Table 4.
CEC2017 test results: 30 dimensions. Bold text indicates the optimal values.
| Dim = 30 | |||||||||
|---|---|---|---|---|---|---|---|---|---|
| SSA | HHO | BOA | OMA | WOA | SCA | DBO | ADBO | ||
| F1 | min | 1.83E+08 | 3.14E+10 | 2.75E+11 | 7.68E+10 | 2.70E+10 | 1.87E+11 | 2.24E+10 | 1.33E+10 |
| mean | 3.83E+08 | 4.95E+10 | 2.95E+11 | 1.18E+11 | 6.48E+10 | 2.17E+11 | 7.86E+10 | 3.76E+10 | |
| std | 1.07E+16 | 6.42E+19 | 2.20E+19 | 4.76E+20 | 1.95E+20 | 2.38E+20 | 4.78E+21 | 1.34E+20 | |
| degree | 1 | 3 | 8 | 6 | 4 | 7 | 5 | 2 | |
| F2 | min | 3.48E+05 | 3.15E+05 | 8.62E+05 | 3.56E+05 | 1.75E+05 | 4.74E+05 | 3.56E+05 | 3.27E+05 |
| mean | 7.35E+05 | 3.61E+05 | 1.88E+10 | 4.17E+05 | 2.43E+05 | 6.01E+05 | 7.75E+05 | 4.00E+05 | |
| std | 1.43E+10 | 6.12E+09 | 3.30E+21 | 1.13E+09 | 4.18E+08 | 5.73E+09 | 9.76E+10 | 1.24E+10 | |
| degree | 6 | 2 | 8 | 4 | 1 | 5 | 7 | 3 | |
| F3 | min | 8.59E+02 | 6.66E+03 | 9.04E+04 | 1.06E+04 | 2.01E+03 | 3.79E+04 | 3.75E+03 | 1.01E+03 |
| mean | 1.01E+03 | 8.99E+03 | 1.18E+05 | 1.74E+04 | 7.45E+03 | 5.11E+04 | 1.56E+04 | 2.97E+03 | |
| std | 9.17E+03 | 1.62E+06 | 1.59E+08 | 1.76E+07 | 9.11E+06 | 4.62E+07 | 3.00E+08 | 2.87E+06 | |
| degree | 1 | 4 | 8 | 6 | 3 | 7 | 5 | 2 | |
| F4 | min | 1.29E+03 | 1.56E+03 | 2.20E+03 | 1.46E+03 | 1.33E+03 | 1.97E+03 | 1.19E+03 | 1.14E+03 |
| mean | 1.37E+03 | 1.67E+03 | 2.29E+03 | 1.72E+03 | 1.46E+03 | 2.07E+03 | 1.70E+03 | 1.31E+03 | |
| std | 1.78E+03 | 2.69E+03 | 3.29E+03 | 1.32E+04 | 3.95E+03 | 3.14E+03 | 5.44E+04 | 5.53E+03 | |
| degree | 2 | 4 | 8 | 6 | 3 | 7 | 5 | 1 | |
| F5 | min | 6.62E+02 | 6.85E+02 | 7.09E+02 | 6.72E+02 | 6.64E+02 | 6.95E+02 | 6.62E+02 | 6.07E+02 |
| mean | 6.66E+02 | 6.91E+02 | 7.27E+02 | 6.87E+02 | 6.71E+02 | 7.02E+02 | 6.77E+02 | 6.51E+02 | |
| std | 7.00E+00 | 1.84E+01 | 7.51E+01 | 6.23E+01 | 1.14E+01 | 1.07E+01 | 1.15E+02 | 3.18E+01 | |
| degree | 2 | 6 | 8 | 5 | 3 | 7 | 4 | 1 | |
| F6 | min | 2.58E+03 | 3.46E+03 | 4.05E+03 | 3.33E+03 | 2.96E+03 | 3.57E+03 | 2.55E+03 | 2.73E+03 |
