PERM for solving circle packing problem

In this paper, we develop a new algorithm that incorporates the improved PERM into an already existing simple deterministic heuristic, the principle of maximum cave degree for corner-occupying actions, to solve the problem of packing equal or unequal circles into a larger circle container. We compare the performance of our algorithm on several problem instances taken from the literature with previous algorithms. The computational results show that the proposed approach produces high-quality solutions within reasonable computational times. Although our algorithm is less efficient than Zhangʹs for several large-scale equal-size instances, it is noteworthy that for several unequal circle instances we found new lower bounds missed in previous papers.