Algorithm 3 Pseudocode of ABBFGO

1:Initialize the parameters of BFGO: N (number of search agents), T (maximum iteration), n (number of bamboo shoots) and K (number of bamboo whips)   2:Initialize the positions of the search agents   3:Calculate the fitness of each search agent   4:The search agents are sorted in descending order of fitness and divided into K groups according to the uniform grouping in Figure 2   5:Update $X_G$, $X_{P\left(k\right)}$, $f\left(X_G\right)$ and $f\left(X_{P\left(k\right)}\right)$   6:$t=2$   7:while$t<T+1$do   8:   if $t>10$&&Convergence(t)==Convergence(t-3) then   9:     Use the long-mutation strategy to generate new solutions 10:     If the fitness value of the new solution is greater than the global optimal value, replace it 11:     Update $X_G$, $X_{P\left(k\right)}$, $f\left(X_G\right)$ and $f\left(X_{P\left(k\right)}\right)$ 12:   end if 13:   for i = 1;i ≤ k;i++ do 14:     if $X_{P\left(k\right)}$ not updated then 15:        P++ 16:     end if 17:   end for 18:   if P = k then 19:     Do Random grouping 20:   end if 21:   for each bamboo whip do 22:     Update $C\left(k\right)$ using Equation (1) 23:     Update the $X_{t+1}$ using Equations (2)–(6) 24:     Calculate the position under binary conditions of each search agent by Equations (11)–(21) 25:     Calculate $f\left(X_{t+1}\right)$ 26:   end for 27:   Update $X_G$, $X_{P\left(k\right)}$, $f\left(X_G\right)$ and $f\left(X_{P\left(k\right)}\right)$ 28:   for each bamboo whip do 29:     Update $C\left(k\right)$ using Equation (1) 30:     Update the $X_{temp}$ using Equations (7)–(10) 31:     Calculate the position under binary conditions of each search agent by Equations (11)–(21) 32:     Calculate $f\left(X_{temp}\right)$ 33:   end for 34:   Update $X_G$, $X_{P\left(k\right)}$, $f\left(X_G\right)$ and $f\left(X_{P\left(k\right)}\right)$ 35:   Convergence(t) = $f\left(X_G\right)$ 36:   $t=t+1$ 37:   Repeat step 4 38:end while