(c) Hunting

The grey wolf has the ability to identify the position of the potential prey (optimal solution). However, the solution space characteristics of many problems are unknown, and the grey wolf cannot determine the precise position of the prey.

In order to ge<sup>t</sup> the best optimization plan, it is assumed that α, β, δ have the ability to identify the possible location of prey to simulate the behavior of grey wolf. Therefore, keep the best three grey wolves (<sup>α</sup>, β, δ) in the current population during iterating, then update their positions according to

the positions of other search agents (including ω). The mathematical model of this behavior can be expressed as follows [29]:

$$\begin{array}{l} D\_{a} = \mathbb{C}\_{1} \circ X\_{a} - X, \; D\_{\beta} = \mathbb{C}\_{2} \circ X\_{\beta} - X, \; D\_{\delta} = \mathbb{C}\_{3} \circ X\_{\delta} - X \\ X\_{1} = X\_{a} - A\_{1} \circ D\_{a}, \; X\_{2} = X\_{\beta} - A\_{2} \circ D\_{\delta}, \; X\_{3} = X\_{\delta} - A\_{3} \circ D\_{\delta} \\ X(t+1) = \frac{X\_{1} + X\_{2} + X\_{3}}{\frac{3}{\delta}} \end{array} \tag{19}$$

where *X*<sup>α</sup>, *<sup>X</sup>*β, *X*δ represent the position vector of α, β, δ in the current population; *X* represent the position vector of the grey wolf; *D*<sup>α</sup>, *<sup>D</sup>*β, *D*δ represent the distance between the current search agen<sup>t</sup> and the best three wolves; when the |*A*>1|, the gray wolf searches for prey in di fferent areas as much as possible. When |*A*<1|, grey wolves focused on searching for prey within a certain area.
