Mixed integer quadratically-constrained programming model to solve the irregular strip packing problem with continuous rotations
Autor(a) principal: | |
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Data de Publicação: | 2018 |
Outros Autores: | , |
Tipo de documento: | Artigo |
Idioma: | eng |
Título da fonte: | Repositório Institucional da UNESP |
Texto Completo: | http://dx.doi.org/10.1007/s10898-018-0638-x http://hdl.handle.net/11449/160523 |
Resumo: | The irregular strip packing problem consists of cutting a set of convex and non-convex two-dimensional polygonal pieces from a board with a fixed height and infinite length. Owing to the importance of this problem, a large number of mathematical models and solution methods have been proposed. However, only few papers consider that the pieces can be rotated at any angle in order to reduce the board length used. Furthermore, the solution methods proposed in the literature are mostly heuristic. This paper proposes a novel mixed integer quadratically-constrained programming model for the irregular strip packing problem considering continuous rotations for the pieces. In the model, the pieces are allocated on the board using a reference point and its allocation is given by the translation and rotation of the pieces. To reduce the number of symmetric solutions for the model, sets of symmetry-breaking constraints are proposed. Computational experiments were performed on the model with and without symmetry-breaking constraints, showing that symmetry elimination improves the quality of solutions found by the solution methods. Tests were performed with instances from the literature. For two instances, it was possible to compare the solutions with a previous model from the literature and show that the proposed model is able to obtain numerically accurate solutions in competitive computational times. |
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Mixed integer quadratically-constrained programming model to solve the irregular strip packing problem with continuous rotationsMixed integer non-linear programmingNesting problemsIrregular piecesContinuous rotationsThe irregular strip packing problem consists of cutting a set of convex and non-convex two-dimensional polygonal pieces from a board with a fixed height and infinite length. Owing to the importance of this problem, a large number of mathematical models and solution methods have been proposed. However, only few papers consider that the pieces can be rotated at any angle in order to reduce the board length used. Furthermore, the solution methods proposed in the literature are mostly heuristic. This paper proposes a novel mixed integer quadratically-constrained programming model for the irregular strip packing problem considering continuous rotations for the pieces. In the model, the pieces are allocated on the board using a reference point and its allocation is given by the translation and rotation of the pieces. To reduce the number of symmetric solutions for the model, sets of symmetry-breaking constraints are proposed. Computational experiments were performed on the model with and without symmetry-breaking constraints, showing that symmetry elimination improves the quality of solutions found by the solution methods. Tests were performed with instances from the literature. For two instances, it was possible to compare the solutions with a previous model from the literature and show that the proposed model is able to obtain numerically accurate solutions in competitive computational times.Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)Univ Sao Paulo, Av Trabalhador Sao Carlense 400, BR-13566590 Sao Carlos, SP, BrazilUniv Estadual Paulista, Av Eng Luiz Edmundo Carrijo Coube 14-01, BR-17033360 Bauru, SP, BrazilODM, Rua Alfredo Lopes 1717,Sala E10, BR-13560460 Sao Carlos, SP, BrazilUniv Estadual Paulista, Av Eng Luiz Edmundo Carrijo Coube 14-01, BR-17033360 Bauru, SP, BrazilFAPESP: 2015/24987-4FAPESP: 2015/03066-8FAPESP: 2013/07375-0CNPq: 477481/2013-2SpringerUniversidade de São Paulo (USP)Universidade Estadual Paulista (Unesp)ODMCherri, Luiz H.Cherri, Adriana C. [UNESP]Soler, Edilaine M. [UNESP]2018-11-26T16:04:51Z2018-11-26T16:04:51Z2018-09-01info:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/article89-107application/pdfhttp://dx.doi.org/10.1007/s10898-018-0638-xJournal Of Global Optimization. Dordrecht: Springer, v. 72, n. 1, p. 89-107, 2018.0925-5001http://hdl.handle.net/11449/16052310.1007/s10898-018-0638-xWOS:000442604900006WOS000442604900006.pdf1965031529508280000-0002-7615-5768Web of Sciencereponame:Repositório Institucional da UNESPinstname:Universidade Estadual Paulista (UNESP)instacron:UNESPengJournal Of Global Optimization1,311info:eu-repo/semantics/openAccess2024-01-19T06:33:35Zoai:repositorio.unesp.br:11449/160523Repositório InstitucionalPUBhttp://repositorio.unesp.br/oai/requestopendoar:29462024-01-19T06:33:35Repositório Institucional da UNESP - Universidade Estadual Paulista (UNESP)false |
