explain all updates in the basic algorithm of differential evolution. i am not able to find all versions of this algorithm. explain all versions of this algorithm as a survey and i am not clearly understand the theory behind this algorithm as given in the Wikipedia. Wikipedia also define only basic algorithm of differential evolution but i want to all updates of this algorithm
All versions of differential evolution algorithm
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For complete survey in Differential Evolution, I suggest you the paper entitled Differential Evolution: A Survey of the State-of-the-Art but the brief explanation is :
DE has 2 basic crossover and 5 basic mutation operators, so we have 2*5=10 basic DE variants.
Two crossover operators are
ExponentialandBinomial.Exponential Crossover:
Dis problem space dimensionality,nis randomly chosen from [1,D],Cris crossover rate andLis drawn from [1,D] according to above pseudocode.Binomial Crossover:
jis refer to j-th dimension,iis vector number andGis generation number andjrandis randomly chosen index from [1,D].Five mutation operators are
DE/rand/1,DE/best/1,DE/target-to-best/1,DE/best/2andDE/rand/2.DE/rand/1:
V(i)=X(r1)+F*(X(r2)-X(r3))DE/best/1:
V(i)=X(best)+F*(X(r1)-X(r2))DE/target-to-best/1:
V(i)=X(i)+F*(X(best)-X(i))+F*(X(r1)-X(r2))DE/best/2:
V(i)=X(best)+F*(X(r1)-X(r2))+F*(X(r3)-X(r4))DE/rand/2:
V(i)=X(r1)+F*(X(r2)-X(r3))+F*(x(r4)-X(r5))V(i)is donor(mutant) vector for target vectorX(i),Fis difference vector's scale factor,r1,r2,r3,r4,r5are mutually exclusive, randomly chosen from [1,NP] and differ fromi,bestis the fittest vector's index in the current population, finallyNPis population size.