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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Vydáno v:	Journal of global optimization Ročník 72; číslo 1; s. 89 - 107
Hlavní autoři:	Cherri, Luiz H., Cherri, Adriana C., Soler, Edilaine M.
Médium:	Journal Article
Jazyk:	angličtina
Vydáno:	New York Springer US 01.09.2018 Springer Springer Nature B.V
Témata:	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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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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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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