All versions of differential evolution algorithm

Question

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

Answer 1

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 Exponential and Binomial.

  Exponential Crossover:
  
  D is problem space dimensionality, n is randomly chosen from [1,D], Cr is crossover rate and L is drawn from [1,D] according to above pseudocode.

  Binomial Crossover:
  
  j is refer to j-th dimension, i is vector number and G is generation number and jrand is randomly chosen index from [1,D].

• Five mutation operators are DE/rand/1 , DE/best/1 , DE/target-to-best/1 , DE/best/2 and DE/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 vector X(i), F is difference vector's scale factor, r1,r2,r3,r4,r5 are mutually exclusive, randomly chosen from [1,NP] and differ from i, best is the fittest vector's index in the current population, finally NP is population size.

• These are all of things you can know about basic variants of DE.
• DE also has many variants for many purposes which has explained in the mentioned paper.