Abstract
Particle Swarm Optimization (PSO) algorithms are widely used in a plethora of optimization problems. In this chapter, we focus on applications of PSO algorithms to optimization problems arising in the theory of wave scattering by inhomogeneous media. More precisely, we consider scattering problems concerning the excitation of a layered spherical medium by an external dipole. The goal is to optimize the physical and geometrical parameters of the medium’s internal composition for varying numbers of layers (spherical shells) so that the core of the medium is substantially cloaked. For the solution of the associated optimization problem, PSO algorithms have been specifically applied to effectively search for optimal solutions corresponding to realizable parameters values. We performed rounds of simulations for the the basic version of the original PSO algorithm, as well as a newer variant of the Accelerated PSO (known as “Chaos Enhanced APSO”/ “Chaotic APSO”). Feasible solutions were found leading to significantly reduced values of the employed objective function, which is the normalized total scattering cross section of the layered medium. Remarks regarding the differences and particularities among the different PSO algorithms as well as the fine-tuning of their parameters are also pointed out.
Highlights
Particle Swarm Optimization (PSO) is a population-based, stochastic optimization algorithm
The model originates from the behavior of flocks of birds when in search of food sources. It was inspired by research carried out by Heppner and Grenander [2], in order to experiment on a “cornfield model”. Exploiting these studies, Kennedy and Eberhart developed the PSO algorithm, in which the members of the swarm, called particles have some form of memory and common knowledge and are motivated by a common goal; in the mathematical framework this goal is the global optimum of the objective function of the optimization problem
In order to clearly establish the link between PSO and Swarm Intelligence, we present a comprehensible list of Swarm Intelligence principles, in reference to Millonas’ categorization [1, 18, 20]
Summary
Particle Swarm Optimization (PSO) is a population-based, stochastic optimization algorithm It is modelled after the intelligent behavior patterns found in swarms of animals when they manage their biological needs. The original PSO, which utilizes a global best position g ∗ and an individual best position x ∗ for the particles, which are described by both their position and velocity This is considered to be the basic PSO algorithm, and the version chosen [3] utilizes an inertia mechanism to describe the particles’ movement. The basic principles of Particle Swarm Optimization (PSO) are presented and an in depth description of the algorithms that have been developed and applied for the considered cloaking problems is given.
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