Can Individuals be Repeatedly Selected for Mutation in Matrix-Based DE? A Comparative Study

Evolutionary Computation (EC) is a class of algorithms derived from the simulation of natural phenomena, which faces the challenges of long running times and high computing loads resulting from large-scale problems. For this reason, the matrix-based EC (MEC) has been presented as an extension of classic EC algorithms to address large-scale optimization. The MEC can be implemented directly on high-performance computing resources, thus accelerating the computation of evolutionary operators. However, MEC is still in its infancy and lacks deeper analysis. Hence, this paper analyzes and investigates matrix-based differential evolution (MDE) and advances the development of related research through theoretical analysis and experimental validation, which has two contributions. First, through the comprehensive comparison of MDE and DE in different problems, we compare the solution quality and computational speed of MDE and DE, and show that the solution quality of MDE is not significantly different from that of DE, but the computational speed of MDE is much faster than that of DE. Second, we also further analyze the mutation mechanism of MDE, focusing on the effect of the repeatability of individuals in the mutation process on the performance of the algorithms, which provides a basis for future research on MDE of MEC.