| mean | 3.19E+03 | 3.75E+03 | 4.27E+03 | 4.25E+03 | 3.20E+03 | 4.05E+03 | 2.98E+03 | 3.14E+03 | |
| std | 2.80E+04 | 1.67E+04 | 6.47E+03 | 1.82E+05 | 1.35E+04 | 4.95E+04 | 4.38E+04 | 3.08E+04 | |
| degree | 3 | 5 | 8 | 7 | 4 | 6 | 1 | 2 | |
| F7 | min | 1.64E+03 | 2.00E+03 | 2.62E+03 | 1.81E+03 | 1.77E+03 | 2.29E+03 | 1.75E+03 | 1.69E+03 |
| mean | 1.84E+03 | 2.13E+03 | 2.77E+03 | 2.02E+03 | 1.89E+03 | 2.43E+03 | 2.10E+03 | 1.79E+03 | |
| std | 2.58E+03 | 3.14E+03 | 7.42E+03 | 1.65E+04 | 5.02E+03 | 4.60E+03 | 6.04E+04 | 1.47E+04 | |
| degree | 2 | 6 | 8 | 4 | 3 | 7 | 5 | 1 | |
| F8 | min | 2.42E+04 | 6.06E+04 | 8.96E+04 | 6.11E+04 | 2.59E+04 | 6.99E+04 | 4.75E+04 | 3.95E+04 |
| mean | 2.53E+04 | 6.95E+04 | 1.08E+05 | 7.36E+04 | 3.04E+04 | 8.98E+04 | 7.60E+04 | 4.96E+04 | |
| std | 3.99E+05 | 2.19E+07 | 7.46E+07 | 7.56E+07 | 8.36E+06 | 9.74E+07 | 1.03E+08 | 1.45E+08 | |
| degree | 1 | 4 | 8 | 5 | 2 | 7 | 6 | 3 | |
| F9 | min | 1.40E+04 | 2.05E+04 | 3.33E+04 | 2.82E+04 | 1.75E+04 | 3.09E+04 | 1.94E+04 | 1.70E+04 |
| mean | 1.73E+04 | 2.47E+04 | 3.51E+04 | 3.21E+04 | 1.94E+04 | 3.31E+04 | 2.84E+04 | 1.79E+04 | |
| std | 1.25E+06 | 5.18E+06 | 9.98E+05 | 8.34E+05 | 1.52E+06 | 4.17E+05 | 2.36E+07 | 1.58E+07 | |
| degree | 1 | 4 | 8 | 6 | 3 | 7 | 5 | 2 | |
| F10 | min | 3.08E+04 | 7.34E+04 | 6.10E+05 | 6.63E+04 | 1.26E+04 | 1.34E+05 | 1.40E+05 | 4.26E+04 |
| mean | 7.62E+04 | 1.41E+05 | 9.69E+06 | 1.03E+05 | 3.57E+04 | 1.85E+05 | 2.30E+05 | 5.47E+04 | |
| std | 5.12E+08 | 1.10E+09 | 1.40E+15 | 2.89E+08 | 9.99E+07 | 9.62E+08 | 3.30E+09 | 8.87E+08 | |
| degree | 3 | 5 | 8 | 4 | 1 | 6 | 7 | 2 | |
| F11 | min | 7.17E+07 | 5.31E+09 | 2.11E+11 | 1.01E+10 | 1.19E+09 | 7.93E+10 | 2.95E+09 | 2.48E+08 |
| mean | 1.88E+08 | 1.14E+10 | 2.51E+11 | 2.05E+10 | 8.44E+09 | 1.03E+11 | 7.34E+09 | 2.64E+09 | |
| std | 4.75E+15 | 2.29E+19 | 2.12E+20 | 3.51E+19 | 4.61E+19 | 1.32E+20 | 4.52E+18 | 1.02E+19 | |
| degree | 1 | 5 | 8 | 6 | 4 | 7 | 3 | 2 | |
| F12 | min | 2.24E+04 | 6.36E+07 | 5.08E+10 | 3.47E+08 | 4.79E+05 | 9.56E+09 | 1.81E+07 | 7.67E+04 |
