Table 2 Mean and SD obtained by JADE, SaDE, EPSDE, CoBiDE and CCDE through 30 independent runs on 30 test functions in 10 dimension with 300,000 FEs
From: Covariance and crossover matrix guided differential evolution for global numerical optimization
Function | JADE mean ± SD | SaDE mean ± SD | EPSDE mean ± SD | CoBiDE mean ± SD | CCDE mean ± SD |
|---|---|---|---|---|---|
Unimodal functions | |||||
F1 | 0.00E+00 ± 0.00E+00 | 0.00E+00 ± 0.00E+00 | 1.57E+04 ± 3.88E+04 | 0.00E+00 ± 0.00E+00 | 0.00E+00 ± 0.00E+00 |
F2 | 0.00E+00 ± 0.00E+00 | 0.00E+00 ± 0.00E+00 | 2.22E+03 ± 3.24E+03 | 0.00E+00 ± 0.00E+00 | 0.00E+00 ± 0.00E+00 |
F3 | 0.00E+00 ± 0.00E+00 | 0.00E+00 ± 0.00E+00 | 7.65E−04 ± 2.30E−03 | 0.00E+00 ± 0.00E+00 | 0.00E+00 ± 0.00E+00 |
Multimodal functions | |||||
F4 | 1.01E+00 ± 1.87E+00 | 1.69E+01 ± 1.71E+01 | 2.64E+01 ± 1.42E+01 | 3.13E+01 ± 1.06E+01 | 0.00E+00 ± 0.00E+00 |
F5 | 2.01E+02 ± 5.60E−03 | 2.03E+01 ± 9.91E−02 | 1.99E+01 ± 9.07E−01 | 1.95E+01 ± 2.25E+00 | 1.91E+01 ± 3.88E+00 |
F6 | 3.02E−02 ± 1.65E+00 | 3.76E+01 ± 1.55E+00 | 9.85E−01 ± 7.78E−01 | 1.31E−01 ± 3.30E−01 | 0.00E+00 ± 0.00E+00 |
F7 | 3.73E−02 ± 3.83E−02 | 2.11E−01 ± 1.57E−01 | 1.47E−01 ± 1.19E−01 | 3.20E−03 ± 4.00E−03 | 0.00E+00 ± 0.00E+00 |
F8 | 7.01E−01 ± 9.48E−01 | 1.58E+01 ± 5.93E+00 | 7.24E+00 ± 3.64E+00 | 0.00E+00 ± 0.00E+00 | 0.00E+00 ± 0.00E+00 |
F9 | 8.46E+00 ± 3.79E+00 | 2.04E+01 ± 6.50E+00 | 7.22E+00 ± 3.79E+00 | 3.47E+00 ± 1.03E+00 | 2.49E+00 ± 1.92E+00 |
F10 | 6.21E+01 ± 6.82E+01 | 3.09E+02 ± 2.02E+02 | 1.67E+02 ± 1.13E+02 | 1.52E−01 ± 7.16E−02 | 7.29E+00 ± 1.25E+00 |
F11 | 2.93E+02 ± 1.86E+02 | 6.71E+02 ± 3.37E+02 | 2.08E+02 ± 1.61E+02 | 1.91E+02 ± 9.64E+01 | 1.73E+02 ± 1.51E+02 |
F12 | 2.17E−01 ± 1.36E−01 | 7.19E−01 ± 3.48E−01 | 2.78E−01 ± 6.29E−02 | 1.31E−01 ± 3.91E−02 | 1.50E−03 ± 5.90E−03 |
F13 | 1.33E−01 ± 2.81E−02 | 3.67E−01 ± 1.94E−01 | 1.14E−01 ± 3.88E−02 | 5.92E−02 ± 1.60E−02 | 8.91E−03 ± 7.13E−03 |
