Research Article
Improved Quantum-Behaved Particle Swarm Algorithm Based on Levy Flight
Table 2
Test function optimization results.
| Number of particles | Function | QPSO | G-QPSO | PSO | Mean values | Worst values | Best values | Mean values | Worst values | Best values | Mean values | Worst values | Best values |
| 20 | f1 | 0.0042 | 0.0715 | 2.45E−06 | 4.31E−05 | 1.30E−03 | 2.15E−08 | 0.0014 | 0.0182 | 1.10E−05 | f2 | −19.1694 | −18.6488 | −19.2085 | −19.2084 | −19.2065 | −19.2085 | −19.1876 | −19.0235 | −19.2084 | f3 | −1 | −0.9998 | −1 | −1 | −1 | −1 | −0.9727 | −0.936 | −1 | f4 | −182.8896 | −154.8117 | −186.7246 | −186.6805 | −186.1052 | −186.7309 | −185.2191 | −175.6943 | −186.7203 | f5 | −2.0626 | −2.0623 | −2.0626 | −2.0626 | −2.0626 | −2.0626 | −2.0626 | −2.0622 | −2.0626 | f6 | 8.68E−10 | 8.07E−09 | 0 | 0 | 0 | 0 | 4.40E−06 | 3.05E−04 | 2.83E−09 | f7 | 0.0016 | 0.0189 | 7.96E−06 | 3.31E−06 | 4.25E−05 | 8.12E−11 | 5.30E−03 | 2.88E−02 | 4.15E−06 | f8 | 1.20E−15 | 8.38E−14 | 6.72E−27 | 1.12E−30 | 6.47E−29 | 4.24E−50 | 6.47E−05 | 5.90E−04 | 1.26E−07 |
| 40 | f1 | 0.0013 | 0.0235 | 3.15E−07 | 3.63E−06 | 1.08E−04 | 1.09E−10 | 3.58E−04 | 1.90E−03 | 1.32E−06 | f2 | −19.1941 | −19.0671 | −19.2085 | −19.2085 | −19.2084 | −19.2085 | −19.202 | −19.1424 | −19.2085 | f3 | −1 | −0.9998 | −1 | −1 | −1 | −1 | −0.9917 | −0.9362 | −0.9998 | f4 | −185.3481 | −178.7177 | −186.7302 | −186.7195 | −186.4609 | −186.7309 | −186.059 | −182.093 | −186.7298 | f5 | −2.0626 | −2.0625 | −2.0626 | −2.0626 | −2.0626 | −2.0626 | −2.0626 | −2.0625 | −2.0626 | f6 | 5.14E−10 | 9.69E−08 | 2.94E−13 | 0 | 0 | 0 | 2.53E−07 | 3.45E−06 | 2.08E−09 | f7 | 3.53E−04 | 0.0039 | 2.14E−07 | 2.80E−07 | 9.30E−06 | 4.22E−15 | 0.0018 | 0.0338 | 5.52E−06 | f8 | 2.90E−16 | 1.56E−14 | 3.93E−23 | 1.35E−42 | 7.40E−41 | 1.52E−64 | 1.64E−05 | 1.07E−04 | 2.41E−07 |
| 60 | f1 | 3.51E−04 | 0.009 | 1.21E−06 | 1.19E−06 | 4.62E−05 | 7.16E−11 | 1.65E−04 | 1.20E−03 | ..3956E−06 | f2 | −19.1961 | −19.0343 | −19.2085 | −19.2085 | −19.2085 | −19.2085 | −19.2033 | −19.1754 | −19.2085 | f3 | −1 | −0.9999 | −1 | −1 | −1 | −1 | −0.9964 | −0.9362 | −0.9999 | f4 | −185.1436 | −167.6131 | −186.7304 | −186.7277 | −186.6912 | −186.7309 | −186.3031 | −182.273 | −186.0393 | f5 | −2.0626 | −2.0626 | −2.0626 | −2.0626 | −2.0626 | −2.0626 | −2.0626 | −2.0624 | −2.0626 | f6 | 2.47E−10 | 1.68E−09 | 5.04E−14 | 0 | 0 | 0 | 1.11E−07 | 1.70E−06 | 3.90E−10 | f7 | 9.21E−05 | 0.0025 | 2.20E−08 | 8.73E−08 | 1.81E−06 | 2.04E−14 | 9.24E−04 | 6.90E−03 | 8.38E−06 | f8 | 5.50E−17 | 1.63E−15 | 1.20E−23 | 1.85E−47 | 1.08E−45 | 1.25E−65 | 7.78E−06 | 4.71E−05 | 9.21E−10 |
| 80 | f1 | 9.92E−05 | 9.92E−05 | 5.15E−07 | 2.13E−07 | 4.47E−05 | 2.25E−12 | 1.33E−04 | 1.10E−03 | 1.02E−07 | f2 | −19.2018 | −19.1234 | −19.2084 | −19.2085 | −19.2085 | −19.2085 | −19.2063 | −19.1933 | −19.2085 | f3 | −1 | −0.9998 | −1 | −1 | −1 | −1 | −0.9985 | −0.9884 | −1 | f4 | −185.7209 | −172.3019 | −186.7214 | −186.7289 | −186.6909 | −186.7309 | −186.4336 | −184.4008 | −186.7298 | f5 | −2.0626 | −2.0626 | −2.0626 | −2.0626 | −2.0626 | −2.0626 | −2.0626 | −2.0626 | −2.0626 | f6 | 3.00E−10 | 2.19E−09 | 5.51E−13 | 0 | 0 | 0 | 7.06E−08 | 7.35E−07 | 1.28E−10 | f7 | 3.36E−05 | 7.75E−04 | 1.72E−07 | 4.36E−08 | 1.07E−06 | 4.72E−20 | 7.21E−04 | 1.33E−02 | 3.03E−06 | f8 | 9.73E−17 | 4.21E−15 | 1.38E−23 | 3.24E−53 | 1.64E−51 | 1.84E−73 | 4.52E−06 | 3.52E−05 | 1.97E−08 |
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