Table 14 The IEEE CEC2005 benchmark results use the newest and most effective methods.
Function | MGO | HHO | HGS | INFO | EOBAVO | |
|---|---|---|---|---|---|---|
F1 | Mean | 9.30E−71 | 1.01E−92 | 3.90E−167 | 1.09E−53 | 0.00E+00 |
Std | 5.03E−70 | 5.50E−92 | 0.00E+00 | 6.69E−54 | 0.00E+00 | |
t-values | − 1.01E+00 | − 1.00E+00 | N.A | − 8.91E+00 | NA | |
F2 | Mean | 2.65E−41 | 2.33E−50 | 2.75E−76 | 1.13E−26 | 1.85E−256 |
Std | 1.35E−40 | 1.23E−49 | 1.50E−75 | 3.73E−27 | 0.00E+00 | |
t-values | − 1.07E+00 | − 1.04E+00 | − 1.00E+00 | − 1.66E+01 | NA | |
F3 | Mean | 2.57E−08 | 7.53E−75 | 2.12E−76 | 1.42E−50 | 0.00E+00 |
Std | 9.38E−08 | 3.30E−74 | 1.16E−75 | 1.16E−50 | 0.00E+00 | |
t-values | − 1.50E+00 | − 1.25E+00 | − 1.00E+00 | − 6.66E+00 | NA | |
F4 | Mean | 3.27E−24 | 5.86E−49 | 2.31E−65 | 1.78E−27 | 7.40E−263 |
Std | 1.12E−23 | 2.20E−48 | 1.27E−64 | 1.08E−27 | 0.00E+00 | |
t-values | − 1.60E+00 | − 1.46E+00 | − 1.00E+00 | − 9.00E+00 | NA | |
F5 | Mean | 1.06E−20 | 2.18E−02 | 1.17E+01 | 2.28E+01 | 3.75E−05 |
Std | 4.87E−20 | 3.07E−02 | 1.28E+01 | 6.37E−01 | 2.83E− 05 | |
t-values | 7.24E+00 | −3.88E+00 | −5.04E+00 | −1.96E+02 | NA | |
F6 | Mean | 1.64E−08 | 1.51E−04 | 6.63E−06 | 6.06E−09 | 3.54E−07 |
Std | 5.25E−08 | 2.30E−04 | 1.10E−05 | 1.00E−08 | 3.27E−07 | |
t-values | 5.59E+00 | − 3.60E+00 | − 3.11E+00 | 5.83E+00 | NA | |
F7 | Mean | 3.13E−04 | 1.20E−04 | 1.70E−03 | 1.56E−03 | 1.15E−04 |
Std | 2.31E−04 | 1.39E−04 | 2.39E−03 | 1.20E−03 | 9.45E−05 | |
t-values | − 4.32E+00 | − 1.34E−01 | − 3.63E+00 | − 6.59E+00 | NA | |
F8 | Mean | − 1.26E+04 | − 1.24E+04 | − 1.22E+04 | − 8.88E+03 | − 1.24E+04 |
Std | 1.02E−07 | 5.53E+02 | 1.07E+03 | 8.35E+02 | 3.44E+02 | |
t-values | 2.90E+00 | 3.10E−01 | −8.26E−01 | −2.13E+01 | NA | |
F9 | Mean | 0.00E+00 | 0.00E+00 | 0.00E+00 | 0.00E+00 | 0.00E+00 |
Std | 0.00E+00 | 0.00E+00 | 0.00E+00 | 0.00E+00 | 0.00E+00 | |
t- values | N. A | N. A | N. A | N. A | N. A | |
F10 | Mean | 1.04E−15 | 4.44E−16 | 4.44E−16 | 4.44E−16 | 4.44E−16 |
Std | 1.35E−15 | 1.50E−31 | 1.50E−31 | 1.50E−31 | 3.01E−31 | |
t-values | − 2.41E+00 | 8.83E+00 | 8.83E+00 | 8.83E+00 | NA | |
F11 | Mean | 0.00E+00 | 0.00E+00 | 0.00E+00 | 0.00E+00 | 0.00E+00 |
Std | 0.00E+00 | 0.00E+00 | 0.00E+00 | 0.00E+00 | 0.00E+00 | |
t-values | N.A | N.A | N. A | N.A | NA | |
F12 | Mean | 6.09E−26 | 1.44E−05 | 1.19E−07 | 9.42E−10 | 1.94E−08 |
