An improved test set approach to nonlinear integer problems with applications to engineering design

Many problems in engineering design involve the use of nonlinearities and some integer variables. Methods based on test sets have been proposed to solve some particular problems with integer variables, but they have not been frequently applied because of computation costs. The walk-back procedure ba...

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Detalles Bibliográficos
Autores: Gago Vargas, Manuel Jesús, Hartillo Hermoso, Isabel, Puerto Albandoz, Justo, Ucha Enríquez, José María
Tipo de recurso: artículo
Fecha de publicación:2015
País:España
Institución:Universidad de Sevilla (US)
Repositorio:idUS. Depósito de Investigación de la Universidad de Sevilla
OAI Identifier:oai:idus.us.es:11441/29474
Acceso en línea:http://hdl.handle.net/11441/29474
https://doi.org/10.1007/s10589-015-9739-3
Access Level:acceso abierto
Palabra clave:Non-linear Integer Programming
test set
Gröbner basis
chance constrained programming
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spelling An improved test set approach to nonlinear integer problems with applications to engineering designGago Vargas, Manuel JesúsHartillo Hermoso, IsabelPuerto Albandoz, JustoUcha Enríquez, José MaríaNon-linear Integer Programmingtest setGröbner basischance constrained programmingMany problems in engineering design involve the use of nonlinearities and some integer variables. Methods based on test sets have been proposed to solve some particular problems with integer variables, but they have not been frequently applied because of computation costs. The walk-back procedure based on a test set gives an exact method to obtain an optimal point of an integer programming problem with linear and nonlinear constraints, but the calculation of this test set and the identification of an optimal solution using the test set directions are usually computationally intensive. In problems for which obtaining the test set is reasonably fast, we show how the effectiveness can still be substantially improved. This methodology is presented in its full generality and illustrated on two specific problems: (1) minimizing cost in the problem of scheduling jobs on parallel machines given restrictions on demands and capacity, and (2) minimizing cost in the series parallel redundancy allocation problem, given a target reliability. Our computational results are promising and suggest the applicability of this approach to deal with other problems with similar characteristics or to combine it with mainstream solvers to certify optimalityJunta de Andalucía FQM- 5849Ministerio de Ciencia e Innovación MTM2010-19336Ministerio de Ciencia e Innovación MTM2010-19576Ministerio de Ciencia e Innovación MTM2013-46962- C2-1-PFEDERSpringerÁlgebra2015info:eu-repo/semantics/articleapplication/pdfapplication/pdfhttp://hdl.handle.net/11441/29474https://doi.org/10.1007/s10589-015-9739-3reponame:idUS. Depósito de Investigación de la Universidad de Sevillainstname:Universidad de Sevilla (US)InglésComputational Optimization and Applications, 62 (2), 565-588.http://link.springer.com/article/10.1007/s10589-015-9739-3info:eu-repo/semantics/openAccessoai:idus.us.es:11441/294742026-06-17T12:51:07Z
dc.title.none.fl_str_mv An improved test set approach to nonlinear integer problems with applications to engineering design
title An improved test set approach to nonlinear integer problems with applications to engineering design
spellingShingle An improved test set approach to nonlinear integer problems with applications to engineering design
Gago Vargas, Manuel Jesús
Non-linear Integer Programming
test set
Gröbner basis
chance constrained programming
title_short An improved test set approach to nonlinear integer problems with applications to engineering design
title_full An improved test set approach to nonlinear integer problems with applications to engineering design
title_fullStr An improved test set approach to nonlinear integer problems with applications to engineering design
title_full_unstemmed An improved test set approach to nonlinear integer problems with applications to engineering design
title_sort An improved test set approach to nonlinear integer problems with applications to engineering design
dc.creator.none.fl_str_mv Gago Vargas, Manuel Jesús
Hartillo Hermoso, Isabel
Puerto Albandoz, Justo
Ucha Enríquez, José María
author Gago Vargas, Manuel Jesús
author_facet Gago Vargas, Manuel Jesús
Hartillo Hermoso, Isabel
Puerto Albandoz, Justo
Ucha Enríquez, José María
author_role author
author2 Hartillo Hermoso, Isabel
Puerto Albandoz, Justo
Ucha Enríquez, José María
author2_role author
author
author
dc.contributor.none.fl_str_mv Álgebra
dc.subject.none.fl_str_mv Non-linear Integer Programming
test set
Gröbner basis
chance constrained programming
topic Non-linear Integer Programming
test set
Gröbner basis
chance constrained programming
description Many problems in engineering design involve the use of nonlinearities and some integer variables. Methods based on test sets have been proposed to solve some particular problems with integer variables, but they have not been frequently applied because of computation costs. The walk-back procedure based on a test set gives an exact method to obtain an optimal point of an integer programming problem with linear and nonlinear constraints, but the calculation of this test set and the identification of an optimal solution using the test set directions are usually computationally intensive. In problems for which obtaining the test set is reasonably fast, we show how the effectiveness can still be substantially improved. This methodology is presented in its full generality and illustrated on two specific problems: (1) minimizing cost in the problem of scheduling jobs on parallel machines given restrictions on demands and capacity, and (2) minimizing cost in the series parallel redundancy allocation problem, given a target reliability. Our computational results are promising and suggest the applicability of this approach to deal with other problems with similar characteristics or to combine it with mainstream solvers to certify optimality
publishDate 2015
dc.date.none.fl_str_mv 2015
dc.type.none.fl_str_mv info:eu-repo/semantics/article
format article
dc.identifier.none.fl_str_mv http://hdl.handle.net/11441/29474
https://doi.org/10.1007/s10589-015-9739-3
url http://hdl.handle.net/11441/29474
https://doi.org/10.1007/s10589-015-9739-3
dc.language.none.fl_str_mv Inglés
language_invalid_str_mv Inglés
dc.relation.none.fl_str_mv Computational Optimization and Applications, 62 (2), 565-588.
http://link.springer.com/article/10.1007/s10589-015-9739-3
dc.rights.none.fl_str_mv info:eu-repo/semantics/openAccess
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv application/pdf
application/pdf
dc.publisher.none.fl_str_mv Springer
publisher.none.fl_str_mv Springer
dc.source.none.fl_str_mv reponame:idUS. Depósito de Investigación de la Universidad de Sevilla
instname:Universidad de Sevilla (US)
instname_str Universidad de Sevilla (US)
reponame_str idUS. Depósito de Investigación de la Universidad de Sevilla
collection idUS. Depósito de Investigación de la Universidad de Sevilla
repository.name.fl_str_mv
repository.mail.fl_str_mv
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score 15.300719

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