Analyzes an electromagnetic model of radar-absorbing layered structures for several stacking sequences of a woven glass/vinyl ester laminate, foam layers, and resistive sheets. It considers configurations that are either deposited on different backing materials or embedded in a laminated sandwich plate. Through-the-thickness layer dimensions and sheet resistances offering the best signal absorption over a specified frequency range are found for each configuration by minimizing an objective function with an enhanced genetic algorithm. The objective function includes selected values of minimum reflection coefficients and novel weight function distributions. In contrast to other optimization methods, this approach works with a population of initially selected values of the objective function and explores in parallel new areas in the search space, thus reducing the probability of being trapped in a local minimum. The procedure also yields the maximum reflection coefficient of -38.9 dB for a 0° incident wave passing through an optimized Jaumann absorber deposited on a metallic backing in the 7.5- to 18-GHz range, which corresponds to 5.2 times smaller reflected signal than a patented design. Two additional surface-mounted designs and three sandwich plate configurations are analyzed in a frequency band used by marine radars. In general, the surface-mounted designs have much lower reflection coefficients.