On the use of particle swarm optimization with multimodal functions

We present two hybrid particle swarm optimization (PSO) algorithms that incorporate a mutation operator similar to the one used with evolutionary algorithms. We study our hybridized PSO algorithm with two schemes called g/spl I.bar/best and l/spl I.bar/best, and we apply them to multimodal functions. The proposed approaches are validated using test functions taken from the specialized literature, and our results are compared with respect to those obtained by other highly competitive PSO algorithms. Our comparative study indicates that the hybridization of PSO with a nonuniform mutation operator significantly improves its performance when dealing with multimodal functions.