| mean | 6.46E+04 | 2.32E+08 | 6.25E+10 | 1.21E+09 | 1.52E+08 | 1.69E+10 | 3.22E+08 | 2.89E+06 | |
| std | 9.55E+09 | 3.62E+16 | 1.52E+19 | 9.75E+17 | 7.87E+16 | 1.83E+19 | 4.87E+16 | 3.46E+13 | |
| degree | 1 | 4 | 8 | 6 | 3 | 7 | 5 | 2 | |
| F13 | min | 8.28E+05 | 4.89E+06 | 1.09E+08 | 1.18E+06 | 5.08E+05 | 1.76E+07 | 2.85E+06 | 1.01E+06 |
| mean | 2.10E+06 | 1.12E+07 | 4.40E+08 | 3.96E+06 | 1.72E+06 | 6.25E+07 | 2.00E+07 | 2.05E+06 | |
| std | 7.27E+11 | 1.19E+13 | 5.79E+16 | 4.22E+12 | 8.34E+11 | 8.33E+14 | 1.68E+14 | 1.39E+13 | |
| degree | 3 | 5 | 8 | 4 | 1 | 7 | 6 | 2 | |
| F14 | min | 9.59E+03 | 6.90E+06 | 1.99E+10 | 6.79E+06 | 1.22E+04 | 3.10E+09 | 1.81E+05 | 2.64E+04 |
| mean | 2.21E+04 | 2.13E+07 | 3.56E+10 | 4.96E+07 | 6.13E+06 | 5.94E+09 | 1.02E+08 | 3.88E+05 | |
| std | 1.44E+08 | 6.13E+14 | 3.00E+19 | 2.08E+15 | 4.57E+14 | 2.93E+18 | 2.48E+16 | 1.05E+12 | |
| degree | 1 | 4 | 8 | 5 | 3 | 7 | 6 | 2 | |
| F15 | min | 4.61E+03 | 7.96E+03 | 1.61E+04 | 7.59E+03 | 5.48E+03 | 1.30E+04 | 7.13E+03 | 4.05E+03 |
| mean | 6.17E+03 | 1.03E+04 | 2.39E+04 | 9.97E+03 | 7.40E+03 | 1.48E+04 | 9.34E+03 | 5.75E+03 | |
| std | 6.19E+05 | 1.42E+06 | 9.70E+06 | 1.57E+06 | 1.09E+06 | 6.51E+05 | 1.82E+06 | 1.14E+06 | |
| degree | 2 | 6 | 8 | 5 | 3 | 7 | 4 | 1 | |
| F16 | min | 4.82E+03 | 6.14E+03 | 3.10E+06 | 4.64E+03 | 5.02E+03 | 1.41E+04 | 7.59E+03 | 3.02E+03 |
| mean | 5.98E+03 | 9.17E+03 | 3.43E+07 | 6.61E+03 | 6.80E+03 | 9.06E+04 | 9.58E+03 | 5.74E+03 | |
| std | 4.71E+05 | 6.12E+07 | 1.25E+15 | 7.55E+05 | 1.18E+06 | 9.13E+09 | 4.03E+06 | 1.09E+06 | |
| degree | 2 | 5 | 8 | 3 | 4 | 7 | 6 | 1 | |
| F17 | min | 3.81E+05 | 2.54E+06 | 1.92E+08 | 1.05E+06 | 1.05E+06 | 4.79E+07 | 3.84E+06 | 1.58E+06 |
| mean | 2.68E+06 | 9.22E+06 | 7.52E+08 | 6.05E+06 | 2.94E+06 | 1.34E+08 | 1.97E+07 | 1.79E+06 | |
| std | 1.42E+12 | 1.84E+13 | 1.27E+17 | 1.23E+13 | 3.39E+12 | 2.90E+15 | 1.11E+14 | 1.24E+13 | |
| degree | 2 | 5 | 8 | 4 | 3 | 7 | 6 | 1 | |
| F18 | min | 2.88E+03 | 1.33E+07 | 2.44E+10 | 4.57E+06 | 7.51E+04 | 3.14E+09 | 1.43E+07 | 4.15E+04 |
