Symmetries in Rectangular Block-Packing
نویسندگان
چکیده
The block-packing problem has applications in chip design, factory layout, container shipment optimization, scheduling and other areas. It has been actively studied in the last 20 years, but symmetry in packings has been neglected. Our work deals with symmetry in several formulations of block-packing, including optimization and constraint-satisfaction variants, as well as slicing and non-slicing packings. We establish the presence of symmetries and show that symmetry-breaking improves the performance of our optimal block-packer BloBB, that is based on branch-and-bound and can solve small instances of the problem. Using this optimal solver we compare the efficiency of symmetry-breaking in different variants of block-packing.
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