Optimization Modulo Theories

Since ancient times, humanity has sought methods for optimizing their resources and their costs, leading to the study of optimization problems. In this thesis Discrete Optimization Problems are dealt with, which are well-known to have a huge economical impact. In order to tackle these problems, we i...

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Detalhes bibliográficos
Autor: Oliver Vendrell, Roc
Formato: tesis de maestría
Fecha de publicación:2011
País:España
Recursos:Universitat Politècnica de Catalunya (UPC)
Repositorio:UPCommons. Portal del coneixement obert de la UPC
Idioma:inglés
OAI Identifier:oai:upcommons.upc.edu:2099.1/14204
Acesso em linha:https://hdl.handle.net/2099.1/14204
Access Level:acceso abierto
Palavra-chave:Mathematical optimization
OMT (Optimization Modulo Theories)
Optimització matemàtica
Àrees temàtiques de la UPC::Matemàtiques i estadística::Investigació operativa::Optimització
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spelling Optimization Modulo TheoriesOliver Vendrell, RocMathematical optimizationOMT (Optimization Modulo Theories)Optimització matemàticaÀrees temàtiques de la UPC::Matemàtiques i estadística::Investigació operativa::OptimitzacióSince ancient times, humanity has sought methods for optimizing their resources and their costs, leading to the study of optimization problems. In this thesis Discrete Optimization Problems are dealt with, which are well-known to have a huge economical impact. In order to tackle these problems, we introduce the Optimization Modulo Theories (OMT) framework, an extension of Satisfiability Modulo Theories (SMT). OMT allows one to model Discrete Optimization Problems as optimization problems of a cost function subject to a quantifier-free first-order formula whose atoms are constraints of Linear Integer Arithmetic (LIA), i.e., linear inequalities over integer variables. Thus, this language exploits the advantages of propositional logic and LIA. Two methods based on the DPLL(T ) approach for SMT are proposed so as to solve problems expressed in OMT: first, by means of an off-the-shelf integer linear programming tool used as a theory solver; and second, by adding new optimization functionalities to satisfiability LIA-solving algorithms originally developed for SMT. Finally, in order to assess the practical value of these approaches, an experimental evaluation has been carried out, whose results are reported in this document.Universitat Politècnica de CatalunyaOliveras Llunell, AlbertRodríguez-Carbonell, Enric20112011-01-0120122012-02-15master thesishttp://purl.org/coar/resource_type/c_bdccNAhttp://purl.org/coar/version/c_be7fb7dd8ff6fe43info:eu-repo/semantics/masterThesisapplication/ziphttps://hdl.handle.net/2099.1/14204reponame:UPCommons. Portal del coneixement obert de la UPCinstname:Universitat Politècnica de Catalunya (UPC)Inglésengopen accesshttp://purl.org/coar/access_right/c_abf2Attribution-NonCommercial-NoDerivs 3.0 Spainhttp://creativecommons.org/licenses/by-nc-nd/3.0/es/info:eu-repo/semantics/openAccessoai:upcommons.upc.edu:2099.1/142042026-05-27T15:37:01Z
dc.title.none.fl_str_mv Optimization Modulo Theories
title Optimization Modulo Theories
spellingShingle Optimization Modulo Theories
Oliver Vendrell, Roc
Mathematical optimization
OMT (Optimization Modulo Theories)
Optimització matemàtica
Àrees temàtiques de la UPC::Matemàtiques i estadística::Investigació operativa::Optimització
title_short Optimization Modulo Theories
title_full Optimization Modulo Theories
title_fullStr Optimization Modulo Theories
title_full_unstemmed Optimization Modulo Theories
title_sort Optimization Modulo Theories
dc.creator.none.fl_str_mv Oliver Vendrell, Roc
author Oliver Vendrell, Roc
author_facet Oliver Vendrell, Roc
author_role author
dc.contributor.none.fl_str_mv Oliveras Llunell, Albert
Rodríguez-Carbonell, Enric
dc.subject.none.fl_str_mv Mathematical optimization
OMT (Optimization Modulo Theories)
Optimització matemàtica
Àrees temàtiques de la UPC::Matemàtiques i estadística::Investigació operativa::Optimització
topic Mathematical optimization
OMT (Optimization Modulo Theories)
Optimització matemàtica
Àrees temàtiques de la UPC::Matemàtiques i estadística::Investigació operativa::Optimització
description Since ancient times, humanity has sought methods for optimizing their resources and their costs, leading to the study of optimization problems. In this thesis Discrete Optimization Problems are dealt with, which are well-known to have a huge economical impact. In order to tackle these problems, we introduce the Optimization Modulo Theories (OMT) framework, an extension of Satisfiability Modulo Theories (SMT). OMT allows one to model Discrete Optimization Problems as optimization problems of a cost function subject to a quantifier-free first-order formula whose atoms are constraints of Linear Integer Arithmetic (LIA), i.e., linear inequalities over integer variables. Thus, this language exploits the advantages of propositional logic and LIA. Two methods based on the DPLL(T ) approach for SMT are proposed so as to solve problems expressed in OMT: first, by means of an off-the-shelf integer linear programming tool used as a theory solver; and second, by adding new optimization functionalities to satisfiability LIA-solving algorithms originally developed for SMT. Finally, in order to assess the practical value of these approaches, an experimental evaluation has been carried out, whose results are reported in this document.
publishDate 2011
dc.date.none.fl_str_mv 2011
2011-01-01
2012
2012-02-15
dc.type.none.fl_str_mv master thesis
http://purl.org/coar/resource_type/c_bdcc
NA
http://purl.org/coar/version/c_be7fb7dd8ff6fe43
dc.type.openaire.fl_str_mv info:eu-repo/semantics/masterThesis
format masterThesis
dc.identifier.none.fl_str_mv https://hdl.handle.net/2099.1/14204
url https://hdl.handle.net/2099.1/14204
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
Attribution-NonCommercial-NoDerivs 3.0 Spain
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
Attribution-NonCommercial-NoDerivs 3.0 Spain
http://creativecommons.org/licenses/by-nc-nd/3.0/es/
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv application/zip
dc.publisher.none.fl_str_mv Universitat Politècnica de Catalunya
publisher.none.fl_str_mv Universitat Politècnica de Catalunya
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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score 15.198674

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