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In this paper, an evolutionary optimization technique Craziness based Particle Swarm Optimization (CRPSO) is adopted for the complex synthesis of three-ring Concentric Circular Antenna Arrays (CCAA) with non-isotropic elements and without and with central element feeding. It is shown that by selection of a fitness function which controls more than one parameter of the array pattern, and also by proper setting of weight factors in fitness function, one can achieve very good results. For each optimal design, optimal current excitation weights and optimal radii are determined having the objective of maximum Sidelobe Level (SLL) reduction. The extensive computational results show that the CCAA designs having central element feeding with non-isotropic elements yield much more reduction in SLL as compared to the same not having central element feeding. Moreover, the particular CCAA containing 4, 6 and 8 number of elements in three successive rings along with central element feeding yields grand minimum SLL (-46.0 dB). Standard Particle Swarm Optimization (PSO) is adopted to compare the results of the proposed CRPSO algorithm.