所有版本的差分进化算法 [英] All versions of differential evolution algorithm

问题描述

解释差分演化的基本算法中的所有更新.我无法找到此算法的所有版本.在调查中解释该算法的所有版本，但我对Wikipedia中给出的该算法背后的理论尚不清楚.维基百科还只定义了差分进化的基本算法，但我想对该算法进行所有更新

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

推荐答案

对于差异演化中的完整调查，我建议您使用标题为

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有2个基本的交叉和5个基本的变异运算符，因此我们有2 * 5 = 10个基本的DE变体.

• 两个交叉运算符是Exponential和Binomial.

指数交叉:

根据上面的伪代码，D是问题空间的维数，n是从[1，D]中随机选择的，Cr是交叉速率，而L是从[1，D]中绘制的.

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.

二项式交叉:

j是第j维，i是向量数，G是世代数，jrand是从[1，D]中随机选择的索引.

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].

五个突变算子是DE/rand/1，DE/best/1，DE/target-to-best/1，DE/best/2和DE/rand/2.

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/最佳目标/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)是目标向量X(i)的施主(突变)向量，F是差分向量的比例因子，r1,r2,r3,r4,r5是互斥的，是从[1，NP]中随机选择的，并且与i不同， best是当前总体中最适向量的索引，最后NP是总体大小.

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.

• 关于DE的基本变体，这些都是您所知道的.
• DE出于多种目的还具有许多变体，已在上述论文中进行了解释.

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