Algorithm 1. Pseudo code of SRW-PO

Input: $\mathit{f}\left(\mathit{x}\right),\mathit{L}\mathit{B},\mathit{U}\mathit{B},\mathit{N},\mathit{T}$

Output: ${\mathit{X}}_{\mathit{b}\mathit{e}\mathit{s}\mathit{t}}$, ${\mathit{f}}_{\mathit{b}\mathit{e}\mathit{s}\mathit{t}}$

1.    Initialize $X_i$, $i=1,\dots ,N,$ within $\left[LB,UB\right]$

2.    Evaluate all individuals and determine $X_{best}$

3.    Set stagnation counter $s=0$

4.    for $t=1$ to $T$ do

5.            Compute progress ratio $p$ using Equation (16)

6.            Compute elite mean $X_{elite}$ using Equation (17)

7.            for $i=1$ to $N$ do

8.                    Select a random peer $X_{peer}$

9.                    Generate the exploration candidate using Equation (18)

10.                  Generate the exploitation candidate using Equation (19)

11.                  Select the basic puma candidate using Equation (20)

12.                  Apply boundary control using Equation (26)

13.                  Update $X_i$ by greedy selection using Equation (27)

14.              end for

15.              Update $X_{best}$ and $f_{best}$

16.              Update stagnation counter $s$

17.              if $p<0.68$ or $s>0$ then

18.                  Select weak individuals

19.                  Generate random walk candidates using Equations (21)–(23)

20.                  Apply boundary control using Equation (26)

21.                  Accept improved candidates using Equation (27)

22.              end if

23.              if $p>0.18$ then

24.                  Select weak individuals

25.                  Generate spiral candidates using Equations (24) and (25)

26.                  Apply boundary control using Equation (26)

27.                  Accept improved candidates using Equation (27)

28.              end if

29.              Update $X_{best}$ and $f_{best}$

30. end for

31. return ${\mathit{X}}_{\mathit{b}\mathit{e}\mathit{s}\mathit{t}}$, ${\mathit{f}}_{\mathit{b}\mathit{e}\mathit{s}\mathit{t}}$