The results of HBWO-JS and other algorithms for CEC2020 test functions (the dimension dim = 30).
| Function . | Index . | Algorithms . | ||||||||
|---|---|---|---|---|---|---|---|---|---|---|
| HBWO-JS . | JS . | BWO . | AHA . | ARO . | DO . | SO . | WSO . | RSA . | ||
| cec01 | Best | 1.77E+05 | 3.08E+07 | 4.50E+10 | 7.09E+06 | 6.41E+06 | 2.73E+05 | 7.88E+05 | 5.88E+09 | 2.97E+10 |
| Worst | 1.66E+06 | 3.83E+09 | 5.99E+10 | 4.42E+08 | 8.80E+07 | 2.72E+06 | 6.39E+07 | 2.15E+10 | 6.39E+10 | |
| Mean | 6.01E+05 | 2.98E+08 | 5.30E+10 | 6.02E+07 | 2.88E+07 | 9.07E+05 | 9.75E+06 | 1.28E+10 | 4.74E+10 | |
| Std | 3.55E+05 | 6.87E+08 | 4.17E+09 | 8.70E+07 | 1.76E+07 | 6.27E+05 | 1.22E+07 | 4.16E+09 | 6.65E+09 | |
| Rank | 1 | 6 | 9 | 5 | 4 | 2 | 3 | 7 | 8 | |
| cec02 | Best | 2.54E+03 | 5.27E+03 | 7.97E+03 | 3.19E+03 | 3.22E+03 | 3.13E+03 | 2.88E+03 | 4.95E+03 | 7.18E+03 |
| Worst | 4.73E+03 | 9.03E+03 | 9.37E+03 | 5.42E+03 | 5.21E+03 | 6.22E+03 | 7.04E+03 | 8.90E+03 | 8.53E+03 | |
| Mean | 4.02E+03 | 8.12E+03 | 8.67E+03 | 4.31E+03 | 4.21E+03 | 4.94E+03 | 4.07E+03 | 7.59E+03 | 7.94E+03 | |
| Std | 4.67E+02 | 8.88E+02 | 3.51E+02 | 5.16E+02 | 5.27E+02 | 7.08E+02 | 8.17E+02 | 1.06E+03 | 4.24E+02 | |
| Rank | 1 | 8 | 9 | 4 | 3 | 5 | 2 | 6 | 7 | |
| cec03 | Best | 8.48E+02 | 8.61E+02 | 1.34E+03 | 8.82E+02 | 8.47E+02 | 8.71E+02 | 7.86E+02 | 1.03E+03 | 1.32E+03 |
| Worst | 1.22E+03 | 1.20E+03 | 1.47E+03 | 1.32E+03 | 1.22E+03 | 1.11E+03 | 1.05E+03 | 1.37E+03 | 1.48E+03 | |
| Mean | 9.09E+02 | 9.86E+02 | 1.40E+03 | 1.05E+03 | 9.52E+02 | 1.01E+03 | 9.11E+02 | 1.14E+03 | 1.40E+03 | |
| Std | 6.83E+01 | 7.21E+01 | 3.33E+01 | 1.07E+02 | 8.78E+01 | 6.11E+01 | 5.00E+01 | 8.98E+01 | 3.80E+01 | |
| Rank | 1 | 4 | 9 | 6 | 3 | 5 | 2 | 7 | 8 | |
| cec04 | Best | 1.90E+03 | 1.90E+03 | 1.90E+03 | 1.90E+03 | 1.90E+03 | 1.90E+03 | 1.90E+03 | 1.91E+03 | 1.90E+03 |
| Worst | 1.90E+03 | 1.90E+03 | 1.90E+03 | 1.90E+03 | 1.90E+03 | 1.92E+03 | 1.90E+03 | 1.99E+03 | 1.90E+03 | |
| Mean | 1.90E+03 | 1.90E+03 | 1.90E+03 | 1.90E+03 | 1.90E+03 | 1.91E+03 | 1.90E+03 | 1.94E+03 | 1.90E+03 | |
| Std | 0.00E+00 | 4.12E-03 | 0.00E+00 | 0.00E+00 | 0.00E+00 | 4.60E+00 | 1.34E-01 | 1.45E+01 | 0.00E+00 | |
| Rank | 1 | 6 | 1 | 1 | 1 | 8 | 7 | 9 | 1 | |
| cec05 | Best | 1.02E+05 | 1.10E+05 | 2.48E+07 | 3.41E+05 | 4.12E+05 | 1.26E+05 | 6.62E+04 | 7.56E+04 | 2.62E+07 |
| Worst | 2.91E+06 | 2.55E+06 | 1.31E+08 | 5.27E+06 | 3.95E+06 | 6.65E+06 | 4.20E+06 | 1.96E+07 | 1.51E+08 | |
| Mean | 9.02E+05 | 7.99E+05 | 7.32E+07 | 2.41E+06 | 1.55E+06 | 1.71E+06 | 1.63E+06 | 2.67E+06 | 8.25E+07 | |
| Std | 7.19E+05 | 5.12E+05 | 2.33E+07 | 1.44E+06 | 1.02E+06 | 1.33E+06 | 1.12E+06 | 4.07E+06 | 3.39E+07 | |
