Table 4 Experimental results (dim = 30).
Function | Metric | MSDBO | DBO | AOA | PSO | GWO | WOA | HHO |
|---|---|---|---|---|---|---|---|---|
F1 | Best | 0 | 9.66E-172 | 9.59E-159 | 2.67E + 02 | 1.14E-29 | 1.54E-84 | 1.04E-113 |
Std | 0 | 6.85E-101 | 1.95E-21 | 3.79E + 02 | 5.72E-28 | 6.08E-72 | 4.20E-96 | |
Average | 0 | 1.25E-101 | 3.60E-22 | 7.70E + 02 | 6.35E-28 | 1.46E-72 | 7.79E-97 | |
F2 | Best | 5.81E-296 | 1.91E-81 | 0 | 1.94E + 01 | 1.37E-17 | 9.59E-61 | 1.95E-60 |
Std | 0 | 1.69E-50 | 0 | 1.02E + 01 | 8.32E-17 | 9.04E-51 | 2.19E-50 | |
Average | 7.72E-235 | 3.18E-51 | 0 | 3.50E + 01 | 1.12E-16 | 2.68E-51 | 4.92E-51 | |
F3 | Best | 0 | 9.72E-156 | 3.62E-123 | 2.45E + 03 | 1.43E-08 | 2.10E + 04 | 2.32E-104 |
Std | 0 | 1.23E-75 | 7.34E-03 | 3.41E + 03 | 7.81E-05 | 1.40E + 04 | 3.96E-73 | |
Average | 0 | 2.27E-76 | 3.88E-03 | 7.26E + 03 | 2.40E-05 | 4.54E + 04 | 9.99E-74 | |
F4 | Best | 1.28E-286 | 1.00E-82 | 1.01E-76 | 8.63E + 00 | 5.17E-08 | 6.24E-03 | 1.12E-58 |
Std | 0 | 6.81E-50 | 1.93E-02 | 2.46E + 00 | 3.92E-07 | 2.94E + 01 | 5.64E-49 | |
Average | 5.46E-245 | 1.24E-50 | 2.09E-02 | 1.31E + 01 | 6.49E-07 | 4.11E + 01 | 2.17E-49 | |
F5 | Best | 2.38E-04 | 2.54E + 01 | 2.78E + 01 | 2.68E + 04 | 2.56E + 01 | 2.67E + 01 | 2.35E-05 |
Std | 1.33E + 01 | 3.14E-01 | 2.62E-01 | 1.81E + 05 | 8.34E-01 | 5.05E-01 | 1.35E-02 | |
Average | 1.32E + 01 | 2.58E + 01 | 2.85E + 01 | 2.45E + 05 | 2.70E + 01 | 2.79E + 01 | 9.83E-03 | |
F6 | Best | 4.30E-08 | 1.35E-06 | 2.63E + 00 | 2.55E + 02 | 1.40E-04 | 1.00E-01 | 5.34E-09 |
Std | 4.34E-03 | 6.23E-02 | 2.59E-01 | 3.52E + 02 | 3.10E-01 | 2.71E-01 | 1.79E-04 | |
Average | 1.65E-03 | 1.72E-02 | 3.25E + 00 | 8.49E + 02 | 7.29E-01 | 4.01E-01 | 1.46E-04 | |
F7 | Best | 2.34E-05 | 2.74E-04 | 6.97E-06 | 4.60E-01 | 9.18E-04 | 2.16E-04 | 2.52E-06 |
Std | 2.64E-04 | 7.41E-04 | 5.32E-05 | 1.51E + 00 | 7.82E-04 | 3.43E-03 | 1.43E-04 | |
Average | 3.13E-04 | 1.30E-03 | 6.81E-05 | 2.39E + 00 | 1.91E-03 | 3.35E-03 | 1.41E-04 | |
F8 | Best | −1.26E + 04 | −1.21E + 04 | −6.37E + 03 | −4.30E + 03 | −7.52E + 03 | −1.26E + 04 | −1.26E + 04 |
Std | 3.88E + 00 | 1.61E + 03 | 5.56E + 02 | 4.69E + 02 | 6.59E + 02 | 1.61E + 03 | 3.55E + 02 | |
Average | −1.26E + 04 | −8.42E + 03 | −5.22E + 03 | −3.25E + 03 | −6.21E + 03 | −1.05E + 04 | −1.25E + 04 | |
F9 | Best | 0 | 0 | 0 | 8.17E + 01 | 5.68E-14 | 0 | 0 |
Std | 0 | 8.54E + 00 | 0 | 2.46E + 01 | 7.33E + 00 | 1.04E-14 | 0 | |
Average | 0 | 1.56E + 00 | 0 | 1.33E + 02 | 3.83E + 00 | 1.89E-15 | 0 | |
F10 | Best | 4.44E-16 | 4.44E-16 | 4.44E-16 | 7.12E + 00 | 6.44E-14 | 4.44E-16 | 4.44E-16 |
Std | 0 | 6.49E-16 | 0 | 1.32E + 00 | 1.48E-14 | 2.27E-15 | 0 | |
Average | 4.44E-16 | 5.63E-16 | 4.44E-16 | 9.14E + 00 | 9.87E-14 | 3.76E-15 | 4.44E-16 | |
F11 | Best | 0 | 0 | 4.66E-03 | 7.03E + 00 | 0 | 0 | 0 |
Std | 0 | 1.52E-02 | 1.44E-01 | 3.82E + 00 | 8.50E-03 | 7.40E-02 | 0 | |
Average | 0 | 2.78E-03 | 2.01E-01 | 1.34E + 01 | 2.87E-03 | 1.35E-02 | 0 | |
