(b) Encircling Prey

The grey wolf will gradually approach the prey and surround it when it searches for the prey. The functional expression for this behavior is as follows [29]:

$$\begin{aligned} D &= \mathbb{C} \circ X\_p(t) - X(t) \\ X(t+1) &= X\_p(t) - A \circ D \\ A &= 2a \circ r\_1 - a \\ \mathbb{C} &= 2r\_2 \end{aligned} \tag{18}$$

where *t* is the current number of iterations, *A* and *C* are the synergy coefficients; vector *Xp* represents the position vector of the prey; *X*(*t*) represents the current grey wolf's position vector; a linearly decreases from 2 to 0 during the entire iteration process; *r*1 and *r*2 are the random vector in [0, 1].
