The results of HBWO-JS and other algorithms for CEC2020 test functions (the dimension dim = 100).
| Function . | Index . | Algorithms . | ||||||||
|---|---|---|---|---|---|---|---|---|---|---|
| HBWO-JS . | JS . | BWO . | AHA . | ARO . | DO . | SO . | WSO . | RSA . | ||
| cec01 | Best | 1.31E+09 | 5.78E+10 | 2.48E+11 | 3.71E+10 | 3.58E+10 | 3.66E+08 | 9.68E+09 | 1.46E+11 | 2.05E+11 |
| Worst | 3.79E+09 | 1.06E+11 | 2.70E+11 | 8.91E+10 | 7.55E+10 | 1.34E+09 | 2.38E+10 | 2.08E+11 | 2.61E+11 | |
| Mean | 2.34E+09 | 7.83E+10 | 2.59E+11 | 6.65E+10 | 5.23E+10 | 7.30E+08 | 1.44E+10 | 1.73E+11 | 2.47E+11 | |
| Std | 6.43E+08 | 1.28E+10 | 6.03E+09 | 1.31E+10 | 1.05E+10 | 2.46E+08 | 3.55E+09 | 1.53E+10 | 9.84E+09 | |
| Rank | 2 | 6 | 9 | 5 | 4 | 1 | 3 | 7 | 8 | |
| cec02 | Best | 1.29E+04 | 2.37E+04 | 3.14E+04 | 1.49E+04 | 1.75E+04 | 1.47E+04 | 2.34E+04 | 2.14E+04 | 3.11E+04 |
| Worst | 2.05E+04 | 3.32E+04 | 3.37E+04 | 1.94E+04 | 2.28E+04 | 2.21E+04 | 3.34E+04 | 3.31E+04 | 3.41E+04 | |
| Mean | 1.73E+04 | 3.18E+04 | 3.28E+04 | 1.71E+04 | 2.01E+04 | 1.89E+04 | 3.09E+04 | 2.83E+04 | 3.25E+04 | |
| Std | 1.65E+03 | 1.74E+03 | 5.70E+02 | 1.36E+03 | 1.35E+03 | 1.89E+03 | 2.07E+03 | 3.86E+03 | 7.65E+02 | |
| Rank | 2 | 7 | 9 | 1 | 4 | 3 | 6 | 5 | 8 | |
| cec03 | Best | 2.03E+03 | 2.55E+03 | 3.68E+03 | 2.59E+03 | 2.48E+03 | 2.31E+03 | 1.98E+03 | 3.31E+03 | 3.73E+03 |
| Worst | 3.17E+03 | 3.52E+03 | 4.05E+03 | 3.39E+03 | 3.41E+03 | 3.32E+03 | 2.47E+03 | 4.15E+03 | 4.12E+03 | |
| Mean | 2.54E+03 | 3.11E+03 | 3.89E+03 | 3.08E+03 | 2.93E+03 | 2.81E+03 | 2.25E+03 | 3.65E+03 | 3.90E+03 | |
| Std | 2.93E+02 | 2.70E+02 | 9.31E+01 | 2.00E+02 | 2.05E+02 | 2.73E+02 | 1.19E+02 | 2.24E+02 | 8.96E+01 | |
| Rank | 2 | 6 | 8 | 5 | 4 | 3 | 1 | 7 | 9 | |
| cec04 | Best | 1.90E+03 | 1.90E+03 | 1.90E+03 | 1.90E+03 | 1.90E+03 | 1.96E+03 | 1.90E+03 | 2.07E+03 | 1.90E+03 |
| Worst | 1.90E+03 | 1.90E+03 | 1.90E+03 | 1.90E+03 | 1.90E+03 | 2.09E+03 | 1.90E+03 | 2.76E+03 | 1.90E+03 | |
| Mean | 1.90E+03 | 1.90E+03 | 1.90E+03 | 1.90E+03 | 1.90E+03 | 2.01E+03 | 1.90E+03 | 2.24E+03 | 1.90E+03 | |
| Std | 0.00E+00 | 9.14E-02 | 0.00E+00 | 0.00E+00 | 0.00E+00 | 3.17E+01 | 0.00E+00 | 1.39E+02 | 0.00E+00 | |
| Rank | 1 | 7 | 1 | 1 | 1 | 8 | 1 | 9 | 1 | |
| cec05 | Best | 2.02E+07 | 3.55E+07 | 1.11E+09 | 3.60E+07 | 3.01E+07 | 1.62E+07 | 2.06E+07 | 4.00E+07 | 7.17E+08 |
| Worst | 7.07E+07 | 8.60E+07 | 1.89E+09 | 1.72E+08 | 1.04E+08 | 4.99E+07 | 1.12E+08 | 5.58E+08 | 2.01E+09 | |
| Mean | 4.21E+07 | 6.06E+07 | 1.62E+09 | 8.95E+07 | 6.32E+07 | 2.98E+07 | 6.05E+07 | 2.18E+08 | 1.29E+09 | |
| Std | 1.22E+07 | 1.16E+07 | 1.91E+08 | 3.63E+07 | 2.12E+07 | 9.38E+06 | 2.24E+07 | 1.21E+08 | 3.66E+08 | |
