Ranking-based hierarchical random mutation in differential evolution

In order to improve the performance of differential evolution (DE), this paper proposes a ranking-based hierarchical random mutation in differential evolution (abbreviated as RHRMDE), in which two improvements are presented. First, RHRMDE introduces a hierarchical random mutation mechanism to apply the classic "DE/rand/1" and its variant on the non-inferior and inferior group determined by the fitness value. The non-inferior group employs the traditional mutation operator "DE/rand/1" with global and random characteristics, which increases the global exploration ability and population diversity. The inferior group uses the improved mutation operator "DE/rand/1" with elite and random characteristics, which enhances the local exploitation ability and convergence speed. Second, the control parameter adaptation of RHRMDE not only considers the complexity differences of various problems but also takes individual differences into account. The proposed RHRMDE is compared with five DE variants and five non-DE algorithms on 32 universal benchmark functions, and the results show that the RHRMDE is superior over the compared algorithms.