Enhanced Particle Swarm Optimization for Design and Optimization of Frequency Selective Surfaces and Artificial Magnetic Conductors

Optimization methods are invaluable tools for the engineer who has to face the increasing complexity in the design of electromagnetic devices, or has to deal with inverse problems. Basically, an objective function f(x) is defined where x is the set of parameters that has to be optimized in order to satisfy the imposed requirements. In design problems the parameters defined in x completely describe the features of the device (a printed antenna for example), and f(x) is a measure of the system performance (gain or return loss). However, the objective function for a real-world problem may be nonlinear, may have many local extrema and may even be nondifferentiable. Numerous optimization methods that have been proposed in the literature can be divided into two groups − deterministic and stochastic. The former performs a local search which yields results that are highly influenced by the starting point, and sometimes requires the objective function to be differentiable. They might lead to a rapid convergence to a local extremum, as opposed to the global one and impose constraints on the solution domain that may be difficult to handle. The latter are largely independent of the initial conditions and place few constraints on the solution domain. They carry out a global search, and are able to deal with solution spaces with discontinuities, as well as a large number of dimensions and hence many potential local minima and maxima. Among the stochastic methods, for instance Monte Carlo and Simulated Annealing techniques, a particular subset also referred to as evolutionary algorithms have been recently growing in importance and interest. This class comprises the Genetic Algorithms (GA) (Goldberg, 1989), the Ant Colony Optimization (ACO) (Dorigo and Stutzle, 2004) and the Particle Swarm Optimization (PSO). The PSO algorithm has been originally proposed by Kennedy and his colleagues (Kennedy and Eberhart, 1995) and it is inspired by a zoological metaphor of the social behavior of animals (birds, insects, or fishes) that are organized in groups (flocks, swarms, or schools). All of the basic units of the swarm, called particles (or agents) are trial solutions for the problem to be optimized, and are free to fly through the multidimensional search-space toward the optimal solution. The search-space represents the global set of potential results, where each dimension of this space corresponds to a