Estimating mineral abundances from coarse hyperspectral data (e.g. EnMAP and PRISMA) is challenging due to the loss of pure spectral signatures (endmembers) in mixed pixels. Multi-objective optimization algorithms (MOAs) provide a robust solution in terms of efficiently exploring high-dimensional spaces to identify optimal spectral bands and index expressions to predict spectral abundances. This study evaluates Bayesian and evolutionary MOAs for predicting mineral abundances with a set of optimal spectral bands at coarse resolutions. The results indicate that while Bayesian MOA offers slightly higher accuracy and faster convergence, the evolutionary MOA achieves comparable accuracy with sparser selection of spectral bands. Both approaches achieve accurate mapping of mineral abundances with a nominal feature spectrum for eliminating spectral redundancy without compromising on information. This comparison underscores the complementary strengths of Bayesian and evolutionary MOAs in supporting hyperspectral data analysis for mineralogical applications, offering scalable solutions for large datasets.