Table 8 The p-Values of the Wilcoxon rank-sum test over 23 benchmark functions.

From: Enhancing grasshopper optimization algorithm (GOA) with levy flight for engineering applications

F

AHA

AO

DA

DMOA

GBO

HGS

HHO

MVO

F1

1.33E-29

1.12E-30

1.10E-03

1.36E-04

4.92E-04

1.66E-27

3.81E-29

1.07E-02

F2

9.55E-05

2.89E-01

1.72E-34

2.39E-31

3.18E-01

1.65E-01

5.83E-04

5.94E-34

F3

3.71E-26

2.20E-29

9.50E-09

1.83E-34

1.52E-14

1.24E-23

4.49E-19

3.11E-07

F4

2.00E-30

5.28E-31

9.68E-01

4.04E-11

2.07E-34

8.90E-30

8.74E-27

1.83E-01

F5

5.63E-15

1.06E-28

6.79E-29

2.17E-34

4.57E-09

8.19E-15

6.66E-21

5.05E-31

F6

3.07E-34

1.76E-32

3.17E-12

6.34E-01

3.17E-08

1.93E-26

1.01E-28

8.20E-03

F7

1.14E-02

1.30E-03

9.41E-35

8.51E-35

4.41E-23

3.21E-31

7.59E-30

2.60E-34

F8

7.48E-39

1.34E-36

7.30E-39

8.07E-39

8.08E-39

7.95E-39

8.06E-39

4.71E-39

F9

2.15E-05

9.75E-01

1.01E-36

2.79E-38

4.14E-31

4.55E-01

2.44E-05

1.15E-36

F10

2.62E-23

9.46E-27

6.68E-09

9.96E-18

3.73E-11

4.66E-23

7.46E-24

1.71E-28

F11

1.53E-29

7.68E-33

9.95E-04

1.68E-01

2.57E-34

7.94E-28

3.83E-27

2.63E-01

F12

1.85E-04

7.78E-35

3.61E-13

3.93E-16

3.70E-03

5.03E-32

5.03E-32

5.71E-16

F13

1.76E-34

2.18E-33

2.72E-13

2.11E-23

4.80E-09

3.18E-24

1.97E-27

9.16E-15

F14

1.56E-16

2.73E-01

1.34E-01

1.29E-05

5.18E-26

4.46E-32

8.75E-29

2.08E-28

F15

1.27E-24

2.31E-04

9.33E-10

7.59E-14

9.82E-04

2.00E-19

7.58E-29

7.45E-12

F16

3.80E-19

7.14E-33

4.09E-27

3.11E-29

2.82E-33

2.05E-30

5.70E-28

8.30E-08

F17

5.99E-12

6.12E-08

9.03E-01

1.05E-24

1.52E-20

9.27E-26

2.03E-21

7.26E-01

F18

3.38E-11

3.17E-41

3.94E-02

1.19E-25

7.84E-36

4.45E-26

1.09E-26

2.20E-03

F19

7.38E-39

1.21E-40

4.98E-39

7.74E-39

8.06E-39

8.09E-39

8.10E-39

7.54E-39

F20

1.77E-35

5.95E-37

1.26E-35

1.82E-35

1.88E-35

1.89E-35

1.89E-35

1.78E-35

F21

3.67E-22

3.59E-36

4.94E-06

3.29E-17

2.56E-31

1.25E-25

3.58E-20

6.52E-23

F22

6.72E-26

3.38E-38

6.45E-16

2.06E-29

9.21E-25

6.63E-34

6.22E-26

7.86E-16

F23

1.59E-22

2.73E-38

1.48E-12

8.93E-33

9.58E-25

6.51E-33

2.71E-28

4.35E-14