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多种群协方差学习差分进化算法

杜永兆 范宇凌 柳培忠 唐加能 骆炎民

引用本文: 杜永兆, 范宇凌, 柳培忠, 唐加能, 骆炎民. 多种群协方差学习差分进化算法[J]. 电子与信息学报, 2019, 41(6): 1488-1495. doi: 10.11999/JEIT180670 shu
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 shu

多种群协方差学习差分进化算法

    作者简介: 杜永兆: 男,1985年生,副教授,博士,研究方向为智能计算、光学成像优化、医学图像处理;
    范宇凌: 男,1995年生,硕士生,研究方向为智能计算、图像处理;
    柳培忠: 男,1976年生,副教授,博士,研究方向为智能计算、视觉媒体检索、深度学习、信息安全;
    唐加能: 男,1983年生,副教授,博士,研究方向为智能计算、混沌同步和控制、网络同步和控制、信息安全、语音信号处理;
    骆炎民: 男,1975年生,副教授,博士,研究方向为机器学习、图像处理、智能计算、模式识别
    通讯作者: 唐加能,2812280164@qq.com
  • 基金项目: 国家自然科学基金(61605048, 61231002, 51075068),福建省教育厅项目(JA15035),泉州市科技局项目(2014Z103, 2015Z114),华侨大学研究生科研创新能力培养计划资助项目(1611422002)

摘要: 种群多样性与交叉算子在差分进化(DE)算法求解全局优化问题中具有重要作用,该文提出一种多种群协方差学习差分进化(MCDE)算法。首先,采用多种群机制的种群结构,利用每一子种群结合相应的变异策略保证进化过程个体多样性。然后,通过种群间的协方差学习,为交叉操作建立一个适当旋转的坐标系统;同时,使用自适应控制参数来平衡种群的勘测与收敛能力。最后,在单峰函数、多峰函数、偏移函数和高维函数的25个基准测试函数上进行测试,并同其他先进的进化算法对比,实验结果表明该文算法相较于其他算法在求解全局优化问题上达到最优效果。

English

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  • 图 1  种群进化过程坐标系

    图 2  4种演化算法在8个测试函数上的平均函数误差

    表 1  D=30下3种算法与MCDE的Wilcoxon’s检测结果比较

    比较算法R+RP$\alpha $=0.05$\alpha $=0.10
    JADE240.559.50.007012
    CoDE264.560.50.005181
    CoBiDE251.074.00.016633
    下载: 导出CSV

    表 2  D=30下各算法的Friedman平均排名

    算法显著值最终排名
    JADE3.783
    CoDE3.804
    CoBiDE3.342
    MCDE2.741
    下载: 导出CSV

    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JADECoDECoBiDEMCDE
    F10.00E+00±0.00E+00≈0.00E+00±0.00E+00≈0.00E+00±0.00E+00≈0.00E+00±0.00E+00
    F21.26E–28±1.22E–28+6.77E–15±3.44E–15–1.60E–12±2.90E–12–8.49E–28±3.75E–28
    F38.42E+03±6.58E+03–5.65E+05±5.66E+04–7.26E+04±5.64E+04–2.74E–12±2.82E–11
    F44.13E–16±3.45E–16–6.21E–03±4.67E–02–1.16E–03±2.74E–03–7.57E–22±4.26E–21
    F57.59E–08±5.65E–07–3.16E+02±3.62E+02–8.03E+02±1.51E+01–5.38E–10±7.12E–10
    F61.16E+01±3.16E+01–3.32E–01±6.57E–01–4.13E–02±9.21E–02+3.19E–01±1.09E–01
    F78.27E–03±8.22E–03–7.39E–03±6.45E–03–1.77E–03±3.73E–03–1.52E–03±4.11E–03
    F82.09E+01±1.68E–01≈2.01E+01±1.25E–01+2.07E+01±3.75E–01+2.09E+01±4.21E–02
    F90.00E+00±0.00E+00+0.00E+00±0.00E+00+0.00E+00±0.00E+00+2.64E–07±5.87E–07
    F102.42E+01±5.44E+00–4.21E+01±2.84E+01–4.41E+01±1.29E+01–2.28E+01±4.27E+00
    F112.57E+01±2.21E+00–1.24E+01±3.55E+00+5.62E+00±2.19E+00+1.51E+01±6.81e+00
    F126.45E+03±2.89E+03–3.21E+03±4.48E+03–2.94E+03±3.93E+03–2.12E+03±1.34E+03
    F131.47E+00±1.15E–01+1.66E+00±3.25E–01+2.64E+00±1.13E+00–1.74E+00±2.04E–01
    F141.23E+01±3.21E–01≈1.23E+01±3.56E–01≈1.23E+01±4.90E–01≈1.23E+01±2.66E–01
    F153.61E+02±2.24E+02+4.00E+02±5.24E+01≈4.04E+02±5.03E+01–4.00E+02±1.09E+02
    F169.33E+01±1.31E+02–7.25E+01±6.22E+01+7.38E+01±3.66E+01–5.37E+01±3.01E+01
    F171.21E+02±1.08E+02–7.16E+01±2.35E+01–7.25E+01±2.02e+01–6.36E+01±6.41E+01
    F189.04E+02±1.24E–01≈9.04E+02±1.34E+00≈9.03E+02±1.05E+01≈9.03E+02±6.01E–01
    F199.04E+02±8.32E+00≈9.04E+02±3.22E–01≈9.03E+02±1.04E+01≈9.03E+02±2.31E–01
    F209.04E+02±7.65E–01≈9.04E+02±7.11E–01≈9.04E+02±5.95E–01≈9.03E+02±2.45E–01
    F215.00E+02±4.67E–13≈5.00E+02±4.68E–13≈5.00E+02±4.62E–13≈5.00E+02±4.51E–14
    F228.68E+02±2.24E+01≈8.78E+02±3.54E+01≈8.69E+02±2.80E+01≈8.69E+02±1.89E+01
    F235.48E+02±8.62E+01–5.34E+02±4.45E–04≈5.34E+02±1.30E–04≈5.34E+02±2.49E–13
    F242.00E+02±2.12E–14≈2.00E+02±2.62E–14≈2.00E+02±2.90E–14≈2.00E+02±2.90E–14
    F252.11E+02±7.35E–01–2.11E+02±6.82E–01–2.10E+02±7.73E–01–2.09E+02±2.78E–01
    +/–/≈3/13/95/10/104/13/8
    下载: 导出CSV

