Movement patterns of a particle swarm in high dimensional spaces

Abstract

In high dimensional problem spaces, particle swarm optimization (PSO) is prone to unwanted roaming behaviour due to initial velocity explosion. A particle swarm’s movement patterns are strongly influenced by the inertia weight and acceleration coefficients. This paper investigates whether the initial velocity explosion can be curbed by appropriate choice of the inertia weight and the acceleration coefficients, which restrict the standard deviation of particle positions. It is shown that roaming behaviour cannot be solved by reducing swarm variance directly, but that the relationship between the parameters must also be considered. Furthermore, the paper investigates different movement patterns that may be exhibited by the swarm. It is shown that optimal parameter configurations differ between low and high dimensional problems. Specifically, parameter configurations which produce very smooth particle trajectories and restrict the swarm’s movement range are advantageous in high dimensional spaces. These movement patterns correspond to high inertia weight and low acceleration coefficients (eg. w=0.9694,c1=c2=0.099381). Swarms with smooth particle trajectories exhibited significantly less unwanted roaming behaviour than swarms with chaotic or oscillating particle trajectories.