Table 3.
Comparison between BSO variants on 10-D problems.
| BFs | BSO | GBSO | ADMBSO | GDBSO | COGBSO | |
|---|---|---|---|---|---|---|
| F1 | Mean | 2.17E-22 | 1.69E−22 | 7.27E−38 | 3.13E−39 | 1.57E−67 |
| Std | 8.50E−23 | 7.54E−23 | 1.45E−37 | 5.81E−39 | 2.37E−67 | |
| Min | 5.16E−23 | 5.57E−23 | 8.41E−40 | 5.56E−41 | 3.34E−69 | |
| Max | 3.76E−22 | 3.76E−22 | 5.55E−37 | 2.06E−38 | 8.80E−67 | |
| F2 | Mean | 1.84E+04 | 2.49E−18 | 5.00E−33 | 5.06E−31 | 3.86E−55 |
| Std | 2.24E+04 | 1.30E−18 | 1.19E−32 | 1.22E−30 | 1.18E−54 | |
| Min | 8.99E+01 | 1.16E−18 | 2.14E−35 | 4.83E−35 | 6.71E−58 | |
| Max | 8.62E+04 | 5.12E−18 | 4.67E−32 | 4.48E−30 | 4.64E−54 | |
| F3 | Mean | 2.35E+02 | 1.31E−16 | 2.10E−27 | 7.15E−24 | 2.30E−42 |
| Std | 2.38E+02 | 4.35E−17 | 3.81E−27 | 2.63E−23 | 8.70E−42 | |
| Min | 1.38E−01 | 5.39E−17 | 2.55E−29 | 5.90E−28 | 3.16E−47 | |
| Max | 7.00E+02 | 2.14E−16 | 1.36E−26 | 1.02E−22 | 3.38E−41 | |
| F4 | Mean | 1.13E+03 | 3.18E−20 | 1.71E−36 | 5.34E−38 | 3.37E−66 |
| Std | 8.45E+02 | 2.13E−20 | 1.93E−36 | 5.12E−38 | 6.91E−66 | |
| Min | 2.30E+02 | 1.05E−20 | 1.38E−38 | 3.71E−39 | 9.80E−69 | |
| Max | 3.42E+03 | 8.76E−20 | 7.38E−36 | 1.73E−37 | 2.69E−65 | |
| F5 | Mean | 8.65E−05 | 7.01E−14 | 5.55E−26 | 3.49E−25 | 4.99E−38 |
| Std | 6.80E−05 | 3.97E−14 | 9.69E−26 | 7.51E−25 | 7.29E−38 | |
| Min | 1.03E−06 | 2.14E−14 | 1.28E−29 | 1.89E−28 | 9.06E−40 | |
| Max | 2.27E−04 | 1.52E−13 | 3.53E−25 | 2.68E−24 | 2.22E−37 | |
| F6 | Mean | 6.19E+00 | 5.38E+00 | 4.69E−08 | 5.57E−09 | 6.17E−10 |
| Std | 1.07E+00 | 1.95E+00 | 5.34E−08 | 6.41E−09 | 4.60E−10 | |
| Min | 3.91E+00 | 2.00E−09 | 1.16E−10 | 6.36E−10 | 1.50E−10 | |
| Max | 8.22E+00 | 7.39E+00 | 1.43E−07 | 1.96E−08 | 1.08E−09 | |
| F7 | Mean | 1.88E−11 | 1.55E−11 | 2.93E−15 | 2.93E−15 | 1.87E−15 |
| Std | 3.56E−12 | 3.20E−12 | 6.88E−16 | 6.88E−16 | 1.38E−15 | |
| Min | 1.36E−11 | 7.65E−12 | 4.44E−16 | 4.44E−16 | 4.44E−16 | |
| Max | 2.50E−11 | 1.92E−11 | 3.11E−15 | 3.11E−15 | 3.11E−15 | |
| F8 | Mean | 2.97E−03 | 3.71E−12 | 5.71E−09 | 1.68E−11 | 6.05E−18 |
