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This paper proposes an optimization-design method for the frequency selective surface (FSS) based on the genetic algorithm (GA) incorporated with a geometry-refinement technique. The present method takes the connectivity condition of the elements into consideration, thereby resulting in an easy fabrication. As an example, we design the multiband single-layer FSS for transmitting L band (1.5 GHz band) and S band (2.5 GHz band) and also reflecting Ka band (20/30 GHz band). The designed FSS has bandwidths broader than previous FSSs. Finally, the validity of the present method is proved by the agreement between the calculated and the measured transmission responses for the designed FSS.