In this paper, a new reconfigurable frequency selective surface (RFSS) design concept is introduced. A grid of simple metallic patches interconnected by a matrix of switches is proposed as the unit cell of an RFSS. The switches are independently addressable and provide significant transmission and reflection flexibility over a large range of frequencies. This flexibility is exploited by optimizing the switch settings using a genetic algorithm (GA) to produce a desired frequency response. The versatility of the design technique is demonstrated by presenting several examples of genetically optimized RFSSs. The first geometry to be considered is a linearly polarized FSS that can be reconfigured for either single-, dual-, or tri-band operation. An RFSS design is also introduced that can be optimized to have a frequency response that is polarization independent in one state (i.e., for one combination of switch settings) and polarization dependent in another state.