Work

Symmetry breaking constraints for packing unequal circles into a minimal outer circle

Year: 2026

Type: article

Abstract: The paper addresses the problem of packing pairwise unequal circles into the circle of minimal radius centered at the origin. This problem with an additional balance condition is considered as well. The corresponding optimization models are highly nonconvex. Symmetry breaking constraints are developed to reduce the number of solutions. It is proved that these additional linear constraints avoid solutions coming from rotations and certain reflections. In addition, problems with subsets of equally sized circles are dealt with as well. Computational experiments based on small benchmark instances demonstrate significant savings in runtime for the global solver BARON if models with symmetry breaking constraints are employed.

Source: Journal of Global Optimization

DOI: 10.1007/s10898-025-01584-4

Authors: Andreas Fischer, Tetyana Romanova, Petro Stetsyuk, Stanislav Tyvodar