On the Impact of Symmetry-Breaking Constraints on Spatial Branch-and-Bound for Circle Packing in a Square

, , and

BibTeX reference

We study the problem of packing equal circles in a square from the mathematical programming point of view. We discuss different formulations, we analyse 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.

, 19 pages

Research Axis

Research applications


On the impact of symmetry-breaking constraints on spatial branch-and-bound for circle packing in a square
, , and
Discrete Applied Mathematics, 161(1-2), 96–106, 2013 BibTeX reference