Metallodielectric photonic crystals (MDPCs) consisting of a planar periodic array of metallic patch elements designed by genetic algorithm (GA) optimization were patterned on flexible dielectric substrates and exhibit strong mid- and far-infrared (IR) dual-band response. The GA uses biological principles of natural selection to evolve nonintuitive geometries by optimizing the MDPC scattering response based on a user-defined fitness function. The transmission spectra measured on two different MDPCs optimized for optically thin and thick substrates have two strong stop bands with attenuation greater than 10dB, which agree well with those predicted by full-wave periodic method of moments (PMM) modeling. This versatile GA optimization approach will facilitate design of scaled mid- and near-IR MDPCs with user-defined scattering response.