Table 3.
The mean and standard deviation of the 30 benchmark functions of CEC-2014 across the 4 algorithms.
| Fun | Algorithm | Mean | Std | Fun | Algorithm | Mean | Std |
|---|---|---|---|---|---|---|---|
| F1 | PSO30 | 3.90E+07 | 2.70E+07 | F16 | PSO30 | 1.39E+01 | 1.77E−01 |
| DAIW-PSO34 | 1.788 | 15.735 | DAIW-PSO34 | 7.168 | 18.856 | ||
| HBF-PSO30 | 3.18E+05 | 2.69E+05 | HBF-PSO30 | 1.06E+01 | 5.19E−01 | ||
| HS-PSO | 5.26E−13 | 1.09E−12 | HS-PSO | 3.26E−10 | 1.19E−09 | ||
| F2 | PSO30 | 8.08E+07 | 3.04E+07 | F17 | PSO30 | 3.49E+06 | 3.30E+06 |
| DAIW-PSO34 | 1.075 | 7.227 | DAIW-PSO34 | 2.85E+01 | 2.68E+01 | ||
| HBF-PSO30 | 3.55E−05 | 1.51E−04 | HBF-PSO30 | 2.25E+04 | 1.99E+04 | ||
| HS-PSO | 1.18E−09 | 2.98E−09 | HS-PSO | 2.04E+04 | 1.87E+04 | ||
| F3 | PSO30 | 1.01E+05 | 2.64E+04 | F18 | PSO30 | 5.38E+03 | 8.95E+03 |
| DAIW-PSO34 | 5.121 | 23.7 | DAIW-PSO34 | 4.33E+03 | 6.12E+03 | ||
| HBF-PSO30 | 6.80E−08 | 1.78E−07 | HBF-PSO30 | 2.88E+02 | 4.26E+02 | ||
| HS-PSO | 0.003 | 0.152 | HS-PSO | 2.96E+02 | 4.42E+02 | ||
| F4 | PSO30 | 2.05E+02 | 6.66E+01 | F19 | PSO30 | 3.53E+01 | 3.01E+01 |
| DAIW-PSO34 | 1.074 | 9.916 | DAIW-PSO34 | 2.88E+01 | 2.69E+01 | ||
| HBF-PSO30 | 4.73E+01 | 5.74E+01 | HBF-PSO30 | 1.96E+01 | 2.25E+01 | ||
| HS-PSO | 0.033 | 0.400 | HS-PSO | 1.93E+01 | 2.10E+01 | ||
| F5 | PSO30 | 2.12E+01 | 5.49E−02 | F20 | PSO30 | 1.19E+05 | 1.26E+05 |
| DAIW-PSO34 | 7.899 | 30.106 | DAIW-PSO34 | 0.459 | 7.966 | ||
| HBF-PSO30 | 2.00E+01 | 5.64E−05 | HBF-PSO30 | 7.08E+01 | 2.87E+01 | ||
| HS-PSO | 3.26E−12 | 2.50E−11 | HS-PSO | 1.907E−10 | 1.29E−09 | ||
| F6 | PSO30 | 4.36E+01 | 3.91E+00 | F21 | PSO30 | 8.22E+05 | 8.49E+05 |
| DAIW-PSO34 | 2.83E+01 | 3.41E+01 | DAIW-PSO34 | 0.631 | 8.717 | ||
| HBF-PSO30 | 2.04E+01 | 2.48E+00 | HBF-PSO30 | 7.29E+03 | 7.34E+03 | ||
| HS-PSO | 1.98E+02 | 2.32E+02 | HS-PSO | 0.000 | 0.003 | ||
| F7 | PSO30 | 1.65E+00 | 2.56E−01 | F22 | PSO30 | 1.02E+03 | 3.31E+02 |
| DAIW-PSO34 | 0.005 | 0.108 | DAIW-PSO34 | 3.453 | 8.896 | ||
| HBF-PSO30 | 1.01E−02 | 2.37E−02 | HBF-PSO30 | 6.75E+02 | 2.23E+02 | ||
| HS-PSO | 3.79E−09 | 1.24E−08 | HS-PSO | 0.000 | 0.002 | ||
| F8 | PSO30 | 3.99E+02 | 4.60E+01 | F23 | PSO30 | 3.38E+02 | 1.64E+01 |