| Rank | 2 | 4 | 9 | 6 | 5 | 1 | 3 | 7 | 8 | |
| cec06 | Best | 5.61E+03 | 7.09E+03 | 2.39E+04 | 5.48E+03 | 5.65E+03 | 6.51E+03 | 5.46E+03 | 9.45E+03 | 1.99E+04 |
| Worst | 8.41E+03 | 1.22E+04 | 3.21E+04 | 8.65E+03 | 9.47E+03 | 1.02E+04 | 7.93E+03 | 1.71E+04 | 3.54E+04 | |
| Mean | 6.65E+03 | 9.44E+03 | 2.90E+04 | 6.84E+03 | 7.78E+03 | 8.20E+03 | 6.67E+03 | 1.25E+04 | 2.81E+04 | |
| Std | 6.79E+02 | 1.23E+03 | 1.99E+03 | 7.07E+02 | 1.11E+03 | 8.68E+02 | 5.24E+02 | 1.64E+03 | 4.16E+03 | |
| Rank | 1 | 6 | 9 | 3 | 4 | 5 | 2 | 7 | 8 | |
| cec07 | Best | 2.82E+06 | 1.02E+07 | 2.40E+08 | 1.07E+07 | 1.07E+07 | 6.26E+06 | 5.55E+06 | 1.74E+07 | 2.12E+08 |
| Worst | 1.68E+07 | 4.25E+07 | 3.96E+08 | 5.85E+07 | 5.04E+07 | 2.44E+07 | 4.97E+07 | 1.34E+08 | 7.34E+08 | |
| Mean | 9.61E+06 | 1.85E+07 | 3.44E+08 | 3.20E+07 | 2.36E+07 | 1.18E+07 | 2.52E+07 | 6.35E+07 | 4.40E+08 | |
| Std | 3.06E+06 | 6.48E+06 | 3.56E+07 | 1.24E+07 | 9.43E+06 | 4.24E+06 | 1.10E+07 | 3.34E+07 | 1.28E+08 | |
| Rank | 1 | 3 | 8 | 6 | 4 | 2 | 5 | 7 | 9 | |
| cec08 | Best | 1.74E+04 | 2.50E+04 | 3.39E+04 | 1.75E+04 | 2.01E+04 | 1.88E+04 | 2.48E+04 | 2.32E+04 | 3.38E+04 |
| Worst | 2.33E+04 | 3.55E+04 | 3.60E+04 | 2.49E+04 | 2.63E+04 | 2.35E+04 | 3.57E+04 | 3.50E+04 | 3.58E+04 | |
| Mean | 2.09E+04 | 3.22E+04 | 3.50E+04 | 2.15E+04 | 2.29E+04 | 2.13E+04 | 3.29E+04 | 2.86E+04 | 3.48E+04 | |
| Std | 1.44E+03 | 3.10E+03 | 4.53E+02 | 1.80E+03 | 1.49E+03 | 1.22E+03 | 2.40E+03 | 3.77E+03 | 5.88E+02 | |
| Rank | 1 | 6 | 9 | 3 | 4 | 2 | 7 | 5 | 8 | |
| cec09 | Best | 4.26E+03 | 4.38E+03 | 8.45E+03 | 4.51E+03 | 4.62E+03 | 4.34E+03 | 4.31E+03 | 6.78E+03 | 7.22E+03 |
| Worst | 4.57E+03 | 5.99E+03 | 1.03E+04 | 5.24E+03 | 5.21E+03 | 5.68E+03 | 5.33E+03 | 1.02E+04 | 1.46E+04 | |
| Mean | 4.36E+03 | 5.38E+03 | 9.37E+03 | 4.82E+03 | 4.94E+03 | 4.79E+03 | 4.79E+03 | 7.83E+03 | 9.71E+03 | |
| Std | 7.54E+01 | 3.23E+02 | 4.56E+02 | 1.61E+02 | 1.67E+02 | 2.73E+02 | 2.23E+02 | 6.71E+02 | 2.60E+03 | |
| Rank | 1 | 6 | 8 | 4 | 5 | 3 | 2 | 7 | 9 | |
| cec10 | Best | 3.94E+03 | 5.70E+03 | 2.65E+04 | 5.27E+03 | 5.07E+03 | 3.74E+03 | 4.50E+03 | 1.19E+04 | 2.05E+04 |
| Worst | 4.68E+03 | 1.05E+04 | 3.04E+04 | 1.01E+04 | 7.65E+03 | 3.94E+03 | 7.69E+03 | 2.13E+04 | 2.89E+04 | |
| Mean | 4.16E+03 | 7.96E+03 | 2.82E+04 | 7.55E+03 | 6.48E+03 | 3.84E+03 | 5.37E+03 | 1.61E+04 | 2.54E+04 | |
| Std | 1.64E+02 | 1.21E+03 | 9.97E+02 | 1.20E+03 | 6.23E+02 | 5.87E+01 | 6.73E+02 | 2.19E+03 | 1.85E+03 | |
| Rank | 2 | 6 | 9 | 5 | 4 | 1 | 3 | 7 | 8 | |
| Mean rank | 1.5 | 5.7 | 7.9 | 3.9 | 3.9 | 2.9 | 3.3 | 6.8 | 7.6 | |
| Final ranking | 1 | 6 | 9 | 4 | 4 | 2 | 3 | 7 | 8 | |
| +/=/– | –/–/– | 0/0/10 | 0/1/9 | 0/4/6 | 0/1/9 | 2/2/5 | 1/2/7 | 0/0/10 | 0/1/9 | |
