SYMMETRY BREAKING IN PACKING EQUAL SPHERES IN A UNIT CUBE

Abstract

The structure of symmetric solutions for some optimization problems leads to a notable increase in computation time and memory consumption for most solving algorithms. To address this disadvantage, various symmetry breaking methods have been developed over the past decades. Among them, the addition of symmetry breaking constraints to the problem formulation. In this work, we propose new symmetry breaking constraints for the packing problem of equal spheres in a unit cube. We also show that the integration of these constraints leads to a narrowing of the original formulation. The numerical results highlight a significant performance improvement, both in computing time and memory usage.