4. Grey Wolf Optimization (GWO)

The GWO imitates the hunting techniques of grey wolves using a meta-heuristic optimization approach [132–135]. Four parameters, alpha (*α*), beta (*β*), delta (*δ*), and omega (*ω*), are used to represent the attaching techniques of the wolves. The fittest solution in the optimization is assumed to be *α* and followed by *β*. The third and fourth fit solutions are *δ* and *ω,* respectively. Figure 10 presents the flow chart of the GWO algorithm. Equation (18) presents the model of the hunting mechanism of grey wolves.

$$\begin{array}{c} \underset{E}{\longrightarrow} = \left| \begin{array}{c} \underset{\mathbb{C}\ \cdot \ X\_{P}}{\longrightarrow} \ \end{array} \begin{array}{c} \left(t\right) \longrightarrow \underset{X\_{P}}{\longrightarrow} \left(t\right) \end{array} \right. \\ \underset{X}{\longrightarrow} \left(t+1\right) = \underset{X}{\longrightarrow} \left(t\right) \text{---} \underset{F}{\longrightarrow} \text{.} \end{array} \tag{18}$$

where

*E*, *F*, and *C* are the coefficient vectors, *Xp* is the position vector of the hunting prey, *X* is the position vector for the Grey wolf, and *t* is the current iteration.

The vectors *C* and *F* are calculated as follows:

$$\begin{array}{c} \underset{F}{\longrightarrow} = \mathbf{2} \underset{a}{\longrightarrow} . \underset{r\_1}{\longrightarrow} - \underset{a}{\longrightarrow} \\ \longrightarrow = \mathbf{2}. \underset{r\_2}{\longrightarrow} \end{array} \tag{19}$$

The GWO fitness function is calculated as follows:

$$\begin{cases} d\_i(k+1) = d\_i(k) - F.E\\ P(d\_i^k) > P(d\_i^{k-1}) \end{cases} \tag{20}$$

where

*d* is the duty cycle,

*k* represents the iteration count,

*i* is the number of the current individual grey wolves, and *P* is the power.

The major advantages of the GWO technique are higher tracking efficiency and elimination of transient and steady-state oscillations [136,137].

**Figure 10.** Flowchart of Grey Wolf Optimization.
