The National Aeronautics and Space Administration (NASA) has proposed the launch of a new space-borne sensor called HyspIRI (Hyperspectral and Infrared Imager) which will cover the spectral range from 0.4–12 μm. Two instruments will be mounted on HyspIRI platform: 1) a hyperspectral instrument which can sense earth surface between 0.4 and 2.5 μm at 10 nm intervals and 2) a multispectral infrared sensor will acquire images between 3 and 12 μm in eight spectral bands (one in Mid infrared (MIR) and seven in Thermal Infrared (TIR)). The TIR spectral wavebands will be positioned based on their importance in various applications. This study aimed to identify HyspIRI optimal TIR wavebands position for earth compositional mapping. A Genetic Algorithm coupled with the Spectral Angle Mapper (GA-SAM) was used as a spectral bands selector. High dimensional HyTES (Hyperspectral Thermal Emission Spectrometer) emissivity spectra comprised of 202 spectral bands of Cuprite and Death Valley regions were used to select meaningful subsets of bands for earth compositional mapping. The GA-SAM was trained for fifteen mineral classes and the algorithms were run iteratively 50 times. High calibration (> 95%) and validation (> 90%) accuracies were achieved with a limited number (seven) of spectral bands selected by GA-SAM. The knowledge of important band positions will help the scientists of the HyspIRI group to place spectral bands in regions where accuracies of earth compositional mapping can be enhanced.