Abstract: In this paper we are concerned with the synthesis techni-ques of array antenna radiation pattern where the optimization parametersare subject to fixed tolerance.The mathematic models for array antennaradiation pattern optimization are given,the discrete method for solvingthe worst-case problem is presented and the physics models for arbitrarytolerance distribution of array elements are initiated,finally,the imp-roved regular polyhedron method is employed to optimize the broadsidearray in which the excitation amplitude have tolerance.In the presentwork the deviations of th actual performance from its desired one areminimized if the design parameters deviate from its nominal values.