4.1.2. Catch Stage

When the number of iterations is greater than two-thirds of the maximum iterations, the aquila individual updates the position by Equation (28) or Equation (29). Again, the specific position update equation is determined by judging the size of the random number. The catch stage is as follows:

$$X\_3(t+1) = (X\_{\text{best}}(t) - X\_M(t) \times a - rand + ((LB - LB) \times rand + LB) \times \delta \tag{28}$$

where *X*3(*t* + 1) denotes the position of the individual after the update, *α* and *δ* are adjustment parameters taking fixed values of 0.1, and *UB* and *LB* denote the upper and lower bounds of the search space.

$$X\_4(t+1) = QF(t) \times X\_{best}(t) - \left(G\_1 \times X(t) \times rand - G\_2 \times Levy(D)\right) + rand \times G\_1 \tag{29}$$

$$\begin{cases} QF(t) = t^{\frac{2 \times rand - 1}{\left(1 - T\right)^2}}\\ G\_1 = 2 \times rand - 1\\ G\_2 = 2 \times \left(1 - \frac{t}{T}\right) \end{cases} \tag{30}$$

where *X*4(*t* + 1) denotes the position of the individual after the update, *QF*(*t*) denotes the search function, *G*1 denotes the movement parameter, and *G*2 denotes the flight slope.