| Function . | Index . | Algorithms . | ||||||||
|---|---|---|---|---|---|---|---|---|---|---|
| HBWO-JS . | JS . | BWO . | AHA . | ARO . | DO . | SO . | WSO . | RSA . | ||
| cec01 | Best | 1.31E+09 | 5.78E+10 | 2.48E+11 | 3.71E+10 | 3.58E+10 | 3.66E+08 | 9.68E+09 | 1.46E+11 | 2.05E+11 |
| Worst | 3.79E+09 | 1.06E+11 | 2.70E+11 | 8.91E+10 | 7.55E+10 | 1.34E+09 | 2.38E+10 | 2.08E+11 | 2.61E+11 | |
| Mean | 2.34E+09 | 7.83E+10 | 2.59E+11 | 6.65E+10 | 5.23E+10 | 7.30E+08 | 1.44E+10 | 1.73E+11 | 2.47E+11 | |
| Std | 6.43E+08 | 1.28E+10 | 6.03E+09 | 1.31E+10 | 1.05E+10 | 2.46E+08 | 3.55E+09 | 1.53E+10 | 9.84E+09 | |
| Rank | 2 | 6 | 9 | 5 | 4 | 1 | 3 | 7 | 8 | |
| cec02 | Best | 1.29E+04 | 2.37E+04 | 3.14E+04 | 1.49E+04 | 1.75E+04 | 1.47E+04 | 2.34E+04 | 2.14E+04 | 3.11E+04 |
| Worst | 2.05E+04 | 3.32E+04 | 3.37E+04 | 1.94E+04 | 2.28E+04 | 2.21E+04 | 3.34E+04 | 3.31E+04 | 3.41E+04 | |
| Mean | 1.73E+04 | 3.18E+04 | 3.28E+04 | 1.71E+04 | 2.01E+04 | 1.89E+04 | 3.09E+04 | 2.83E+04 | 3.25E+04 | |
| Std | 1.65E+03 | 1.74E+03 | 5.70E+02 | 1.36E+03 | 1.35E+03 | 1.89E+03 | 2.07E+03 | 3.86E+03 | 7.65E+02 | |
| Rank | 2 | 7 | 9 | 1 | 4 | 3 | 6 | 5 | 8 | |
| cec03 | Best | 2.03E+03 | 2.55E+03 | 3.68E+03 | 2.59E+03 | 2.48E+03 | 2.31E+03 | 1.98E+03 | 3.31E+03 | 3.73E+03 |
| Worst | 3.17E+03 | 3.52E+03 | 4.05E+03 | 3.39E+03 | 3.41E+03 | 3.32E+03 | 2.47E+03 | 4.15E+03 | 4.12E+03 | |
| Mean | 2.54E+03 | 3.11E+03 | 3.89E+03 | 3.08E+03 | 2.93E+03 | 2.81E+03 | 2.25E+03 | 3.65E+03 | 3.90E+03 | |
| Std | 2.93E+02 | 2.70E+02 | 9.31E+01 | 2.00E+02 | 2.05E+02 | 2.73E+02 | 1.19E+02 | 2.24E+02 | 8.96E+01 | |
| Rank | 2 | 6 | 8 | 5 | 4 | 3 | 1 | 7 | 9 | |
| cec04 | Best | 1.90E+03 | 1.90E+03 | 1.90E+03 | 1.90E+03 | 1.90E+03 | 1.96E+03 | 1.90E+03 | 2.07E+03 | 1.90E+03 |
| Worst | 1.90E+03 | 1.90E+03 | 1.90E+03 | 1.90E+03 | 1.90E+03 | 2.09E+03 | 1.90E+03 | 2.76E+03 | 1.90E+03 | |
| Mean | 1.90E+03 | 1.90E+03 | 1.90E+03 | 1.90E+03 | 1.90E+03 | 2.01E+03 | 1.90E+03 | 2.24E+03 | 1.90E+03 | |
| Std | 0.00E+00 | 9.14E-02 | 0.00E+00 | 0.00E+00 | 0.00E+00 | 3.17E+01 | 0.00E+00 | 1.39E+02 | 0.00E+00 | |
| Rank | 1 | 7 | 1 | 1 | 1 | 8 | 1 | 9 | 1 | |
| cec05 | Best | 2.02E+07 | 3.55E+07 | 1.11E+09 | 3.60E+07 | 3.01E+07 | 1.62E+07 | 2.06E+07 | 4.00E+07 | 7.17E+08 |
| Worst | 7.07E+07 | 8.60E+07 | 1.89E+09 | 1.72E+08 | 1.04E+08 | 4.99E+07 | 1.12E+08 | 5.58E+08 | 2.01E+09 | |
| Mean | 4.21E+07 | 6.06E+07 | 1.62E+09 | 8.95E+07 | 6.32E+07 | 2.98E+07 | 6.05E+07 | 2.18E+08 | 1.29E+09 | |
| Std | 1.22E+07 | 1.16E+07 | 1.91E+08 | 3.63E+07 | 2.12E+07 | 9.38E+06 | 2.24E+07 | 1.21E+08 | 3.66E+08 | |
| Rank | 2 | 4 | 9 | 6 | 5 | 1 | 3 | 7 | 8 | |
| cec06 | Best | 5.61E+03 | 7.09E+03 | 2.39E+04 | 5.48E+03 | 5.65E+03 | 6.51E+03 | 5.46E+03 | 9.45E+03 | 1.99E+04 |