F14 | 1.26E−01 ± 4.70E−02 | 3.49E−01 ± 2.02E−01 | 2.84E−01 ± 1.29E−01 | 9.18E−02 ± 3.22E−02 | 7.91E−02 ± 2.83E−02 |
F15 | 9.79E−01 ± 3.29E−01 | 1.48E+00 ± 8.25E−01 | 7.28E−01 ± 2.76E−01 | 6.15E−01 ± 9.45E−02 | 6.69E−01 ± 1.82E−01 |
F16 | 2.31E+00 ± 4.25E−01 | 3.25E+01 ± 2.38E−01 | 1.52E+00 ± 5.31E−01 | 2.02E+00 ± 2.67E−01 | 1.62E+01 ± 6.23E−01 |
Hybrid function | |||||
F17 | 5.19E+01 ± 6.23E+01 | 2.96E+02 ± 1.79E+02 | 2.48E+02 ± 1.76E+02 | 1.04E+01 ± 5.86E+00 | 1.58E+00 ± 2.57E+00 |
F18 | 1.96E+01 ± 8.62E−01 | 2.36E+01 ± 1.74E+01 | 2.51E+01 ± 2.13E+01 | 2.37E−01 ± 2.08E−01 | 7.63E−01 ± 8.13E−01 |
F19 | 9.48E−01 ± 3.38E−01 | 2.75E+00 ± 1.73E+00 | 1.97E+00 ± 1.18E+00 | 2.61E−01 ± 1.18E−01 | 2.32E−01 ± 3.51E−01 |
F20 | 6.78E−01 ± 5.25E−01 | 1.66E+01 ± 1.13E+01 | 1.39E+01 ± 1.29E+01 | 4.26E−01 ± 1.64E−01 | 3.62E−01 ± 4.69E−01 |
F21 | 1.33E+00 ± 4.16E+00 | 1.27E+02 ± 1.29E+02 | 9.97E+01 ± 1.18E+02 | 4.98E−01 ± 2.25E−01 | 4.09E−01 ± 4.06E−01 |
F22 | 1.07E+01 ± 9.64E+00 | 2.78E+01 ± 1.42E+01 | 3.27E+01 ± 3.48E+01 | 3.18E+00 ± 8.64E−01 | 2.72E−01 ± 2.15E−01 |
Composition functions | |||||
F23 | 3.29E+02 ± 0.00E+00 | 3.29E+02 ± 0.00E+00 | 3.29E+02 ± 3.28E−04 | 3.29E+02 ± 0.00E+00 | 3.29E+02 ± 0.00E+00 |
F24 | 1.20E+02 ± 7.47E+00 | 1.37E+02 ± 1.06E+01 | 1.24E+02 ± 2.65E+01 | 1.09E+02 ± 1.83E+00 | 1.08E+02 ± 2.25E+00 |
F25 | 1.28E+02 ± 1.56E+01 | 1.86E+02 ± 2.52E+01 | 1.85E+02 ± 2.79E+02 | 1.65E+02 ± 4.19E+01 | 1.20E+02 ± 1.79E+01 |
F26 | 1.00E+02 ± 3.75E−02 | 1.00E+02 ± 1.69E−01 | 1.00E+02 ± 2.79E−02 | 1.00E+02 ± 1.27E−02 | 1.00E+02 ± 7.71E−03 |
F27 | 9.39E+01 ± 1.43E+02 | 4.79E+01 ± 1.16E+02 | 2.47E+02 ± 1.78E+02 | 1.15E+02 ± 1.77E+02 | 3.82E+01 ± 1.12E+02 |
F28 | 3.88E+02 ± 5.38E+01 | 4.57E+02 ± 7.84E+01 | 4.16E+02 ± 5.57E+01 | 3.91E+02 ± 3.93E+01 | 3.25E+02 ± 3.38E+01 |
F29 | 2.13E+02 ± 2.63E+01 | 5.77E+04 ± 3.15E+05 | 4.25E+05 ± 1.02E+06 | 2.22E+02 ± 6.66E−01 | 1.95E+02 ± 2.08E+01 |
F30 | 5.06E+02 ± 1.25E+02 | 8.67E+02 ± 3.98E+02 | 6.33E+02 ± 1.39E+02 | 4.66E+02 ± 1.72E+01 | 2.40E+02 ± 4.41E+01 |