| Rank | 2 | 1 | 8 | 6 | 3 | 5 | 4 | 7 | 9 | |
| cec06 | Best | 1.74E+03 | 1.80E+03 | 4.13E+03 | 1.76E+03 | 1.81E+03 | 1.86E+03 | 1.76E+03 | 1.90E+03 | 3.44E+03 |
| Worst | 2.07E+03 | 2.79E+03 | 5.85E+03 | 2.56E+03 | 2.52E+03 | 2.80E+03 | 2.69E+03 | 3.03E+03 | 6.91E+03 | |
| Mean | 1.92E+03 | 2.21E+03 | 5.07E+03 | 2.13E+03 | 2.15E+03 | 2.28E+03 | 2.17E+03 | 2.36E+03 | 4.71E+03 | |
| Std | 8.38E+01 | 2.49E+02 | 3.82E+02 | 2.01E+02 | 1.91E+02 | 2.49E+02 | 2.26E+02 | 2.84E+02 | 7.84E+02 | |
| Rank | 1 | 5 | 9 | 2 | 3 | 6 | 4 | 7 | 8 | |
| cec07 | Best | 1.85E+04 | 2.75E+04 | 3.63E+06 | 5.18E+04 | 5.91E+04 | 4.58E+04 | 1.92E+04 | 6.04E+03 | 5.78E+06 |
| Worst | 8.13E+05 | 9.05E+05 | 6.08E+07 | 1.61E+06 | 3.17E+06 | 2.02E+06 | 1.10E+06 | 2.73E+06 | 9.49E+07 | |
| Mean | 2.48E+05 | 2.39E+05 | 3.03E+07 | 5.18E+05 | 5.17E+05 | 6.41E+05 | 5.07E+05 | 2.88E+05 | 4.40E+07 | |
| Std | 1.85E+05 | 1.96E+05 | 1.51E+07 | 3.78E+05 | 6.08E+05 | 4.63E+05 | 3.25E+05 | 5.19E+05 | 2.57E+07 | |
| Rank | 2 | 1 | 8 | 6 | 5 | 7 | 4 | 3 | 9 | |
| cec08 | Best | 2.30E+03 | 2.34E+03 | 7.64E+03 | 2.32E+03 | 2.32E+03 | 2.30E+03 | 2.33E+03 | 3.16E+03 | 6.89E+03 |
| Worst | 2.31E+03 | 2.70E+03 | 9.97E+03 | 7.18E+03 | 2.43E+03 | 7.65E+03 | 7.45E+03 | 7.45E+03 | 1.03E+04 | |
| Mean | 2.31E+03 | 2.43E+03 | 8.91E+03 | 2.65E+03 | 2.34E+03 | 5.93E+03 | 4.28E+03 | 5.05E+03 | 8.57E+03 | |
| Std | 2.24E+00 | 1.01E+02 | 5.87E+02 | 1.19E+03 | 2.04E+01 | 1.90E+03 | 1.70E+03 | 1.21E+03 | 9.31E+02 | |
| Rank | 1 | 3 | 9 | 4 | 2 | 7 | 5 | 6 | 8 | |
| cec09 | Best | 2.88E+03 | 2.94E+03 | 3.45E+03 | 2.96E+03 | 2.89E+03 | 2.95E+03 | 2.88E+03 | 3.17E+03 | 3.30E+03 |
| Worst | 3.00E+03 | 3.12E+03 | 3.91E+03 | 3.29E+03 | 3.06E+03 | 3.26E+03 | 3.08E+03 | 3.66E+03 | 4.46E+03 | |
| Mean | 2.94E+03 | 3.01E+03 | 3.60E+03 | 3.06E+03 | 2.96E+03 | 3.10E+03 | 2.96E+03 | 3.36E+03 | 3.53E+03 | |
| Std | 3.01E+01 | 4.89E+01 | 9.03E+01 | 6.53E+01 | 4.90E+01 | 7.97E+01 | 4.70E+01 | 1.21E+02 | 2.63E+02 | |
| Rank | 1 | 4 | 9 | 5 | 2 | 6 | 3 | 7 | 8 | |
| cec10 | Best | 2.89E+03 | 2.95E+03 | 4.21E+03 | 2.89E+03 | 2.92E+03 | 2.88E+03 | 2.89E+03 | 3.08E+03 | 3.95E+03 |
| Worst | 2.96E+03 | 3.08E+03 | 4.69E+03 | 3.02E+03 | 3.05E+03 | 2.97E+03 | 2.97E+03 | 3.82E+03 | 6.12E+03 | |
| Mean | 2.91E+03 | 3.00E+03 | 4.45E+03 | 2.96E+03 | 2.96E+03 | 2.91E+03 | 2.93E+03 | 3.32E+03 | 5.02E+03 | |
| Std | 1.82E+01 | 3.34E+01 | 1.37E+02 | 3.31E+01 | 3.20E+01 | 2.14E+01 | 2.36E+01 | 1.88E+02 | 6.18E+02 | |
| Rank | 2 | 6 | 8 | 4 | 5 | 1 | 3 | 7 | 9 | |
| Mean rank | 1.3 | 4.4 | 7.9 | 4.3 | 3.1 | 5.2 | 3.7 | 6.6 | 7.5 | |
| Final ranking | 1 | 5 | 9 | 4 | 2 | 6 | 3 | 7 | 8 | |
| +/=/– | –/–/– | 0/2/8 | 0/1/9 | 0/1/9 | 0/3/7 | 0/2/8 | 0/3/7 | 0/2/8 | 0/1/9 | |
