Greedy vacancy search algorithm for packing equal circles in a square

This paper considers the problem of finding the densest packings of N(N=1,2,…) equal circles in a square. We propose a physically inspired model to formulate this problem and a new heuristic algorithm to solve this problem. The approach is tested on the instances of N=1,2,…,200N=1,2,…,200. Though many researchers have searched these instances using various methods, we can still find 41 better packings than the best-known ones reported in literature.