Locating All the Global Minima Using Multi-Species Particle Swarm Optimizer: The Inertia Weight and The Constriction Factor Variants

This paper reports further simplification and improvement of a modified particle swarm optimizer (PSO) called the multi-species particle swarm optimizer (MSPSO) proposed by the author. MSPSO extends the original PSO by dividing the particle swarm spatially into a multiple cluster called a species in a multi-dimensional search space. Each species explores a different area of the search space and tries to find out the global or local optima of that area. Therefore it can be used to locate all the global minima of multi-modal functions in parallel. The previous version of MSPSO relies strongly on the inertia-weight annealing and its performance depends on the annealing schedule. In this paper, instead, we use the constriction factor proposed by Clerc. Our new MSPSO could locate, for example, all 18 global optima of the two-dimensional Shubert function, yet it is free from annealing-schedule optimization of the inertia weight.