Algorithm 1. Pseudo-Code of MFISOA.

1: Initialize the parameters (population size (N), dimension (dim), upper bound ($ub$), lower bound ($lb$), Max iterations (T)). 2: Initialize the solutions’ positions randomly. 3: while $t\le T$ do 4:        Calculate the fitness value of each individual, and determine the global optimal individual $X_{best}$ , global worst individual $X_{worst}$ and population average fitness mean(fit). 5:      Calculate the population centroid ${centroid}_j$ for each dimension $j$ using Equation (8). 6:  for i = 1:N do 7:  Classify the individual as “high-quality” $\left(fit\right(i) \le mean(fit)$ ) or “poor-quality” ( $fit\left(i\right) > mean\left(fit\right)$ ) based on its fitness. 8: $\mathit{i}\mathit{f} fit\left(i\right) > mean\left(fit\right)$ then 9:     Compute weights $AFL1$ and $AFL2$ using Equation (2). 10:   Update the position by Equation (3). 11: else 12:         Generate the Levy flight disturbance matrix $RL$ using Equation (4). 13:   Update the position by Equation (3). 14: end if 15:        Randomly select two distinct individuals $X_{r2}$ and $X_{r3}$( $r2\ne r3\ne i$). 16:   Generate the binary mask vector F1 using Equation (5). 17:   Fine-tune the position by Equation (6). 18:     if $X_{ij}<{lb}_j$ or $X_{ij}>{ub}_j$ then 19:   Map $X_{ij}$ to the valid range by Equation (9). 20:  end if 21:  Enforce the secondary boundary constraint by Equation (10). 22: End for 23: Update the fitness values, $X_{best}$, $X_{worst}$ and mean(fit) for the new population. 24: End while 25: Return  $X_{best}$.