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The design of linear and circular antenna arrays is one of the important electromagnetic optimization problems. In this paper, the problem of designing these arrays for specific radiation properties is dealt with. The biogeography based optimization (BBO) method, which represents a new evolutionary algorithm, is used in the optimization process. BBO is used to minimize the maximum side lobe level (SLL) and null control for isotropic linear antenna arrays by optimizing different array parameters (position, amplitude, and phase). Similarly, for non-uniform circular antenna arrays (CAA), BBO is used to determine an optimum set of weights and positions that provide a radiation pattern with maximum SLL reduction with the constraint of a fixed major lobe beam width. The results obtained show the effectiveness of BBO compared to other optimization methods.