Research Article
Hybrid Genetic Grey Wolf Algorithm for Large-Scale Global Optimization
Table 4
Comparison results of 10 high-dimensional benchmark functions by WOA, SSA, ALO, and HGGWA.
| | Function | Dim | WOA | SSA | ALO | HGGWA | | Mean | Std | SR | Mean | Std | SR | Mean | Std | SR | Mean | Std | SR |
| | 100 | 5.77E-96 | 4.69E-96 | 100% | 1.01E-02 | 1.24E-02 | 0 | 3.04E-01 | 2.31E-01 | 0 | 4.85E-53 | 2.41E-52 | 100% | | 500 | 7.24E-93 | 2.98E-94 | 100% | 3.24E+04 | 2.18E+04 | 0 | 7.34E+04 | 1.32E+04 | 0 | 8.35E-25 | 8.86E-25 | 100% | | 1000 | 2.05E-89 | 3.16E-90 | 100% | 1.19E+05 | 1.04E+05 | 0 | 2.48E+05 | 2.12E+05 | 0 | 1.75E-17 | 2.73E-17 | 100% |
| | 100 | 1.89E-99 | 2.33E-99 | 100% | 8.85E+00 | 2.37E+00 | 0 | 4.29E+02 | 3.25E+02 | 0 | 4.01E-33 | 4.34E-33 | 100% | | 500 | 1.38E-99 | 2.16E-99 | 100% | 3.37E+02 | 2.17E+02 | 0 | 2.31E+03 | 2.03E+03 | 0 | 9.58E-18 | 2.36E-18 | 100% | | 1000 | 1.80E-99 | 1.37E-98 | 100% | 8.45E+02 | 3.43E+02 | 0 | 3.25E+04 | 4.13E+04 | 0 | 2.50E-11 | 1.66E-11 | 100% |
| | 100 | 3.84E+01 | 2.17E+00 | 0 | 2.22E+01 | 1.05E+01 | 0 | 2.47E+01 | 1.34E+01 | 0 | 4.55E+01 | 3.69E+01 | 0 | | 500 | 9.32E+01 | 5.32E+01 | 0 | 3.27E+01 | 2.33E+01 | 0 | 3.92E+01 | 2.34E+01 | 0 | 7.22E+01 | 5.01E+00 | 0 | | 1000 | 9.86E+01 | 3.24E+01 | 0 | 3.31E+01 | 1.28E+01 | 0 | 4.93E+01 | 3.99E+01 | 0 | 8.31E+01 | 4.36E+00 | 0 |
| | 100 | 9.67E+01 | 3.98E+01 | 0 | 9.00E+02 | 5.16E+02 | 0 | 1.40E+03 | 1.03E+03 | 0 | 6.82E+01 | 1.25E-01 | 100% | | 500 | 4.95E+02 | 3.14E+01 | 0 | 7.18E+06 | 1.46E+06 | 0 | 2.09E+07 | 1.37E+07 | 0 | 3.67E+02 | 8.23E-01 | 0 | | 1000 | 9.91E+02 | 2.48E+02 | 0 | 2.98E+07 | 1.35E+07 | 0 | 1.52E+08 | 1.00E+07 | 0 | 9.64E+02 | 3.74E+01 | 0 |
| | 100 | 7.83E+05 | 2.36E+05 | 0 | 2.17E+04 | 1.03E+04 | 0 | 3.60E+04 | 2.16E+04 | 0 | 3.45E-05 | 2.77E-05 | 100% | | 500 | 1.98E+07 | 1.32E+07 | 0 | 4.29E+05 | 3.16E+05 | 0 | 1.18E+06 | 1.03E+06 | 0 | 2.67E-03 | 4.38E-03 | 80% | | 1000 | 6.68E+07 | 3.44E+07 | 0 | 2.48E+06 | 1.23E+06 | 0 | 3.72E+06 | 3.49E+06 | 0 | 8.33E+00 | 5.12E+00 | 0 |
| | 100 | 2.65E-04 | 1.43E-04 | 100% | 1.12E+00 | 1.03E+00 | 0 | 8.28E-01 | 2.68E-01 | 0 | 2.34E-09 | 3.17E-10 | 100% | | 500 | 3.94E-04 | 3.22E-04 | 60% | 4.97E+01 | 3.66E+01 | 0 | 1.13E+02 | 1.01E+02 | 0 | 5.73E-05 | 4.33E-06 | 100% | | 1000 | 2.16E-03 | 1.36E-03 | 0 | 3.93E+02 | 2.78E+02 | 0 | 1.77E+03 | 2.33E+03 | 0 | 1.08E-04 | 1.62E-03 | 80% |
| | 100 | 0.00E+00 | 0.00E+00 | 100% | 6.27E+01 | 4.36E+01 | 0 | 3.54E+02 | 3.32E+02 | 0 | 0.00E+00 | 0.00E+00 | 100% | | 500 | 0.00E+00 | 0.00E+00 | 100% | 2.04E+03 | 1.97E+03 | 0 | 3.34E+03 | 4.56E+03 | 0 | 0.00E+00 | 0.00E+00 | 100% | | 1000 | 0.00E+00 | 0.00E+00 | 100% | 5.69E+03 | 1.66E+03 | 0 | 7.19E+03 | 2.14E+03 | 0 | 5.57E-11 | 3.15E-12 | 100% |
| | 100 | 4.44E-15 | 3.12E-15 | 100% | 5.15E+00 | 4.13E+00 | 0 | 4.93E+00 | 3.49E+00 | 0 | 2.15E-15 | 3.48E-15 | 100% | | 500 | 4.44E-15 | 3.05E-15 | 100% | 1.26E+01 | 1.00E+01 | 0 | 1.28E+01 | 2.28E+01 | 0 | 8.74E-12 | 5.39E-12 | 100% | | 1000 | 8.88E-16 | 2.88E-15 | 100% | 1.28E+01 | 1.44E+01 | 0 | 1.46E+01 | 2.03E+01 | 0 | 1.59E-07 | 1.63E-07 | 100% |
| | 100 | 0.00E+00 | 0.00E+00 | 100% | 1.52E-01 | 2.44E-01 | 0 | 4.54E-01 | 3.16E-01 | 0 | 0.00E+00 | 0.00E+00 | 100% | | 500 | 0.00E+00 | 0.00E+00 | 100% | 2.82E+02 | 2.13E+02 | 0 | 3.92E+02 | 1.08E+02 | 0 | 1.84E-16 | 8.44E-17 | 100% | | 1000 | 0.00E+00 | 0.00E+00 | 100% | 1.10E+03 | 1.34E+03 | 0 | 3.61E+03 | 1.17E+03 | 0 | 2.31E-13 | 3.29E-14 | 100% |
| | 100 | 8.16E-03 | 4.32E-03 | 100% | 1.10E+01 | 2.19E+01 | 0 | 1.74E+01 | 1.33E+01 | 0 | 2.73E-07 | 3.11E-07 | 100% | | 500 | 2.52E-02 | 1.99E-02 | 80% | 5.16E+01 | 3.33E+01 | 0 | 3.97E+05 | 2.96E+05 | 0 | 8.12E-05 | 4.98E-06 | 100% | | 1000 | 1.43E-02 | 1.03E-02 | 80% | 1.00E+05 | 2.13E+04 | 0 | 6.96E+06 | 1.34E+06 | 0 | 6.33E-04 | 3.77E-03 | 100% |
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