Table 2.
The experimental results from different algorithms.
| Function | Metric | GDSAO | SAO | MSAO | DESAO | MPA | EO | CMA-ES | jSO |
|---|---|---|---|---|---|---|---|---|---|
| F1 | Mean | 2.23E+00 | 3.90E+03 | 2.89E+00 | 6.30E+01 | 5.99E+01 | 4.91E+03 | 2.24E+05 | 0.00E+00 |
| Std | 4.82E+02 | 4.73E+03 | 2.62E+00 | 6.65E+01 | 6.25E+01 | 5.45E+03 | 1.94E+05 | 0.00E+00 | |
| F2 | Mean | 0.00E+00 | 6.44E+00 | 2.46E−12 | 1.05E+09 | 1.05E+09 | 1.40E+08 | 4.58E+31 | 0.00E+00 |
| Std | 3.82E+06 | 1.56E+01 | 7.29E+16 | 3.41E+09 | 3.46E+09 | 2.10E+08 | 7.19E+31 | 0.00E+00 | |
| F3 | Mean | 0.00E+00 | 4.09E+04 | 3.18E+04 | 6.06E+04 | 5.97E+04 | 7.11E+02 | 3.59E+05 | 5.94E−14 |
| Std | 2.66E+03 | 9.51E+03 | 9.89E+03 | 1.01E+04 | 1.07E+04 | 9.53E+02 | 4.73E+04 | 0.00E+00 | |
| F4 | Mean | 2.00E−01 | 8.18E+01 | 6.41E+01 | 8.97E+01 | 8.54E+01 | 8.81E+01 | 2.33E+01 | 6.86E+01 |
| Std | 1.21E+01 | 9.25E+00 | 3.90E+01 | 1.99E+01 | 1.65E+01 | 2.25E+01 | 8.98E−01 | 0.00E+00 | |
| F5 | Mean | 4.90E+00 | 4.75E+01 | 8.22E+01 | 5.35E+01 | 5.17E+01 | 6.52E+01 | 2.49E+02 | 2.44E+01 |
| Std | 2.81E+01 | 1.48E+01 | 6.55E+01 | 1.57E+01 | 1.22E+01 | 1.89E+01 | 1.52E+01 | 0.00E+00 | |
| F6 | Mean | 0.00E+00 | 3.57E−03 | 3.72E−04 | 5.72E−02 | 6.15E−02 | 3.40E−03 | 0.00E+00 | 3.25E−06 |
| Std | 7.39E−08 | 7.75E−03 | 1.56E−03 | 1.14E−01 | 1.50E−01 | 8.40E−03 | 0.00E+00 | 3.82E−06 | |
| F7 | Mean | 5.36E+01 | 7.47E+01 | 1.89E+02 | 6.74E+01 | 7.17E+01 | 9.26E+01 | 2.54E+02 | 4.32E+01 |
| Std | 2.31E+01 | 1.43E+01 | 5.37E+01 | 5.67E+00 | 6.13E+00 | 3.13E+01 | 1.17E+01 | 8.82E−01 | |
| F8 | Mean | 2.62E+01 | 4.98E+01 | 8.01E+01 | 4.81E+01 | 3.84E+01 | 6.31E+01 | 1.56E+02 | 6.45E+00 |
| Std | 7.81E+01 | 1.82E+01 | 5.84E+01 | 1.29E+01 | 1.28E+01 | 1.53E+01 | 4.54E+00 | 7.62E−01 | |
| F9 | Mean | 0.00E+00 | 7.46E+00 | 2.77E+00 | 2.70E+00 | 3.09E+00 | 2.26E+01 | 0.00E+00 | 0.00E+00 |
| Std | 9.03E−01 | 1.25E+01 | 4.60E+00 | 4.39E+00 | 4.55E+00 | 4.60E+01 | 0.00E+00 | 0.00E+00 | |
| F10 | Mean | 2.29E+02 | 3.00E+03 | 7.35E+03 | 2.68E+03 | 2.76E+03 | 3.76E+03 | 7.48E+03 | 2.85E+03 |