| Function . | Index . | Algorithms . | ||||||||
|---|---|---|---|---|---|---|---|---|---|---|
| HBWO-JS . | JS . | BWO . | AHA . | ARO . | DO . | SO . | WSO . | RSA . | ||
| cec01 | Best | 1.77E+05 | 3.08E+07 | 4.50E+10 | 7.09E+06 | 6.41E+06 | 2.73E+05 | 7.88E+05 | 5.88E+09 | 2.97E+10 |
| Worst | 1.66E+06 | 3.83E+09 | 5.99E+10 | 4.42E+08 | 8.80E+07 | 2.72E+06 | 6.39E+07 | 2.15E+10 | 6.39E+10 | |
| Mean | 6.01E+05 | 2.98E+08 | 5.30E+10 | 6.02E+07 | 2.88E+07 | 9.07E+05 | 9.75E+06 | 1.28E+10 | 4.74E+10 | |
| Std | 3.55E+05 | 6.87E+08 | 4.17E+09 | 8.70E+07 | 1.76E+07 | 6.27E+05 | 1.22E+07 | 4.16E+09 | 6.65E+09 | |
| Rank | 1 | 6 | 9 | 5 | 4 | 2 | 3 | 7 | 8 | |
| cec02 | Best | 2.54E+03 | 5.27E+03 | 7.97E+03 | 3.19E+03 | 3.22E+03 | 3.13E+03 | 2.88E+03 | 4.95E+03 | 7.18E+03 |
| Worst | 4.73E+03 | 9.03E+03 | 9.37E+03 | 5.42E+03 | 5.21E+03 | 6.22E+03 | 7.04E+03 | 8.90E+03 | 8.53E+03 | |
| Mean | 4.02E+03 | 8.12E+03 | 8.67E+03 | 4.31E+03 | 4.21E+03 | 4.94E+03 | 4.07E+03 | 7.59E+03 | 7.94E+03 | |
| Std | 4.67E+02 | 8.88E+02 | 3.51E+02 | 5.16E+02 | 5.27E+02 | 7.08E+02 | 8.17E+02 | 1.06E+03 | 4.24E+02 | |
| Rank | 1 | 8 | 9 | 4 | 3 | 5 | 2 | 6 | 7 | |
| cec03 | Best | 8.48E+02 | 8.61E+02 | 1.34E+03 | 8.82E+02 | 8.47E+02 | 8.71E+02 | 7.86E+02 | 1.03E+03 | 1.32E+03 |
| Worst | 1.22E+03 | 1.20E+03 | 1.47E+03 | 1.32E+03 | 1.22E+03 | 1.11E+03 | 1.05E+03 | 1.37E+03 | 1.48E+03 | |
| Mean | 9.09E+02 | 9.86E+02 | 1.40E+03 | 1.05E+03 | 9.52E+02 | 1.01E+03 | 9.11E+02 | 1.14E+03 | 1.40E+03 | |
| Std | 6.83E+01 | 7.21E+01 | 3.33E+01 | 1.07E+02 | 8.78E+01 | 6.11E+01 | 5.00E+01 | 8.98E+01 | 3.80E+01 | |
| Rank | 1 | 4 | 9 | 6 | 3 | 5 | 2 | 7 | 8 | |
| cec04 | Best | 1.90E+03 | 1.90E+03 | 1.90E+03 | 1.90E+03 | 1.90E+03 | 1.90E+03 | 1.90E+03 | 1.91E+03 | 1.90E+03 |
| Worst | 1.90E+03 | 1.90E+03 | 1.90E+03 | 1.90E+03 | 1.90E+03 | 1.92E+03 | 1.90E+03 | 1.99E+03 | 1.90E+03 | |
| Mean | 1.90E+03 | 1.90E+03 | 1.90E+03 | 1.90E+03 | 1.90E+03 | 1.91E+03 | 1.90E+03 | 1.94E+03 | 1.90E+03 | |
| Std | 0.00E+00 | 4.12E-03 | 0.00E+00 | 0.00E+00 | 0.00E+00 | 4.60E+00 | 1.34E-01 | 1.45E+01 | 0.00E+00 | |
| Rank | 1 | 6 | 1 | 1 | 1 | 8 | 7 | 9 | 1 | |
| cec05 | Best | 1.02E+05 | 1.10E+05 | 2.48E+07 | 3.41E+05 | 4.12E+05 | 1.26E+05 | 6.62E+04 | 7.56E+04 | 2.62E+07 |
| Worst | 2.91E+06 | 2.55E+06 | 1.31E+08 | 5.27E+06 | 3.95E+06 | 6.65E+06 | 4.20E+06 | 1.96E+07 | 1.51E+08 | |
| Mean | 9.02E+05 | 7.99E+05 | 7.32E+07 | 2.41E+06 | 1.55E+06 | 1.71E+06 | 1.63E+06 | 2.67E+06 | 8.25E+07 | |
| Std | 7.19E+05 | 5.12E+05 | 2.33E+07 | 1.44E+06 | 1.02E+06 | 1.33E+06 | 1.12E+06 | 4.07E+06 | 3.39E+07 | |
| Rank | 2 | 1 | 8 | 6 | 3 | 5 | 4 | 7 | 9 | |
| cec06 | Best | 1.74E+03 | 1.80E+03 | 4.13E+03 | 1.76E+03 | 1.81E+03 | 1.86E+03 | 1.76E+03 | 1.90E+03 | 3.44E+03 |
