Algorithm 4 MSBKA

Begin

Step 1. Initialize BKA population $X_i(i=1,2,\dots ,n)$

Step 2. Corroborate fitness of each black-winged kite

Retrieve $X_{best}$ and $F_{best}$

Step 3. while ($t<T$) do

Ranking-based differential mutation of “DE/rand/1” is incorporated into BKA

for each black-winged kite do

/*Meticulous attacking phase*/

Simplex method and elite opposition-based learning strategy are incorporated into BKA

if $p<r$

Recalibrate the attacking location via Equation (5)

$y_{t+1}^{i,j}=y_t^{i,j}+n\left(1+sin\left(r\right)\right)\times y_t^{i,j}$

else if do

Recalibrate attacking location via Equation (5)

$y_{t+1}^{i,j}=y_t^{i,j}+n\times \left(2r-1\right)\times y_t^{i,j}$

end if

/*Swarm migration phase*/

Simplex method and elite opposition-based learning strategy are incorporated into BKA

if $Fi<Fri$

Recalibrate migration location via Equation (7)

$y_{t+1}^{i,j}=y_t^{i,j}+C\left(0,1\right)\times \left(y_t^{i,j}-L_t^j\right)$

else if do

Recalibrate migration location via Equation (7)

$y_{t+1}^{i,j}=y_t^{i,j}+C\left(0,1\right)\times \left(L_t^j-m\times y_t^{i,j}\right)$

end if

/* Handpick the fittest individual*/

if $y_{t+1}^{i,j}<L_t^j$

$X_{best}=y_{t+1}^{i,j},F_{best}=f\left(y_{t+1}^{i,j}\right)$

else if do

$X_{best}=L_t^j,F_{best}=f\left(L_t^j\right)$

end if

Enforce boundary constraints by detecting and correcting violations

Corroborate fitness of each black-winged kite

Recalibrate $X_{best}$ if there is a superior black-winged kite

end for

$t=t+1$

end while

Retrieve $X_{best}$ and $F_{best}$

End