Solving packing identical spheres into a smallest sphere with a particle swarm optimization

摘要

In this paper, the identical sphere packing is tackled by applying a particle swarm optimization-based method. An instance of the problem is characterized by a set of equal spheres and a large sphere with unlimited radius. The aim of the problem is to determine a minimum radius of the spherical container that contains all spheres without overlapping. The particle swarm optimization cooperates with an efficient continuous local optimization that serves either to repair the non-feasibility of solutions or improve their quality. The behavior of the proposed method is evaluated on a set of standard benchmark instances taken from the literature and its achieved results are compared to those obtained by the best methods available in the literature. As shown in the experimental part, the proposed approach is very competitive.