Table 4.
Friedman ranking test for the optimization algorithms using the various benchmark functions.
| Function | F1 | F2 | F3 | F4 | F5 | F6 | F7 | F8 | F9 | F10 | F11 | F12 |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| AOA | 1 | 1 | 1 | 1 | 3 | 1 | 1 | 1 | 2 | 4 | 1 | 6 |
| AOAs | 2 | 3 | 2 | 4 | 2 | 3 | 2 | 2 | 6 | 3 | 4 | 1 |
| ATOAc | 3 | 4 | 3 | 3 | 6 | 2 | 5 | 3 | 5 | 1 | 6 | 2 |
| ATOAt | 1 | 2 | 1 | 6 | 4 | 6 | 6 | 1 | 3 | 6 | 2 | 4 |
| ATOAsc | 1 | 5 | 1 | 2 | 5 | 4 | 4 | 1 | 1 | 2 | 3 | 5 |
| ATOAcs | 1 | 1 | 1 | 5 | 1 | 5 | 3 | 1 | 4 | 5 | 5 | 3 |
| Function | F13 | F14 | F15 | F16 | F17 | F18 | F19 | F20 | F21 | F22 | F23 | F24 |
| AOA | 1 | 5 | 4 | 5 | 3 | 6 | 5 | 6 | 6 | 3 | 3 | 6 |
| AOAs | 2 | 4 | 2 | 1 | 2 | 1 | 1 | 4 | 5 | 1 | 1 | 3 |
| AOAc | 1 | 1 | 1 | 6 | 5 | 2 | 4 | 1 | 3 | 1 | 2 | 4 |
| ATOAt | 3 | 2 | 5 | 3 | 4 | 3 | 6 | 5 | 1 | 4 | 1 | 5 |
| ATOAsc | 1 | 1 | 3 | 4 | 6 | 4 | 2 | 3 | 4 | 1 | 2 | 1 |
| ATOAcs | 2 | 3 | 2 | 2 | 1 | 5 | 3 | 2 | 2 | 2 | 1 | 2 |
| Function | F25 | F26 | F27 | F28 | F29 | F30 | F31 | F32 | F33 | Final Mean | Final Rank | |
| AOA | 6 | 5 | 6 | 6 | 6 | 3 | 5 | 3 | 6 | 3.696 | 6 | |
| ATOAs | 3 | 3 | 2 | 5 | 5 | 1 | 3 | 2 | 2 | 2.636 | 2 | |
| ATOAc | 1 | 1 | 1 | 4 | 4 | 6 | 6 | 5 | 5 | 3.242 | 4 | |
| ATOAt | 5 | 4 | 5 | 1 | 3 | 4 | 2 | 4 | 3 | 3.484 | 5 | |
| ATOAsc | 2 | 1 | 4 | 2 | 1 | 5 | 4 | 6 | 4 | 2.878 | 3 | |
| ATOAcs | 4 | 2 | 3 | 3 | 2 | 2 | 1 | 1 | 1 | 2.454 | 1 |