| Std | 2.39E−03 | 8.06E−13 | 2.11E−08 | 4.10E−11 | 1.61E−17 | |
| Min | 3.79E−12 | 2.50E−12 | 4.48E−15 | 2.91E−15 | 1.25E−33 | |
| Max | 7.31E−03 | 5.31E−12 | 8.18E−08 | 1.26E−10 | 5.15E−17 | |
| F9 | Mean | 4.30E+00 | 1.13E−01 | 1.38E−01 | 3.41E−01 | 5.64E−02 |
| Std | 1.86E+00 | 7.84E−02 | 1.38E−01 | 1.27E−01 | 3.48E−02 | |
| Min | 2.57E+00 | 2.95E−02 | 1.48E−02 | 4.94E−02 | 9.86E−03 | |
| Max | 7.70E+00 | 2.61E−01 | 4.85E−01 | 5.26E−01 | 1.21E−01 | |
| F10 | Mean | 5.97E+00 | 4.78E+00 | 1.03E+01 | 2.14E+01 | 4.31E+00 |
| Std | 1.88E+00 | 1.20E+00 | 6.45E+00 | 6.93E+00 | 2.15E+00 | |
| Min | 2.98E+00 | 2.98E+00 | 1.99E+00 | 4.98E+00 | 9.95E−01 | |
| Max | 8.95E+00 | 7.96E+00 | 2.39E+01 | 3.04E+01 | 6.96E+00 | |
| F11 | Mean | 3.57E+01 | 3.30E−11 | 6.36E−12 | 5.37E−12 | 3.37E−23 |
| Std | 6.13E+01 | 9.03E−12 | 1.75E−11 | 1.99E−11 | 7.75E−23 | |
| Min | 3.65E−11 | 1.23E−11 | 1.12E−16 | 2.51E−16 | 1.33E−33 | |
| Max | 1.52E+02 | 4.60E−11 | 6.42E−11 | 7.72E−11 | 2.97E−22 | |
| F12 | Mean | 9.14E−12 | 7.51E−12 | 8.95E−15 | 1.88E−15 | 3.76E−23 |
| Std | 1.72E−12 | 1.09E−12 | 5.57E−15 | 1.67E−15 | 3.76E−23 | |
| Min | 6.09E−12 | 5.45E−12 | 1.42E−15 | 2.60E−16 | 4.06E−24 | |
| Max | 1.18E−11 | 9.12E−12 | 2.03E−14 | 6.39E−15 | 1.46E−22 | |
| F13 | Mean | 1.45E−110 | 4.33E−111 | 3.71E−157 | 4.73E−168 | 1.48E−267 |
| Std | 1.75E−110 | 6.41E−111 | 0.00E+00 | 0.00E+00 | 0.00E+00 | |
| Min | 1.12E−111 | 1.18E−113 | 3.64E−169 | 1.21E−178 | 2.43E−283 | |
| Max | 6.72E−110 | 2.43E−110 | 3.23E−156 | 6.47E−167 | 1.11E−266 | |
| F14 | Mean | 4.06E−11 | 3.12E−11 | 1.32E−17 | 3.74E−18 | 3.71E−25 |
| Std | 5.91E−12 | 5.16E−12 | 1.06E−17 | 3.92E−18 | 4.45E−25 | |
| Min | 3.17E−11 | 2.53E−11 | 1.27E−18 | 4.24E−19 | 1.89E−26 | |
| Max | 5.05E−11 | 4.45E−11 | 4.10E−17 | 1.47E−17 | 1.67E−24 | |
| F15 | Mean | 1.17E−11 | 9.62E−22 | 0.00E+00 | 0.00E+00 | 0.00E+00 |
| Std | 4.55E−11 | 2.18E−22 | 0.00E+00 | 0.00E+00 | 0.00E+00 | |
| Min | 1.01E−21 | 5.95E−22 | 0.00E+00 | 0.00E+00 | 0.00E+00 | |
| Max | 1.76E−10 | 1.36E−21 | 0.00E+00 | 0.00E+00 | 0.00E+00 | |
Optimal mean values are in bold.