| mean | 2.87E+04 | 3.92E+07 | 3.44E+10 | 4.83E+07 | 1.26E+07 | 5.30E+09 | 1.48E+08 | 1.46E+06 | |
| std | 5.28E+09 | 3.32E+14 | 2.75E+19 | 1.31E+15 | 2.93E+15 | 1.81E+18 | 1.43E+16 | 1.33E+12 | |
| degree | 1 | 4 | 8 | 5 | 3 | 7 | 6 | 2 | |
| F19 | min | 4.58E+03 | 4.92E+03 | 8.72E+03 | 6.65E+03 | 4.16E+03 | 7.41E+03 | 5.45E+03 | 4.02E+03 |
| mean | 6.06E+03 | 6.12E+03 | 9.26E+03 | 7.45E+03 | 5.25E+03 | 8.14E+03 | 7.28E+03 | 5.25E+03 | |
| std | 3.60E+05 | 2.69E+05 | 6.94E+04 | 1.10E+05 | 3.39E+05 | 1.11E+05 | 6.12E+05 | 5.82E+05 | |
| degree | 3 | 4 | 8 | 6 | 2 | 7 | 5 | 1 | |
| F20 | min | 3.35E+03 | 4.03E+03 | 4.46E+03 | 3.18E+03 | 3.33E+03 | 3.99E+03 | 3.73E+03 | 3.03E+03 |
| mean | 3.66E+03 | 4.40E+03 | 4.96E+03 | 3.45E+03 | 3.58E+03 | 4.21E+03 | 4.04E+03 | 3.39E+03 | |
| std | 4.69E+04 | 3.34E+04 | 4.69E+04 | 2.00E+04 | 2.36E+04 | 1.18E+04 | 3.73E+04 | 4.87E+04 | |
| degree | 4 | 7 | 8 | 2 | 3 | 6 | 5 | 1 | |
| F21 | min | 1.40E+04 | 2.45E+04 | 3.54E+04 | 3.31E+04 | 1.85E+04 | 3.38E+04 | 2.07E+04 | 2.01E+04 |
| mean | 1.94E+04 | 2.78E+04 | 3.76E+04 | 3.48E+04 | 2.35E+04 | 3.53E+04 | 2.82E+04 | 2.73E+04 | |
| std | 2.89E+06 | 2.01E+06 | 1.30E+06 | 4.72E+05 | 2.94E+06 | 6.16E+05 | 2.46E+07 | 9.05E+06 | |
| degree | 1 | 4 | 8 | 6 | 2 | 7 | 5 | 3 | |
| F22 | min | 3.75E+03 | 5.43E+03 | 5.55E+03 | 3.93E+03 | 3.98E+03 | 5.05E+03 | 4.49E+03 | 3.75E+03 |
| mean | 4.24E+03 | 5.95E+03 | 6.53E+03 | 4.20E+03 | 4.59E+03 | 5.26E+03 | 4.81E+03 | 4.17E+03 | |
| std | 3.78E+04 | 1.33E+05 | 4.27E+05 | 2.43E+04 | 8.34E+04 | 1.69E+04 | 3.07E+04 | 1.15E+05 | |
| degree | 3 | 7 | 8 | 2 | 4 | 6 | 5 | 1 | |
| F23 | min | 4.56E+03 | 7.05E+03 | 7.35E+03 | 5.23E+03 | 5.43E+03 | 6.93E+03 | 5.28E+03 | 4.91E+03 |
| mean | 5.23E+03 | 8.57E+03 | 9.45E+03 | 5.92E+03 | 5.98E+03 | 7.43E+03 | 6.30E+03 | 5.19E+03 | |
| std | 1.26E+05 | 2.61E+05 | 3.70E+06 | 1.86E+05 | 9.61E+04 | 8.67E+04 | 2.40E+05 | 2.54E+05 | |
| degree | 2 | 7 | 8 | 3 | 4 | 6 | 5 | 1 | |
