A methodology is presented for the design synthesis of metamaterials that act as thin multifrequency artificial magnetic conductors. These structures are realized by placing a frequency-selective surface above a conventional prefect electric conductor, separated by a thin dielectric layer. The frequency-selective surface design is optimized using a microgenetic algorithm to operate at multiple, narrow frequency bands. Two examples of genetically engineered multiband high-impedance frequency-selective surfaces (that is, artificial magnetic conductors) are presented and discussed.