Algorithm 2. Binary Reinforced Cuckoo Search Algorithm.

Input: Total Population of the nest ( $N$), dimensions $\left(d\right),$ objective function $f()$

Output: $Fitness\mathrm{\_}{x}_{best}$ and $x_{best}$

Each $x$ consists of dimensions (1… d)

$Po{p}_{Nest}$, Termination Criteria, $\alpha =0.1,P_a$

1: Initialize individuals in host nest $x$

2: for $i\leftarrow 1toN$ do

3:   $x_i\leftarrow randi\left(\left[0,1\right],d,1\right)$

4:   Calculate $Fitness\mathrm{\_}{x}_i\leftarrow f\left(x_i\right)$

5: end for

6: while (Termination Condition not met) do

7:     for $i\leftarrow 1toN$

9:         $\mathit{L}\mathit{e}\mathit{v}\mathit{y}=randi\left(\left[0,1\right],1,1\right)$

10:      $x_{t_{!}}\leftarrow randi\left(\left[0,1\right],d,1\right)$

11:       $x_{t_2}\leftarrow randi\left(\left[0,1\right],d,1\right)$

12:       $y_i$ = $x_{t_{!}}\bowtie x_{t_2}$

13:    end for

14:   Calculate $Fitness\mathrm{\_}{y}_i\leftarrow f\left(y_i\right)$ where $i\in 1\dots N$

15:   for $i\leftarrow 1toN$

16:      if ( $Fitness\mathrm{\_}{y}_i\le Fitness\mathrm{\_}{x}_i$)

17:          $x_i\leftarrow y_i$

18:          $Fitness\mathrm{\_}{x}_i\leftarrow Fitness\mathrm{\_}{y}_i$

19:     end if

20:  end for

21:  Compute mean value ${\sigma }_t={\displaystyle \frac{{\sum }_{i=1}^{N}f\left(x_i\right)}{N}}$

22:  Compute Fitness Difference ${\vartheta }_t=C\times \left({\sigma }_t-f\left(x_t^{best}\right)\right)$

23:  Compute Threshold Value ${\mathrm{\Theta }}_t=f\left(x_t^{best}\right)+{\vartheta }_t$

24:  Find the index of abandon solutions ${\stackrel{\circ }{A}}_{t,k}=index(f(x_i))>{\mathrm{\Theta }}_t|\mathrm{\forall }andk\in \{1$

25:  Find the index of qualified solutions ${\mathbb{Q}}_{t,L}={\stackrel{\circ }{A}}_{t,k}$

26:  Calculate $\alpha ={\left|{\displaystyle \frac{f\left(x_t^{best}\right)}{{\sigma }_t\times \omega }}\right|}^{\phi }$

27:  for $i=1tosize({\stackrel{\circ }{A}}_{t,k})$, then

28:        $\mathrm{\Delta }X=\sqrt{{\displaystyle \frac{{\sum }_{j=1}^m{\left(x_j-x_i\right)}^2}{m}}}$ where $m\in {\mathbb{Q}}_{t,K}$

29:       if $\alpha >0.5,$then

30:          $x_i=Sum(x_{new}\oplus \mathrm{\Delta }X)$

31:       else

32:          $x_i=Carry(x_{new}\oplus \mathrm{\Delta }X)$

33:       end if

34:  end for

35:   $Fitness\mathrm{\_}{x}_{best}=\mathrm{m}\mathrm{i}\mathrm{n}\left(f\left(x_i\right)\right)$

36:   $x_{best}=index\left(Fitness\mathrm{\_}{x}_{best}\right)$

37: end while