Particle swarm convergence: An empirical investigation

This paper performs a thorough empirical investigation of the conditions placed on particle swarm optimization control parameters to ensure convergent behavior. At present there exists a large number of theoretically derived parameter regions that will ensure particle convergence, however, selecting which region to utilize in practice is not obvious. The empirical study is carried out over a region slightly larger than that needed to contain all the relevant theoretically derived regions. It was found that there is a very strong correlation between one of the theoretically derived regions and the empirical evidence. It was also found that parameters near the edge of the theoretically derived region converge at a very slow rate, after an initial population explosion. Particle convergence is so slow, that in practice, the edge parameter settings should not really be considered useful as convergent parameter settings.