Algorithm 2 The pseudocode of the BGO algorithm.

Input: $N\left(populationsize\right),D\left(populationdimension\right),ub,lb,P_1=5$, $P_2=0.001$, $P_3=0.3$, $FEs=0$ Output: Global optimal solution: $\overrightarrow{gbestx}$ 1. Initialize the population using $\overrightarrow{x}=\mathrm{randint}(N,D)$ and evaluate $(i=1,\cdots ,N)$ while $FEs\le \mathrm{MaxFEs}$ do     $[\sim ,ind]=\mathrm{sort}\left(GR\right)$     $\overrightarrow{xbest}=\overrightarrow{x}(ind\left(1\right),:)$     %Learning phase:     for $i=1$ to N do         $\overrightarrow{x_{better}}=\overrightarrow{x}(ind\left(\mathrm{randi}([2,1+P_1],1)\right),:)$         $\overrightarrow{x_{worse}}=\overrightarrow{x}(ind\left(\mathrm{randi}([N-P_1,N],1)\right),:)$         Find two random individuals that are different from ${\overrightarrow{x}}_i$: $\overrightarrow{x_{L1}}$ and $\overrightarrow{x_{L2}}$         Compute ${\mathrm{Gap}}_k$, $k=1,2,3,4$ by Equation (4)         Compute ${\mathrm{LF}}_k$, $k=1,2,3,4$ according to Equation (5)         Compute $S{F}_i$ according to Equation (6)         Compute ${\overrightarrow{KA}}_k$, $k=1,2,3,4$ according to Equation (8)         Complete the learning process for the i-th individual once according to Equation (7)         Complete the update of the i-th individual according to Equation (9)         Real-time update $\overrightarrow{gbestx}$         $FEs=FEs+1$     end for     %Reflection phase:     for $i=1$ to N do         Complete the reflection process for the i-th individual once according to Equations (10) and (11)         Complete the update of the i-th individual according to Equation (9)         Real-time update $\overrightarrow{gbestx}$         $FEs=FEs+1$     end for     %Two-Step Binarization:     for $i=1$ to N do         Compute the transfer function of the i-th individual         Complete the binarization of the i-th individual based on the binarization function selected     end for end while Output: $\overrightarrow{gbestx}$