Ensemble of Similar Differential Evolution Algorithms With Independent Option on Operators for Individuals
Chengjun Li · 2022
L-SHADE [3], the winner in 2014, is a version of Differential Evolution (DE) [4].• L-SHADE-EpSin [5], one of the two joint winners in 2016, is a variant of L-SHADE.• UMOEAs-II [6], the other joint winner in 2016, is ensemble of DE and CMA-ES.• EBOwithCMAR [7], the winner in 2017, is a version of self-adaptive butterfly optimizer; • HSES [8], the winner in 2018, is also a variant of CMA-ES.• IMODE [9], the winner in 2020, is ensemble of three DE algorithms.• APGSK-IMODE [10], the winner for non-shifted cases in 2021, is ensemble of gaining-sharing knowledge based algorithm with adaptive parameters (APGSK) and IMODE.• NL-SHADE-RSP [10], the winner for shifted cases and rotated shifted cases in 2021, is a variant of L-SHADE.• jDE-21 [11], the winner for non-rotated shifted cases in 2021, is a DE algorithm with two subpopulations.Among the ten winners, seven algorithms -L-SHADE (2014), L-SHADE-EpSin (2016), UMOEAs-II (2016), IMODE (2020), APGSK-IMODE (2021), NL-SHADE-RSP (2021), and jDE-21 (2021) -are based on DE.In brief, DE-based algorithms perform outstandingly in the CEC competition.DE is based on operators such as mutation, crossover, and selection.In the initial generation of population, individuals, i.e., target vectors x i,0 = (x 1,i,0 , x 2,i,0 , ..., x D,i,0 ), where i is from 1 to N P and N P denotes the population size with dimensionality as D, are produced randomly.In the g-th generation, mutant vector v i,g is produced based on target vector x i,g by mutation.An early mutation strategy, DE/rand/1, is presented in Equation (1), for instance