| Worst | 8.41E+03 | 1.22E+04 | 3.21E+04 | 8.65E+03 | 9.47E+03 | 1.02E+04 | 7.93E+03 | 1.71E+04 | 3.54E+04 | |
| Mean | 6.65E+03 | 9.44E+03 | 2.90E+04 | 6.84E+03 | 7.78E+03 | 8.20E+03 | 6.67E+03 | 1.25E+04 | 2.81E+04 | |
| Std | 6.79E+02 | 1.23E+03 | 1.99E+03 | 7.07E+02 | 1.11E+03 | 8.68E+02 | 5.24E+02 | 1.64E+03 | 4.16E+03 | |
| Rank | 1 | 6 | 9 | 3 | 4 | 5 | 2 | 7 | 8 | |
| cec07 | Best | 2.82E+06 | 1.02E+07 | 2.40E+08 | 1.07E+07 | 1.07E+07 | 6.26E+06 | 5.55E+06 | 1.74E+07 | 2.12E+08 |
| Worst | 1.68E+07 | 4.25E+07 | 3.96E+08 | 5.85E+07 | 5.04E+07 | 2.44E+07 | 4.97E+07 | 1.34E+08 | 7.34E+08 | |
| Mean | 9.61E+06 | 1.85E+07 | 3.44E+08 | 3.20E+07 | 2.36E+07 | 1.18E+07 | 2.52E+07 | 6.35E+07 | 4.40E+08 | |
| Std | 3.06E+06 | 6.48E+06 | 3.56E+07 | 1.24E+07 | 9.43E+06 | 4.24E+06 | 1.10E+07 | 3.34E+07 | 1.28E+08 | |
| Rank | 1 | 3 | 8 | 6 | 4 | 2 | 5 | 7 | 9 | |
| cec08 | Best | 1.74E+04 | 2.50E+04 | 3.39E+04 | 1.75E+04 | 2.01E+04 | 1.88E+04 | 2.48E+04 | 2.32E+04 | 3.38E+04 |
| Worst | 2.33E+04 | 3.55E+04 | 3.60E+04 | 2.49E+04 | 2.63E+04 | 2.35E+04 | 3.57E+04 | 3.50E+04 | 3.58E+04 | |
| Mean | 2.09E+04 | 3.22E+04 | 3.50E+04 | 2.15E+04 | 2.29E+04 | 2.13E+04 | 3.29E+04 | 2.86E+04 | 3.48E+04 | |
| Std | 1.44E+03 | 3.10E+03 | 4.53E+02 | 1.80E+03 | 1.49E+03 | 1.22E+03 | 2.40E+03 | 3.77E+03 | 5.88E+02 | |
| Rank | 1 | 6 | 9 | 3 | 4 | 2 | 7 | 5 | 8 | |
| cec09 | Best | 4.26E+03 | 4.38E+03 | 8.45E+03 | 4.51E+03 | 4.62E+03 | 4.34E+03 | 4.31E+03 | 6.78E+03 | 7.22E+03 |
| Worst | 4.57E+03 | 5.99E+03 | 1.03E+04 | 5.24E+03 | 5.21E+03 | 5.68E+03 | 5.33E+03 | 1.02E+04 | 1.46E+04 | |
| Mean | 4.36E+03 | 5.38E+03 | 9.37E+03 | 4.82E+03 | 4.94E+03 | 4.79E+03 | 4.79E+03 | 7.83E+03 | 9.71E+03 | |
| Std | 7.54E+01 | 3.23E+02 | 4.56E+02 | 1.61E+02 | 1.67E+02 | 2.73E+02 | 2.23E+02 | 6.71E+02 | 2.60E+03 | |
| Rank | 1 | 6 | 8 | 4 | 5 | 3 | 2 | 7 | 9 | |
| cec10 | Best | 3.94E+03 | 5.70E+03 | 2.65E+04 | 5.27E+03 | 5.07E+03 | 3.74E+03 | 4.50E+03 | 1.19E+04 | 2.05E+04 |
| Worst | 4.68E+03 | 1.05E+04 | 3.04E+04 | 1.01E+04 | 7.65E+03 | 3.94E+03 | 7.69E+03 | 2.13E+04 | 2.89E+04 | |
| Mean | 4.16E+03 | 7.96E+03 | 2.82E+04 | 7.55E+03 | 6.48E+03 | 3.84E+03 | 5.37E+03 | 1.61E+04 | 2.54E+04 | |
| Std | 1.64E+02 | 1.21E+03 | 9.97E+02 | 1.20E+03 | 6.23E+02 | 5.87E+01 | 6.73E+02 | 2.19E+03 | 1.85E+03 | |
| Rank | 2 | 6 | 9 | 5 | 4 | 1 | 3 | 7 | 8 | |
| Mean rank | 1.5 | 5.7 | 7.9 | 3.9 | 3.9 | 2.9 | 3.3 | 6.8 | 7.6 | |
| Final ranking | 1 | 6 | 9 | 4 | 4 | 2 | 3 | 7 | 8 | |
| +/=/– | –/–/– | 0/0/10 | 0/1/9 | 0/4/6 | 0/1/9 | 2/2/5 | 1/2/7 | 0/0/10 | 0/1/9 | |
The results of HBWO-JS and other algorithms for CEC2020 test functions (the dimension dim = 100).
