Improved particle swarm optimization technique using hard boundary conditions

The terminology of hard and soft boundary conditions is suggested in this paper to describe the way in which particles are enforced to stay inside the desired domain of interest. Specifically, hard boundary conditions use position-clipping criterion, while soft boundary conditions do not use this criterion. All soft domains employed before in the PSO literature rely on velocity clipping rather than position clipping. Traditionally, a velocity-clipping technique is used to prevent particles from explosion. In this paper, we investigate the hard-wall boundary conditions together with other velocity-termination criteria. The application into linear-array synthesis shows that the choice of the way in which the velocity is treated at the boundary of the problem can dramatically improve the convergence of the PSO algorithm.