Comparison of evolutionary algorithms for LPDA antenna optimization

Broadband log-periodic antenna optimization is a very challenging problem for antenna design. However, up to now, the universal method for log-periodic antenna design is Carrel´s method dating from the 1960s. This paper compares five antenna design optimization algorithms (Differential Evolution, Particle Swarm, Taguchi, Invasive Weed, Adaptive Invasive Weed) as solutions to the broadband antenna design problem. The algorithms compared are evolutionary algorithms which use mechanisms inspired by biological evolution, such as reproduction, mutation, recombination, and selection. The focus of the comparison is given to the algorithm with the best results, nevertheless, it becomes obvious that the algorithm which produces the best fitness values (Invasive Weed Optimization) requires very substantial computational resources due to its random search nature. Log-periodic antennas (LPDA: Log-Periodic Dipole Arrays) are frequently preferred for broadband applications due to their very good directivity characteristics and flat gain curve. The purpose of this study is, in the first place, the accurate modelling of the log-periodic type of antennas, the detailed calculation of the important characteristics of the antennas under test (gain, vswr, front-to-back ratio) and the confrontation with accurate measurements results. In the second place, various evolutionary optimization algorithms are used, and notably the relatively new (2006) Invasive Weed Optimization (IWO) algorithm of Mehrabian & Lucas, for optimizing the performance of a log-periodic antenna with respect to maximum gain, Side-Lobe-Levels (SLL) and matching to 50 Ohms, VSWR. The multi-objective optimization algorithm is minimising a so-called fitness function including all the above requirements and leads to the optimum dipole lengths, spacing between the dipoles, and dipole wire diameters. In some optimization cases, a constant dipole wire radius is used in order to simplify the construction of the antenna. Fig. 1 is depicting the main antenna geometrical characteristics.