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We discuss the design of a frequency selective surface (FSS) with low cross-polarization discrimination. In the past, FSS screens have been employed to improve the cross-polarization performance. The objective of this paper is to synthesize an FSS subreflector with low cross-polarization via the application of a parallel binary coded micro-genetic algorithm (PMGA). The PMGA optimizes the metallization pattern and the periodicity of the FSS screen in both the x- and y-directions to maintain a low cross-polarization level for a wide band of frequencies and a range of incident angles.