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Over the years, frequency selective surfaces (FSSs) have found frequent use as radomes and spatial filters in both commercial and military applications. In the literature, the problem of synthesizing broadband microwave absorbers using multilayered dielectrics through the application of genetic algorithms (GAs) have been dealt with successfully. Recently, spatial filters employing multiple, freestanding, FSS screens have been successfully designed by utilizing a domain-decomposed GA. In this paper, we present a procedure for synthesizing broadband microwave absorbers by using multiple FSS screens buried in a dielectric composite. A binary coded microgenetic algorithm (MGA) is applied to optimize various parameters, viz., the thickness and relative permittivity of each dielectric layer; the FSS screen designs and materials; their-and-periodicities; and their placement within the dielectric composite. The result is a multilayer composite that provides maximum absorption of both transverse electric (TE) and transverse magnetic (TM) waves simultaneously for a prescribed range of frequencies and incident angles. This technique automatically places an upper bound on the total thickness of the composite. While a single FSS screen is analyzed using the electric field integral equation (EFIE), multiple FSS screens are analyzed using the scattering matrix technique.