Global optimization method for finding dense packings of equal circles in a circle

This paper considers the problem of finding the densest packing of N (N = 1, 2, ...) equal circles in a circle. This problem is perhaps the most classical packing problem. It is also a natural and challenging test system for evaluating various global optimization methods. We propose a quasi-physical global optimization method by simulating two kinds of movements of N elastic disks: smooth movement driven by elastic pressures and abrupt movement driven by strong repulsive forces and attractive forces. The algorithm is tested on the instances of N = 1, 2, ... , 200. Using the best-known record of the radius of the container as an upper bound, we find 63 new packings better than the best-known ones reported in literature.