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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Shrnutí: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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ISSN:0925-5001
1573-2916
DOI:10.1007/s10898-018-0638-x