| Worst | 2.07E+03 | 2.79E+03 | 5.85E+03 | 2.56E+03 | 2.52E+03 | 2.80E+03 | 2.69E+03 | 3.03E+03 | 6.91E+03 | |
| Mean | 1.92E+03 | 2.21E+03 | 5.07E+03 | 2.13E+03 | 2.15E+03 | 2.28E+03 | 2.17E+03 | 2.36E+03 | 4.71E+03 | |
| Std | 8.38E+01 | 2.49E+02 | 3.82E+02 | 2.01E+02 | 1.91E+02 | 2.49E+02 | 2.26E+02 | 2.84E+02 | 7.84E+02 | |
| Rank | 1 | 5 | 9 | 2 | 3 | 6 | 4 | 7 | 8 | |
| cec07 | Best | 1.85E+04 | 2.75E+04 | 3.63E+06 | 5.18E+04 | 5.91E+04 | 4.58E+04 | 1.92E+04 | 6.04E+03 | 5.78E+06 |
| Worst | 8.13E+05 | 9.05E+05 | 6.08E+07 | 1.61E+06 | 3.17E+06 | 2.02E+06 | 1.10E+06 | 2.73E+06 | 9.49E+07 | |
| Mean | 2.48E+05 | 2.39E+05 | 3.03E+07 | 5.18E+05 | 5.17E+05 | 6.41E+05 | 5.07E+05 | 2.88E+05 | 4.40E+07 | |
| Std | 1.85E+05 | 1.96E+05 | 1.51E+07 | 3.78E+05 | 6.08E+05 | 4.63E+05 | 3.25E+05 | 5.19E+05 | 2.57E+07 | |
| Rank | 2 | 1 | 8 | 6 | 5 | 7 | 4 | 3 | 9 | |
| cec08 | Best | 2.30E+03 | 2.34E+03 | 7.64E+03 | 2.32E+03 | 2.32E+03 | 2.30E+03 | 2.33E+03 | 3.16E+03 | 6.89E+03 |
| Worst | 2.31E+03 | 2.70E+03 | 9.97E+03 | 7.18E+03 | 2.43E+03 | 7.65E+03 | 7.45E+03 | 7.45E+03 | 1.03E+04 | |
| Mean | 2.31E+03 | 2.43E+03 | 8.91E+03 | 2.65E+03 | 2.34E+03 | 5.93E+03 | 4.28E+03 | 5.05E+03 | 8.57E+03 | |
| Std | 2.24E+00 | 1.01E+02 | 5.87E+02 | 1.19E+03 | 2.04E+01 | 1.90E+03 | 1.70E+03 | 1.21E+03 | 9.31E+02 | |
| Rank | 1 | 3 | 9 | 4 | 2 | 7 | 5 | 6 | 8 | |
| cec09 | Best | 2.88E+03 | 2.94E+03 | 3.45E+03 | 2.96E+03 | 2.89E+03 | 2.95E+03 | 2.88E+03 | 3.17E+03 | 3.30E+03 |
| Worst | 3.00E+03 | 3.12E+03 | 3.91E+03 | 3.29E+03 | 3.06E+03 | 3.26E+03 | 3.08E+03 | 3.66E+03 | 4.46E+03 | |
| Mean | 2.94E+03 | 3.01E+03 | 3.60E+03 | 3.06E+03 | 2.96E+03 | 3.10E+03 | 2.96E+03 | 3.36E+03 | 3.53E+03 | |
| Std | 3.01E+01 | 4.89E+01 | 9.03E+01 | 6.53E+01 | 4.90E+01 | 7.97E+01 | 4.70E+01 | 1.21E+02 | 2.63E+02 | |
| Rank | 1 | 4 | 9 | 5 | 2 | 6 | 3 | 7 | 8 | |
| cec10 | Best | 2.89E+03 | 2.95E+03 | 4.21E+03 | 2.89E+03 | 2.92E+03 | 2.88E+03 | 2.89E+03 | 3.08E+03 | 3.95E+03 |
| Worst | 2.96E+03 | 3.08E+03 | 4.69E+03 | 3.02E+03 | 3.05E+03 | 2.97E+03 | 2.97E+03 | 3.82E+03 | 6.12E+03 | |
| Mean | 2.91E+03 | 3.00E+03 | 4.45E+03 | 2.96E+03 | 2.96E+03 | 2.91E+03 | 2.93E+03 | 3.32E+03 | 5.02E+03 | |
| Std | 1.82E+01 | 3.34E+01 | 1.37E+02 | 3.31E+01 | 3.20E+01 | 2.14E+01 | 2.36E+01 | 1.88E+02 | 6.18E+02 | |
| Rank | 2 | 6 | 8 | 4 | 5 | 1 | 3 | 7 | 9 | |
| Mean rank | 1.3 | 4.4 | 7.9 | 4.3 | 3.1 | 5.2 | 3.7 | 6.6 | 7.5 | |
| Final ranking | 1 | 5 | 9 | 4 | 2 | 6 | 3 | 7 | 8 | |
| +/=/– | –/–/– | 0/2/8 | 0/1/9 | 0/1/9 | 0/3/7 | 0/2/8 | 0/3/7 | 0/2/8 | 0/1/9 | |
The results of HBWO-JS and other algorithms for CEC2020 test functions (the dimension dim = 30).
