Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
421180 | Discrete Applied Mathematics | 2013 | 11 Pages |
Abstract
We study the problem of packing equal circles in a square from the mathematical programming point of view. We discuss different formulations, we analyze formulation symmetries, we propose some symmetry breaking constraints and show that not only do they tighten the convex relaxation bound, but they also ease the task of local NLP solution algorithms in finding feasible solutions. We solve the problem by means of a standard spatial Branch-and-Bound implementation, and show that our formulation improvements allow the algorithm to find very good solutions at the root node.
Related Topics
Physical Sciences and Engineering
Computer Science
Computational Theory and Mathematics
Authors
Alberto Costa, Pierre Hansen, Leo Liberti,