Std | 1.70E−25 | 2.15E−05 | 1.21E−07 | 2.01E−09 | 1.36E−08 | |
t-values | 7.79E+00 | − 3.67E+00 | − 4.47E+00 | 7.34E+00 | NA | |
F13 | Mean | 1.61E−32 | 1.44E−05 | 2.05E−02 | 5.75E−02 | 3.89E−08 |
Std | 4.35E−33 | 2.15E−05 | 6.83E−02 | 8.76E−02 | 3.30E−08 | |
t-values | 6.45E+00 | − 3.67E+00 | − 1.64E+00 | − 3.60E+00 | NA | |
F14 | Mean | 9.98E−01 | 1.50E+00 | 1.98E+00 | 1.46E+00 | 1.13E+00 |
Std | 3.39E−16 | 9.97E−01 | 2.98E+00 | 9.29E−01 | 5.03E−01 | |
t-values | 1.44E+00 | − 1.79E+00 | − 1.53E+00 | − 1.71E+00 | NA | |
F15 | Mean | 3.85E−04 | 3.38E−04 | 5.83E−04 | 1.23E−03 | 3.33E−04 |
Std | 2.42E−04 | 2.75E−05 | 2.53E−04 | 3.64E−03 | 8.33E−05 | |
t- values | − 1.10E+00 | − 3.12E−01 | − 5.14E+00 | − 1.35E+00 | NA | |
F16 | Mean | − 1.03E+00 | − 1.03E+00 | − 1.03E+00 | − 1.03E+00 | − 1.03E+00 |
Std | 6.78E−16 | 2.94E−09 | 6.78E−16 | 6.78E−16 | 0.00E+00 | |
t- values | − 8.62E+01 | − 2.16E+00 | − 8.62E+01 | − 8.62E+01 | NA | |
F17 | Mean | 3.98E−01 | 3.98E−01 | 3.98E−01 | 3.98E−01 | 3.98E−01 |
Std | 1.13E−16 | 2.55E−05 | 1.13E−16 | 1.13E−16 | 1.13E−16 | |
t- values | 0.00E+00 | − 2.40E+00 | 0.00E+00 | 0.00E+00 | NA | |
F18 | Mean | 3.00E+00 | 3.00E+00 | 3.00E+00 | 3.00E+00 | 3.00E+00 |
Std | 2.57E−15 | 1.84E−07 | 3.40E−15 | 3.20E−10 | 3.06E−06 | |
t-values | 3.40E+00 | 3.19E+00 | 3.40E+00 | 3.40E+00 | NA | |
F19 | Mean | − 3.86E+00 | − 3.86E+00 | − 3.86E+00 | − 3.86E+00 | − 3.86E+00 |
Std | 1.36E−15 | 4.00E−03 | 1.36E−15 | 1.36E−15 | 2.53E−12 | |
t-values | 1.28E+00 | −4.30E+00 | 1.28E+00 | 1.28E+00 | NA | |
F20 | Mean | − 3.27E+00 | − 3.10E+00 | − 3.24E+00 | − 3.27E+00 | − 3.30E+00 |
Std | 5.99E−02 | 9.74E−02 | 7.95E−02 | 6.03E−02 | 4.51E−02 | |
t-values | − 2.32E+00 | − 1.05E+01 | − 3.90E+00 | − 2.59E+00 | NA | |
F21 | Mean | − 1.02E+01 | − 5.22E+00 | − 9.47E+00 | − 9.06E+00 | − 1.02E+01 |
Std | 1.81E−15 | 9.01E−01 | 1.76E+00 | 2.53E+00 | 5.29E−13 | |
t-values | 1.66E+00 | − 3.00E+01 | − 2.11E+00 | − 2.36E+00 | NA | |
F22 | Mean | − 1.04E+01 | − 5.08E+00 | − 9.69E+00 | − 8.40E+00 | − 1.04E+01 |
Std | 9.03E−15 | 6.73E−03 | 1.84E+00 | 3.40E+00 | 3.20E−12 | |
t-values | 1.24E+00 | − 4.33E+03 | − 2.11E+00 | − 3.23E+00 | NA | |
F23 | Mean | − 1.05E+01 | − 5.64E+00 | − 1.04E+01 | − 7.13E+00 | − 1.05E+01 |
Std | 9.03E−15 | 1.60E+00 | 9.87E−01 | 3.77E+00 | 4.56E−13 | |
t-values | 1.98E+00 | − 1.67E+01 | − 1.01E+00 | − 4.95E+00 | NA | |
w/t/l | Â | 4/12/7 | 13/7/3 | 10/11/2 | 14/5/4 | Â |