| Std | 1.66E+03 | 6.43E+02 | 8.82E+02 | 5.14E+02 | 4.53E+02 | 5.72E+02 | 2.97E+02 | 2.44E+02 | |
| F11 | Mean | 3.88E+01 | 4.68E+01 | 3.44E+01 | 4.48E+01 | 4.21E+01 | 5.69E+01 | 2.51E+03 | 2.04E+01 |
| Std | 4.14E+01 | 3.59E+01 | 4.06E+01 | 3.26E+01 | 3.63E+01 | 3.47E+01 | 9.03E+02 | 7.56E−01 | |
| F12 | Mean | 1.65E+04 | 6.88E+04 | 6.82E+04 | 3.15E+04 | 3.01E+04 | 7.68E+04 | 2.13E+07 | 1.45E+03 |
| Std | 1.86E+04 | 3.64E+04 | 5.97E+04 | 9.04E+03 | 8.57E+03 | 5.54E+04 | 8.01E+06 | 3.93E+02 | |
| F13 | Mean | 3.21E+02 | 9.26E+03 | 1.56E+04 | 2.45E+04 | 2.54E+04 | 2.23E+04 | 4.85E+06 | 3.29E+02 |
| Std | 2.18E+03 | 1.09E+04 | 9.31E+03 | 2.37E+04 | 2.13E+04 | 2.77E+04 | 4.12E+06 | 5.87E+00 | |
| F14 | Mean | 6.27E+02 | 1.87E+04 | 2.57E+02 | 1.21E+02 | 1.97E+02 | 8.90E+03 | 2.12E+05 | 2.55E+01 |
| Std | 5.32E+02 | 1.43E+04 | 6.10E+01 | 2.39E+01 | 3.18E+01 | 6.61E+03 | 2.71E+05 | 1.66E+00 | |
| F15 | Mean | 5.21E+02 | 3.92E+03 | 4.96E+02 | 2.49E+03 | 1.78E+03 | 4.43E+03 | 2.58E+06 | 2.02E+01 |
| Std | 1.49E+03 | 3.29E+03 | 6.09E+02 | 1.92E+03 | 2.13E+03 | 3.75E+03 | 1.98E+06 | 1.72E+01 | |
| F16 | Mean | 5.54E+01 | 7.42E+02 | 5.25E+02 | 8.34E+02 | 8.33E+02 | 7.14E+02 | 1.55E+03 | 3.27E+02 |
| Std | 4.71E+02 | 2.92E+02 | 4.08E+02 | 2.48E+02 | 2.42E+02 | 2.44E+02 | 1.85E+02 | 1.90E+02 | |
| F17 | Mean | 3.19E+01 | 2.65E+02 | 1.91E+02 | 3.18E+02 | 2.44E+02 | 2.73E+02 | 5.93E+02 | 5.54E+01 |
| Std | 2.43E+02 | 1.69E+02 | 7.20E+01 | 2.42E+02 | 2.14E+02 | 2.44E+02 | 2.86E+02 | 4.10E+00 | |
| F18 | Mean | 9.27E+03 | 1.82E+05 | 3.67E+05 | 7.00E+04 | 7.03E+04 | 1.62E+05 | 3.80E+06 | 2.96E+01 |
| Std | 1.45E+04 | 6.04E+04 | 3.79E+05 | 6.96E+04 | 6.85E+04 | 8.45E+04 | 3.53E+06 | 3.14E+00 | |
| F19 | Mean | 9.99E+01 | 3.79E+03 | 2.03E+03 | 2.94E+03 | 2.96E+03 | 4.29E+03 | 2.87E+06 | 2.46E+01 |
| Std | 9.92E+01 | 3.81E+03 | 2.76E+03 | 2.27E+03 | 2.49E+03 | 5.30E+03 | 1.61E+06 | 3.75E+00 | |
| F20 | Mean | 1.90E+01 | 2.54E+02 | 2.28E+02 | 3.17E+02 | 2.89E+02 | 3.66E+02 | 6.32E+02 | 9.39E+01 |
| Std | 2.76E+02 | 2.11E+02 | 1.39E+02 | 1.89E+02 | 2.04E+02 | 2.12E+02 | 1.78E+02 | 7.59E+01 | |