| Function . | Index . | Algorithms . | ||||||||
|---|---|---|---|---|---|---|---|---|---|---|
| HBWO-JS . | JS . | BWO . | AHA . | ARO . | DO . | SO . | WSO . | RSA . | ||
| cec01 | Best | 1.31E+09 | 5.78E+10 | 2.48E+11 | 3.71E+10 | 3.58E+10 | 3.66E+08 | 9.68E+09 | 1.46E+11 | 2.05E+11 |
| Worst | 3.79E+09 | 1.06E+11 | 2.70E+11 | 8.91E+10 | 7.55E+10 | 1.34E+09 | 2.38E+10 | 2.08E+11 | 2.61E+11 | |
| Mean | 2.34E+09 | 7.83E+10 | 2.59E+11 | 6.65E+10 | 5.23E+10 | 7.30E+08 | 1.44E+10 | 1.73E+11 | 2.47E+11 | |
| Std | 6.43E+08 | 1.28E+10 | 6.03E+09 | 1.31E+10 | 1.05E+10 | 2.46E+08 | 3.55E+09 | 1.53E+10 | 9.84E+09 | |
| Rank | 2 | 6 | 9 | 5 | 4 | 1 | 3 | 7 | 8 | |
| cec02 | Best | 1.29E+04 | 2.37E+04 | 3.14E+04 | 1.49E+04 | 1.75E+04 | 1.47E+04 | 2.34E+04 | 2.14E+04 | 3.11E+04 |
| Worst | 2.05E+04 | 3.32E+04 | 3.37E+04 | 1.94E+04 | 2.28E+04 | 2.21E+04 | 3.34E+04 | 3.31E+04 | 3.41E+04 | |
| Mean | 1.73E+04 | 3.18E+04 | 3.28E+04 | 1.71E+04 | 2.01E+04 | 1.89E+04 | 3.09E+04 | 2.83E+04 | 3.25E+04 | |
| Std | 1.65E+03 | 1.74E+03 | 5.70E+02 | 1.36E+03 | 1.35E+03 | 1.89E+03 | 2.07E+03 | 3.86E+03 | 7.65E+02 | |
| Rank | 2 | 7 | 9 | 1 | 4 | 3 | 6 | 5 | 8 | |
| cec03 | Best | 2.03E+03 | 2.55E+03 | 3.68E+03 | 2.59E+03 | 2.48E+03 | 2.31E+03 | 1.98E+03 | 3.31E+03 | 3.73E+03 |
| Worst | 3.17E+03 | 3.52E+03 | 4.05E+03 | 3.39E+03 | 3.41E+03 | 3.32E+03 | 2.47E+03 | 4.15E+03 | 4.12E+03 | |
| Mean | 2.54E+03 | 3.11E+03 | 3.89E+03 | 3.08E+03 | 2.93E+03 | 2.81E+03 | 2.25E+03 | 3.65E+03 | 3.90E+03 | |
| Std | 2.93E+02 | 2.70E+02 | 9.31E+01 | 2.00E+02 | 2.05E+02 | 2.73E+02 | 1.19E+02 | 2.24E+02 | 8.96E+01 | |
| Rank | 2 | 6 | 8 | 5 | 4 | 3 | 1 | 7 | 9 | |
| cec04 | Best | 1.90E+03 | 1.90E+03 | 1.90E+03 | 1.90E+03 | 1.90E+03 | 1.96E+03 | 1.90E+03 | 2.07E+03 | 1.90E+03 |
| Worst | 1.90E+03 | 1.90E+03 | 1.90E+03 | 1.90E+03 | 1.90E+03 | 2.09E+03 | 1.90E+03 | 2.76E+03 | 1.90E+03 | |
| Mean | 1.90E+03 | 1.90E+03 | 1.90E+03 | 1.90E+03 | 1.90E+03 | 2.01E+03 | 1.90E+03 | 2.24E+03 | 1.90E+03 | |
| Std | 0.00E+00 | 9.14E-02 | 0.00E+00 | 0.00E+00 | 0.00E+00 | 3.17E+01 | 0.00E+00 | 1.39E+02 | 0.00E+00 | |
| Rank | 1 | 7 | 1 | 1 | 1 | 8 | 1 | 9 | 1 | |
| cec05 | Best | 2.02E+07 | 3.55E+07 | 1.11E+09 | 3.60E+07 | 3.01E+07 | 1.62E+07 | 2.06E+07 | 4.00E+07 | 7.17E+08 |
| Worst | 7.07E+07 | 8.60E+07 | 1.89E+09 | 1.72E+08 | 1.04E+08 | 4.99E+07 | 1.12E+08 | 5.58E+08 | 2.01E+09 | |
| Mean | 4.21E+07 | 6.06E+07 | 1.62E+09 | 8.95E+07 | 6.32E+07 | 2.98E+07 | 6.05E+07 | 2.18E+08 | 1.29E+09 | |
| Std | 1.22E+07 | 1.16E+07 | 1.91E+08 | 3.63E+07 | 2.12E+07 | 9.38E+06 | 2.24E+07 | 1.21E+08 | 3.66E+08 | |
| Rank | 2 | 4 | 9 | 6 | 5 | 1 | 3 | 7 | 8 | |
| cec06 | Best | 5.61E+03 | 7.09E+03 | 2.39E+04 | 5.48E+03 | 5.65E+03 | 6.51E+03 | 5.46E+03 | 9.45E+03 | 1.99E+04 |
