Page 205 - 2024-Vol20-Issue2

201 | Al-mtory, Alnahwi & Ali

55

D=5 D=5

D=10 D=10

4 D=15 4 D=15

D=20 D=20

Fitness Function Value 33 Fitness Function Value

22

11

00

-1 -1
50 100 150 200 250 300 350 400 450 500 100 200 300 400 500 600 700 800 900 1000
No. of iteration No. of Iteration

(a) (b)

Fitness Function Value 4.5 Fitness Function Value 5
4 D=5
D=10
3.5
3 4 D=15
D=20
2.5
2 3

1.5 2
1
1
0.5
0 0
50 100 150 200 250 300 350 400 450 500
No. of Iteration -1
50 100 150 200 250 300 350 400 450 500
(c) No. of Iteration

(d)

Fig. 3. curve of convergence (cost value with iteration) for different variable dimensions and different fitness function a: De
Jong’s sphere function, b: Ackley’s function, c: Griewangk’s function, and d: Rastrigin’s function

Set point Proportional = ????. ?????? T_ term P_ term Process G(s) of the proposed algorithm. With the aid of some unimodal
r(t) + + and multimodal benchmark functions, it is found that the algo-
Integral = ???? * rithm gives the best solution compared with PSO, CA, CSA,
e(t) ???0?? ?????????? ?. and SCA for the unimodal problems at any dimension for the
?. optimization variable. However, the optimum solution of the
Y(t) proposed algorithm is the best compared to other solutions
Derivative = ???? ?? ?????? + Control signal only for dimension of variable less than or equal to 20. For
???? D_ term the PID kind of close loop control systems, the proposed algo-
rithm provides a negligible amount of rise time, settling time,
Feedback and overshoot. Finally, CDOA results in a minimum fitness
function for the cantilever beam compared to PSO, GA, MVO,
Fig. 4. PID controller of a closed loop system WWO, SCA, and WOA algorithms.
- Future Works As a future work, the chaos based initializa-
tion and pitting spreading will be used instead of the random