| F21 | Mean | 2.71E+02 | 2.94E+02 | 2.60E+02 | 3.14E+02 | 3.17E+02 | 3.36E+02 | 3.75E+02 | 1.67E+02 |
| Std | 7.71E+01 | 1.73E+01 | 5.55E+01 | 1.41E+01 | 2.00E+01 | 2.49E+01 | 7.46E+00 | 4.81E−01 | |
| F22 | Mean | 1.93E+02 | 1.13E+02 | 1.59E+03 | 1.94E+02 | 1.35E+02 | 6.43E+02 | 8.03E+03 | 1.61E+02 |
| Std | 2.16E+02 | 1.66E+00 | 3.88E+03 | 1.78E−11 | 1.45E−11 | 1.62E+03 | 3.67E+02 | 0.00E+00 | |
| F23 | Mean | 3.98E+02 | 4.48E+02 | 4.13E+02 | 4.51E+02 | 4.04E+02 | 4.30E+02 | 5.54E+02 | 3.64E+02 |
| Std | 2.01E+01 | 2.02E+01 | 4.74E+01 | 7.40E+00 | 7.91E+00 | 2.77E+01 | 1.78E+01 | 4.61E+00 | |
| F24 | Mean | 3.45E+02 | 5.46E+02 | 5.87E+02 | 5.72E+02 | 5.27E+02 | 5.22E+02 | 5.92E+02 | 5.33E+02 |
| Std | 4.76E+01 | 2.77E+01 | 6.72E+01 | 2.27E+01 | 2.61E+01 | 2.57E+01 | 7.15E+01 | 1.89E+01 | |
| F25 | Mean | 4.26E+02 | 4.14E+02 | 4.74E+02 | 4.82E+02 | 4.82E+02 | 4.36E+02 | 3.99E+02 | 4.12E+02 |
| Std | 5.89E−01 | 2.82E+00 | 2.39E+00 | 2.22E+00 | 1.96E+00 | 1.90E+01 | 3.22E−01 | 5.74E−02 | |
| F26 | Mean | 2.16E+02 | 2.53E+03 | 2.05E+03 | 1.62E+03 | 2.04E+03 | 2.56E+03 | 2.78E+03 | 2.03E+03 |
| Std | 1.05E+02 | 2.02E+02 | 8.19E+01 | 6.02E+02 | 6.31E+02 | 2.51E+02 | 1.66E+02 | 3.03E+02 | |
| F27 | Mean | 3.92E+02 | 6.14E+02 | 5.32E+02 | 5.49E+02 | 5.65E+02 | 6.12E+02 | 5.08E+02 | 5.55E+02 |
| Std | 1.77E+01 | 7.37E+00 | 2.46E−05 | 1.73E+01 | 1.72E+01 | 1.90E+01 | 4.31E−05 | 6.33E−01 | |
| F28 | Mean | 4.24E+02 | 4.75E+02 | 5.83E+02 | 4.13E+02 | 4.77E+02 | 4.15E+02 | 5.19E+02 | 3.74E+02 |
| Std | 6.14E+01 | 6.50E+01 | 1.77E−05 | 6.08E+01 | 5.72E+01 | 4.71E+01 | 6.49E−05 | 8.99E+01 | |
| F29 | Mean | 5.13E+02 | 7.21E+02 | 5.94E+02 | 6.82E+02 | 7.22E+02 | 7.01E+02 | 2.40E+03 | 3.04E+02 |
| Std | 2.51E+02 | 2.41E+02 | 8.79E+01 | 1.47E+02 | 1.74E+02 | 1.62E+02 | 2.63E+02 | 5.02E+01 | |
| F30 | Mean | 2.83E+03 | 5.67E+03 | 4.72E+03 | 6.01E+03 | 5.51E+03 | 6.42E+03 | 3.12E+06 | 2.82E+03 |
| Std | 3.51E+02 | 2.62E+03 | 3.35E+03 | 3.68E+03 | 4.33E+03 | 3.05E+03 | 2.01E+06 | 2.71E+02 | |
| Friedman | Ranking | 2.0667 | 5.1333 | 4.4333 | 4.9000 | 4.8000 | 5.8000 | 6.9333 | 1.9333 |
Significant values are in bold.