Table 10.
Results of fixed-dimension multimodal benchmark functions (F14-F23).
| F | CBFO | PSOBFO | BFO | FA | FPA | BA | DA | PSO | |
|---|---|---|---|---|---|---|---|---|---|
| F14 | Avg | 9.83E+00 | 3.11E+00 | 2.96E+00 | 1.82E+00 | 1.04E+00 | 4.53E+00 | 1.30E+00 | 4.41E+00 |
| Stdv | 4.51E+00 | 1.71E+00 | 2.22E+00 | 8.42E-01 | 1.56E-01 | 3.91E+00 | 6.96E-01 | 3.20E+00 | |
| Rank | 8 | 5 | 4 | 3 | 1 | 7 | 2 | 6 | |
|
| |||||||||
| F15 | Avg | 4.33E-04 | 9.49E-04 | 6.24E-04 | 2.85E-03 | 7.44E-04 | 8.29E-03 | 3.73E-03 | 1.41E-03 |
| Stdv | 1.65E-04 | 3.00E-04 | 2.25E-04 | 4.71E-03 | 1.41E-04 | 1.35E-02 | 5.95E-03 | 4.04E-04 | |
| Rank | 1 | 4 | 2 | 6 | 3 | 8 | 7 | 5 | |
|
| |||||||||
| F16 | Avg | -1.03E+00 | -1.03E+00 | -1.03E+00 | -1.03E+00 | -1.03E+00 | -1.03E+00 | -1.03E+00 | -1.03E+00 |
| Stdv | 5.23E-06 | 1.60E-04 | 7.96E-06 | 3.36E-09 | 2.55E-08 | 8.94E-04 | 3.47E-06 | 2.49E-03 | |
| Rank | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | |
|
| |||||||||
| F17 | Avg | 3.98E-01 | 3.98E-01 | 3.98E-01 | 3.98E-01 | 3.98E-01 | 3.98E-01 | 3.98E-01 | 3.99E-01 |
| Stdv | 2.24E-06 | 4.80E-05 | 2.02E-06 | 1.76E-09 | 6.28E-09 | 5.45E-04 | 1.84E-07 | 1.65E-03 | |
| Rank | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | |
|
| |||||||||
| F18 | Avg | 3.00E+00 | 3.01E+00 | 3.00E+00 | 3.00E+00 | 3.00E+00 | 3.10E+00 | 3.00E+00 | 3.24E+00 |
| Stdv | 2.00E-04 | 6.53E-03 | 3.13E-04 | 2.59E-08 | 1.60E-06 | 8.65E-02 | 6.09E-07 | 3.61E-01 | |
| Rank | 1 | 6 | 1 | 1 | 1 | 6 | 1 | 8 | |
|
| |||||||||
| F19 | Avg | -3.86E+00 | -3.86E+00 | -3.86E+00 | -3.86E+00 | -3.86E+00 | -3.83E+00 | -3.86E+00 | -3.84E+00 |
| Stdv | 4.86E-04 | 4.56E-03 | 5.87E-04 | 1.03E-09 | 2.38E-06 | 2.49E-02 | 1.16E-03 | 2.10E-02 | |
| Rank | 1 | 1 | 1 | 1 | 1 | 8 | 1 | 7 | |
|
| |||||||||
| F20 | Avg | -3.29E+00 | -3.24E+00 | -3.27E+00 | -3.28E+00 | -3.31E+00 | -2.89E+00 | -3.25E+00 | -2.71E+00 |
| Stdv | 2.41E-02 | 2.38E-02 | 2.48E-02 | 6.10E-02 | 6.06E-03 | 1.31E-01 | 1.01E-01 | 3.54E-01 | |
| Rank | 2 | 6 | 4 | 3 | 1 | 7 | 5 | 8 | |
|
| |||||||||
| F21 | Avg | -6.03E+00 | -1.01E+01 | -9.80E+00 | -7.92E+00 | -1.01E+01 | -4.64E+00 | -6.61E+00 | -3.67E+00 |
| Stdv | 9.74E-01 | 4.27E-02 | 1.28E+00 | 3.47E+00 | 1.30E-01 | 2.43E+00 | 2.62E+00 | 1.31E+00 | |
| Rank | 6 | 1 | 3 | 4 | 1 | 7 | 5 | 8 | |
|
| |||||||||
| F22 | Avg | -6.45E+00 | -1.01E+01 | -1.02E+01 | -9.89E+00 | -1.02E+01 | -5.03E+00 | -7.35E+00 | -4.33E+00 |
| Stdv | 1.22E+00 | 9.60E-01 | 9.61E-01 | 1.94E+00 | 4.87E-01 | 2.93E+00 | 2.98E+00 | 1.67E+00 | |
| Rank | 6 | 3 | 1 | 4 | 1 | 7 | 5 | 8 | |
|
| |||||||||
| F23 | Avg | -6.91E+00 | -9.73E+00 | -9.98E+00 | -1.05E+01 | -1.02E+01 | -5.36E+00 | -6.35E+00 | -4.42E+00 |
| Stdv | 1.30E+00 | 1.82E+00 | 1.63E+00 | 1.07E-06 | 4.94E-01 | 2.90E+00 | 3.36E+00 | 1.33E+00 | |
| Rank | 5 | 4 | 3 | 1 | 2 | 7 | 6 | 8 | |
|
| |||||||||
| Sum of ranks | 32 | 32 | 21 | 25 | 13 | 59 | 34 | 60 | |
| Average rank | 3.2 | 3.2 | 2.1 | 2.5 | 1.3 | 5.9 | 3.4 | 6 | |
| Overall rank | 4 | 4 | 2 | 3 | 1 | 7 | 6 | 8 | |