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A new method for the genetic algorithm (GA) based design of broadband, high-performance electromagnetic absorbers is discussed. The method gives rise to novel absorber designs with a geometrical complexity greater than that of absorbers typically in use today. The finite element-boundary integral method is applied to efficiently analyze the scattering from complex geometries occupied by given lossy material, and genetic algorithms are adopted to optimize the geometry parameters to minimize the overall reflection coefficients. In addition, a method is proposed for accelerating the convergence of the GA. Numerical results for absorbers are presented for wide-angle incidence over a broad frequency range considering both polarizations, and demonstrate the new technique's power and robustness.