Theoretical Analysis of Initial Particle Swarm Behavior

In this paper, particle trajectories of PSO algorithms in the first iteration are studied. We will prove that many particles leave the search space at the beginning of the optimization process when solving problems with boundary constraints in high-dimensional search spaces. Three different velocity initialization strategies will be investigated, but even initializing velocities to zero cannot prevent this particle swarm explosion. The theoretical analysis gives valuable insight into PSO in highdimensional bounded spaces, and highlights the importance of bound handling for PSO: As many particles leave the search space in the beginning, bound handling strongly influences particle swarm behavior. Experimental investigations confirm the theoretical results.