Table 3.
Parameter evaluations of the optimization algorithms on benchmark functions.
| F 1 | P 2 | PSO | GWO | WOA | MA | SSA | CASSA | CDLSSA | PERSSA |
|---|---|---|---|---|---|---|---|---|---|
| Uni-modal benchmark functions | |||||||||
| Best | 1.40E-10 | 4.73E-45 | 6.32E-127 | 1.82E-10 | 4.94E-299 | 0 | 0 | 0 | |
| Avg | 5.15E-09 | 7.10E-43 | 1.25E-109 | 1.12E-08 | 9.82E-40 | 7.39E-59 | 0 | 0 | |
| SD | 1.44E-08 | 1.40E-42 | 6.72E-109 | 3.06E-08 | 7.60E-48 | 4.79E-57 | 0 | 0 | |
| T | 7.00E+01 | 6.32E+01 | 2.29E+01 | 9.53E+01 | 1.98E+01 | 1.82E+01 | 4.06E+01 | 2.06E+01 | |
| Best | 6.20E-01 | 5.56E-12 | 3.58E-04 | 3.32E+01 | 2.19E-14 | 3.84E-27 | 1.51E-259 | 0 | |
| Avg | 1.54E+00 | 8.40E-10 | 1.62E+01 | 5.25E+01 | 6.93E-10 | 4.59E-13 | 2.87E-200 | 0 | |
| SD | 7.85E-01 | 1.74E-10 | 1.65E+01 | 8.05E+00 | 4.11E-09 | 3.43E-12 | 0 | 0 | |
| T | 6.74E+01 | 5.98E+01 | 2.30E+01 | 8.17E+01 | 1.99E+01 | 2.04E+01 | 4.04E+01 | 2.04E+01 | |
| Best | 1.68E+01 | 2.52E+01 | 2.62E+01 | 1.89E+00 | 2.71E-04 | 7.87E-05 | 7.04E-03 | 1.16E-09 | |
| Avg | 2.19E+02 | 2.66E+01 | 2.72E+01 | 4.78E+01 | 5.21E-02 | 3.84E-02 | 1.41E-03 | 4.45E-04 | |
| SD | 6.64E+02 | 7.68E-01 | 7.02E-01 | 4.07E+01 | 1.05E-02 | 8.05E-02 | 4.42E-03 | 8.99E-04 | |
| T | 7.18E+01 | 6.36E+01 | 2.53E+01 | 1.05E+02 | 2.20E+01 | 2.19E+01 | 4.33E+01 | 2.26E+01 | |
| Multi-modal benchmark functions | |||||||||
| Best | −9.33E+03 | −7.71E+03 | −1.26E+04 | −1.15E+04 | −1.24E+03 | −1.06E+03 | −1.91E+03 | −1.26E+04 | |
| Avg | −8.22E+03 | −6.21E+03 | −9.01E+03 | −1.08E+04 | −1.04E+03 | −9.18E+03 | −1.88E+03 | −1.23E+04 | |
| SD | 4.84E+02 | 8.06E+02 | 1.25E+03 | 3.66E+02 | 2.02E+03 | 1.68E+03 | 1.01E+02 | 9.48E+01 | |
| T | 7.26E+01 | 6.49E+01 | 2.57E+01 | 1.17E+02 | 2.22E+01 | 2.26E+01 | 4.35E+01 | 2.29E+01 | |
| Best | 2.18E-06 | 1.51E-14 | 8.88E-16 | 4.47E-07 | 8.57E-14 | 8.98E-14 | 8.88E-16 | 8.88E-16 | |
| Avg | 5.59E-01 | 2.53E-14 | 4.09E-15 | 5.84E-02 | 8.47E-16 | 1.18E-15 | 8.88E-16 | 8.88E-16 | |
| SD | 6.74E-01 | 4.39E-15 | 2.75E-15 | 6.79E-02 | 4.59E-16 | 9.90E-16 | 0 | 0 | |
| T | 7.10E+01 | 6.28E+01 | 2.39E+01 | 9.22E+01 | 2.09E+01 | 2.07E+01 | 4.10E+01 | 2.16E+01 | |
| Best | 6.28E-11 | 2.00E-06 | 5.45E-04 | 6.00E-08 | 5.62E-12 | 3.33E-13 | 4.65E-10 | 6.58E-14 | |
| Avg | 1.32E-01 | 2.52E-02 | 2.79E-02 | 5.36E-02 | 4.94E-07 | 4.13E-07 | 2.84E-06 | 3.70E-08 | |
| SD | 2.75E-01 | 1.48E-02 | 6.97E-02 | 9.09E-02 | 2.06E-06 | 1.27E-06 | 1.25E-06 | 1.52E-06 | |
| T | 9.95E+01 | 9.37E+01 | 5.13E+01 | 1.54E+02 | 4.86E+01 | 4.87E+01 | 8.85E+01 | 4.86E+01 | |
1 F is the function. 2 P is the parameter.