| Worst | 8.41E+03 | 1.22E+04 | 3.21E+04 | 8.65E+03 | 9.47E+03 | 1.02E+04 | 7.93E+03 | 1.71E+04 | 3.54E+04 | |
| Mean | 6.65E+03 | 9.44E+03 | 2.90E+04 | 6.84E+03 | 7.78E+03 | 8.20E+03 | 6.67E+03 | 1.25E+04 | 2.81E+04 | |
| Std | 6.79E+02 | 1.23E+03 | 1.99E+03 | 7.07E+02 | 1.11E+03 | 8.68E+02 | 5.24E+02 | 1.64E+03 | 4.16E+03 | |
| Rank | 1 | 6 | 9 | 3 | 4 | 5 | 2 | 7 | 8 | |
| cec07 | Best | 2.82E+06 | 1.02E+07 | 2.40E+08 | 1.07E+07 | 1.07E+07 | 6.26E+06 | 5.55E+06 | 1.74E+07 | 2.12E+08 |
| Worst | 1.68E+07 | 4.25E+07 | 3.96E+08 | 5.85E+07 | 5.04E+07 | 2.44E+07 | 4.97E+07 | 1.34E+08 | 7.34E+08 | |
| Mean | 9.61E+06 | 1.85E+07 | 3.44E+08 | 3.20E+07 | 2.36E+07 | 1.18E+07 | 2.52E+07 | 6.35E+07 | 4.40E+08 | |
| Std | 3.06E+06 | 6.48E+06 | 3.56E+07 | 1.24E+07 | 9.43E+06 | 4.24E+06 | 1.10E+07 | 3.34E+07 | 1.28E+08 | |
| Rank | 1 | 3 | 8 | 6 | 4 | 2 | 5 | 7 | 9 | |
| cec08 | Best | 1.74E+04 | 2.50E+04 | 3.39E+04 | 1.75E+04 | 2.01E+04 | 1.88E+04 | 2.48E+04 | 2.32E+04 | 3.38E+04 |
| Worst | 2.33E+04 | 3.55E+04 | 3.60E+04 | 2.49E+04 | 2.63E+04 | 2.35E+04 | 3.57E+04 | 3.50E+04 | 3.58E+04 | |
| Mean | 2.09E+04 | 3.22E+04 | 3.50E+04 | 2.15E+04 | 2.29E+04 | 2.13E+04 | 3.29E+04 | 2.86E+04 | 3.48E+04 | |
| Std | 1.44E+03 | 3.10E+03 | 4.53E+02 | 1.80E+03 | 1.49E+03 | 1.22E+03 | 2.40E+03 | 3.77E+03 | 5.88E+02 | |
| Rank | 1 | 6 | 9 | 3 | 4 | 2 | 7 | 5 | 8 | |
| cec09 | Best | 4.26E+03 | 4.38E+03 | 8.45E+03 | 4.51E+03 | 4.62E+03 | 4.34E+03 | 4.31E+03 | 6.78E+03 | 7.22E+03 |
| Worst | 4.57E+03 | 5.99E+03 | 1.03E+04 | 5.24E+03 | 5.21E+03 | 5.68E+03 | 5.33E+03 | 1.02E+04 | 1.46E+04 | |
| Mean | 4.36E+03 | 5.38E+03 | 9.37E+03 | 4.82E+03 | 4.94E+03 | 4.79E+03 | 4.79E+03 | 7.83E+03 | 9.71E+03 | |
| Std | 7.54E+01 | 3.23E+02 | 4.56E+02 | 1.61E+02 | 1.67E+02 | 2.73E+02 | 2.23E+02 | 6.71E+02 | 2.60E+03 | |
| Rank | 1 | 6 | 8 | 4 | 5 | 3 | 2 | 7 | 9 | |
| cec10 | Best | 3.94E+03 | 5.70E+03 | 2.65E+04 | 5.27E+03 | 5.07E+03 | 3.74E+03 | 4.50E+03 | 1.19E+04 | 2.05E+04 |
| Worst | 4.68E+03 | 1.05E+04 | 3.04E+04 | 1.01E+04 | 7.65E+03 | 3.94E+03 | 7.69E+03 | 2.13E+04 | 2.89E+04 | |
| Mean | 4.16E+03 | 7.96E+03 | 2.82E+04 | 7.55E+03 | 6.48E+03 | 3.84E+03 | 5.37E+03 | 1.61E+04 | 2.54E+04 | |
| Std | 1.64E+02 | 1.21E+03 | 9.97E+02 | 1.20E+03 | 6.23E+02 | 5.87E+01 | 6.73E+02 | 2.19E+03 | 1.85E+03 | |
| Rank | 2 | 6 | 9 | 5 | 4 | 1 | 3 | 7 | 8 | |
| Mean rank | 1.5 | 5.7 | 7.9 | 3.9 | 3.9 | 2.9 | 3.3 | 6.8 | 7.6 | |
| Final ranking | 1 | 6 | 9 | 4 | 4 | 2 | 3 | 7 | 8 | |
| +/=/– | –/–/– | 0/0/10 | 0/1/9 | 0/4/6 | 0/1/9 | 2/2/5 | 1/2/7 | 0/0/10 | 0/1/9 | |
| Function . | Index . | Algorithms . | ||||||||
|---|---|---|---|---|---|---|---|---|---|---|
