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The purpose of this paper is to find the desired pattern of uniform circular antenna array with uniformly spaced isotropic elements having identical excitation amplitudes. For this purpose, angular position of array elements simulated in binary codes and populations representing the circular array are created. Afterwards, the selection, crossover and mutation operators of the Genetic Algorithm are performed on these populations. Fixed mutation rate method, which is used in the conventional Genetic Algorithm, is compared with the variable mutation rate method. In conclusion, mutation rate decreasing along with the generations is found to outperform to the fixed mutation rate for this particular type of antenna array application.