3.2.1. Initialization

DE optimizes the problem by using different formulas for creating new particles and also by maintaining the population size at the same time. In the search space, out of the existing particles and newly updated particles, the best fitness value particles only remain and others having the least fitness value are replaced. In DE optimization, various control processes are carried out step by step as discussed below. For optimization using DE, at first, initial parameters, population, and number of generations must be initialized [37,41,42].

If a function with "P" real parameters must be optimized, then the population size is taken as "N", where the "N" value should not be less than 4.

Hence, the parameter vectors can be written as:

$$\mathbf{x}\_{\mathrm{i},\mathrm{G}} = \begin{bmatrix} \mathbf{x}\_{\mathrm{i},\mathrm{i},\mathrm{G},\prime} \mathbf{x}\_{\mathrm{2},\mathrm{i},\mathrm{G},\prime} \mathbf{x}\_{\mathrm{3},\mathrm{i},\mathrm{G},\prime} \dots \dots \mathbf{x}\_{\mathrm{P},\mathrm{i},\mathrm{G}} \end{bmatrix} \tag{9}$$

In the above equation i = 1, 2, ... , N; and G is the number of generations.

During initialization process, the user sets a predefined upper and lower boundary value for each particle:

$$\mathbf{x}\_{\mathbf{j}}^{\mathcal{L}} \le \mathbf{x}\_{\mathbf{j},1} \le \mathbf{x}\_{\mathbf{j}}^{\mathcal{U}} \tag{10}$$

The initial values are chosen randomly for each particle but in uniform intervals between the upper and lower interval of the particle.
