Differential Evolutionary algorithm

Original link: Differential evolutionary algorithm
The differential evolutionary algorithm (differential evolution,de) is a vector-based meta-heuristic algorithm, which has good convergence. The DE variant has many, and has been applied in a wide range of disciplines. Here is a brief introduction to basic differential evolution and its main implementation details and variants. The basic convergence of population variance is discussed. Introduction

Differential Evolution (differential evolution,de) was developed in the papers of R.storn and K.price in 1996 and 1997 [7, 8]. DE is a vector-based meta-heuristic algorithm, which has some similarity with pattern search and genetic algorithm because of its crossover and mutation characteristics. In fact, the DE algorithm can be regarded as the further development of the genetic algorithm with explicit updating equations, which makes the theory analysis possible. The DE algorithm is a random search algorithm with self-organizing tendency and does not use derivative information. Therefore, it is a group-based, non-derivative approach. In addition, the DE uses real numbers as the deserializer, so no coding and decoding is required.

As with genetic algorithms, design parameters in D-dimensional search space are represented as vectors, and various genetic operators operate on their bit strings. However, unlike genetic algorithms, differential evolution performs operations on each component (or each dimension of the solution). Almost everything is done with vectors. For example, in a genetic algorithm, mutations are performed at one or more loci of the chromosome, while in differential evolution, the existing vectors are adjusted using the difference vectors of two randomly selected population vectors. From an implementation point of view, this vectorization mutation can be seen as a more efficient method. This disturbance is performed on each population vector and can therefore be expected to be more efficient. Similarly, a crossover is also a branch exchange of a vector-based chromosome or vector segment.

In addition to using mutation and crossover as the difference operator, the DE also has an explicit update equation. This also makes it straightforward to implement and design new variants. Differential Evolution

For a D-dimensional optimization problem with D parameters, a population with n solution vectors is first generated. We have XI X i x_i, where i=1,2,..., n i = 1, 2, ..., n i=1, 2,..., N. For the solution XI X i x_i of the T generation, we use the regular notation as:

Xti= (xt1,i,xt2,i,..., xtd,i), (1) (1) x i t = (x 1, I t, x 2, I t, ..., x D, I t), x_i^t = (x_{1,i}^t, x_{2,i}^t, ..., X_{d, i}^t), \tag 1

It is made up of D components in D-dimensional space. Such vectors can be thought of as chromosomes or genomes.

Differential evolution consists of three main steps: Mutation, crossover, and selection.

Mutation is made through the mutation scheme. For each vector xi X i x_i of Generation T, we first randomly selected three different vectors xp x P x_p, XQ x q x_q and XR x r x_r (see
Figure 1), and then we produce the mutant individual (donor vector) through the mutation scheme

Vt+1i=xt