| HBWO-JS . | JS . | BWO . | AHA . | ARO . | DO . | SO . | WSO . | RSA . | ||
| cec01 | Best | 1.31E+09 | 5.78E+10 | 2.48E+11 | 3.71E+10 | 3.58E+10 | 3.66E+08 | 9.68E+09 | 1.46E+11 | 2.05E+11 |
| Worst | 3.79E+09 | 1.06E+11 | 2.70E+11 | 8.91E+10 | 7.55E+10 | 1.34E+09 | 2.38E+10 | 2.08E+11 | 2.61E+11 | |
| Mean | 2.34E+09 | 7.83E+10 | 2.59E+11 | 6.65E+10 | 5.23E+10 | 7.30E+08 | 1.44E+10 | 1.73E+11 | 2.47E+11 | |
| Std | 6.43E+08 | 1.28E+10 | 6.03E+09 | 1.31E+10 | 1.05E+10 | 2.46E+08 | 3.55E+09 | 1.53E+10 | 9.84E+09 | |
| Rank | 2 | 6 | 9 | 5 | 4 | 1 | 3 | 7 | 8 | |
| cec02 | Best | 1.29E+04 | 2.37E+04 | 3.14E+04 | 1.49E+04 | 1.75E+04 | 1.47E+04 | 2.34E+04 | 2.14E+04 | 3.11E+04 |
| Worst | 2.05E+04 | 3.32E+04 | 3.37E+04 | 1.94E+04 | 2.28E+04 | 2.21E+04 | 3.34E+04 | 3.31E+04 | 3.41E+04 | |
| Mean | 1.73E+04 | 3.18E+04 | 3.28E+04 | 1.71E+04 | 2.01E+04 | 1.89E+04 | 3.09E+04 | 2.83E+04 | 3.25E+04 | |
| Std | 1.65E+03 | 1.74E+03 | 5.70E+02 | 1.36E+03 | 1.35E+03 | 1.89E+03 | 2.07E+03 | 3.86E+03 | 7.65E+02 | |
| Rank | 2 | 7 | 9 | 1 | 4 | 3 | 6 | 5 | 8 | |
| cec03 | Best | 2.03E+03 | 2.55E+03 | 3.68E+03 | 2.59E+03 | 2.48E+03 | 2.31E+03 | 1.98E+03 | 3.31E+03 | 3.73E+03 |
| Worst | 3.17E+03 | 3.52E+03 | 4.05E+03 | 3.39E+03 | 3.41E+03 | 3.32E+03 | 2.47E+03 | 4.15E+03 | 4.12E+03 | |
| Mean | 2.54E+03 | 3.11E+03 | 3.89E+03 | 3.08E+03 | 2.93E+03 | 2.81E+03 | 2.25E+03 | 3.65E+03 | 3.90E+03 | |
| Std | 2.93E+02 | 2.70E+02 | 9.31E+01 | 2.00E+02 | 2.05E+02 | 2.73E+02 | 1.19E+02 | 2.24E+02 | 8.96E+01 | |
| Rank | 2 | 6 | 8 | 5 | 4 | 3 | 1 | 7 | 9 | |
| cec04 | Best | 1.90E+03 | 1.90E+03 | 1.90E+03 | 1.90E+03 | 1.90E+03 | 1.96E+03 | 1.90E+03 | 2.07E+03 | 1.90E+03 |
| Worst | 1.90E+03 | 1.90E+03 | 1.90E+03 | 1.90E+03 | 1.90E+03 | 2.09E+03 | 1.90E+03 | 2.76E+03 | 1.90E+03 | |
| Mean | 1.90E+03 | 1.90E+03 | 1.90E+03 | 1.90E+03 | 1.90E+03 | 2.01E+03 | 1.90E+03 | 2.24E+03 | 1.90E+03 | |
| Std | 0.00E+00 | 9.14E-02 | 0.00E+00 | 0.00E+00 | 0.00E+00 | 3.17E+01 | 0.00E+00 | 1.39E+02 | 0.00E+00 | |
| Rank | 1 | 7 | 1 | 1 | 1 | 8 | 1 | 9 | 1 | |
| cec05 | Best | 2.02E+07 | 3.55E+07 | 1.11E+09 | 3.60E+07 | 3.01E+07 | 1.62E+07 | 2.06E+07 | 4.00E+07 | 7.17E+08 |
| Worst | 7.07E+07 | 8.60E+07 | 1.89E+09 | 1.72E+08 | 1.04E+08 | 4.99E+07 | 1.12E+08 | 5.58E+08 | 2.01E+09 | |
| Mean | 4.21E+07 | 6.06E+07 | 1.62E+09 | 8.95E+07 | 6.32E+07 | 2.98E+07 | 6.05E+07 | 2.18E+08 | 1.29E+09 | |
| Std | 1.22E+07 | 1.16E+07 | 1.91E+08 | 3.63E+07 | 2.12E+07 | 9.38E+06 | 2.24E+07 | 1.21E+08 | 3.66E+08 | |
| Rank | 2 | 4 | 9 | 6 | 5 | 1 | 3 | 7 | 8 | |
| cec06 | Best | 5.61E+03 | 7.09E+03 | 2.39E+04 | 5.48E+03 | 5.65E+03 | 6.51E+03 | 5.46E+03 | 9.45E+03 | 1.99E+04 |
