The evolution of optimal linear polyfractal arrays using genetic algorithms

Recently, in order to successfully combine the positive attributes of both periodic and random arrays into one design, a novel class of arrays, known as fractal-random arrays, has been introduced. In addition, several researchers have successfully used genetic algorithms, robust global optimization techniques based on natural selection, to find solutions to complex array layout problems. This paper introduces a type of nature-based design process that applies a specially formulated genetic algorithm to evolve optimal layouts of an important subset of fractal-random arrays, which we call polyfractal arrays. Also, this paper discusses how the underlying self-similar properties of polyfractal arrays can be exploited to increase the speed of the associated array factor calculations. This speed increase dramatically reduces the time required for the genetic algorithm to converge thereby making it possible to effectively evolve optimal array configurations which are much larger than has been previously possible. Moreover, the fractal-random properties of these polyfractal arrays are shown to provide substantially wider bandwidth performance than their conventional counterparts. Finally, several design examples of genetically optimized linear polyfractal arrays with narrow beamwidths, improved sidelobe suppression and wide bandwidths are presented.