Algorithm 1 The ISCHNOA

Input: population size N, the lower limits of variables ${\mathrm{u}}_b$, the upper limits of variables $u_l$,

the current number of iteration t = 0, and

the maximum number of iteration T

Output: the best solution

1. Initialize N nutcracker using Equation (10)

2. Identifying the optimal individual based on fitness values.

3.    While (t < T)

4.       Generate random numbers ${\sigma }_1$ and ${\sigma }_2$ between 0 and 1.

5.       If ${\sigma }_1$ < ${\sigma }_2$

6.          $\varphi$ is a random number between 0 and 1.

7.          for i = 1:N

8.             for j = i:d

9.             if $\varphi >P_{a1}$

10.                Updating ${\overrightarrow{X}}_i^{t+1}$ using Equation (11), (27) and (28).

11.             else

12.                Updating ${\overrightarrow{X}}_i^{t+1}$ using Equations (27) and (32).

13.             end if

14.          end for

15.          t = t + 1

16.       end for

17.    Else

18.       The reference point matrix is generated using Equations (15)–(17).

19.       Generate random numbers $\phi$ between 0 and 1.

20.       for i = 1:N

21.          if $\phi >P_{a2}$

22.             Updating ${\overrightarrow{X}}_i^{t+1}$ using Equations (24), (27) and (33).

23.          else

24.             Updating ${\overrightarrow{X}}_i^{t+1}$ using Equations (25), (27) and (33).

25.          end if

26.          t = t + 1

27.       end for

28.    end while