Table 4.
Comparison between BSO variants on 20-D problems.
| BFs | BSO | GBSO | ADMBSO | GDBSO | COGBSO | |
|---|---|---|---|---|---|---|
| F1 | Mean | 3.31E−43 | 1.56E−43 | 2.89E−50 | 9.73E−51 | 8.07E−66 |
| Std | 9.04E−44 | 3.34E−44 | 3.69E−50 | 3.49E−50 | 1.87E−65 | |
| Min | 1.95E−43 | 1.09E−43 | 2.73E−52 | 1.36E−54 | 8.53E−69 | |
| Max | 5.15E−43 | 2.20E−43 | 1.30E−49 | 1.36E−49 | 7.12E−65 | |
| F2 | Mean | 9.36E+04 | 2.07E−39 | 7.98E−45 | 2.59E−45 | 1.10E−64 |
| Std | 4.97E+04 | 1.06E−39 | 1.27E−44 | 2.82E−45 | 1.88E−64 | |
| Min | 2.53E+04 | 8.94E−40 | 2.47E−46 | 8.16E−48 | 1.61E−67 | |
| Max | 2.14E+05 | 4.80E−39 | 3.99E−44 | 8.36E−45 | 6.33E−64 | |
| F3 | Mean | 4.08E+02 | 6.64E−34 | 5.39E−34 | 1.91E−32 | 3.11E−55 |
| Std | 5.66E+02 | 2.08E−33 | 1.53E−33 | 5.19E−32 | 7.43E−55 | |
| Min | 3.76E+00 | 1.74E−37 | 6.39E−36 | 2.56E−37 | 4.17E−59 | |
| Max | 2.05E+03 | 8.09E−33 | 6.02E−33 | 1.98E−31 | 2.19E−54 | |
| F4 | Mean | 5.28E+02 | 1.44E−41 | 2.11E−49 | 3.71E−51 | 3.48E−66 |
| Std | 3.13E+02 | 1.14E−41 | 3.16E−49 | 5.93E−51 | 8.20E−66 | |
| Min | 3.20E+01 | 1.58E−42 | 3.25E−52 | 9.64E−54 | 1.16E−69 | |
| Max | 1.03E+03 | 3.74E−41 | 1.22E−48 | 2.28E−50 | 3.23E−65 | |
| F5 | Mean | 1.41E−03 | 1.28E−24 | 5.37E−37 | 1.98E−38 | 2.09E−49 |
| Std | 4.97E−04 | 5.74E−25 | 1.75E−36 | 4.26E−38 | 3.46E−49 | |
| Min | 6.07E−04 | 4.20E−25 | 9.23E−41 | 1.90E−43 | 2.18E−52 | |
| Max | 2.51E−03 | 2.34E−24 | 6.85E−36 | 1.43E−37 | 1.00E−48 | |
| F6 | Mean | 1.77E+01 | 1.67E+01 | 2.66E−01 | 2.41E−07 | 5.43E−08 |
| Std | 9.01E−01 | 4.70E+00 | 1.03E+00 | 3.52E−07 | 2.15E−08 | |
| Min | 1.60E+01 | 1.31E−07 | 1.03E−07 | 4.22E−08 | 2.09E−08 | |
| Max | 1.92E+01 | 1.93E+01 | 3.99E+00 | 1.41E−06 | 8.46E−08 | |
| F7 | Mean | 3.64E−15 | 2.22E−15 | 2.46E−15 | 2.22E−15 | 2.22E−15 |
| Std | 1.80E−15 | 8.17E−31 | 9.17E−16 | 8.17E−31 | 8.17E−31 | |
| Min | 2.22E−15 | 2.22E−15 | 2.22E−15 | 2.22E−15 | 2.22E−15 | |
| Max | 5.77E−15 | 2.22E−15 | 5.77E−15 | 2.22E−15 | 2.22E−15 | |
| F8 | Mean | 6.81E−02 | 8.14E−17 | 5.71E−17 | 1.22E−16 | 1.48E−17 |
