Symmetry-breaking constraints for packing identical rectangles within polyhedra |
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Authors: | R Andrade E G Birgin |
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Institution: | 1. Department of Computer Science, Institute of Mathematics and Statistics, University of S?o Paulo, Rua do Mat?o 1010, Cidade Universitária, S?o Paulo, SP, 05508-090, Brazil
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Abstract: | Two problems related to packing identical rectangles within a polyhedron are tackled in the present work. Rectangles are allowed to differ only by horizontal or vertical translations and possibly 90° rotations. The first considered problem consists in packing as many identical rectangles as possible within a given polyhedron, while the second problem consists in finding the smallest polyhedron of a given type that accommodates a fixed number of identical rectangles. Both problems are modeled as mixed integer programming problems. Symmetry-breaking constraints that facilitate the solution of the MIP models are introduced. Numerical results are presented. |
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