    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

    FunctionCLPSOCMA-ESGL-25MCDE
    F10.00E+00±0.00e+00≈1.58E–25±3.35E–26–5.60E–27±1.76E–26–0.00E+00±0.00E+00
    F28.40E+02±1.90E+02–1.12E–24±2.93E–25–4.04E+01±6.28E+01–8.49E–28±3.75E–28
    F31.42E+07±4.19E+06–5.54E–21±1.69E–21+2.19E+06±1.08E+06–2.74E–12±2.82E–11
    F46.99E+03±1.73E+03–9.15E+05±2.16E+06–9.07E+02±4.25E+02–7.57E–22±4.26E–21
    F53.86E+03±4.35E+02–2.77E–10±5.04E–11+2.51E+03±1.96E+02–5.38E–10±7.12E–10
    F64.16E+00±3.48E+00–4.78E–01±1.32E+00–2.15E+01±1.17E+00–3.19E–01±1.09E–01
    F74.51E–01±8.47E–02–1.82E–03±4.33E–03–2.78E–02±3.62E–02–1.52E–03±4.11E–03
    F82.09E+01±4.41E–02–2.03E+01±5.72E–01+2.09E+01±5.94E–02–2.09E+01±4.21E–02
    F90.00e+00±0.00e+00+4.45E+02±7.12E+01–2.45E+01±7.35E+00–2.64E–07±5.87E–07
    F101.04E+02±1.53E+01–4.63E+01±1.16E+01–1.42E+02±6.45E+01–2.28E+01±4.27E+00
    F112.60E+01±1.63E+00–7.11E+00±2.14E+00+3.27E+01±7.79E+00–1.51E+01±6.81e+00
    F121.79E+04±5.24E+03–1.26E+04±1.74E+04–6.53E+04±4.69E+04–2.12E+03±1.34E+03
    F132.06E+00±2.15E–01–3.43E+00±7.60E–01–6.23E+00±4.88E+00–1.74E+00±2.04E–01
    F141.28E+01±2.48E–01–1.47E+01±3.31E–01–1.31E+01±1.84E–01–1.23E+01±2.66E–01
    F155.77E+01±2.76E+01–5.55E+02±3.32E+02–3.04E+02±1.99E+01+4.00E+02±1.09E+02
    F161.74E+02±2.82E+01–2.98E+02±2.08E+02–1.32E+02±7.60E+01–5.37E+01±3.01E+01
    F172.46E+02±4.81E+01–4.43E+02±3.34E+02–1.61E+02±6.80E+01–6.36E+01±6.41E+01
    F189.13E+02±1.42E+00–9.04E+02±3.01E–01≈9.07E+02±1.48E+00–9.03E+02±6.01E–01
    F199.14E+02±1.45E+00–9.16E+02±6.03E+01–9.06E+02±1.24E+00–9.03E+02±2.31E–01
    F209.14E+02±3.62E+00–9.04E+02±2.71E–01≈9.07E+02±1.35E+00–9.03E+02±2.45E–01
    F215.00E+02±3.39E–13≈5.00E+02±2.68E–12≈5.00E+02±4.83E–13≈5.00E+02±4.51E–14
    F229.72E+02±1.20E+01–8.26E+02±1.46E+01+9.28E+02±7.04E+01–8.69E+02±1.89E+01
    F235.34E+02±2.19E–04≈5.36E+02±5.44E+00≈5.34E+02±4.66E–04≈5.34E+02±2.49E–13
    F242.00E+02±1.49E–12≈2.12E+02±6.00E+01–2.00E+02±5.52E–11≈2.00E+02±2.90E–14
    F252.00E+02±1.96E+00+2.07E+02±6.07E+00≈2.17E+02±1.36E–01–2.09E+02±2.78E–01
    +/–/≈2/19/45/15/51/21/3
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  • 通讯作者:  唐加能, 2812280164@qq.com
  • 收稿日期:  2018-07-06
  • 录用日期:  2019-01-28
  • 网络出版日期:  2019-02-18
  • 刊出日期:  2019-06-01
通讯作者: 陈斌, bchen63@163.com
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