Particle swarm, genetic algorithm, and their hybrids: optimization of a profiled corrugated horn antenna

Abstract

Introduction Genetic Algorithms (CA) have proven to be a useful method of optimization for difficult and discontinuous multidimensional engineering problem. A new method of optimization, Particle Swarm Optimization (PSO), is able to accomplish the same goal as GA optimization in a new and faster way [l]. The purpose of this paper is to investigate: the foundations and performance of the two algorithms when qplied to the design of a profiled corrugated horn antcnna. Also investigated is the possibility of hybridizing the two algorithms.GA Background GA is an evolutionary optimizer (EO) that takes a sample of possible solutions (individuals) and employs mutation, crossover, and selection as the primary operator!: for optimization [2]. For the case of a profiled corrugated horn antenna, there are five parameters being optimized for the design of a profiled corrugated horn antenna. The optimization parameters are the '3'' paramcter relating to the length, the number of corrugations per wavelength, the ratio of tooth width to total corrugation width, profile parameter, and matching section parameter.The fitness function takes the values of each parameter and returns a single number representing how good the solution is. For this example the design parameters are fed into a hom simulation program that creates a horn cross section and simulates the far field pattern. A representative fitness function is definedas:The BWtaTg, is the desired beamwidth of the horn. In this case 34' is chosen because that was the desired outcome for a particular project. Weight is the wight of the horn, and Xpol is the peak crosspolarization within a reflector subtended angle of +36 '. Additional constraints are made to discourage unrealistic dcsigns. Any design with a tooth thickness of lcss than I mm is given a fitness value of -100 bccause 1 mm is the thinnest tooth that can be effectively manufactured. If the value of SI I was lcss than -30 dB, the fitness is evaluated using -30 as the value of S I I.PSO Background PSO is in principle a much simpler algorithm. It operates on the principle that each solution can be rcprcsentcd as a particle (agcnt) in a swarm. Each agcnt has a position and velocity vector. Each position coordinate represents a paramctcr value. Thus for an n-dimensional optimization, each agcnt will have a position in n-dimensional space that reprcscnts a solution [3]. For this case the position corresponds to thc horn design parainetcrs. Figurc la shows a flow chart of the PSO algorithm.Like GA, PSO must also have a fitncss evaluation function that takes thc agent's positiori and assigns to it a fitness value. For consistency the fitncss function IS the same as for CA. Thc position with the highest fitness value in the entire run is called the global bcst (ghcrt). Each :agent also keeps track of its highest fitness value. The location of this value is called its personal bcst (pbcit). Each agent is initialized with a random position and random velocity. The velocity in each of n dimensions is accelerated toward the globa...

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