In this paper, optimal designs of non-uniform single-ring circular antenna array (CAA) and non-uniform threering concentric circular antenna array (CCAA) have been dealt with, which gives rise to optimal improvement of far-field radiation characteristics. An evolutionary optimization technique based on opposition-based bat algorithm (OBA) is applied to determine an optimum set of current excitation weights and antenna inter-element spacing for CAA of 8, 10, and 12 elements and optimal current excitation weights for CCAA, respectively. Two three-ring CCAAs, one having the set of 4, 6, and 8 elements and the other having 8, 10, and 12 elements with and without center element, are considered. The results show a considerable reduction of side lobe level, 3-dB beamwidth, and improved directivity of CAA and better side lobe level of CCAA, with respect to the results of some recent literature reported in this paper. The BAT is a metaheuristic algorithm, based on the echolocation behavior of bats. The capability of echolocation of microbats is fascinating as the bats can find their prey and discriminate different types of insects even in complete darkness. By idealizing the echolocation behavior of bats, BAT is recently introduced in the literature. In the present paper, opposition-based learning is employed for population initialization and also for the generation jumping along with the original BAT for further improving the convergence performance of BAT. This new variant of BAT is termed as opposition-based BAT.