A New Heuristic Algorithm for Packing Equal Circles into A Larger Equilateral Triangular Container

This paper studies the problem of packing equal circles into a larger equilateral triangular container, which is concerned with how to pack these circles into the container without overlapping. Its aim is to minimize the edge length of the container as much as possible. By incorporating some heuristic configuration update strategies, a local search strategy based on the gradient method and the dichotomous search (DS) strategy into the simulated annealing (SA) algorithm, a new heuristic algorithm, the heuristic simulated annealing algorithm based on dichotomous search (HSADS), is put forward for solving this problem. In HSADS, the heuristic configuration update strategies are used to produce new configurations, and the gradient method is used to search for lower-energy minima near newly generated configurations, and the dichotomous search strategy is used to gain the minimal edge length of the equilateral triangular container. By testing six equal circles instances from the literature, the proposed algorithm improves the best known results of them so far. The experimental results show that HSADS is an effective algorithm for the problem of packing equal circles into a larger equilateral triangular container.