| Std | 6.97E−02 | 2.15E−16 | 1.63E−16 | 2.53E−16 | 5.73E−17 | |
| Min | 1.42E−02 | 3.63E−23 | 1.30E−21 | 2.93E−21 | 1.02E−39 | |
| Max | 2.76E−01 | 6.11E−16 | 6.11E−16 | 6.11E−16 | 2.22E−16 | |
| F9 | Mean | 2.35E−02 | 8.21E−03 | 8.54E−03 | 7.88E−03 | 1.31E−03 |
| Std | 2.27E−02 | 1.09E−02 | 6.37E−03 | 9.36E−03 | 5.09E−03 | |
| Min | 0.00E+00 | 0.00E+00 | 0.00E+00 | 0.00E+00 | 0.00E+00 | |
| Max | 7.14E−02 | 2.96E−02 | 1.97E−02 | 2.95E−02 | 1.97E−02 | |
| F10 | Mean | 1.92E+01 | 1.30E+01 | 3.10E+01 | 5.02E+01 | 1.05E+01 |
| Std | 4.40E+00 | 5.33E+00 | 2.71E+01 | 3.82E+01 | 3.94E+00 | |
| Min | 1.29E+01 | 4.97E+00 | 6.96E+00 | 5.97E+00 | 2.89E+00 | |
| Max | 2.89E+01 | 2.39E+01 | 8.95E+01 | 1.05E+02 | 1.89E+01 | |
| F11 | Mean | 2.20E+02 | 2.36E−21 | 2.33E−17 | 1.28E−17 | 3.70E−36 |
| Std | 5.76E+01 | 3.95E−22 | 4.40E−17 | 4.88E−17 | 7.08E−36 | |
| Min | 9.75E+01 | 1.82E−21 | 1.75E−19 | 4.93E−21 | 1.34E−46 | |
| Max | 3.17E+02 | 3.01E−21 | 1.52E−16 | 1.89E−16 | 2.15E−35 | |
| F12 | Mean | 1.20E−03 | 2.05E−17 | 6.05E−15 | 5.91E−16 | 2.72E−16 |
| Std | 1.46E−03 | 2.30E−17 | 6.08E−15 | 4.95E−16 | 4.11E−16 | |
| Min | 6.47E−07 | 4.08E−19 | 1.00E−15 | 5.54E−17 | 2.28E−17 | |
| Max | 4.43E−03 | 7.74E−17 | 2.24E−14 | 1.71E−15 | 1.59E−15 | |
| F13 | Mean | 3.51E−45 | 2.11E−212 | 6.03E−180 | 4.58E−192 | 1.58E−211 |
| Std | 1.36E−44 | 0.00E+00 | 0.00E+00 | 0.00E+00 | 0.00E+00 | |
| Min | 2.56E−216 | 7.00E−216 | 4.79E−198 | 1.05E−206 | 2.32E−223 | |
| Max | 5.26E−44 | 3.00E−211 | 9.04E−179 | 4.06E−191 | 2.01E−210 | |
| F14 | Mean | 2.69E−09 | 1.37E−21 | 7.89E−23 | 8.46E−24 | 8.69E−34 |
| Std | 1.04E−08 | 1.54E−22 | 5.82E−23 | 1.02E−23 | 1.55E−33 | |
| Min | 1.67E−21 | 1.17E−21 | 1.08E−23 | 7.67E−25 | 5.97E−35 | |
| Max | 4.03E−08 | 1.73E−21 | 1.94E−22 | 2.99E−23 | 6.28E−33 | |
| F15 | Mean | 5.57E−03 | 0.00E+00 | 0.00E+00 | 0.00E+00 | 1.04E−30 |
| Std | 4.88E−03 | 0.00E+00 | 0.00E+00 | 0.00E+00 | 1.12E−30 | |
| Min | 1.13E−03 | 0.00E+00 | 0.00E+00 | 0.00E+00 | 0.00E+00 | |
| Max | 1.87E−02 | 0.00E+00 | 0.00E+00 | 0.00E+00 | 4.19E−30 | |
Optimal mean values are in bold.