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In this paper, an optimal design of linear antenna arrays having microstrip patch antenna elements has been carried out. Cat swarm optimization (CSO) has been applied for the optimization of the control parameters of radiation patte of an antenna array. The optimal radiation pattes of isotropic antenna elements are obtained by optimizing the current excitation weight of each element and the inter-element spacing. The antenna arrays of 12, 16, and 20 elements are taken as examples. The arrays are de-signed by using MATLAB computation and are validated through Computer Simulation Technology-Microwave Studio (CST-MWS). From the simulation results it is evident that CSO is able to yield the optimal design of linear antenna arrays of patch antenna elements.