Mixed integer quadratically-constrained programming model to solve the irregular strip packing problem with continuous rotations

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. Howeve...

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Veröffentlicht in:	Journal of global optimization Jg. 72; H. 1; S. 89 - 107
Hauptverfasser:	Cherri, Luiz H., Cherri, Adriana C., Soler, Edilaine M.
Format:	Journal Article
Sprache:	Englisch
Veröffentlicht:	New York Springer US 01.09.2018 Springer Springer Nature B.V
Schlagworte:	Broken symmetry Computation Computer Science Constraint modelling Heuristic methods Mathematics Mathematics and Statistics Mixed integer Operations Research/Decision Theory Optimization Packing problem Production scheduling Real Functions Strip Symmetry Test procedures Nesting problems Mixed integer non-linear programming Continuous rotations Irregular pieces
ISSN:	0925-5001, 1573-2916
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Abstract	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.
AbstractList	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.
Audience	Academic
Author	Cherri, Luiz H. Soler, Edilaine M. Cherri, Adriana C.
Author_xml	– sequence: 1 givenname: Luiz H. surname: Cherri fullname: Cherri, Luiz H. email: lhcherri@icmc.usp.br organization: University of São Paulo, Optimized Decision Making (ODM) – sequence: 2 givenname: Adriana C. surname: Cherri fullname: Cherri, Adriana C. organization: Universidade Estadual Paulista – sequence: 3 givenname: Edilaine M. surname: Soler fullname: Soler, Edilaine M. organization: Universidade Estadual Paulista
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CitedBy_id	crossref_primary_10_3390_math12172670 crossref_primary_10_1016_j_ejor_2019_04_045 crossref_primary_10_1109_ACCESS_2018_2876546 crossref_primary_10_3389_fmech_2022_966691 crossref_primary_10_1007_s10845_024_02329_y crossref_primary_10_3390_app132212474 crossref_primary_10_1007_s10878_025_01351_x crossref_primary_10_1016_j_cor_2025_107209 crossref_primary_10_1007_s10479_024_06335_4 crossref_primary_10_1016_j_cor_2023_106398 crossref_primary_10_1016_j_ejor_2023_08_009 crossref_primary_10_1038_s41598_024_81749_5 crossref_primary_10_1016_j_cor_2023_106476 crossref_primary_10_1016_j_eswa_2022_118207 crossref_primary_10_1007_s11804_025_00644_1 crossref_primary_10_1016_j_ejor_2025_05_019 crossref_primary_10_3390_math12152414
Cites_doi	10.1016/j.comgeo.2009.12.003 10.1016/j.ejor.2016.03.009 10.1016/S0377-2217(02)00130-3 10.1007/s10898-014-0192-0 10.1016/j.ifacol.2015.06.131 10.1016/j.ijpe.2013.04.009 10.1016/j.ejor.2006.11.038 10.1016/0020-0190(81)90111-3 10.1057/jors.2015.94 10.1177/1687814016652080 10.1016/j.ijpe.2013.04.007 10.1007/s10898-013-0129-z 10.1007/978-1-4613-0215-5_8 10.1111/1475-3995.00434 10.3182/20130522-3-BR-4036.00081 10.1016/j.ejor.2013.06.020 10.1007/s10898-007-9274-6 10.1007/s10732-008-9088-9 10.1115/DETC1993-0337
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Copyright	Springer Science+Business Media, LLC, part of Springer Nature 2018 COPYRIGHT 2018 Springer Journal of Global Optimization is a copyright of Springer, (2018). All Rights Reserved.
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Keywords	Nesting problems Mixed integer non-linear programming Continuous rotations Irregular pieces
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Snippet	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...
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SubjectTerms	Broken symmetry Computation Computer Science Constraint modelling Heuristic methods Mathematics Mathematics and Statistics Mixed integer Operations Research/Decision Theory Optimization Packing problem Production scheduling Real Functions Strip Symmetry Test procedures
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Title	Mixed integer quadratically-constrained programming model to solve the irregular strip packing problem with continuous rotations
URI	https://link.springer.com/article/10.1007/s10898-018-0638-x https://www.proquest.com/docview/2015562156
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