Table 8 Statistical results of CEAHA compared with other optimization algorithms in CEC2019.
From: Enhanced artificial hummingbird algorithm with chaotic traversal flight
Fun | Index | CEAHA | AHA | DGSAHA | IAHA | LCAHA | AOA | COA | CS | CSBO | EEFO | EMA |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
CF1 | Mean | 1.00E+00 | 1.00E+00≈ | 1.00E+00≈ | 1.00E+00≈ | 1.00E+00≈ | 2.94E+04+ | 1.00E+00≈ | 6.88E+08+ | 1.00E+00+ | 1.00E+00+ | 1.79E+05+ |
|  | Std | 0.00E+00 | 0.00E+00 | 0.00E+00 | 0.00E+00 | 0.00E+00 | 9.74E+04 | 0.00E+00 | 3.09E+08 | 1.04E−03 | 5.44E−11 | 3.41E+05 |
CF2 | Mean | 4.19E+00 | 4.33E+00+ | 4.38E+00+ | 4.35E+00+ | 4.41E+00+ | 1.02E+04+ | 4.78E+00+ | 2.05E+04+ | 2.49E+01+ | 4.34E+00+ | 1.23E+03+ |
|  | Std | 1.42E−01 | 2.30E−01 | 2.84E−01 | 2.60E−01 | 3.01E−01 | 3.25E+03 | 3.40E−01 | 5.03E+03 | 2.86E+01 | 2.29E−01 | 9.58E+02 |
CF3 | Mean | 1.33E+00 | 1.58E+00+ | 1.53E+00+ | 1.41E+00+ | 1.51E+00+ | 9.65E+00+ | 7.21E+00+ | 1.18E+01+ | 5.85E+00+ | 2.40E+00+ | 3.63E+00+ |
|  | Std | 1.66E−01 | 4.50E−01 | 1.58E−01 | 4.93E−03 | 3.65E−01 | 1.10E+00 | 1.99E+00 | 3.33E−01 | 7.28E−01 | 6.85E−01 | 2.16E+00 |
CF4 | Mean | 1.01E+01 | 1.70E+01+ | 2.11E+01+ | 2.05E+01+ | 2.04E+01+ | 4.87E+01+ | 3.44E+01+ | 1.16E+02+ | 1.71E+01+ | 1.25E+01+ | 1.80E+01+ |
| Â | Std | 3.99E+00 | 9.64E+00 | 7.81E+00 | 8.08E+00 | 8.32E+00 | 1.38E+01 | 2.07E+01 | 1.69E+01 | 3.38E+00 | 5.27E+00 | 7.47E+00 |
CF5 | Mean | 1.06E+00 | 1.07E+00≈ | 1.18E+00+ | 1.11E+00+ | 1.10E+00+ | 6.52E+01+ | 1.22E+00+ | 1.31E+02+ | 1.15E+00+ | 1.10E+00+ | 1.09E+00+ |
|  | Std | 3.18E−02 | 5.64E−02 | 5.16E−02 | 6.90E−02 | 6.50E−02 | 2.11E+01 | 1.40E−01 | 4.32E+01 | 4.91E−02 | 5.64E−02 | 4.90E−02 |
CF6 | Mean | 1.26E+00 | 1.37E+00≈ | 1.28E+00+ | 1.09E+00- | 1.44E+00≈ | 1.04E+01+ | 3.75E+00+ | 1.31E+01+ | 1.79E+00+ | 1.53E+00+ | 2.87E+00+ |
|  | Std | 4.71E−01 | 4.72E−01 | 1.78E−01 | 2.57E−01 | 6.43E−01 | 1.54E+00 | 1.62E+00 | 1.02E+00 | 6.57E−01 | 6.89E−01 | 1.46E+00 |
CF7 | Mean | 2.13E+02 | 6.26E+02+ | 4.61E+02+ | 5.46E+02+ | 6.27E+02+ | 1.29E+03+ | 1.12E+03+ | 2.15E+03+ | 8.80E+02+ | 4.65E+02+ | 5.85E+02+ |
