3.2.3. Crossover

Here, the next generation is formed from the parent particles. Therefore, recombination is performed between the target and mutant vector to ge<sup>t</sup> the next generation vector, which is a trial vector. In other words, the trial vector ui,G+<sup>1</sup> is formed by considering the elements of the target vector xi,G and also from the elements of the mutant vector/donor vector ui,G+1.

Crossover may be reached on the D variables when an arbitrarily chosen number between 0 to 1 lies in the range of the CR value, where CR is a constant value and is used for controlling DE parameters. The condition is given as:

$$\mathbf{u}\_{\text{j},\text{j},\text{G}+1} = \begin{cases} \mathbf{u}\_{\text{j},\text{i},\text{G}+1} & \text{if } \text{rand}\_{\text{j}\text{i}} \le \text{CR and j} = \text{I}\_{\text{rand}} \\\\ \mathbf{x}\_{\text{j},\text{i},\text{G}} & \text{if } \text{rand}\_{\text{j}\text{i}} > \text{CR and j} \ne \text{I}\_{\text{rand}} \end{cases} \tag{12}$$

where

> i = 1, 2, ... , N j = 1, 2, ... ., D

randj,i is any value randomly chosen within [0,1]

Irand is a random integer whose value lies within (1, 2, ... , D). This value makes sure that ui,G+<sup>1</sup> - xi,G.
