Two optimization techniques from the class of direct search solvers, the genetic and generalized pattern search algorithms, are applied to hyperspectral source prediction. The number of filter bands to be sampled and their placements are the variables subject to optimization. The algorithms provide the optimal placements by sampling the stable source radiances at multispectral resolution, estimating the original source spectrum upon interpolation to hyperspectral resolution, and retaining the most accurate prediction. The integrated absolute error between the source prediction and the hyperspectral source truth is minimized. The interpolation estimate of the source approaches zero error asymptotically, as the number of allowed band samples is increased. The source spectrum of 2.15 μm bandwidth is reconstructed with 13 bands and relative absolute error of less than 0.5%. The method can be applied to any radiance spectrum or subspectrum partition, and is useful in transfer radiometer design or minimizing the number of spectrometer measurements required for hyperspectral source prediction.