A dynamic programming approach for a class of robust optimization problems
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/10773/16478 |
Resumo: | Common approaches to solving a robust optimization problem decompose the problem into a master problem (MP) and adversarial problems (APs). The MP contains the original robust constraints, written, however, only for nite numbers of scenarios. Additional scenarios are generated on the y by solving the APs. We consider in this work the budgeted uncertainty polytope from Bertsimas and Sim, widely used in the literature, and propose new dynamic programming algorithms to solve the APs that are based on the maximum number of deviations allowed and on the size of the deviations. Our algorithms can be applied to robust constraints that occur in various applications such as lot-sizing, the traveling salesman problem with time windows, scheduling problems, and inventory routing problems, among many others. We show how the simple version of the algorithms leads to a fully polynomial time approximation scheme when the deterministic problem is convex. We assess numerically our approach on a lot-sizing problem, showing a comparison with the classical mixed integer linear programming reformulation of the AP. |
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Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) |
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7160 |
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A dynamic programming approach for a class of robust optimization problemsRobust optimizationBudgeted uncertaintyDynamic programmingRow-andcolumn generationFPTASCommon approaches to solving a robust optimization problem decompose the problem into a master problem (MP) and adversarial problems (APs). The MP contains the original robust constraints, written, however, only for nite numbers of scenarios. Additional scenarios are generated on the y by solving the APs. We consider in this work the budgeted uncertainty polytope from Bertsimas and Sim, widely used in the literature, and propose new dynamic programming algorithms to solve the APs that are based on the maximum number of deviations allowed and on the size of the deviations. Our algorithms can be applied to robust constraints that occur in various applications such as lot-sizing, the traveling salesman problem with time windows, scheduling problems, and inventory routing problems, among many others. We show how the simple version of the algorithms leads to a fully polynomial time approximation scheme when the deterministic problem is convex. We assess numerically our approach on a lot-sizing problem, showing a comparison with the classical mixed integer linear programming reformulation of the AP.Society for Industrial and Applied Mathematics2016-12-13T12:17:34Z2016-09-01T00:00:00Z2016-09info:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/articleapplication/pdfhttp://hdl.handle.net/10773/16478eng1052-623410.1137/15M1007070Agra, AgostinhoSantos, Márcio CostaNace, DritanPoss, Michaelinfo: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:10773/16478Portal AgregadorONGhttps://www.rcaap.pt/oai/openaireopendoar:71602024-03-20T02:51:37.493557Repositório 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 |
A dynamic programming approach for a class of robust optimization problems |
title |
A dynamic programming approach for a class of robust optimization problems |
spellingShingle |
A dynamic programming approach for a class of robust optimization problems Agra, Agostinho Robust optimization Budgeted uncertainty Dynamic programming Row-andcolumn generation FPTAS |
title_short |
A dynamic programming approach for a class of robust optimization problems |
title_full |
A dynamic programming approach for a class of robust optimization problems |
title_fullStr |
A dynamic programming approach for a class of robust optimization problems |
title_full_unstemmed |
A dynamic programming approach for a class of robust optimization problems |
title_sort |
A dynamic programming approach for a class of robust optimization problems |
author |
Agra, Agostinho |
author_facet |
Agra, Agostinho Santos, Márcio Costa Nace, Dritan Poss, Michael |
author_role |
author |
author2 |
Santos, Márcio Costa Nace, Dritan Poss, Michael |
author2_role |
author author author |
dc.contributor.author.fl_str_mv |
Agra, Agostinho Santos, Márcio Costa Nace, Dritan Poss, Michael |
dc.subject.por.fl_str_mv |
Robust optimization Budgeted uncertainty Dynamic programming Row-andcolumn generation FPTAS |
topic |
Robust optimization Budgeted uncertainty Dynamic programming Row-andcolumn generation FPTAS |
description |
Common approaches to solving a robust optimization problem decompose the problem into a master problem (MP) and adversarial problems (APs). The MP contains the original robust constraints, written, however, only for nite numbers of scenarios. Additional scenarios are generated on the y by solving the APs. We consider in this work the budgeted uncertainty polytope from Bertsimas and Sim, widely used in the literature, and propose new dynamic programming algorithms to solve the APs that are based on the maximum number of deviations allowed and on the size of the deviations. Our algorithms can be applied to robust constraints that occur in various applications such as lot-sizing, the traveling salesman problem with time windows, scheduling problems, and inventory routing problems, among many others. We show how the simple version of the algorithms leads to a fully polynomial time approximation scheme when the deterministic problem is convex. We assess numerically our approach on a lot-sizing problem, showing a comparison with the classical mixed integer linear programming reformulation of the AP. |
publishDate |
2016 |
dc.date.none.fl_str_mv |
2016-12-13T12:17:34Z 2016-09-01T00:00:00Z 2016-09 |
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/10773/16478 |
url |
http://hdl.handle.net/10773/16478 |
dc.language.iso.fl_str_mv |
eng |
language |
eng |
dc.relation.none.fl_str_mv |
1052-6234 10.1137/15M1007070 |
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 |
Society for Industrial and Applied Mathematics |
publisher.none.fl_str_mv |
Society for Industrial and Applied Mathematics |
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 |
repository.mail.fl_str_mv |
|
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1799137565993861120 |