Greedy heuristic algorithm for packing equal circles into a circular container

This paper presents a greedy heuristic algorithm for solving the circle packing problem whose objective is to pack a set of unit circles into the smallest circular container. The proposed algorithm can be divided into two stages. In the first stage, a greedy packing procedure is introduced to determine whether the given set of circles can be packed into a fixed container. According to the greedy packing procedure, the circles are packed into the container one by one and each circle is packed into the container by a corner-occupying placement with maximal global benefit. In the second stage, the greedy packing procedure is embedded in a heuristic enumeration strategy to find the smallest container to accommodate all given circles. Tested on two sets of 20 public benchmark instances, the proposed algorithm achieves competitive results compared with existing algorithms in the literature. Furthermore, the effects of important parameter setting and essential components of the proposed algorithm are analyzed.