**Step-2: Tracking and Encircling the Prey**

Grey wolves frequently encircle prey all through the hunting phase, expressed mathematically by Equations (22) and (23) (with iteration "i"). Equation (22) calculates a wolf's distance vector <sup>→</sup> d from prey with current iteration.

$$\stackrel{\rightarrow}{d} = \left| \stackrel{\rightarrow}{B} . X\_{P\_{GW}}^{\rightarrow}(i) - \stackrel{\rightarrow}{X}\_{P}^{\rightarrow}(i) \right| \tag{22}$$

$$
\stackrel{\rightarrow}{X}\_P(i+1) = X\_{P\_{\overrightarrow{GW}}}(i) - \stackrel{\rightarrow}{A}\_{\cdot}\stackrel{\rightarrow}{d}\tag{23}
$$

$$
\overrightarrow{\vec{A}} = 2\overrightarrow{\vec{a}}\,\overrightarrow{r\_1} - \overrightarrow{\vec{a}}\tag{24}
$$

$$
\stackrel{\rightarrow}{B} = 2\stackrel{\rightarrow}{r\_2} \tag{25}
$$

→ r1&<sup>→</sup> r2 ranges between [0, 1], and <sup>→</sup> a = linearly decreases from 2 to 0 during each iteration. **Step-3: Hunting**

Using arbitrary vectors <sup>→</sup> r1 and <sup>→</sup> r2, any place in between the points can be reached by a wolf. The first three best solutions (i.e., α, β, and δ wolves' locations) are initially saved. Other probing wolves alter their locations based on the top solution knowledge. As a result, a grey wolf can use this technique to improve its position in any arbitrary direction.
