Table 8.
Comparison between different swarm intelligence algorithms on 30-D problems.
| BFs | SSA | MSWOA | MSCA | COGBSO | |
|---|---|---|---|---|---|
| F1 | Mean | 5.84E−09 | 1.13E−77 | 5.16E−74 | 5.40E−78 |
| Std | 1.03E−09 | 1.35E−77 | 2.00E−73 | 1.06E−77 | |
| Min | 4.31E−09 | 1.22E−78 | 7.04E−75 | 5.03E−80 | |
| Max | 7.57E−09 | 3.45E−77 | 7.74E−73 | 3.45E−77 | |
| F2 | Mean | 5.59E+03 | 1.02E−78 | 6.09E−76 | 3.47E−79 |
| Std | 3.07E+03 | 1.34E−78 | 2.36E−75 | 8.70E−79 | |
| Min | 1.62E+03 | 1.55E−79 | 2.03E−84 | 7.15E−83 | |
| Max | 1.07E+04 | 5.36E−78 | 9.13E−75 | 3.27E−78 | |
| F3 | Mean | 1.26E+01 | 5.61E−67 | 1.35E−58 | 2.25E−67 |
| Std | 1.78E+01 | 9.67E−67 | 5.24E−58 | 6.44E−67 | |
| Min | 6.52E−03 | 3.40E−69 | 4.27E−67 | 8.86E−72 | |
| Max | 6.16E+01 | 3.41E−66 | 2.03E−57 | 2.41E−66 | |
| F4 | Mean | 2.66E+01 | 3.73E−77 | 3.53E−75 | 3.18E−77 |
| Std | 2.03E+01 | 1.33E−77 | 1.36E−74 | 8.82E−77 | |
| Min | 9.68E+00 | 1.64E−78 | 8.74E−82 | 8.31E−80 | |
| Max | 9.09E+01 | 1.02E−76 | 5.27E−74 | 3.48E−76 | |
| F5 | Mean | 5.62E−04 | 0.00E+00 | 2.33E−54 | 2.01E−58 |
| Std | 6.51E−05 | 0.00E+00 | 9.03E−54 | 5.05E−58 | |
| Min | 4.58E−04 | 0.00E+00 | 2.39E−56 | 8.26E−62 | |
| Max | 6.74E−04 | 0.00E+00 | 3.50E−53 | 1.99E−57 | |
| F6 | Mean | 1.48E−10 | 1.07E+00 | 2.68E+01 | 6.36E−06 |
| Std | 4.13E−18 | 2.32E+00 | 7.93E−01 | 9.87E−06 | |
| Min | 1.48E−10 | 3.05E−09 | 2.58E+01 | 5.41E−07 | |
| Max | 1.48E−10 | 7.76E+00 | 2.80E+01 | 2.83E−05 | |
| F7 | Mean | 3.57E+00 | − 4.44E−16 | − 4.44E−16 | 3.35E−15 |
| Std | 1.23E−05 | 0.00E+00 | 0.00E+00 | 9.17E−16 | |
| Min | 3.57E+00 | −4.44E−16 | −4.44E−16 | 3.11E−15 | |
| Max | 3.57E+00 | −4.44E−16 | −4.44E−16 | 6.66E−15 | |
| F8 | Mean | 1.18E−04 | 9.10E−05 | 2.52E−56 | 1.11E−16 |
| Std | 1.23E−05 | 2.37E−04 | 9.69E−56 | 2.33E−16 | |
| Min | 1.00E−04 | 0.00E+00 | 3.43E−70 | 4.77E−43 | |
| Max | 1.47E−04 | 8.91E−04 | 3.75E−55 | 6.11E−16 | |
| F9 | Mean | 1.31E−08 | 0.00E+00 | 0.00E+00 | 8.21E−04 |
| Std | 3.30E−09 | 0.00E+00 | 0.00E+00 | 3.18E−03 | |
| Min | 9.17E−09 | 0.00E+00 | 0.00E+00 | 0.00E+00 | |
| Max | 2.06E−08 | 0.00E+00 | 0.00E+00 | 1.23E−02 | |
| F10 | Mean | 2.98E+01 | 1.83E+01 | 1.93E+01 | 1.70E+01 |
| Std | 4.52E−10 | 6.10E+00 | 6.84E+00 | 5.51E+00 | |
| Min | 2.98E+01 | 9.95E+00 | 1.09E+01 | 9.95E+00 | |
| Max | 2.98E+01 | 2.29E+01 | 2.79E+01 | 2.79E+01 | |
| F11 | Mean | 3.51E−04 | 1.14E−34 | 1.12E−39 | 7.95E−40 |
| Std | 3.69E−05 | 3.73E−34 | 4.31E−39 | 3.08E−39 | |
| Min | 2.88E−04 | 9.40E−35 | 7.64E−48 | 2.69E−47 | |
| Max | 4.34E−04 | 1.40E−33 | 1.67E−38 | 1.19E−38 | |
| F12 | Mean | 1.00E+00 | 4.90E−15 | 2.46E−24 | 4.67E−15 |
| Std | 2.30E−16 | 0.00E+00 | 9.52E−24 | 2.74E−15 | |
| Min | 1.00E+00 | 4.90E−15 | 4.72E−34 | 7.76E−16 | |
| Max | 1.00E+00 | 4.90E−15 | 3.69E−23 | 1.08E−14 | |
| F13 | Mean | 6.25E−55 | 0.00E+00 | 0.00E+00 | 2.33E−203 |
| Std | 7.53E−55 | 0.00E+00 | 0.00E+00 | 0.00E+00 | |
| Min | 7.62E−56 | 0.00E+00 | 0.00E+00 | 1.43E−218 | |
| Max | 2.86E−54 | 0.00E+00 | 0.00E+00 | 2.66E−202 | |
| F14 | Mean | 3.77E−04 | 1.20E−272 | 2.31E−49 | 1.83E−42 |
| Std | 4.96E−05 | 0.00E+00 | 8.95E−49 | 4.60E−42 | |
| Min | 3.12E−04 | 9.40E−273 | 7.87E−58 | 8.36E−45 | |
| Max | 4.60E−04 | 1.40E−272 | 3.47E−48 | 1.82E−41 | |
| F15 | Mean | 2.94E−12 | 1.39E+00 | 2.38E+01 | 1.54E−29 |
| Std | 8.86E−19 | 1.27E+00 | 1.12E+00 | 1.76E−29 | |
| Min | 2.94E−12 | 1.44E−02 | 2.20E+01 | 1.43E−30 | |
| Max | 2.94E−12 | 3.42E+00 | 2.62E+01 | 6.54E−29 | |
Optimal mean values are in bold.