A hybrid genetic algorithm/local optimization technique for designing cascaded planar periodic structures such as frequency selective surfaces is developed. The genetic algorithm optimizes the shape and size of the periodic metallization in each of the screens as well as the thickness and dielectric constant of intervening dielectric layers in order to achieve a desired frequency response characteristic. Careful local optimization to fine-tune the dielectric layer thicknesses is shown to accelerate both the spectral analysis of the cascades and the convergence of the stochastic search. Results are presented for the design of a satellite subreflector with a 3:1 ratio of stop band center to passband center, a circular polarizer with an axial ratio of less than 1 dB between 47 and 64 GHz, and a twist polarizer with a better than -1-dB reflection into the cross-polarized field component for 47--65 GHz. ¿ 1999 American Geophysical Union