Pattern Search optimization with applications on synthesis of linear antenna arrays

In this work, Pattern Search (PSearch) method is introduced as a direct, efficient and derivative-free optimization tool with the applications on the antenna array synthesis in the antenna engineering. PSearch is a nonrandom method which can be exploited as a direct searching tool for minimization of a function which is not necessarily differentiable, stochastic, or even continuous. Thus, firstly antenna array synthesis is defined as a multi-objective optimization problem with its feasible variable and target spaces. For this aim, maximum amount of the side-lobe suppressions and broad/narrow null generations in any desired directions are simultaneously expressed as objectives in the target space while ensuring maximization in the gain performance of the antenna array. At the same time, the inter-element spacings and excitation amplitudes are considered as optimization variables that results in determination of the physical layout and feeding network of the array. In the optimization procedure, a fitness function is defined based on the target and synthesis variable spaces that can be applied into various antenna array designs, combining part by part with the different requirements. Besides convergence is made fast by a seeding process which consists of running “genetic” algorithm once with the random initial values. Finally, the whole PSearch synthesis method is verified by applying into the many linear antenna arrays synthesizes with various multi-objective requirements, and all of the optimized arrays are observed to outperform uniform arrays and representative designs.