| Function . | Index . | Algorithms . | ||||||||
|---|---|---|---|---|---|---|---|---|---|---|
| HBWO-JS . | JS . | BWO . | AHA . | ARO . | DO . | SO . | WSO . | RSA . | ||
| cec01 | Best | 1.77E+05 | 3.08E+07 | 4.50E+10 | 7.09E+06 | 6.41E+06 | 2.73E+05 | 7.88E+05 | 5.88E+09 | 2.97E+10 |
| Worst | 1.66E+06 | 3.83E+09 | 5.99E+10 | 4.42E+08 | 8.80E+07 | 2.72E+06 | 6.39E+07 | 2.15E+10 | 6.39E+10 | |
| Mean | 6.01E+05 | 2.98E+08 | 5.30E+10 | 6.02E+07 | 2.88E+07 | 9.07E+05 | 9.75E+06 | 1.28E+10 | 4.74E+10 | |
| Std | 3.55E+05 | 6.87E+08 | 4.17E+09 | 8.70E+07 | 1.76E+07 | 6.27E+05 | 1.22E+07 | 4.16E+09 | 6.65E+09 | |
| Rank | 1 | 6 | 9 | 5 | 4 | 2 | 3 | 7 | 8 | |
| cec02 | Best | 2.54E+03 | 5.27E+03 | 7.97E+03 | 3.19E+03 | 3.22E+03 | 3.13E+03 | 2.88E+03 | 4.95E+03 | 7.18E+03 |
| Worst | 4.73E+03 | 9.03E+03 | 9.37E+03 | 5.42E+03 | 5.21E+03 | 6.22E+03 | 7.04E+03 | 8.90E+03 | 8.53E+03 | |
| Mean | 4.02E+03 | 8.12E+03 | 8.67E+03 | 4.31E+03 | 4.21E+03 | 4.94E+03 | 4.07E+03 | 7.59E+03 | 7.94E+03 | |
| Std | 4.67E+02 | 8.88E+02 | 3.51E+02 | 5.16E+02 | 5.27E+02 | 7.08E+02 | 8.17E+02 | 1.06E+03 | 4.24E+02 | |
| Rank | 1 | 8 | 9 | 4 | 3 | 5 | 2 | 6 | 7 | |
| cec03 | Best | 8.48E+02 | 8.61E+02 | 1.34E+03 | 8.82E+02 | 8.47E+02 | 8.71E+02 | 7.86E+02 | 1.03E+03 | 1.32E+03 |
| Worst | 1.22E+03 | 1.20E+03 | 1.47E+03 | 1.32E+03 | 1.22E+03 | 1.11E+03 | 1.05E+03 | 1.37E+03 | 1.48E+03 | |
| Mean | 9.09E+02 | 9.86E+02 | 1.40E+03 | 1.05E+03 | 9.52E+02 | 1.01E+03 | 9.11E+02 | 1.14E+03 | 1.40E+03 | |
| Std | 6.83E+01 | 7.21E+01 | 3.33E+01 | 1.07E+02 | 8.78E+01 | 6.11E+01 | 5.00E+01 | 8.98E+01 | 3.80E+01 | |
| Rank | 1 | 4 | 9 | 6 | 3 | 5 | 2 | 7 | 8 | |
| cec04 | Best | 1.90E+03 | 1.90E+03 | 1.90E+03 | 1.90E+03 | 1.90E+03 | 1.90E+03 | 1.90E+03 | 1.91E+03 | 1.90E+03 |
| Worst | 1.90E+03 | 1.90E+03 | 1.90E+03 | 1.90E+03 | 1.90E+03 | 1.92E+03 | 1.90E+03 | 1.99E+03 | 1.90E+03 | |
| Mean | 1.90E+03 | 1.90E+03 | 1.90E+03 | 1.90E+03 | 1.90E+03 | 1.91E+03 | 1.90E+03 | 1.94E+03 | 1.90E+03 | |
| Std | 0.00E+00 | 4.12E-03 | 0.00E+00 | 0.00E+00 | 0.00E+00 | 4.60E+00 | 1.34E-01 | 1.45E+01 | 0.00E+00 | |
| Rank | 1 | 6 | 1 | 1 | 1 | 8 | 7 | 9 | 1 | |
| cec05 | Best | 1.02E+05 | 1.10E+05 | 2.48E+07 | 3.41E+05 | 4.12E+05 | 1.26E+05 | 6.62E+04 | 7.56E+04 | 2.62E+07 |
| Worst | 2.91E+06 | 2.55E+06 | 1.31E+08 | 5.27E+06 | 3.95E+06 | 6.65E+06 | 4.20E+06 | 1.96E+07 | 1.51E+08 | |
| Mean | 9.02E+05 | 7.99E+05 | 7.32E+07 | 2.41E+06 | 1.55E+06 | 1.71E+06 | 1.63E+06 | 2.67E+06 | 8.25E+07 | |
| Std | 7.19E+05 | 5.12E+05 | 2.33E+07 | 1.44E+06 | 1.02E+06 | 1.33E+06 | 1.12E+06 | 4.07E+06 | 3.39E+07 | |
| Rank | 2 | 1 | 8 | 6 | 3 | 5 | 4 | 7 | 9 | |
