A New Multi-Swarm Particle Swarm Optimization and Its Application to Lennard-Jones Problem

Abstract

Particle swarm optimization (PSO) algorithm is a modern heuristic technique for global optimization. Due to its ease of implementation, excellent effectiveness, and few parameters to adjust it has gained a lot of attention in the recent years. However, with the increasing size and computational complexity of real life optimization problems it takes long solution times and the solution quality also degrades, so there is a constant need to improve its effectiveness and robustness to find better solution in the shortest possible computational time. Parallel computing is a possible way to fulfill this requirement. In this paper we propose a multi-swarm approach to parallelize PSO algorithm (MSPSO). The performance of the proposed algorithm is evaluated using several well-known numerical test problems taken from literature. Then, it is applied to the challenging problem of finding the minimum energy configuration of a cluster of identical atoms interacting through the Lennard-Jones potential. Finding the global minimum of this function is very difficult because of the presence of a large number of local minima, which grows exponentially with molecule size. Computational results for clusters containing 8 and 9 atoms are obtained. The parallel algorithm shows significant speed-up without compromising the accuracy, when compared to the sequential PSO.