Table 2.
Comparisons of VGHHO and other six approaches for 18 classical problems with 30D in Table 1
| Function | Index | BOA | SOA | HHO | AGDE | EEGWO | ISCA | VGHHO |
|---|---|---|---|---|---|---|---|---|
| f1 | Mean | 2.64E-11 | 4.17E-13 | 6.59E-102 | 4.87E-03 | 0 | 0 | 0 |
| Std | 3.10E-12 | 4.36E-13 | 2.94E-102 | 3.63E-03 | 0 | 0 | 0 | |
| Ranking | 6 | 5 | 4 | 7 | 1 | 1 | 1 | |
| f2 | Mean | 8.65E-09 | 1.30E-08 | 9.20E-50 | 1.09E-02 | 5.42E-240 | 8.99E-211 | 0 |
| Std | 4.62E-09 | 1.14E-08 | 2.06E-49 | 5.10E-03 | 0 | 0 | 0 | |
| Ranking | 5 | 6 | 4 | 7 | 2 | 3 | 1 | |
| f3 | Mean | 1.27E-08 | 3.44E-03 | 1.46E-48 | 8.73E + 00 | 8.80E-228 | 1.36E-207 | 0 |
| Std | 2.22E-09 | 4.09E-03 | 3.26E-48 | 8.09E-01 | 0 | 0 | 0 | |
| Ranking | 5 | 6 | 4 | 7 | 2 | 3 | 1 | |
| f4 | Mean | 2.90E + 01 | 2.81E + 01 | 7.15E-02 | 6.19E + 01 | 2.89E + 01 | 2.89E + 01 | 4.40E-03 |
| Std | 2.58E-02 | 6.22E-01 | 6.67E-02 | 5.65E + 01 | 2.61E-02 | 1.81E-02 | 4.43E-03 | |
| Ranking | 6 | 3 | 2 | 7 | 4 | 4 | 1 | |
| f5 | Mean | 1.23E-03 | 2.08E-03 | 2.27E-04 | 7.60E-02 | 2.56E-05 | 4.24E-05 | 5.17E-06 |
| Std | 5.41E-04 | 1.55E-03 | 1.66E-04 | 4.53E-02 | 3.85E-05 | 5.55E-05 | 1.15E-05 | |
| Ranking | 5 | 6 | 4 | 7 | 2 | 3 | 1 | |
| f6 | Mean | 2.65E-11 | 8.30E-13 | 1.87E-107 | 3.55E-04 | 0 | 0 | 0 |
| Std | 3.25E-12 | 6.74E-13 | 2.88E-107 | 1.46E-04 | 0 | 0 | 0 | |
| Ranking | 6 | 5 | 4 | 7 | 1 | 1 | 1 | |
| f7 | Mean | 2.87E-13 | 1.41E-47 | 2.12E-129 | 3.10E-22 | 0 | 0 | 0 |
| Std | 2.19E-13 | 3.06E-47 | 4.63E-129 | 1.38E-22 | 0 | 0 | 0 | |
| Ranking | 7 | 5 | 4 | 6 | 1 | 1 | 1 | |
| f8 | Mean | 2.79E-11 | 3.71E-09 | 7.36E-96 | 8.33E + 00 | 0 | 0 | 0 |
| Std | 3.05E-12 | 5.66E-09 | 1.64E-95 | 6.30E + 00 | 0 | 0 | 0 | |
| Ranking | 5 | 6 | 4 | 7 | 1 | 1 | 1 | |
| f9 | Mean | 1.20E + 02 | 2.96E + 00 | 0 | 4.26E + 01 | 0 | 0 | 0 |
| Std | 1.11E + 02 | 4.62E + 00 | 0 | 3.95E + 00 | 0 | 0 | 0 | |
| Ranking | 7 | 5 | 1 | 6 | 1 | 1 | 1 | |
| f10 | Mean | 1.23E-08 | 2.00E + 01 | 8.88E-16 | 1.53E-02 | 8.88E-16 | 8.88E-16 | 8.88E-16 |
| Std | 1.40E-09 | 6.20E-04 | 0 | 1.83E-03 | 0 | 0 | 0 | |
| Ranking | 5 | 7 | 1 | 6 | 1 | 1 | 1 | |
| f11 | Mean | 1.55E-11 | 2.61E-02 | 0 | 1.42E-02 | 0 | 0 | 0 |
| Std | 1.05E-11 | 3.64E-02 | 0 | 9.85E-03 | 0 | 0 | 0 | |
| Ranking | 5 | 7 | 1 | 6 | 1 | 1 | 1 | |
| f12 | Mean | 1.68E-09 | 4.24E-04 | 1.71E-57 | 2.57E-02 | 8.44E-239 | 2.03E-210 | 0 |
| Std | 1.02E-09 | 7.29E-04 | 2.59E-57 | 3.38E-03 | 0 | 0 | 0 | |
| Ranking | 5 | 6 | 4 | 7 | 2 | 3 | 1 | |
| f13 | Mean | 4.20E-12 | 1.31E-13 | 3.17E-99 | 3.30E-01 | 0 | 0 | 0 |
| Std | 4.36E-12 | 1.19E-13 | 1.42E-98 | 5.71E-01 | 0 | 0 | 0 | |
| Ranking | 6 | 5 | 4 | 7 | 1 | 1 | 1 | |
| f14 | Mean | 3.29E-01 | 1.42E-01 | 8.18E-49 | 1.10E + 00 | 5.39E-63 | 0 | 0 |
| Std | 4.26E-02 | 8.55E-02 | 1.82E-48 | 2.00E-01 | 4.52E-63 | 0 | 0 | |
| Ranking | 6 | 5 | 4 | 7 | 3 | 1 | 1 | |
| f15 | Mean | 2.38E-12 | 3.47E-16 | 2.34E-105 | 2.71E-06 | 0 | 0 | 0 |
| Std | 8.81E-13 | 4.68E-16 | 3.92E-105 | 1.39E-06 | 0 | 0 | 0 | |
| Ranking | 6 | 5 | 4 | 7 | 1 | 1 | 1 | |
| f16 | Mean | 2.08E-11 | 1.30E-13 | 3.60E-100 | 9.69E-06 | 0 | 0 | 0 |
| Std | 4.44E-12 | 2.81E-13 | 8.05E-100 | 7.84E-06 | 0 | 0 | 0 | |
| Ranking | 6 | 5 | 4 | 7 | 1 | 1 | 1 | |
| f17 | Mean | 5.01E-05 | 1.46E-02 | 2.28E-27 | 4.96E + 00 | 0 | 0 | 0 |
| Std | 8.06E-05 | 5.10E-03 | 7.11E-27 | 8.73E-01 | 0 | 0 | 0 | |
| Ranking | 5 | 6 | 4 | 7 | 1 | 1 | 1 | |
| f18 | Mean | 5.27E-10 | 3.53E-37 | 0 | 9.73E-16 | 0 | 0 | 0 |
| Std | 4.76E-10 | 7.31E-37 | 0 | 8.57E-16 | 0 | 0 | 0 | |
| Ranking | 7 | 5 | 1 | 6 | 1 | 1 | 1 | |
| Average ranking | 5.72 | 5.44 | 3.22 | 6.72 | 1.50 | 1.61 | 1.00 | |
| Total ranking | 6 | 5 | 4 | 7 | 2 | 3 | 1 | |
The best value of each function is highlighted in bold in the table