| cec06 | Best | 1.74E+03 | 1.80E+03 | 4.13E+03 | 1.76E+03 | 1.81E+03 | 1.86E+03 | 1.76E+03 | 1.90E+03 | 3.44E+03 |
| Worst | 2.07E+03 | 2.79E+03 | 5.85E+03 | 2.56E+03 | 2.52E+03 | 2.80E+03 | 2.69E+03 | 3.03E+03 | 6.91E+03 | |
| Mean | 1.92E+03 | 2.21E+03 | 5.07E+03 | 2.13E+03 | 2.15E+03 | 2.28E+03 | 2.17E+03 | 2.36E+03 | 4.71E+03 | |
| Std | 8.38E+01 | 2.49E+02 | 3.82E+02 | 2.01E+02 | 1.91E+02 | 2.49E+02 | 2.26E+02 | 2.84E+02 | 7.84E+02 | |
| Rank | 1 | 5 | 9 | 2 | 3 | 6 | 4 | 7 | 8 | |
| cec07 | Best | 1.85E+04 | 2.75E+04 | 3.63E+06 | 5.18E+04 | 5.91E+04 | 4.58E+04 | 1.92E+04 | 6.04E+03 | 5.78E+06 |
| Worst | 8.13E+05 | 9.05E+05 | 6.08E+07 | 1.61E+06 | 3.17E+06 | 2.02E+06 | 1.10E+06 | 2.73E+06 | 9.49E+07 | |
| Mean | 2.48E+05 | 2.39E+05 | 3.03E+07 | 5.18E+05 | 5.17E+05 | 6.41E+05 | 5.07E+05 | 2.88E+05 | 4.40E+07 | |
| Std | 1.85E+05 | 1.96E+05 | 1.51E+07 | 3.78E+05 | 6.08E+05 | 4.63E+05 | 3.25E+05 | 5.19E+05 | 2.57E+07 | |
| Rank | 2 | 1 | 8 | 6 | 5 | 7 | 4 | 3 | 9 | |
| cec08 | Best | 2.30E+03 | 2.34E+03 | 7.64E+03 | 2.32E+03 | 2.32E+03 | 2.30E+03 | 2.33E+03 | 3.16E+03 | 6.89E+03 |
| Worst | 2.31E+03 | 2.70E+03 | 9.97E+03 | 7.18E+03 | 2.43E+03 | 7.65E+03 | 7.45E+03 | 7.45E+03 | 1.03E+04 | |
| Mean | 2.31E+03 | 2.43E+03 | 8.91E+03 | 2.65E+03 | 2.34E+03 | 5.93E+03 | 4.28E+03 | 5.05E+03 | 8.57E+03 | |
| Std | 2.24E+00 | 1.01E+02 | 5.87E+02 | 1.19E+03 | 2.04E+01 | 1.90E+03 | 1.70E+03 | 1.21E+03 | 9.31E+02 | |
| Rank | 1 | 3 | 9 | 4 | 2 | 7 | 5 | 6 | 8 | |
| cec09 | Best | 2.88E+03 | 2.94E+03 | 3.45E+03 | 2.96E+03 | 2.89E+03 | 2.95E+03 | 2.88E+03 | 3.17E+03 | 3.30E+03 |
| Worst | 3.00E+03 | 3.12E+03 | 3.91E+03 | 3.29E+03 | 3.06E+03 | 3.26E+03 | 3.08E+03 | 3.66E+03 | 4.46E+03 | |
| Mean | 2.94E+03 | 3.01E+03 | 3.60E+03 | 3.06E+03 | 2.96E+03 | 3.10E+03 | 2.96E+03 | 3.36E+03 | 3.53E+03 | |
| Std | 3.01E+01 | 4.89E+01 | 9.03E+01 | 6.53E+01 | 4.90E+01 | 7.97E+01 | 4.70E+01 | 1.21E+02 | 2.63E+02 | |
| Rank | 1 | 4 | 9 | 5 | 2 | 6 | 3 | 7 | 8 | |
| cec10 | Best | 2.89E+03 | 2.95E+03 | 4.21E+03 | 2.89E+03 | 2.92E+03 | 2.88E+03 | 2.89E+03 | 3.08E+03 | 3.95E+03 |
| Worst | 2.96E+03 | 3.08E+03 | 4.69E+03 | 3.02E+03 | 3.05E+03 | 2.97E+03 | 2.97E+03 | 3.82E+03 | 6.12E+03 | |
| Mean | 2.91E+03 | 3.00E+03 | 4.45E+03 | 2.96E+03 | 2.96E+03 | 2.91E+03 | 2.93E+03 | 3.32E+03 | 5.02E+03 | |
| Std | 1.82E+01 | 3.34E+01 | 1.37E+02 | 3.31E+01 | 3.20E+01 | 2.14E+01 | 2.36E+01 | 1.88E+02 | 6.18E+02 | |
| Rank | 2 | 6 | 8 | 4 | 5 | 1 | 3 | 7 | 9 | |
| Mean rank | 1.3 | 4.4 | 7.9 | 4.3 | 3.1 | 5.2 | 3.7 | 6.6 | 7.5 | |
| Final ranking | 1 | 5 | 9 | 4 | 2 | 6 | 3 | 7 | 8 | |
| +/=/– | –/–/– | 0/2/8 | 0/1/9 | 0/1/9 | 0/3/7 | 0/2/8 | 0/3/7 | 0/2/8 | 0/1/9 | |
| Function . | Index . | Algorithms . | ||||||||
