Quasi-physical global optimization method for solving the equal circle packing problem

The equal circle packing problem is a well-known challenge in geometry. It is also a natural, clear and fair test system for global optimization. This paper presents a quasi-physical global optimization algorithm for solving the equal circle packing problem. The algorithm simulates two kinds of movements of N elastic disks: smooth movement driven by elastic pressures and violent movement driven by strong repulsive forces and attractive forces. The smooth movement makes the disks reach a locally optimal configuration, while the violent movement makes them jump out of the local optimum trap and reach a more promising place. The algorithm is tested on the widely studied instances of N = 1, 2, ..., 150. We find better packings than the reported best-known ones on 37 instances and reproduce the best-known results on the remaining 113 instances.