期刊
DISCRETE APPLIED MATHEMATICS
卷 161, 期 1-2, 页码 96-106出版社
ELSEVIER
DOI: 10.1016/j.dam.2012.07.020
关键词
Symmetry; Reformulation; Narrowing; Circle packing; Nonconvex NLP
资金
- Digiteo 2009-14D [RMNCCO]
- ARM [Digiteo 2009-55D]
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. (c) 2012 Elsevier B.V. All rights reserved.
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