Since requirements on axial ratio and impedance matching of a circularly polarized antenna are conflicting objectives, a MATLAB-based multi-objective optimization was used to design the feeding system of a two-layer broadband antenna array. Whereas optimum values of state variables were computed by the Non-Dominated Sorting Genetic Algorithm in MATLAB, objective functions were evaluated in CST Microwave Studio using the time-domain solver. Optimizing the antenna array in frequency range from 19 GHz to 21 GHz, the axial-ratio bandwidth 1.44 GHz, and the gain 14.9 dB were achieved. The problem of design sensitivity on fabrication tolerances has not been satisfactorily solved yet.