|---|---|---|---|---|---|---|---|---|---|---|
| HBWO-JS . | JS . | BWO . | AHA . | ARO . | DO . | SO . | WSO . | RSA . | ||
| cec01 | Best | 1.77E+05 | 3.08E+07 | 4.50E+10 | 7.09E+06 | 6.41E+06 | 2.73E+05 | 7.88E+05 | 5.88E+09 | 2.97E+10 |
| Worst | 1.66E+06 | 3.83E+09 | 5.99E+10 | 4.42E+08 | 8.80E+07 | 2.72E+06 | 6.39E+07 | 2.15E+10 | 6.39E+10 | |
| Mean | 6.01E+05 | 2.98E+08 | 5.30E+10 | 6.02E+07 | 2.88E+07 | 9.07E+05 | 9.75E+06 | 1.28E+10 | 4.74E+10 | |
| Std | 3.55E+05 | 6.87E+08 | 4.17E+09 | 8.70E+07 | 1.76E+07 | 6.27E+05 | 1.22E+07 | 4.16E+09 | 6.65E+09 | |
| Rank | 1 | 6 | 9 | 5 | 4 | 2 | 3 | 7 | 8 | |
| cec02 | Best | 2.54E+03 | 5.27E+03 | 7.97E+03 | 3.19E+03 | 3.22E+03 | 3.13E+03 | 2.88E+03 | 4.95E+03 | 7.18E+03 |
| Worst | 4.73E+03 | 9.03E+03 | 9.37E+03 | 5.42E+03 | 5.21E+03 | 6.22E+03 | 7.04E+03 | 8.90E+03 | 8.53E+03 | |
| Mean | 4.02E+03 | 8.12E+03 | 8.67E+03 | 4.31E+03 | 4.21E+03 | 4.94E+03 | 4.07E+03 | 7.59E+03 | 7.94E+03 | |
| Std | 4.67E+02 | 8.88E+02 | 3.51E+02 | 5.16E+02 | 5.27E+02 | 7.08E+02 | 8.17E+02 | 1.06E+03 | 4.24E+02 | |
| Rank | 1 | 8 | 9 | 4 | 3 | 5 | 2 | 6 | 7 | |
| cec03 | Best | 8.48E+02 | 8.61E+02 | 1.34E+03 | 8.82E+02 | 8.47E+02 | 8.71E+02 | 7.86E+02 | 1.03E+03 | 1.32E+03 |
| Worst | 1.22E+03 | 1.20E+03 | 1.47E+03 | 1.32E+03 | 1.22E+03 | 1.11E+03 | 1.05E+03 | 1.37E+03 | 1.48E+03 | |
| Mean | 9.09E+02 | 9.86E+02 | 1.40E+03 | 1.05E+03 | 9.52E+02 | 1.01E+03 | 9.11E+02 | 1.14E+03 | 1.40E+03 | |
| Std | 6.83E+01 | 7.21E+01 | 3.33E+01 | 1.07E+02 | 8.78E+01 | 6.11E+01 | 5.00E+01 | 8.98E+01 | 3.80E+01 | |
| Rank | 1 | 4 | 9 | 6 | 3 | 5 | 2 | 7 | 8 | |
| cec04 | Best | 1.90E+03 | 1.90E+03 | 1.90E+03 | 1.90E+03 | 1.90E+03 | 1.90E+03 | 1.90E+03 | 1.91E+03 | 1.90E+03 |
| Worst | 1.90E+03 | 1.90E+03 | 1.90E+03 | 1.90E+03 | 1.90E+03 | 1.92E+03 | 1.90E+03 | 1.99E+03 | 1.90E+03 | |
| Mean | 1.90E+03 | 1.90E+03 | 1.90E+03 | 1.90E+03 | 1.90E+03 | 1.91E+03 | 1.90E+03 | 1.94E+03 | 1.90E+03 | |
| Std | 0.00E+00 | 4.12E-03 | 0.00E+00 | 0.00E+00 | 0.00E+00 | 4.60E+00 | 1.34E-01 | 1.45E+01 | 0.00E+00 | |
| Rank | 1 | 6 | 1 | 1 | 1 | 8 | 7 | 9 | 1 | |
| cec05 | Best | 1.02E+05 | 1.10E+05 | 2.48E+07 | 3.41E+05 | 4.12E+05 | 1.26E+05 | 6.62E+04 | 7.56E+04 | 2.62E+07 |
| Worst | 2.91E+06 | 2.55E+06 | 1.31E+08 | 5.27E+06 | 3.95E+06 | 6.65E+06 | 4.20E+06 | 1.96E+07 | 1.51E+08 | |
| Mean | 9.02E+05 | 7.99E+05 | 7.32E+07 | 2.41E+06 | 1.55E+06 | 1.71E+06 | 1.63E+06 | 2.67E+06 | 8.25E+07 | |
| Std | 7.19E+05 | 5.12E+05 | 2.33E+07 | 1.44E+06 | 1.02E+06 | 1.33E+06 | 1.12E+06 | 4.07E+06 | 3.39E+07 | |
| Rank | 2 | 1 | 8 | 6 | 3 | 5 | 4 | 7 | 9 | |
| cec06 | Best | 1.74E+03 | 1.80E+03 | 4.13E+03 | 1.76E+03 | 1.81E+03 | 1.86E+03 | 1.76E+03 | 1.90E+03 | 3.44E+03 |
