Table 4 Comparative analysis of the studied algorithms toward the DHGSO algorithm.

Sphere

6.12 ± 2.34

4.78 ± 1.56

2.90 ± 1.23

Ellipsoid

12.34 ± 5.67

10.56 ± 3.45

9.87 ± 4.56

Bent Cigar

9.87 ± 4.56

7.90 ± 3.12

8.45 ± 3.56

Discus

4.56 ± 1.98

3.67 ± 1.23

3.34 ± 1.12

Different Powers

11.34 ± 3.45

9.56 ± 2.67

10.12 ± 3.12

Rosenbrock

2.34 ± 1.23

1.67 ± 0.89

1.45 ± 0.67

Rosenbrock Rotated

3.45 ± 2.34

2.78 ± 1.45

2.56 ± 1.23

Elliptic

15.78 ± 7.56

12.90 ± 5.67

14.23 ± 6.12

Rastrigin

13.56 ± 6.12

10.78 ± 4.56

12.45 ± 5.34

Rastrigin Nonseparable

27.90 ± 13.56

22.67 ± 10.78

25.67 ± 12.45

Ackley

5.67 ± 3.12

4.56 ± 2.34

4.12 ± 1.90

Ackley Rotated

4.56 ± 2.45

3.89 ± 2.12

3.90 ± 1.98

Benchmark Function

DHGSO (Mean ± Std Dev)

MFO (Mean ± Std Dev)

GWO (Mean ± Std Dev)

Sphere

0.56 ± 0.89

3.45 ± 1.67

2.12 ± 1.23

Ellipsoid

6.78 ± 2.34

11.90 ± 4.56

9.01 ± 3.78

Bent Cigar

5.34 ± 2.45

8.90 ± 3.89

7.23 ± 3.12

Discus

2.12 ± 0.89

4.23 ± 1.45

3.56 ± 1.23

Different Powers

7.89 ± 2.56

10.78 ± 3.12

8.90 ± 2.78

Rosenbrock

1.01 ± 0.56

2.12 ± 1.12

1.45 ± 0.78

Rosenbrock Rotated

1.89 ± 0.98

3.12 ± 1.67

2.34 ± 1.12

Elliptic

9.78 ± 4.56

14.67 ± 6.78

11.90 ± 5.34

Rastrigin

8.90 ± 3.78

12.90 ± 5.67

10.12 ± 4.78

Rastrigin Nonseparable

19.90 ± 9.67

26.34 ± 12.12

21.56 ± 10.45

Ackley

3.34 ± 1.56

5.45 ± 2.78

4.23 ± 2.12

Ackley Rotated

3.12 ± 1.67

4.23 ± 2.34

3.56 ± 1.78