| F24 | min | 3.54E+03 | 5.91E+03 | 2.47E+04 | 9.14E+03 | 5.46E+03 | 1.82E+04 | 5.20E+03 | 4.73E+03 |
| mean | 3.69E+03 | 6.78E+03 | 3.22E+04 | 1.23E+04 | 7.67E+03 | 2.28E+04 | 1.15E+04 | 5.72E+03 | |
| std | 6.90E+03 | 2.15E+05 | 9.35E+06 | 5.86E+06 | 1.12E+06 | 5.41E+06 | 5.86E+07 | 7.73E+05 | |
| degree | 1 | 3 | 8 | 6 | 4 | 7 | 5 | 2 | |
| F25 | min | 4.86E+03 | 2.83E+04 | 5.06E+04 | 2.95E+04 | 2.64E+04 | 3.46E+04 | 1.97E+04 | 2.01E+04 |
| mean | 2.10E+04 | 3.23E+04 | 5.81E+04 | 3.65E+04 | 3.18E+04 | 4.16E+04 | 2.63E+04 | 2.61E+04 | |
| std | 5.17E+07 | 6.15E+06 | 1.33E+07 | 1.43E+07 | 6.10E+06 | 8.64E+06 | 1.29E+07 | 1.64E+07 | |
| degree | 1 | 5 | 8 | 6 | 4 | 7 | 3 | 2 | |
| F26 | min | 3.62E+03 | 5.85E+03 | 8.14E+03 | 4.71E+03 | 4.34E+03 | 7.44E+03 | 4.02E+03 | 3.70E+03 |
| mean | 3.89E+03 | 7.65E+03 | 1.16E+04 | 5.47E+03 | 5.41E+03 | 8.70E+03 | 4.63E+03 | 4.59E+03 | |
| std | 6.25E+04 | 2.59E+06 | 2.17E+06 | 2.16E+05 | 3.44E+05 | 4.26E+05 | 2.51E+05 | 2.80E+05 | |
| degree | 1 | 6 | 8 | 5 | 4 | 7 | 3 | 2 | |
| F27 | min | 3.65E+03 | 7.61E+03 | 3.03E+04 | 1.09E+04 | 6.81E+03 | 2.19E+04 | 7.03E+03 | 4.87E+03 |
| mean | 3.80E+03 | 9.27E+03 | 3.70E+04 | 1.47E+04 | 9.63E+03 | 2.66E+04 | 1.93E+04 | 7.56E+03 | |
| std | 9.55E+03 | 7.57E+05 | 6.98E+06 | 3.79E+06 | 2.39E+06 | 4.12E+06 | 3.80E+07 | 2.37E+06 | |
| degree | 1 | 3 | 8 | 5 | 4 | 7 | 6 | 2 | |
| F28 | min | 6.75E+03 | 1.04E+04 | 2.25E+05 | 9.23E+03 | 8.58E+03 | 2.14E+04 | 9.10E+03 | 5.66E+03 |
| mean | 7.73E+03 | 1.31E+04 | 1.41E+06 | 1.27E+04 | 1.05E+04 | 4.15E+04 | 1.23E+04 | 9.81E+03 | |
| std | 2.41E+05 | 2.52E+06 | 1.07E+12 | 3.18E+06 | 8.00E+05 | 6.38E+08 | 2.55E+06 | 8.13E+05 | |
| degree | 1 | 6 | 8 | 5 | 3 | 7 | 4 | 2 | |
| F29 | min | 1.89E+05 | 3.34E+08 | 4.47E+10 | 3.43E+08 | 8.25E+06 | 6.19E+09 | 6.66E+07 | 5.10E+06 |
| mean | 6.18E+05 | 7.95E+08 | 5.66E+10 | 2.09E+09 | 1.36E+08 | 1.33E+10 | 2.66E+08 | 7.45E+07 | |
| std | 1.28E+11 | 1.03E+17 | 2.23E+19 | 2.76E+18 | 3.09E+16 | 9.88E+18 | 1.95E+16 | 6.57E+16 | |
| degree | 1 | 5 | 8 | 6 | 3 | 7 | 4 | 2 |