Table 6.
Comparison between different swarm intelligence algorithms on 10-D problems.
| BFs | SSA | MSWOA | MSCA | COGBSO | |
|---|---|---|---|---|---|
| F1 | Mean | 5.94E−10 | 2.39E−67 | 1.85E−51 | 1.57E−67 |
| Std | 1.81E−10 | 1.44E−67 | 5.14E−51 | 2.37E−67 | |
| Min | 3.76E−10 | 1.18E−67 | 2.67E−70 | 3.34E−69 | |
| Max | 9.73E−10 | 4.54E−67 | 1.81E−50 | 8.80E−67 | |
| F2 | Mean | 9.59E+02 | 1.07E−54 | 1.81E−50 | 3.86E−55 |
| Std | 6.80E+02 | 2.00E−54 | 6.94E−50 | 1.18E−54 | |
| Min | 1.44E+02 | 1.21E−55 | 7.93E−67 | 6.71E−58 | |
| Max | 2.37E+03 | 3.87E−54 | 2.69E−49 | 4.64E−54 | |
| F3 | Mean | 4.03E+00 | 6.59E−39 | 1.59E−40 | 2.30E−42 |
| Std | 4.87E+00 | 1.02E−39 | 6.17E−40 | 8.70E−42 | |
| Min | 3.45E−02 | 9.88E−48 | 2.56E−47 | 3.16E−47 | |
| Max | 1.80E+01 | 3.48E−37 | 2.39E−39 | 3.38E−41 | |
| F4 | Mean | 1.89E+02 | 2.77E−62 | 1.04E−53 | 3.37E−66 |
| Std | 2.30E+02 | 5.48E−62 | 2.43E−53 | 6.91E−66 | |
| Min | 9.14E+00 | 5.12E−68 | 9.56E−73 | 9.80E−69 | |
| Max | 6.87E+02 | 3.78E−61 | 9.12E−53 | 2.69E−65 | |
| F5 | Mean | 1.41E−04 | 0.00E+00 | 1.76E−28 | 4.99E−38 |
| Std | 4.33E−05 | 0.00E+00 | 4.65E−28 | 7.29E−38 | |
| Min | 7.53E−05 | 0.00E+00 | 2.92E−30 | 9.06E−40 | |
| Max | 2.55E−04 | 0.00E+00 | 1.53E−27 | 2.22E−37 | |
| F6 | Mean | 4.58E−08 | 1.20E+00 | 6.47E+00 | 6.17E−10 |
| Std | 1.04E−08 | 2.10E+00 | 3.89E−01 | 4.60E−10 | |
| Min | 4.20E−08 | 1.70E−07 | 6.15E+00 | 1.50E−10 | |
| Max | 4.60E−08 | 5.96E+00 | 7.22E+00 | 1.08E−09 | |
| F7 | Mean | 2.38E−01 | − 4.44E−16 | − 4.44E−16 | 1.87E−15 |
| Std | 2.38E−01 | − 4.44E−16 | − 4.44E−16 | 1.38E−15 | |
| Min | 5.12E−06 | − 4.44E−16 | − 4.44E−16 | 4.44E−16 | |
| Max | 3.57E+00 | − 4.44E−16 | − 4.44E−16 | 3.11E−15 | |
| F8 | Mean | 2.20E−05 | 3.87E−05 | 1.86E−28 | 6.05E−18 |
| Std | 6.21E−06 | 1.50E−04 | 7.20E−28 | 1.61E−17 | |
| Min | 1.55E−05 | 1.52E−17 | 2.91E−40 | 1.25E−33 | |
| Max | 4.22E−05 | 5.80E−04 | 2.79E−27 | 5.15E−17 | |
| F9 | Mean | 1.62E−02 | 0.00E+00 | 0.00E+00 | 5.64E−02 |
| Std | 3.87E−02 | 0.00E+00 | 0.00E+00 | 3.48E−02 | |
| Min | 1.16E−09 | 0.00E+00 | 0.00E+00 | 9.86E−03 | |
| Max | 1.35E−01 | 0.00E+00 | 0.00E+00 | 1.21E−01 | |
| F10 | Mean | 9.95E+00 | 5.62E+00 | 9.95E+00 | 4.31E+00 |
| Std | 8.50E−11 | 3.33E+00 | 9.95E+00 | 2.15E+00 | |
| Min | 9.95E+00 | 9.95E−01 | 9.95E+00 | 9.95E−01 | |
| Max | 9.95E+00 | 6.96E+00 | 9.95E+00 | 6.96E+00 | |
| F11 | Mean | 6.19E−05 | 6.41E−17 | 3.02E−11 | 3.37E−23 |
| Std | 8.24E−06 | 8.85E−17 | 1.10E−10 | 7.75E−23 | |
| Min | 4.33E−05 | 6.86E−18 | 1.39E−19 | 1.33E−33 | |
| Max | 7.46E−05 | 9.02E−17 | 4.27E−10 | 2.97E−22 | |
| F12 | Mean | 1.31E−05 | 7.20E−19 | 4.55E−18 | 3.76E−23 |
| Std | 1.67E−06 | 6.51E−19 | 1.76E−17 | 3.76E−23 | |
| Min | 9.40E−06 | 6.26E−20 | 5.56E−28 | 4.06E−24 | |
| Max | 1.48E−05 | 2.10E−13 | 6.83E−17 | 1.46E−22 | |
| F13 | Mean | 1.40E−58 | 0.00E+00 | 3.25E−229 | 1.48E−267 |
| Std | 2.25E−58 | 0.00E+00 | 0.00E+00 | 0.00E+00 | |
| Min | 8.32E−61 | 0.00E+00 | 1.36E−317 | 2.43E−283 | |
| Max | 7.85E−58 | 0.00E+00 | 4.76E−228 | 1.11E−266 | |
| F14 | Mean | 5.94E−05 | 2.94E−179 | 9.70E−28 | 3.71E−25 |
| Std | 1.13E−05 | 0.00E+00 | 3.73E−27 | 4.45E−25 | |
| Min | 3.89E−05 | 3.59E−182 | 7.51E−41 | 1.89E−26 | |
| Max | 7.54E−05 | 2.50E−178 | 1.45E−26 | 1.67E−24 | |
| F15 | Mean | 9.12E−13 | 1.10E−01 | 4.38E+00 | 0.00E+00 |
| Std | 6.16E−19 | 4.20E−01 | 1.67E+00 | 0.00E+00 | |
| Min | 9.12E−13 | 5.27E−04 | 4.72E−01 | 0.00E+00 | |
| Max | 9.12E−13 | 1.63E+00 | 6.16E+00 | 0.00E+00 | |
Optimal mean values are in bold.