1. Consider the following algorithm (The Arithmetic Optimization Algorithm), analyze it and then find the following:

a. their complexity function, then

b. their Asymptotic analysis functions (i.e. , , ) .

Algorithm 1 Pseudo-code of the AOA algorithm

1: Initialize the Arithmetic Optimization Algorithm parameters , .

2: Initialize the solutions positions randomly. (Solutions: i=1, ..., N.)

3: while (C Iter < M Iter) do

4: Calculate the Fitness Function (F F) for the given solutions

5: Find the best solution (Determined best so far).

6: Update the MOA value using Eq. (2).

7: Update the MOP value using Eq. (4).

8: for (i=1 to Solutions) do

9: for (j=1 to Positions) do

10: Generate a random values between [0, 1] (r1, r2, and r3)

11: if r1 >MOA then

12: Exploration phase

13: if r2 >0.5 then

14: (1) Apply the Division math operator (D ).

15: Update the ith solutions positions using the first rule in Eq. (3).

16: else

17: (2) Apply the Multiplication math operator (M ).

18: Update the ith solutions positions using the second rule in Eq. (3).

19: end if

20: else

21: Exploitation phase

22: if r3 >0.5 then

23: (1) Apply the Subtraction math operator (S ).

24: Update the ith solutions positions using the first rule in Eq. (5).

25: else

26: (2) Apply the Addition math operator (A + ).

27: Update the ith solutions positions using the second rule in Eq. (5).

28: end if

29: end if

30: end for

31: end for

32: C Iter=C Iter+1

33: end while

34: Return the best solution (x).