical, problems. While part of the theory applies in both contexts, numerical problems have specificities that make most of the technical developments inadequate. In this paper, we present the rlex constraints, partial symmetry-breaking inequalities corresponding to a relaxation of the famous lex constraints extensively studied in the discrete case. They allow (partially) breaking any variable symmetry and can be generated in polynomial time. Contrarily to lex constraints that are impractical in general (due to their overwhelming number) and inappropriate in the continuous context (due to their form), rlex constraints can be efficiently handled natively by numerical constraint solvers. Moreover, we demonstrate their pruning power on continuous domains is almost as strong as that of lex constraints, and they subsume several previous work on breaking specific symmetry classes for continuous problems. Their experimental behavior is assessed on a collection of standard numerical problems and the factors influencing their impact are studied. The results confirm rlex constraints are a dependable counterpart to lex constraints for numerical problems.
publishDate 2015
dc.date.none.fl_str_mv 2015
2015-01-01
2016
2016-03-29
dc.type.none.fl_str_mv journal article
http://purl.org/coar/resource_type/c_6501
AM
http://purl.org/coar/version/c_ab4af688f83e57aa
dc.type.openaire.fl_str_mv info:eu-repo/semantics/article
format article
dc.identifier.none.fl_str_mv https://hdl.handle.net/2117/84830
https://dx.doi.org/10.1016/j.artint.2015.08.006
url https://hdl.handle.net/2117/84830
https://dx.doi.org/10.1016/j.artint.2015.08.006
dc.language.none.fl_str_mv Inglés
eng
language_invalid_str_mv Inglés
language eng
dc.rights.none.fl_str_mv open access
http://purl.org/coar/access_right/c_abf2

http://creativecommons.org/licenses/by-nc-nd/3.0/es/
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

http://creativecommons.org/licenses/by-nc-nd/3.0/es/
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv application/pdf
dc.source.none.fl_str_mv reponame:UPCommons. Portal del coneixement obert de la UPC
instname:Universitat Politècnica de Catalunya (UPC)
instname_str Universitat Politècnica de Catalunya (UPC)
reponame_str UPCommons. Portal del coneixement obert de la UPC
collection UPCommons. Portal del coneixement obert de la UPC
repository.name.fl_str_mv
repository.mail.fl_str_mv
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