Particle swarm optimization: A numerical stability analysis and parameter adjustment based on swarm activity

In this paper, swarm activity is defined as the root mean square velocity of the particles in particle swarm optimization (PSO). Using numerical experiments, an investigation of the relationship between swarm activity and intensification/diversification during a PSO search, as well as the similarity between swarm activity and temperature in simulated annealing (SA), was conducted. Furthermore, a new method for determining the numerical stability of PSO based on swarm activity was developed. The stability limit for PSO based on the new numerical stability analysis method was compared with the stability limit based on a conventional analytical stability analysis method. Also, using the results of a numerical stability analysis of PSO, the search of conventional PSO methods was examined. From this analysis, issues related to diversification (global search) and intensification (local search) during the search could be explored. Finally, after showing that swarm activity can be controlled using the stable and unstable regions in PSO, a new PSO method that uses swarm activity feedback to control diversification and intensification during a search was proposed. The versatility and search capabilities of the new PSO were examined based on the results of numerical experiments using five typical benchmark problems.