This paper presents an objective function specially designed for the
convergence analysis of a number of particle swarm optimization (PSO) variants.
It was found that using a specially designed objective function for convergence
analysis is both a simple and valid method for performing assumption free convergence
analysis. It was also found that the canonical particle swarm's topology did
not have an impact on the parameter region needed to ensure convergence. The
parameter region needed to ensure convergent particle behavior was empirically
obtained for the fully informed PSO, the bare bones PSO, and the standard PSO
2011 algorithm. In the case of the bare bones PSO and the standard PSO 2011 the
region needed to ensure convergent particle behavior di ers from previous theoretical
work. The di erence in the obtained regions in the bare bones PSO is a direct
result of the previous theoretical work relying on simplifying assumptions, speci -
cally the stagnation assumption. A number of possible causes for the discrepancy
in the obtained convergent region for the standard PSO 2011 are given.