| Worst | 8.41E+03 | 1.22E+04 | 3.21E+04 | 8.65E+03 | 9.47E+03 | 1.02E+04 | 7.93E+03 | 1.71E+04 | 3.54E+04 | |
| Mean | 6.65E+03 | 9.44E+03 | 2.90E+04 | 6.84E+03 | 7.78E+03 | 8.20E+03 | 6.67E+03 | 1.25E+04 | 2.81E+04 | |
| Std | 6.79E+02 | 1.23E+03 | 1.99E+03 | 7.07E+02 | 1.11E+03 | 8.68E+02 | 5.24E+02 | 1.64E+03 | 4.16E+03 | |
| Rank | 1 | 6 | 9 | 3 | 4 | 5 | 2 | 7 | 8 | |
| cec07 | Best | 2.82E+06 | 1.02E+07 | 2.40E+08 | 1.07E+07 | 1.07E+07 | 6.26E+06 | 5.55E+06 | 1.74E+07 | 2.12E+08 |
| Worst | 1.68E+07 | 4.25E+07 | 3.96E+08 | 5.85E+07 | 5.04E+07 | 2.44E+07 | 4.97E+07 | 1.34E+08 | 7.34E+08 | |
| Mean | 9.61E+06 | 1.85E+07 | 3.44E+08 | 3.20E+07 | 2.36E+07 | 1.18E+07 | 2.52E+07 | 6.35E+07 | 4.40E+08 | |
| Std | 3.06E+06 | 6.48E+06 | 3.56E+07 | 1.24E+07 | 9.43E+06 | 4.24E+06 | 1.10E+07 | 3.34E+07 | 1.28E+08 | |
| Rank | 1 | 3 | 8 | 6 | 4 | 2 | 5 | 7 | 9 | |
| cec08 | Best | 1.74E+04 | 2.50E+04 | 3.39E+04 | 1.75E+04 | 2.01E+04 | 1.88E+04 | 2.48E+04 | 2.32E+04 | 3.38E+04 |
| Worst | 2.33E+04 | 3.55E+04 | 3.60E+04 | 2.49E+04 | 2.63E+04 | 2.35E+04 | 3.57E+04 | 3.50E+04 | 3.58E+04 | |
| Mean | 2.09E+04 | 3.22E+04 | 3.50E+04 | 2.15E+04 | 2.29E+04 | 2.13E+04 | 3.29E+04 | 2.86E+04 | 3.48E+04 | |
| Std | 1.44E+03 | 3.10E+03 | 4.53E+02 | 1.80E+03 | 1.49E+03 | 1.22E+03 | 2.40E+03 | 3.77E+03 | 5.88E+02 | |
| Rank | 1 | 6 | 9 | 3 | 4 | 2 | 7 | 5 | 8 | |
| cec09 | Best | 4.26E+03 | 4.38E+03 | 8.45E+03 | 4.51E+03 | 4.62E+03 | 4.34E+03 | 4.31E+03 | 6.78E+03 | 7.22E+03 |
| Worst | 4.57E+03 | 5.99E+03 | 1.03E+04 | 5.24E+03 | 5.21E+03 | 5.68E+03 | 5.33E+03 | 1.02E+04 | 1.46E+04 | |
| Mean | 4.36E+03 | 5.38E+03 | 9.37E+03 | 4.82E+03 | 4.94E+03 | 4.79E+03 | 4.79E+03 | 7.83E+03 | 9.71E+03 | |
| Std | 7.54E+01 | 3.23E+02 | 4.56E+02 | 1.61E+02 | 1.67E+02 | 2.73E+02 | 2.23E+02 | 6.71E+02 | 2.60E+03 | |
| Rank | 1 | 6 | 8 | 4 | 5 | 3 | 2 | 7 | 9 | |
| cec10 | Best | 3.94E+03 | 5.70E+03 | 2.65E+04 | 5.27E+03 | 5.07E+03 | 3.74E+03 | 4.50E+03 | 1.19E+04 | 2.05E+04 |
| Worst | 4.68E+03 | 1.05E+04 | 3.04E+04 | 1.01E+04 | 7.65E+03 | 3.94E+03 | 7.69E+03 | 2.13E+04 | 2.89E+04 | |
| Mean | 4.16E+03 | 7.96E+03 | 2.82E+04 | 7.55E+03 | 6.48E+03 | 3.84E+03 | 5.37E+03 | 1.61E+04 | 2.54E+04 | |
| Std | 1.64E+02 | 1.21E+03 | 9.97E+02 | 1.20E+03 | 6.23E+02 | 5.87E+01 | 6.73E+02 | 2.19E+03 | 1.85E+03 | |
| Rank | 2 | 6 | 9 | 5 | 4 | 1 | 3 | 7 | 8 | |
| Mean rank | 1.5 | 5.7 | 7.9 | 3.9 | 3.9 | 2.9 | 3.3 | 6.8 | 7.6 | |
| Final ranking | 1 | 6 | 9 | 4 | 4 | 2 | 3 | 7 | 8 | |
| +/=/– | –/–/– | 0/0/10 | 0/1/9 | 0/4/6 | 0/1/9 | 2/2/5 | 1/2/7 | 0/0/10 | 0/1/9 | |
This PDF is available to Subscribers Only
View Article Abstract & Purchase OptionsFor full access to this pdf, sign in to an existing account, or purchase an annual subscription.
