Analysis of mutation vectors selection mechanism in differential evolution

Differential evolution (DE), which is one of the most popular evolution algorithms, has received much attention from researchers and engineers. In DE, mutation operation has a great impact on the performance of the algorithm. It generates mutant vectors by adding difference vectors to the base vector. Obviously, the chosen vectors in the mutation operation should not be equal to each other or to the target vector. This paper designs four experiments to analyze this session of DE and tries to determine whether this constraint is necessary. The theoretical analysis and experimental results show that without this constraint, the DE algorithm may perform better or at least not worse. Moreover, based on the experimental results, we can also summarize some rules for when and how to use this constraint to enhance the performance of the DE algorithm. This can help researchers to improve or apply the DE algorithm well.