Table 6.
The results of the Wilcoxon rank-sum test were obtained by algorithms on 23 benchmark functions.
| Function | ESMA vs. | ||||||
|---|---|---|---|---|---|---|---|
| SMA | ROA | AOA | AO | SSA | WOA | SCA | |
| F1 | 3.51 × 10−01 | 3.97 × 10−02 | 6.87 × 10−07 | 6.87 × 10−07 | 6.87 × 10−07 | 6.87 × 10−07 | 6.87 × 10−07 |
| F2 | 2.33 × 10−05 | 3.39 × 10−06 | 3.39 × 10−06 | 3.39 × 10−06 | 3.39 × 10−06 | 3.39 × 10−06 | 3.39 × 10−06 |
| F3 | 1.64 × 10−01 | 6.87 × 10−07 | 6.87 × 10−07 | 6.87 × 10−07 | 6.87 × 10−07 | 6.87 × 10−07 | 6.87 × 10−07 |
| F4 | 1.92 × 10−05 | 3.36 × 10−06 | 3.36 × 10−06 | 3.36 × 10−06 | 3.36 × 10−06 | 3.36 × 10−06 | 3.36 × 10−06 |
| F5 | 3.39 × 10−06 | 3.39 × 10−06 | 3.39 × 10−06 | 2.15 × 10−03 | 3.39 × 10−06 | 3.39 × 10−06 | 3.39 × 10−06 |
| F6 | 3.39 × 10−06 | 3.39 × 10−06 | 3.39 × 10−06 | 3.39 × 10−06 | 2.23 × 10−04 | 3.39 × 10−06 | 3.39 × 10−06 |
| F7 | 2.02 × 10−02 | 1.98 × 10−01 | 4.81 × 10−01 | 1.46 × 10−01 | 3.39 × 10−06 | 3.39 × 10−06 | 3.39 × 10−06 |
| F8 | 5.05 × 10−06 | 4.02 × 10−05 | 3.39 × 10−06 | 3.39 × 10−06 | 3.39 × 10−06 | 3.39 × 10−06 | 3.39 × 10−06 |
| F9 | NaN | NaN | 2.54 × 10−06 | NaN | 6.87 × 10−07 | 1.64 × 10−02 | 6.87 × 10−07 |
| F10 | NaN | NaN | 6.87 × 10−07 | NaN | 6.87 × 10−07 | 2.10 × 10−04 | 6.87 × 10−07 |
| F11 | NaN | NaN | 6.87 × 10−07 | NaN | 6.87 × 10−07 | 1.64 × 10−01 | 6.87 × 10−07 |
| F12 | 5.74 × 10−05 | 3.39 × 10−06 | 3.39 × 10−06 | 2.79 × 10−02 | 3.39 × 10−06 | 3.39 × 10−06 | 3.39 × 10−06 |
| F13 | 3.39 × 10−06 | 3.39 × 10−06 | 3.39 × 10−06 | 5.74 × 10−05 | 3.39 × 10−06 | 3.39 × 10−06 | 3.39 × 10−06 |
| F14 | 2.19 × 10−06 | 2.19 × 10−06 | 2.18 × 10−06 | 2.19 × 10−06 | 1.23 × 10−03 | 2.19 × 10−06 | 2.19 × 10−06 |
| F15 | 7.72 × 10−01 | 1.99 × 10−01 | 1.25 × 10−01 | 4.64 × 10−02 | 1.28 × 10−02 | 5.90 × 10−01 | 1.89 × 10−04 |
| F16 | 3.37 × 10−06 | 3.37 × 10−06 | 3.37 × 10−06 | 3.37 × 10−06 | 7.72 × 10−04 | 3.37 × 10−06 | 3.37 × 10−06 |
| F17 | 3.37 × 10−06 | 3.37 × 10−06 | 3.37 × 10−06 | 3.37 × 10−06 | 2.41 × 10−04 | 3.37 × 10−06 | 3.37 × 10−06 |
| F18 | 1.35 × 10−01 | 7.72 × 10−01 | 5.07 × 10−01 | 7.72 × 10−01 | 3.69 × 10−03 | 7.72 × 10−01 | 7.72 × 10−01 |
| F19 | 3.39 × 10−06 | 3.39 × 10−06 | 3.39 × 10−06 | 3.39 × 10−06 | 2.79 × 10−05 | 3.39 × 10−06 | 3.39 × 10−06 |
| F20 | 3.69 × 10−03 | 3.69 × 10−03 | 3.10 × 10−02 | 3.69 × 10−03 | 5.45 × 10−03 | 8.97 × 10−03 | 3.39 × 10−06 |
| F21 | 3.39 × 10−06 | 3.39 × 10−06 | 3.39 × 10−06 | 3.39 × 10−06 | 3.62 × 10−01 | 3.39 × 10−06 | 3.39 × 10−06 |
| F22 | 3.39 × 10−06 | 3.39 × 10−06 | 3.39 × 10−06 | 3.39 × 10−06 | 5.45 × 10−03 | 3.39 × 10−06 | 3.39 × 10−06 |
| F23 | 3.39 × 10−06 | 3.39 × 10−06 | 3.39 × 10−06 | 3.39 × 10−06 | 5.45 × 10−03 | 3.39 × 10−06 | 3.39 × 10−06 |