Hyperspectral Endmember Extraction by (μ + λ) Multiobjective Differential Evolution Algorithm Based on Ranking Multiple Mutations

Abstract

Endmember extraction (EE) plays a crucial part in the hyperspectral unmixing (HU) process. To obtain satisfactory EE results, the EE can be considered as the multiobjective optimization problem to optimize the volume maximization (VM) and root-mean-square error (RMSE) simultaneously. However, it is often quite challenging to balance the conflict of these objectives. In order to tackle the challenges of multiobjective EE, we present a <inline-formula> <tex-math notation= LaTeX >$({\\mu + \\lambda })$ </tex-math></inline-formula> multiobjective differential evolution algorithm (<inline-formula> <tex-math notation= LaTeX >$({\\mu +\\lambda })$ </tex-math></inline-formula>-MODE) based on ranking multiple mutations. In the <inline-formula> <tex-math notation= LaTeX >$({\\mu + \\lambda })$ </tex-math></inline-formula>-MODE algorithm, ranking multiple mutations are adopted to create the mutant vectors via the scaling factor pool to enhance the population diversity. Moreover, mutant vectors employ the binary crossover operator to generate the trial vectors through a crossover control parameter pool in <inline-formula> <tex-math notation= LaTeX >$({\\mu + \\lambda })$ </tex-math></inline-formula>-MODE to take advantage of the good information of the population. In addition, <inline-formula> <tex-math notation= LaTeX >$({\\mu + \\lambda })$ </tex-math></inline-formula>-MODE utilizes the fast nondominated sorting approach to sort the parent and trial vectors, and then selects the elitism offspring as the next population via the <inline-formula> <tex-math notation= LaTeX >$({\\mu + \\lambda })$ </tex-math></inline-formula> selection strategy. Eventually, experimental comparative results in three real HSIs reveal that our proposed <inline-formula> <tex-math notation= LaTeX >$({\\mu + \\lambda })$ </tex-math></inline-formula>-MODE is superior to other EE methods.