Open Access
Table 3
Experimental results of high-dimensional test functions with different algorithms
| Function | Dimension | WOA | GWO | HHO | TDHHO | ||||
|---|---|---|---|---|---|---|---|---|---|
| Mean | Std | Mean | Std | Mean | Std | Mean | Std | ||
| F1 | 100 | 3.10E-71 | 1.66E-70 | 1.27E-12 | 8.19E-13 | 3.77E-95 | 1.36E-94 | 0.00E+00 | 0.00E+00 |
| 500 | 1.87E-66 | 1.02E-65 | 1.50E-03 | 4.26E-04 | 6.14E-90 | 3.34E-89 | 0.00E+00 | 0.00E+00 | |
| F2 | 100 | 2.87E-49 | 3.39E-47 | 4.44E-08 | 1.58E-08 | 6.50E-48 | 3.39E-47 | 0.00E+00 | 0.00E+00 |
| 500 | 6.98E-48 | 3.72E-47 | 1.07E-02 | 1.60E-03 | 5.67E-49 | 2.97E-48 | 0.00E+00 | 0.00E+00 | |
| F3 | 100 | 1.02E+06 | 2.85E+05 | 4.85E+02 | 5.19E+02 | 4.11E-51 | 2.45E-50 | 0.00E+00 | 0.00E+00 |
| 500 | 2.82E+07 | 8.42E+06 | 2.91E+05 | 5.82E+04 | 1.94E-37 | 1.06E-36 | 0.00E+00 | 0.00E+00 | |
| F4 | 100 | 8.22E+01 | 1.49E+01 | 9.85E-01 | 6.40E-01 | 1.11E-49 | 2.80E-49 | 0.00E+00 | 0.00E+00 |
| 500 | 8.75E+01 | 1.21E+01 | 6.53E+01 | 4.14E+00 | 2.30E-47 | 1.22E-46 | 0.00E+00 | 0.00E+00 | |
| F5 | 100 | 9.82E+01 | 1.96E-01 | 9.79E+01 | 8.18E-01 | 4.62E-02 | 6.12E-02 | 2.13E-10 | 4.34E-10 |
| 500 | 4.96E+02 | 4.42E-01 | 4.98E+02 | 4.02E-01 | 2.00E-01 | 2.11E-01 | 7.50E-09 | 2.23E-08 | |
| F6 | 100 | 4.16E+00 | 1.23E+00 | 9.93E+00 | 1.08E+00 | 5.76E-04 | 7.99E-04 | 2.70E-11 | 1.31E-10 |
| 500 | 3.26E+01 | 8.04E+00 | 9.13E+01 | 1.92E+00 | 4.90E-03 | 5.30E-03 | 2.33E-10 | 1.02E-09 | |
| F7 | 100 | 3.20E-03 | 3.00E-03 | 7.40E-03 | 3.00E-03 | 1.58E-04 | 1.33E-04 | 3.77E-04 | 3.74E-04 |
| 500 | 5.90E-03 | 5.40E-03 | 4.56E-02 | 1.08E-02 | 1.98E-04 | 2.23E-04 | 2.18E-04 | 2.23E-04 | |
| F8 | 100 | -3.55E+04 | 6.00E+03 | -1.60E+04 | 2.17E+03 | -4.19E+04 | 2.32E+02 | -4.19E+04 | 1.72E+02 |
| 500 | -1.66E+05 | 2.89E+04 | -5.41E+04 | 1.12E+04 | -2.09E+05 | 1.71E+01 | -2.09E+05 | 5.97E+02 | |
| F9 | 100 | 0.00E+00 | 0.00E+00 | 8.55E+00 | 6.55E+00 | 0.00E+00 | 0.00E+00 | 0.00E+00 | 0.00E+00 |
| 500 | 3.03E-14 | 1.66E-13 | 7.86E+01 | 3.21E+01 | 0.00E+00 | 0.00E+00 | 0.00E+00 | 0.00E+00 | |
| F10 | 100 | 4.20E-15 | 2.46E-15 | 1.29E-07 | 4.65E-08 | 8.88E-16 | 0.00E+00 | 8.88E-16 | 0.00E+00 |
| 500 | 4.20E-15 | 2.46E-15 | 2.00E-03 | 3.76E-04 | 8.88E-16 | 0.00E+00 | 8.88E-16 | 0.00E+00 | |
| F11 | 100 | 0.00E+00 | 0.00E+00 | 5.10E-03 | 1.07E-02 | 0.00E+00 | 0.00E+00 | 0.00E+00 | 0.00E+00 |
| 500 | 0.00E+00 | 0.00E+00 | 4.30E-03 | 2.24E-02 | 0.00E+00 | 0.00E+00 | 0.00E+00 | 0.00E+00 | |
| F12 | 100 | 4.58E-02 | 1.95E-02 | 3.00E-01 | 7.53E-02 | 3.35E-06 | 3.87E-06 | 2.31E-12 | 5.95E-12 |
| 500 | 1.02E-01 | 4.99E-02 | 7.50E-01 | 4.70E-02 | 1.45E-06 | 2.24E-06 | 8.31E-13 | 3.00E-12 | |
| F13 | 100 | 2.78E+00 | 9.36E-01 | 7.00E+00 | 4.07E-01 | 1.47E-04 | 2.28E-04 | 2.32E-11 | 9.66E-11 |
| 500 | 2.06E+01 | 6.96E+00 | 5.05E+01 | 1.26E+00 | 4.96E-04 | 7.58E-04 | 3.51E-10 | 1.88E-09 | |
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