| Â | Std | 1.49E+02 | 2.23E+02 | 1.20E+02 | 2.11E+02 | 1.81E+02 | 2.74E+02 | 3.78E+02 | 2.22E+02 | 1.46E+02 | 1.88E+02 | 2.42E+02 |
CF8 | Mean | 2.51E+00 | 3.30E+00+ | 3.42E+00+ | 3.55E+00+ | 3.34E+00+ | 4.69E+00+ | 3.90E+00+ | 5.24E+00+ | 4.00E+00+ | 3.52E+00+ | 3.68E+00+ |
|  | Std | 4.80E−01 | 4.73E−01 | 2.96E−01 | 4.68E−01 | 4.71E−01 | 3.91E−01 | 3.65E−01 | 1.26E−01 | 2.65E−01 | 4.56E−01 | 4.42E−01 |
CF9 | Mean | 1.12E+00 | 1.11E+00≈ | 1.20E+00+ | 1.13E+00≈ | 1.13E+00≈ | 2.32E+00+ | 1.31E+00+ | 5.11E+00+ | 1.21E+00+ | 1.19E+00+ | 1.25E+00+ |
|  | Std | 4.67E−02 | 5.46E−02 | 4.28E−02 | 4.78E−02 | 7.03E−02 | 8.02E−01 | 8.40E−02 | 6.54E−01 | 3.67E−02 | 6.14E−02 | 8.16E−02 |
CF10 | Mean | 1.17E+01 | 1.91E+01+ | 1.73E+01+ | 1.84E+01+ | 1.77E+01+ | 2.11E+01+ | 1.96E+01+ | 2.17E+01+ | 2.12E+01+ | 2.00E+01+ | 2.12E+01+ |
|  | Std | 1.00E+01 | 5.75E+00 | 7.52E+00 | 6.78E+00 | 7.58E+00 | 3.85E−02 | 4.66E+00 | 1.18E−01 | 5.31E−02 | 5.15E+00 | 1.00E−01 |
CEAHA wins | + | 6 | 9 | 7 | 7 | 10 | 9 | 10 | 10 | 10 | 10 | |
Similar | ≈ | 4 | 1 | 2 | 3 | 0 | 1 | 0 | 0 | 0 | 0 | |
Competitor wins | – | 0 | 0 | 1 | 0 | 0 | 0 | 0 | 5 | 0 | 0 | |
Fun | Index | GOA | GTO | PDO | PSO | SCSSA | SHCO | SPBO | SSA | WOA | SaNSDE | JADE |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
CF1 | Mean | 2.05E+06+ | 1.00E+00≈ | 1.00E+00≈ | 1.49E+09+ | 1.00E+00≈ | 1.00E+00≈ | 8.49E+01≈ | 1.58E+06+ | 1.10E+07+ | 2.10E+03+ | 1.40E+07+ |
| Â | Std | 2.45E+06 | 0.00E+00 | 0.00E+00 | 7.67E+08 | 0.00E+00 | 0.00E+00 | 4.60E+02 | 1.53E+06 | 1.23E+07 | 1.15E+04 | 7.52E+06 |
CF2 | Mean | 9.98E+02+ | 4.41E+00+ | 5.00E+00+ | 3.00E+04+ | 5.00E+00+ | 5.00E+00+ | 6.94E+01+ | 8.46E+02+ | 7.51E+03+ | 5.58E+02+ | 4.43E+03+ |
|  | Std | 5.70E+02 | 2.74E−01 | 2.12E−06 | 8.57E+03 | 0.00E+00 | 6.23E−05 | 1.94E+02 | 7.06E+02 | 2.97E+03 | 5.87E+02 | 1.41E+03 |
CF3 | Mean | 8.44E+00+ | 1.38E+00+ | 7.47E+00+ | 8.99E+00+ | 3.16E+00+ | 6.85E+00+ | 5.32E+00+ | 3.39E+00+ | 5.60E+00+ | 4.99E+00+ | 5.95E+00+ |
|  | Std | 2.16E+00 | 1.04E−01 | 1.83E+00 | 8.15E−01 | 2.05E+00 | 2.46E+00 | 1.43E+00 | 1.92E+00 | 2.10E+00 | 9.56E−01 | 9.67E−01 |