dc.title.none.fl_str_mv |
Mixed integer quadratically-constrained programming model to solve the irregular strip packing problem with continuous rotations |
title |
Mixed integer quadratically-constrained programming model to solve the irregular strip packing problem with continuous rotations |
spellingShingle |
Mixed integer quadratically-constrained programming model to solve the irregular strip packing problem with continuous rotations Cherri, Luiz H. Mixed integer non-linear programming Nesting problems Irregular pieces Continuous rotations |
title_short |
Mixed integer quadratically-constrained programming model to solve the irregular strip packing problem with continuous rotations |
title_full |
Mixed integer quadratically-constrained programming model to solve the irregular strip packing problem with continuous rotations |
title_fullStr |
Mixed integer quadratically-constrained programming model to solve the irregular strip packing problem with continuous rotations |
title_full_unstemmed |
Mixed integer quadratically-constrained programming model to solve the irregular strip packing problem with continuous rotations |
title_sort |
Mixed integer quadratically-constrained programming model to solve the irregular strip packing problem with continuous rotations |
author |
Cherri, Luiz H. |
author_facet |
Cherri, Luiz H. Cherri, Adriana C. [UNESP] Soler, Edilaine M. [UNESP] |
author_role |
author |
author2 |
Cherri, Adriana C. [UNESP] Soler, Edilaine M. [UNESP] |
author2_role |
author author |
dc.contributor.none.fl_str_mv |
Universidade de São Paulo (USP) Universidade Estadual Paulista (Unesp) ODM |
dc.contributor.author.fl_str_mv |
Cherri, Luiz H. Cherri, Adriana C. [UNESP] Soler, Edilaine M. [UNESP] |
dc.subject.por.fl_str_mv |
Mixed integer non-linear programming Nesting problems Irregular pieces Continuous rotations |
topic |
Mixed integer non-linear programming Nesting problems Irregular pieces Continuous rotations |
description |
The irregular strip packing problem consists of cutting a set of convex and non-convex two-dimensional polygonal pieces from a board with a fixed height and infinite length. Owing to the importance of this problem, a large number of mathematical models and solution methods have been proposed. However, only few papers consider that the pieces can be rotated at any angle in order to reduce the board length used. Furthermore, the solution methods proposed in the literature are mostly heuristic. This paper proposes a novel mixed integer quadratically-constrained programming model for the irregular strip packing problem considering continuous rotations for the pieces. In the model, the pieces are allocated on the board using a reference point and its allocation is given by the translation and rotation of the pieces. To reduce the number of symmetric solutions for the model, sets of symmetry-breaking constraints are proposed. Computational experiments were performed on the model with and without symmetry-breaking constraints, showing that symmetry elimination improves the quality of solutions found by the solution methods. Tests were performed with instances from the literature. For two instances, it was possible to compare the solutions with a previous model from the literature and show that the proposed model is able to obtain numerically accurate solutions in competitive computational times. |
publishDate |
2018 |
dc.date.none.fl_str_mv |
2018-11-26T16:04:51Z 2018-11-26T16:04:51Z 2018-09-01 |
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://dx.doi.org/10.1007/s10898-018-0638-x Journal Of Global Optimization. Dordrecht: Springer, v. 72, n. 1, p. 89-107, 2018. 0925-5001 http://hdl.handle.net/11449/160523 10.1007/s10898-018-0638-x WOS:000442604900006 WOS000442604900006.pdf 196503152950828 0000-0002-7615-5768 |
url |
http://dx.doi.org/10.1007/s10898-018-0638-x http://hdl.handle.net/11449/160523 |
identifier_str_mv |
Journal Of Global Optimization. Dordrecht: Springer, v. 72, n. 1, p. 89-107, 2018. 0925-5001 10.1007/s10898-018-0638-x WOS:000442604900006 WOS000442604900006.pdf 196503152950828 0000-0002-7615-5768 |
dc.language.iso.fl_str_mv |
eng |
language |
eng |
dc.relation.none.fl_str_mv |
Journal Of Global Optimization 1,311 |
dc.rights.driver.fl_str_mv |
info:eu-repo/semantics/openAccess |
eu_rights_str_mv |
openAccess |
dc.format.none.fl_str_mv |
89-107 application/pdf |
dc.publisher.none.fl_str_mv |
Springer |
publisher.none.fl_str_mv |
Springer |
dc.source.none.fl_str_mv |
Web of Science reponame:Repositório Institucional da UNESP instname:Universidade Estadual Paulista (UNESP) instacron:UNESP |
instname_str |
Universidade Estadual Paulista (UNESP) |
instacron_str |
UNESP |
institution |
UNESP |
reponame_str |
Repositório Institucional da UNESP |
collection |
Repositório Institucional da UNESP |
repository.name.fl_str_mv |
Repositório Institucional da UNESP - Universidade Estadual Paulista (UNESP) |
repository.mail.fl_str_mv |
|
_version_ |
1799965667802218496 |