Particle swarm optimization in electromagnetics

The particle swarm optimization (PSO), new to the electromagnetics community, is a robust stochastic evolutionary computation technique based on the movement and intelligence of swarms. This paper introduces a conceptual overview and detailed explanation of the PSO algorithm, as well as how it can be used for electromagnetic optimizations. This paper also presents several results illustrating the swarm behavior in a PSO algorithm developed by the authors at UCLA specifically for engineering optimizations (UCLA-PSO). Also discussed is recent progress in the development of the PSO and the special considerations needed for engineering implementation including suggestions for the selection of parameter values. Additionally, a study of boundary conditions is presented indicating the invisible wall technique outperforms absorbing and reflecting wall techniques. These concepts are then integrated into a representative example of optimization of a profiled corrugated horn antenna.

I. Introduction

The particle swarm optimization (PSO) has been shown to be effective in optimizing difficult multidimensional discontinuous problems in a variety of fields [1]. Recently, this technique has been successfully applied to antenna design, and results were presented by the authors in a 2002 conference [2]. Additionally, this new stochastic evolutionary computation technique, based on Fig. 1.

(a) Like bees searching a field for the location of the most flowers, particles in a PSO are attracted both to the area of highest concentration found by the entire swarm, and the best location personally encountered by the particle. (b) Eventually, after being attracted to areas of high flower concentration, all the bees swarm around the best location over-flying it only to be pulled back in after failing to find a higher concentration of flowers elsewhere.

the movement and intelligence of swarms, has been shown in certain instances to outperform other methods of optimization like genetic algorithms (GA) [3]. Developed in 1995 by Kennedy and Eberhart [4], the PSO can best be understood through an analogy similar to the one that led to the development of the PSO. Imagine a swarm of bees in a field. Their goal is to find in the field the location with the highest density of flowers. Without any knowledge of the field a priori, the bees begin in random locations with random velocities looking for flowers. Each bee can remember the locations that it found the most flowers, and somehow knows the locations where the other bees found an abundance of flowers. Torn between returning to the location where it had personally found the most flowers, or exploring the location reported by others to have the most flowers, the ambivalent bee accelerates in both directions altering its trajectory to fly somewhere between the two points depending on whether nostalgia or social influence dominates its decision Fig. 1(a). Along the way, a bee might find a place with a higher concentration of flowers than it had found previously. It would then be drawn to this new location as well as the location of the most flowers found by the whole swarm. Occasionally, one bee may fly over a place with more flowers than had been encountered by any bee in the swarm. The whole swarm would then be drawn toward that location in additional to their own personal discovery. In this way the bees explore the field: overflying locations of greatest concentration, then being pulled back toward them. Constantly, they are checking the territory they fly over against previously encountered locations of highest concentration hoping to find the absolute highest concentration of flowers. Eventually, the bees' flight leads them to the one place in the field with the highest concentration of flowers. Soon, all the bees swarm around this point. Unable to find any points of higher flower concentration, they are continually drawn back to the highest flower concentration Fig. 1(b).