Quantum Particle Swarm Optimization for Electromagnetics

Abstract

-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.

Quantum Particle Swarm Optimization for Synthesis of Non-uniformly Spaced Linear Arrays with Broadband Frequency Invariant Pattern

“…A novel optimization algorithm QPSO, which is rooted on the fundamental theory of particle swarm and properties of quantum mechanics, was proposed in [11][12][13]. QPSO is stated only by the position vector and there is no velocity vector.…”

“…Another method for synthesis of nonuniformly spaced linear arrays with wide band frequency-invariant patterns using the generalized matrix pencil methods has been described in [10]. In this paper, a simple method is presented for broadband frequency invariant pattern using Quantum Particle Swarm Optimization (QPSO) algorithm for synthesis of nonuniformly spaced linear array antenna [11][12][13].…”

Physical Theory for Particle Swarm Optimization

“…Little has been done in investigating the possible connections between the PSO algorithms, in its social intelligence context, with fundamental physics, like Newtonian mechanics and quantum theory. Of special importance is the recent work on quantum versions of the PSO in which the laws of physics, Schrodinger's equation in this case, were employed directly in the formulation [13][14][15]. While the incorporation of physics in the quantum version was self-evident and fundamental, the situation with the classical PSO algorithm looks very different.…”

“…The recently introduced quantum version of the PSO has naturally no velocity terms [13][14][15]. This is because in quantum mechanics, according to Heisenberg's principle of uncertainty, it is not possible to determine both the position and the velocity with the same precision.…”

“…This is because in quantum mechanics, according to Heisenberg's principle of uncertainty, it is not possible to determine both the position and the velocity with the same precision. It can be shown that all quantum mechanical calculations will produce a natural conditional pdf for the positions in the swarm environment as solutions of the governing Schrödinger's equation [15]. Therefore, one way to unify both the quantum and classical approaches is to consider their common theme: The existence of certain conditional probability distributions underlying the stochastic dynamics of the problem.…”