Algorithm: Improved whale-optimization algorithm (IWOA)

Objective:

Minimize and maximize the objective function $f\left(x\right)$, $x_i=\left(x_{i1}, x_{i2}, \dots , x_{id}\right)$

Parameters:

iter-iteration number.

Maxiter-the maximum number of iteration.

I-a population pop.

p-the switch probability

1. /*Initialize a population $x_i=\left(x_{i1}, x_{i2}, \dots , x_{id}\right)$

2. WHILEiter < Maxiter

3. FORi = 1 to I  Update $\overrightarrow{A}$, $\overrightarrow{C}$, l and p

4. IFp > 0.5

5. IF$(\left|\overrightarrow{A}\right|<+1)$

6. Update the position of the current solution by Equation (14)

7. ELSE IF$(\left|\overrightarrow{A}\right|>+1)$

8. Randomly choose a search agent

9. Update the position of the current search agent by Equation (16)

10. END IF

11. ELSE IFp > 0.5

12. Update the position of the current search by Equation (15)

13. END IF

14. END FOR

15. /*Jump out of local optimum by using chaotic local search. */

16. Calculate $c{x}_i^{iter}=\frac{x_i^{iter}-x_i^{\min }}{x_i^{\max }-x_i^{\min }}$

17. Calculate the next iteration chaotic variable by Equation (16)

18. Transform $c{x}_i^{iter+1}$ for the next iteration $x_i^{iter+1}=x_i^{\min }+c{x}_i^{iter+1}\left(x_i^{\max }-x_i^{\min }\right)$

19. /*Evaluate $x_i^{iter}$ replace $x_i^{iter}$ by $x_i^{iter+1}$ if the newly generation is better. */

20. /*Find the current best solution gbest*/

21. $iter = iter + 1$

22. END WHILE