| Worst | 2.07E+03 | 2.79E+03 | 5.85E+03 | 2.56E+03 | 2.52E+03 | 2.80E+03 | 2.69E+03 | 3.03E+03 | 6.91E+03 | |
| Mean | 1.92E+03 | 2.21E+03 | 5.07E+03 | 2.13E+03 | 2.15E+03 | 2.28E+03 | 2.17E+03 | 2.36E+03 | 4.71E+03 | |
| Std | 8.38E+01 | 2.49E+02 | 3.82E+02 | 2.01E+02 | 1.91E+02 | 2.49E+02 | 2.26E+02 | 2.84E+02 | 7.84E+02 | |
| Rank | 1 | 5 | 9 | 2 | 3 | 6 | 4 | 7 | 8 | |
| cec07 | Best | 1.85E+04 | 2.75E+04 | 3.63E+06 | 5.18E+04 | 5.91E+04 | 4.58E+04 | 1.92E+04 | 6.04E+03 | 5.78E+06 |
| Worst | 8.13E+05 | 9.05E+05 | 6.08E+07 | 1.61E+06 | 3.17E+06 | 2.02E+06 | 1.10E+06 | 2.73E+06 | 9.49E+07 | |
| Mean | 2.48E+05 | 2.39E+05 | 3.03E+07 | 5.18E+05 | 5.17E+05 | 6.41E+05 | 5.07E+05 | 2.88E+05 | 4.40E+07 | |
| Std | 1.85E+05 | 1.96E+05 | 1.51E+07 | 3.78E+05 | 6.08E+05 | 4.63E+05 | 3.25E+05 | 5.19E+05 | 2.57E+07 | |
| Rank | 2 | 1 | 8 | 6 | 5 | 7 | 4 | 3 | 9 | |
| cec08 | Best | 2.30E+03 | 2.34E+03 | 7.64E+03 | 2.32E+03 | 2.32E+03 | 2.30E+03 | 2.33E+03 | 3.16E+03 | 6.89E+03 |
| Worst | 2.31E+03 | 2.70E+03 | 9.97E+03 | 7.18E+03 | 2.43E+03 | 7.65E+03 | 7.45E+03 | 7.45E+03 | 1.03E+04 | |
| Mean | 2.31E+03 | 2.43E+03 | 8.91E+03 | 2.65E+03 | 2.34E+03 | 5.93E+03 | 4.28E+03 | 5.05E+03 | 8.57E+03 | |
| Std | 2.24E+00 | 1.01E+02 | 5.87E+02 | 1.19E+03 | 2.04E+01 | 1.90E+03 | 1.70E+03 | 1.21E+03 | 9.31E+02 | |
| Rank | 1 | 3 | 9 | 4 | 2 | 7 | 5 | 6 | 8 | |
| cec09 | Best | 2.88E+03 | 2.94E+03 | 3.45E+03 | 2.96E+03 | 2.89E+03 | 2.95E+03 | 2.88E+03 | 3.17E+03 | 3.30E+03 |
| Worst | 3.00E+03 | 3.12E+03 | 3.91E+03 | 3.29E+03 | 3.06E+03 | 3.26E+03 | 3.08E+03 | 3.66E+03 | 4.46E+03 | |
| Mean | 2.94E+03 | 3.01E+03 | 3.60E+03 | 3.06E+03 | 2.96E+03 | 3.10E+03 | 2.96E+03 | 3.36E+03 | 3.53E+03 | |
| Std | 3.01E+01 | 4.89E+01 | 9.03E+01 | 6.53E+01 | 4.90E+01 | 7.97E+01 | 4.70E+01 | 1.21E+02 | 2.63E+02 | |
| Rank | 1 | 4 | 9 | 5 | 2 | 6 | 3 | 7 | 8 | |
| cec10 | Best | 2.89E+03 | 2.95E+03 | 4.21E+03 | 2.89E+03 | 2.92E+03 | 2.88E+03 | 2.89E+03 | 3.08E+03 | 3.95E+03 |
| Worst | 2.96E+03 | 3.08E+03 | 4.69E+03 | 3.02E+03 | 3.05E+03 | 2.97E+03 | 2.97E+03 | 3.82E+03 | 6.12E+03 | |
| Mean | 2.91E+03 | 3.00E+03 | 4.45E+03 | 2.96E+03 | 2.96E+03 | 2.91E+03 | 2.93E+03 | 3.32E+03 | 5.02E+03 | |
| Std | 1.82E+01 | 3.34E+01 | 1.37E+02 | 3.31E+01 | 3.20E+01 | 2.14E+01 | 2.36E+01 | 1.88E+02 | 6.18E+02 | |
| Rank | 2 | 6 | 8 | 4 | 5 | 1 | 3 | 7 | 9 | |
| Mean rank | 1.3 | 4.4 | 7.9 | 4.3 | 3.1 | 5.2 | 3.7 | 6.6 | 7.5 | |
| Final ranking | 1 | 5 | 9 | 4 | 2 | 6 | 3 | 7 | 8 | |
| +/=/– | –/–/– | 0/2/8 | 0/1/9 | 0/1/9 | 0/3/7 | 0/2/8 | 0/3/7 | 0/2/8 | 0/1/9 | |
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