Quantum Particle Swarm Optimization for Electromagnetics

A new particle swarm optimization (PSO) technique for electromagnetic applications is proposed. The method is based on quantum mechanics rather than the Newtonian rules assumed in all previous versions of PSO, which we refer to as classical PSO. A general procedure is suggested to derive many different versions of the quantum PSO algorithm (QPSO). The QPSO is applied first to linear array antenna synthesis, which is one of the standard problems used by antenna engineers. The performance of the QPSO is compared against an improved version of the classical PSO. The new algorithm outperforms the classical one most of the time in convergence speed and achieves better levels for the cost function. As another application, the algorithm is used to find a set of infinitesimal dipoles that produces the same near and far fields of a circular dielectric resonator antenna (DRA). In addition, the QPSO method is employed to find an equivalent circuit model for the DRA that can be used to predict some interesting parameters like the Q-factor. The QPSO contains only one control parameter that can be tuned easily by trial and error or by suggested simple linear variation. Based on our understanding of the physical background of the method, various explanations of the theoretical aspects of the algorithm are presented

I. Introduction

The evolutionary particle swarm optimization (PSO) is a global search strategy that can handle efficiently arbitrary optimization problems. In 1995, Kennedy and Eberhart introduced the PSO method for the first time [1]. Later, it received a considerable attention and proved to be capable of tackling difficult optimization problems. The basic idea of the PSO is to mimic the social interactions between members of biological swarms. One of the good examples illustrating the concept is the analogy with the swarm of bees. Bees (solution candidates) are allowed to fly in a specified field, looking for food. It is believed that after certain time (generations; iterations) all bees will gather around the highest concentration of food in the field (global optimum). At every generation, each bee updates its current location by employing information about the local and global “bests”, achieved so far, received from all other bees. Such social interactions and continuous velocity update will guarantee arriving to the global optimum. The method has received considerable attention by the electromagnetic community because of its simplicity and high capability of searching for the global optimum of hard optimization problems. The classical PSO method was recently applied to electromagnetic problems [2]–[4], [11] and proved to be very competitive compared with other well-established evolutionary computing techniques, such as the genetic algorithm [4].