F12 | Best | 3.11E-07 | 2.10E-07 | 4.19E-01 | 5.79E + 00 | 1.87E-02 | 5.98E-03 | 4.75E-08 |
Std | 7.31E-04 | 3.38E-03 | 4.19E-02 | 4.01E + 00 | 1.68E-02 | 1.20E-02 | 1.99E-05 | |
Average | 3.14E-04 | 1.01E-03 | 5.02E-01 | 1.04E + 01 | 4.35E-02 | 2.40E-02 | 1.21E-05 | |
F13 | Best | 1.13E-06 | 4.31E-03 | 2.61E + 00 | 3.42E + 01 | 1.13E-01 | 1.23E-01 | 1.20E-08 |
Std | 2.87E-03 | 4.90E-01 | 9.00E-02 | 7.11E + 03 | 2.58E-01 | 2.65E-01 | 1.43E-04 | |
Average | 8.35E-04 | 5.92E-01 | 2.86E + 00 | 4.62E + 03 | 6.42E-01 | 5.40E-01 | 8.40E-05 | |
F14 | Best | 9.98E-01 | 9.98E-01 | 1.99E + 00 | 9.98E-01 | 9.98E-01 | 9.98E-01 | 9.98E-01 |
Std | 2.15E + 00 | 1.86E + 00 | 4.23E + 00 | 2.34E + 00 | 3.52E + 00 | 2.92E + 00 | 1.50E + 00 | |
Average | 1.45E + 00 | 1.65E + 00 | 9.13E + 00 | 3.63E + 00 | 3.25E + 00 | 2.40E + 00 | 1.49E + 00 | |
F15 | Best | 3.07E-04 | 3.08E-04 | 3.37E-04 | 5.76E-04 | 3.08E-04 | 3.08E-04 | 3.08E-04 |
Std | 1.67E-04 | 4.17E-04 | 1.45E-02 | 8.25E-03 | 6.10E-03 | 1.90E-03 | 2.84E-05 | |
Average | 3.41E-04 | 7.76E-04 | 9.39E-03 | 5.74E-03 | 2.37E-03 | 1.04E-03 | 3.34E-04 | |
F16 | Best | 3.98E-01 | 3.98E-01 | 3.99E-01 | 3.98E-01 | 3.98E-01 | 3.98E-01 | 3.98E-01 |
Std | 6.71E-06 | 0 | 1.05E-02 | 0 | 5.63E-05 | 1.02E-05 | 4.55E-05 | |
Average | 3.98E-01 | 3.98E-01 | 4.11E-01 | 3.98E-01 | 3.98E-01 | 3.98E-01 | 3.98E-01 | |
F17 | Best | −3.86E + 00 | −3.86E + 00 | −3.86E + 00 | −3.86E + 00 | −3.86E + 00 | −3.86E + 00 | −3.86E + 00 |
Std | 1.41E-01 | 1.44E-03 | 5.60E-03 | 9.03E-06 | 1.86E-03 | 6.48E-03 | 1.43E-03 | |
Average | −3.86E + 00 | −3.86E + 00 | −3.85E + 00 | −3.86E + 00 | −3.86E + 00 | −3.86E + 00 | −3.86E + 00 | |
F18 | Best | −3.32E + 00 | −3.32E + 00 | −3.15E + 00 | −3.32E + 00 | −3.32E + 00 | −3.32E + 00 | −3.32E + 00 |
Std | 2.17E-02 | 8.50E-02 | 1.17E-01 | 6.88E-02 | 8.84E-02 | 1.70E-01 | 8.25E-02 | |
Average | −3.32E + 00 | −3.25E + 00 | −3.03E + 00 | −3.26E + 00 | −3.26E + 00 | −3.22E + 00 | −3.17E + 00 | |
F19 | Best | −1.02E + 01 | −1.02E + 01 | −6.71E + 00 | −1.02E + 01 | −1.02E + 01 | −1.02E + 01 | −5.05E + 00 |
Std | 6.55E-04 | 2.55E + 00 | 1.25E + 00 | 3.37E + 00 | 1.55E + 00 | 2.52E + 00 | 3.98E-03 | |
Average | −1.02E + 01 | −6.88E + 00 | −3.71E + 00 | −5.65E + 00 | −9.64E + 00 | −8.52E + 00 | −5.05E + 00 | |
F20 | Best | −1.04E + 01 | −1.04E + 01 | −6.96E + 00 | −1.04E + 01 | −1.04E + 01 | −1.04E + 01 | −1.02E + 01 |
Std | 3.28E-04 | 2.73E + 00 | 1.54E + 00 | 3.65E + 00 | 9.70E-01 | 3.07E + 00 | 9.38E-01 | |
Average | −1.04E + 01 | −8.38E + 00 | −3.67E + 00 | −6.09E + 00 | −1.02E + 01 | −7.22E + 00 | −5.26E + 00 | |
F21 | Best | −1.05E + 01 | −1.05E + 01 | −7.56E + 00 | −1.05E + 01 | −1.05E + 01 | −1.05E + 01 | −5.13E + 00 |
Std | 5.93E-04 | 2.44E + 00 | 1.35E + 00 | 3.80E + 00 | 7.16E-04 | 2.96E + 00 | 4.98E-01 | |
Average | −1.05E + 01 | −8.98E + 00 | −3.79E + 00 | −6.66E + 00 | −1.05E + 01 | −7.00E + 00 | −5.03E + 00 |
