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In this article, the efficiency of the robust design methods for large array antennas with the simultaneous presence of interval amplitude, phase excitation errors, and antenna position errors is addressed. The CPU time for a single iteration of the robust optimization method is greatly reduced by the proposed prior knowledge-based algorithm ( PKA ). Mathematically, the array factor bounds of array antennas with interval uncertainties can be taken as the bounds of the modulus of the sum of the complex intervals with both the modulus and argument errors ( CIMAS ). The PKA for the modulus of CIMAS consists of three theorems: 1) the necessary conditions for each complex interval for the upper modulus bound of CIMAS ; 2) the method for judging whether the lower modulus bound of CIMAS equals zero; and 3) the necessary conditions for each complex interval for the nonzero lower modulus bound of CIMAS. The efficiency and accuracy of PKA are demonstrated by comparisons with two popular methods. Based on genetic algorithm (GA) and PKA , the robust designs of array antennas under multiple constraints are also presented.