| DAIW-PSO34 | 1.833 | 6.561 | DAIW-PSO34 | 5.208 | 11.848 | ||
| HBF-PSO30 | 7.63E+00 | 2.85E+00 | HBF-PSO30 | 3.15E+02 | 2.72E−12 | ||
| HS-PSO | 1.25E−10 | 7.58E−10 | HS-PSO | 0.000 | 0.001 | ||
| F9 | PSO30 | 4.21E+02 | 3.61E+01 | F24 | PSO30 | 2.41E+02 | 7.08E+00 |
| DAIW-PSO34 | 0.096 | 1.068 | DAIW-PSO34 | 1.722 | 6.804 | ||
| HBF-PSO30 | 1.17E+02 | 2.59E+01 | HBF-PSO30 | 2.33E+02 | 9.27E+00 | ||
| HS-PSO | 5.385E−10 | 2.01E−09 | HS-PSO | 0.000 | 0.003 | ||
| F10 | PSO30 | 8.87E+03 | 4.80E+02 | F25 | PSO30 | 2.20E+02 | 6.34E+00 |
| DAIW-PSO34 | 7.53E+02 | 3.65E+03 | DAIW-PSO34 | 0.274 | 9.397 | ||
| HBF-PSO30 | 4.18E+01 | 5.38E+01 | HBF-PSO30 | 2.16E+02 | 5.29E+00 | ||
| HS-PSO | 3.14E+02 | 4.21E+02 | HS-PSO | 3.126E−10 | 6.79E−10 | ||
| F11 | PSO30 | 9.21E+03 | 6.08E+02 | F26 | PSO30 | 1.77E+02 | 4.29E+01 |
| DAIW-PSO34 | 7.18E+05 | 4.88E+02 | DAIW-PSO34 | 1.963 | 8.457 | ||
| HBF-PSO30 | 2.87E+03 | 6.50E+02 | HBF-PSO30 | 1.35E+02 | 5.07E+01 | ||
| HS-PSO | 2.67E+03 | 5.33E+02 | HS-PSO | 0.000 | 0.003 | ||
| F12 | PSO30 | 5.51E+00 | 9.09E−01 | F27 | PSO30 | 1.22E+03 | 4.27E+02 |
| DAIW-PSO34 | 10.728 | 47.323 | DAIW-PSO34 | 4.691 | 9.931 | ||
| HBF-PSO30 | 1.91E−01 | 5.39E−02 | HBF-PSO30 | 7.63E+02 | 2.48E+02 | ||
| HS-PSO | 17.708 | 76.511 | HS-PSO | 0.000 | 0.001 | ||
| F13 | PSO30 | 5.88E−01 | 1.45E−01 | F28 | PSO30 | 9.26E+03 | 1.15E+03 |
| DAIW-PSO34 | 0.051 | 11.868 | DAIW-PSO34 | 2.927 | 7.048 | ||
| HBF-PSO30 | 2.99E−01 | 7.18E−02 | HBF-PSO30 | 2.33E+03 | 6.18E+02 | ||
| HS-PSO | 2.38E−14 | 9.41E−14 | HS-PSO | 0.001 | 0.005 | ||
| F14 | PSO30 | 2.90E−01 | 1.22E−01 | F29 | PSO30 | 1.36E+08 | 2.83E+08 |
| DAIW-PSO34 | 2.507 | 6.15 | DAIW-PSO34 | 0.353 | 7.058 | ||
| HBF-PSO30 | 1.18E−01 | 5.65E−02 | HBF-PSO30 | 2.90E+05 | 1.58E+06 | ||
| HS-PSO | 0.078 | 0.165 | HS-PSO | 1.788E−11 | 1.62E−10 | ||
| F15 | PSO30 | 5.40E+01 | 2.61E+01 | F30 | PSO30 | 1.59E+05 | 1.56E+05 |
| DAIW-PSO34 | 0.246 | 8.148 | DAIW-PSO34 | 3.53 | 11.204 | ||
| HBF-PSO30 | 1.29E+01 | 4.31E+00 | HBF-PSO30 | 2.37E+03 | 9.61E+02 | ||
| HS-PSO | 3.78E−14 | 1.24E−13 | HS-PSO | 0.000 | 0.003 |
The bold values represent the optimal value for each benchmark function.