Table 4 The standard deviations and Std rank on nine algorithms.

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

 

Index

AHA

AO

DA

DMOA

GBO

HGS

HHO

LFGOA

MVO

 

Std.

1.69E+01

1.43E+03

2.43E+03

1.78E+03

4.95E+08

5.02E+03

7.37E+03

1.25E-08

1.89E+03

F1

Rank

2

3

6

4

9

7

8

1

5

 

Std.

2.07E-01

5.17E+00

7.58E+00

8.06E+00

3.43E+36

9.42E+08

1.88E+09

1.99E-28

1.46E+01

F2

Rank

2

3

4

5

9

7

8

1

6

 

Std.

2.13E+03

9.34E+02

4.18E+03

2.20E+03

4.74E+02

1.33E+04

9.35E+03

4.05E-09

2.27E+03

F3

Rank

4

3

7

5

2

9

8

1

6

 

Std.

8.32E-01

6.23E+00

2.22E+01

1.18E+01

3.07E+07

1.08E+01

9.66E+00

1.36E-05

1.10E+01

F4

Rank

2

3

8

7

9

5

4

1

6

 

Std.

4.20E+02

8.44E+05

6.66E+06

2.51E+06

1.36E+04

2.13E+07

1.77E+07

1.64E-03

3.96E+06

F5

Rank

2

4

7

5

3

9

8

1

6

 

Std.

1.13E+02

1.41E+03

2.99E+03

2.23E+03

6.25E+06

1.05E+04

6.55E+03

2.04E-02

1.44E+03

F6

Rank

2

3

6

5

9

8

7

1

4

 

Std.

5.96E-01

5.37E-01

1.79E+00

3.36E-01

2.56E+00

1.65E+01

1.35E+01

2.87E-01

9.85E-01

F7

Rank

4

3

6

2

7

9

8

1

5

 

Std.

1.20E+03

4.22E+02

3.82E+02

2.53E+13

4.07E+02

1.17E+03

1.96E+03

2.05E+01

2.95E+02

F8

Rank

7

5

3

9

4

6

8

1

2

 

Std.

2.44E+01

1.11E+01

3.44E+01

1.78E+01

1.12E+02

4.78E+01

4.94E+01

0.00E+00

1.58E+01

F9

Rank

5

2

6

4

9

7

8

1

3

 

Std.

1.60E+00

1.93E+00

7.42E+00

5.05E+00

1.04E+00

3.53E+00

2.94E+00

1.47E-08

4.19E+00

F10

Rank

3

4

9

8

2

6

5

1

7

 

Std.

2.63E+00

1.33E+01

2.56E+01

1.71E+01

4.95E-02

5.15E+01

4.76E+01

1.20E-06

1.82E+01

F11

Rank

3

4

7

5

2

9

8

1

6

 

Std.

3.10E+00

3.27E+06

1.24E+07

4.82E+06

6.67E+00

4.66E+07

4.23E+07

8.73E-02

1.08E+07

F12

Rank

2

4

7

5

3

9

8

1

6

 

Std.

1.48E+01

3.38E+06

1.44E+07

1.10E+07

3.70E+02

1.21E+08

9.32E+07

9.20E-03

2.26E+07

F13

Rank

2

4

6

5

3

9

8

1

7

 

Std.

1.34E+00

1.59E+00

2.25E+00

1.46E+00

2.49E+00

1.92E+00

1.05E+00

5.90E+01

2.91E+00

F14

Rank

2

4

6

3

7

5

1

9

8

 

Std.

7.43E-03

7.37E-03

2.15E-02

1.77E-03

1.87E-03

4.16E-03

3.19E-02

4.91E-03

8.15E-03

F15

Rank

6

5

8

1

2

3

9

4

7

 

Std.

1.98E-03

2.72E-02

1.25E-01

7.10E-03

2.56E-02

2.63E-02

1.12E-01

7.49E-03

1.27E-01

F16

Rank

1

6

8

2

4

5

7

3

9

 

Std.

3.62E-02

1.72E-01

9.71E-02

9.61E-02

3.65E-02

1.32E-01

7.35E-02

8.58E-01

1.44E-01

F17

Rank

1

8

5

4

2

6

3

9

7

 

Std.

4.88E-01

5.43E-01

4.64E+00

1.08E+00

5.84E+00

9.35E-01

1.49E+00

6.66E+00

3.90E+00

F18

Rank

1

2

7

4

8

3

5

9

6

 

Std.

6.50E-03

3.48E-02

2.18E-02

2.95E-02

3.10E-02

1.72E-02

7.80E-02

1.50E-04

6.82E-02

F19

Rank

2

7

4

5

6

3

9

1

8

 

Std.

1.60E-01

1.32E-01

2.23E-01

2.09E-01

1.61E-01

2.20E-01

4.77E-02

1.43E-04

3.67E-01

F20

Rank

4

3

8

6

5

7

2

1

9

 

Std.

1.73E+00

1.12E+00

3.62E+00

2.27E+00

3.96E-01

2.64E+00

5.42E-01

1.44E-03

2.71E+00

F21

Rank

5

4

9

6

2

7

3

1

8

 

Std.

2.43E+00

1.02E+00

3.31E+00

2.28E+00

1.55E+00

2.71E+00

6.57E-01

1.32E-02

5.30E-01

F22

Rank

7

4

9

6

5

8

3

1

2

 

Std.

1.64E+00

9.47E-01

3.28E+00

2.82E+00

8.53E-01

1.72E+00

6.13E-01

2.45E-03

3.39E+00

F23

Rank

5

4

8

7

3

6

2

1

9

Friedmans test

3.2174

4.0000

6.6957

4.9130

5.0000

6.6522

6.0870

2.2609

6.1739

  1. The best of the comparison results are in [bold].
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