CF4 | Mean | 2.17E+01+ | 2.56E+01+ | 7.47E+01+ | 1.39E+02+ | 4.49E+01+ | 3.90E+01+ | 3.82E+01+ | 2.52E+01+ | 4.89E+01+ | 1.15E+01+ | 1.23E+01+ |
| Â | Std | 1.02E+01 | 9.69E+00 | 1.39E+01 | 1.94E+01 | 2.34E+01 | 1.49E+01 | 9.44E+00 | 1.09E+01 | 1.89E+01 | 1.88E+00 | 2.66E+00 |
CF5 | Mean | 1.27E+00+ | 1.28E+00+ | 5.52E+01+ | 1.90E+02+ | 1.19E+00+ | 7.05E+00+ | 2.49E+00+ | 1.24E+00+ | 2.07E+00+ | 1.13E+00+ | 1.40E+00+ |
|  | Std | 1.68E−01 | 2.09E−01 | 2.07E+01 | 5.40E+01 | 1.13E−01 | 1.16E+01 | 4.24E−01 | 1.50E−01 | 3.91E−01 | 3.24E−02 | 2.24E−01 |
CF6 | Mean | 4.63E+00+ | 4.74E+00+ | 1.06E+01+ | 1.51E+01+ | 4.08E+00+ | 6.18E+00+ | 7.04E+00+ | 4.23E+00+ | 8.59E+00+ | 1.18E+00≈ | 5.12E+00+ |
|  | Std | 1.98E+00 | 1.30E+00 | 1.17E+00 | 9.62E−01 | 1.65E+00 | 1.53E+00 | 1.18E+00 | 2.34E+00 | 1.68E+00 | 1.98E−01 | 6.64E−01 |
CF7 | Mean | 1.00E+03+ | 9.12E+02+ | 1.70E+03+ | 2.48E+03+ | 1.25E+03+ | 1.03E+03+ | 1.20E+03+ | 1.04E+03+ | 1.25E+03+ | 4.71E+02+ | 8.34E+02+ |
| Â | Std | 2.21E+02 | 2.73E+02 | 3.08E+02 | 2.43E+02 | 3.61E+02 | 3.32E+02 | 2.17E+02 | 3.11E+02 | 3.07E+02 | 1.37E+02 | 2.54E+02 |
CF8 | Mean | 4.11E+00+ | 3.97E+00+ | 4.87E+00+ | 5.24E+00+ | 4.10E+00+ | 4.42E+00+ | 4.32E+00+ | 4.18E+00+ | 4.63E+00+ | 3.63E+00+ | 4.29E+00+ |
|  | Std | 4.37E−01 | 4.71E−01 | 2.23E−01 | 1.94E−01 | 3.95E−01 | 3.73E−01 | 2.80E−01 | 3.03E−01 | 3.61E−01 | 1.87E−01 | 3.67E−01 |
CF9 | Mean | 1.28E+00+ | 1.21E+00+ | 3.00E+00+ | 5.76E+00+ | 1.32E+00+ | 1.40E+00+ | 1.40E+00+ | 1.37E+00+ | 1.34E+00+ | 1.20E+00+ | 1.26E+00+ |
|  | Std | 1.13E−01 | 7.48E−02 | 8.70E−01 | 7.28E−01 | 1.33E−01 | 1.34E−01 | 1.49E−01 | 1.68E−01 | 1.65E−01 | 3.78E−02 | 5.02E−02 |
CF10 | Mean | 2.11E+01+ | 2.11E+01+ | 2.13E+01+ | 2.18E+01+ | 2.07E+01+ | 2.15E+01+ | 2.12E+01+ | 2.03E+01+ | 2.13E+01+ | 2.11E+01+ | 2.11E+01+ |
|  | Std | 7.50E−02 | 1.24E−01 | 1.49E−01 | 1.34E−01 | 3.29E+00 | 1.03E−01 | 8.70E−02 | 3.65E+00 | 1.36E−01 | 2.64E−01 | 2.67E−02 |
CEAHA wins | 10 | 9 | 9 | 10 | 9 | 9 | 9 | 10 | 10 | 9 | 10 | |
Similar | 0 | 1 | 1 | 0 | 1 | 1 | 1 | 0 | 0 | 1 | 0 | |
Competitor wins | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | |
