比较算法 | R+ | R – | P值 | $\alpha $=0.05 | $\alpha $=0.10 |
JADE | 240.5 | 59.5 | 0.007012 | 是 | 是 |
CoDE | 264.5 | 60.5 | 0.005181 | 是 | 是 |
CoBiDE | 251.0 | 74.0 | 0.016633 | 是 | 是 |

Citation: Yongzhao DU, Yuling FAN, Peizhong LIU, Jianeng TANG, Yanmin LUO. Multi-populations Covariance Learning Differential Evolution Algorithm[J]. Journal of Electronics and Information Technology, 2019, 41(6): 1488-1495. doi: 10.11999/JEIT180670

多种群协方差学习差分进化算法
English
Multi-populations Covariance Learning Differential Evolution Algorithm
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表 1 在D=30下3种算法与MCDE的Wilcoxon’s检测结果比较
表 2 在D=30下各算法的Friedman平均排名
算法 显著值 最终排名 JADE 3.78 3 CoDE 3.80 4 CoBiDE 3.34 2 MCDE 2.74 1 表 3 30次独立运行在4种算法的最优解平均值及标准差
函数 JADE CoDE CoBiDE MCDE F1 0.00E+00±0.00E+00≈ 0.00E+00±0.00E+00≈ 0.00E+00±0.00E+00≈ 0.00E+00±0.00E+00 F2 1.26E–28±1.22E–28+ 6.77E–15±3.44E–15– 1.60E–12±2.90E–12– 8.49E–28±3.75E–28 F3 8.42E+03±6.58E+03– 5.65E+05±5.66E+04– 7.26E+04±5.64E+04– 2.74E–12±2.82E–11 F4 4.13E–16±3.45E–16– 6.21E–03±4.67E–02– 1.16E–03±2.74E–03– 7.57E–22±4.26E–21 F5 7.59E–08±5.65E–07– 3.16E+02±3.62E+02– 8.03E+02±1.51E+01– 5.38E–10±7.12E–10 F6 1.16E+01±3.16E+01– 3.32E–01±6.57E–01– 4.13E–02±9.21E–02+ 3.19E–01±1.09E–01 F7 8.27E–03±8.22E–03– 7.39E–03±6.45E–03– 1.77E–03±3.73E–03– 1.52E–03±4.11E–03 F8 2.09E+01±1.68E–01≈ 2.01E+01±1.25E–01+ 2.07E+01±3.75E–01+ 2.09E+01±4.21E–02 F9 0.00E+00±0.00E+00+ 0.00E+00±0.00E+00+ 0.00E+00±0.00E+00+ 2.64E–07±5.87E–07 F10 2.42E+01±5.44E+00– 4.21E+01±2.84E+01– 4.41E+01±1.29E+01– 2.28E+01±4.27E+00 F11 2.57E+01±2.21E+00– 1.24E+01±3.55E+00+ 5.62E+00±2.19E+00+ 1.51E+01±6.81e+00 F12 6.45E+03±2.89E+03– 3.21E+03±4.48E+03– 2.94E+03±3.93E+03– 2.12E+03±1.34E+03 F13 1.47E+00±1.15E–01+ 1.66E+00±3.25E–01+ 2.64E+00±1.13E+00– 1.74E+00±2.04E–01 F14 1.23E+01±3.21E–01≈ 1.23E+01±3.56E–01≈ 1.23E+01±4.90E–01≈ 1.23E+01±2.66E–01 F15 3.61E+02±2.24E+02+ 4.00E+02±5.24E+01≈ 4.04E+02±5.03E+01– 4.00E+02±1.09E+02 F16 9.33E+01±1.31E+02– 7.25E+01±6.22E+01+ 7.38E+01±3.66E+01– 5.37E+01±3.01E+01 F17 1.21E+02±1.08E+02– 7.16E+01±2.35E+01– 7.25E+01±2.02e+01– 6.36E+01±6.41E+01 F18 9.04E+02±1.24E–01≈ 9.04E+02±1.34E+00≈ 9.03E+02±1.05E+01≈ 9.03E+02±6.01E–01 F19 9.04E+02±8.32E+00≈ 9.04E+02±3.22E–01≈ 9.03E+02±1.04E+01≈ 9.03E+02±2.31E–01 F20 9.04E+02±7.65E–01≈ 9.04E+02±7.11E–01≈ 9.04E+02±5.95E–01≈ 9.03E+02±2.45E–01 F21 5.00E+02±4.67E–13≈ 5.00E+02±4.68E–13≈ 5.00E+02±4.62E–13≈ 5.00E+02±4.51E–14 F22 8.68E+02±2.24E+01≈ 8.78E+02±3.54E+01≈ 8.69E+02±2.80E+01≈ 8.69E+02±1.89E+01 F23 5.48E+02±8.62E+01– 5.34E+02±4.45E–04≈ 5.34E+02±1.30E–04≈ 5.34E+02±2.49E–13 F24 2.00E+02±2.12E–14≈ 2.00E+02±2.62E–14≈ 2.00E+02±2.90E–14≈ 2.00E+02±2.90E–14 F25 2.11E+02±7.35E–01– 2.11E+02±6.82E–01– 2.10E+02±7.73E–01– 2.09E+02±2.78E–01 +/–/≈ 3/13/9 5/10/10 4/13/8 表 4 30次独立运行在CLPSO, CMA-ES, GL-25, MCDE最优解平均值及标准差
Function CLPSO CMA-ES GL-25 MCDE F1 0.00E+00±0.00e+00≈ 1.58E–25±3.35E–26– 5.60E–27±1.76E–26– 0.00E+00±0.00E+00 F2 8.40E+02±1.90E+02– 1.12E–24±2.93E–25– 4.04E+01±6.28E+01– 8.49E–28±3.75E–28 F3 1.42E+07±4.19E+06– 5.54E–21±1.69E–21+ 2.19E+06±1.08E+06– 2.74E–12±2.82E–11 F4 6.99E+03±1.73E+03– 9.15E+05±2.16E+06– 9.07E+02±4.25E+02– 7.57E–22±4.26E–21 F5 3.86E+03±4.35E+02– 2.77E–10±5.04E–11+ 2.51E+03±1.96E+02– 5.38E–10±7.12E–10 F6 4.16E+00±3.48E+00– 4.78E–01±1.32E+00– 2.15E+01±1.17E+00– 3.19E–01±1.09E–01 F7 4.51E–01±8.47E–02– 1.82E–03±4.33E–03– 2.78E–02±3.62E–02– 1.52E–03±4.11E–03 F8 2.09E+01±4.41E–02– 2.03E+01±5.72E–01+ 2.09E+01±5.94E–02– 2.09E+01±4.21E–02 F9 0.00e+00±0.00e+00+ 4.45E+02±7.12E+01– 2.45E+01±7.35E+00– 2.64E–07±5.87E–07 F10 1.04E+02±1.53E+01– 4.63E+01±1.16E+01– 1.42E+02±6.45E+01– 2.28E+01±4.27E+00 F11 2.60E+01±1.63E+00– 7.11E+00±2.14E+00+ 3.27E+01±7.79E+00– 1.51E+01±6.81e+00 F12 1.79E+04±5.24E+03– 1.26E+04±1.74E+04– 6.53E+04±4.69E+04– 2.12E+03±1.34E+03 F13 2.06E+00±2.15E–01– 3.43E+00±7.60E–01– 6.23E+00±4.88E+00– 1.74E+00±2.04E–01 F14 1.28E+01±2.48E–01– 1.47E+01±3.31E–01– 1.31E+01±1.84E–01– 1.23E+01±2.66E–01 F15 5.77E+01±2.76E+01– 5.55E+02±3.32E+02– 3.04E+02±1.99E+01+ 4.00E+02±1.09E+02 F16 1.74E+02±2.82E+01– 2.98E+02±2.08E+02– 1.32E+02±7.60E+01– 5.37E+01±3.01E+01 F17 2.46E+02±4.81E+01– 4.43E+02±3.34E+02– 1.61E+02±6.80E+01– 6.36E+01±6.41E+01 F18 9.13E+02±1.42E+00– 9.04E+02±3.01E–01≈ 9.07E+02±1.48E+00– 9.03E+02±6.01E–01 F19 9.14E+02±1.45E+00– 9.16E+02±6.03E+01– 9.06E+02±1.24E+00– 9.03E+02±2.31E–01 F20 9.14E+02±3.62E+00– 9.04E+02±2.71E–01≈ 9.07E+02±1.35E+00– 9.03E+02±2.45E–01 F21 5.00E+02±3.39E–13≈ 5.00E+02±2.68E–12≈ 5.00E+02±4.83E–13≈ 5.00E+02±4.51E–14 F22 9.72E+02±1.20E+01– 8.26E+02±1.46E+01+ 9.28E+02±7.04E+01– 8.69E+02±1.89E+01 F23 5.34E+02±2.19E–04≈ 5.36E+02±5.44E+00≈ 5.34E+02±4.66E–04≈ 5.34E+02±2.49E–13 F24 2.00E+02±1.49E–12≈ 2.12E+02±6.00E+01– 2.00E+02±5.52E–11≈ 2.00E+02±2.90E–14 F25 2.00E+02±1.96E+00+ 2.07E+02±6.07E+00≈ 2.17E+02±1.36E–01– 2.09E+02±2.78E–01 +/–/≈ 2/19/4 5/15/5 1/21/3 -