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多種群協(xié)方差學(xué)習(xí)差分進化算法

杜永兆 范宇凌 柳培忠 唐加能 駱炎民

杜永兆, 范宇凌, 柳培忠, 唐加能, 駱炎民. 多種群協(xié)方差學(xué)習(xí)差分進化算法[J]. 電子與信息學(xué)報, 2019, 41(6): 1488-1495. doi: 10.11999/JEIT180670
引用本文: 杜永兆, 范宇凌, 柳培忠, 唐加能, 駱炎民. 多種群協(xié)方差學(xué)習(xí)差分進化算法[J]. 電子與信息學(xué)報, 2019, 41(6): 1488-1495. doi: 10.11999/JEIT180670
Yongzhao DU, Yuling FAN, Peizhong LIU, Jianeng TANG, Yanmin LUO. Multi-populations Covariance Learning Differential Evolution Algorithm[J]. Journal of Electronics & Information Technology, 2019, 41(6): 1488-1495. doi: 10.11999/JEIT180670
Citation: Yongzhao DU, Yuling FAN, Peizhong LIU, Jianeng TANG, Yanmin LUO. Multi-populations Covariance Learning Differential Evolution Algorithm[J]. Journal of Electronics & Information Technology, 2019, 41(6): 1488-1495. doi: 10.11999/JEIT180670

多種群協(xié)方差學(xué)習(xí)差分進化算法

doi: 10.11999/JEIT180670
基金項目: 國家自然科學(xué)基金(61605048, 61231002, 51075068),福建省教育廳項目(JA15035),泉州市科技局項目(2014Z103, 2015Z114),華僑大學(xué)研究生科研創(chuàng)新能力培養(yǎng)計劃(1611422002)
詳細信息
    作者簡介:

    杜永兆:男,1985年生,副教授,博士,研究方向為智能計算、光學(xué)成像優(yōu)化、醫(yī)學(xué)圖像處理

    范宇凌:男,1995年生,碩士生,研究方向為智能計算、圖像處理

    柳培忠:男,1976年生,副教授,博士,研究方向為智能計算、視覺媒體檢索、深度學(xué)習(xí)、信息安全

    唐加能:男,1983年生,副教授,博士,研究方向為智能計算、混沌同步和控制、網(wǎng)絡(luò)同步和控制、信息安全、語音信號處理

    駱炎民:男,1975年生,副教授,博士,研究方向為機器學(xué)習(xí)、圖像處理、智能計算、模式識別

    通訊作者:

    唐加能 2812280164@qq.com

  • 中圖分類號: TP18

Multi-populations Covariance Learning Differential Evolution Algorithm

Funds: The National Natural Science Foundation of China (61605048, 61231002, 51075068), The Fujian Provincial Department of Education Project (JA15035), The Quanzhou Science and Technology Bureau Project (2014Z103, 2015Z114), Huaqiao University Graduate Research Innovation Capacity Development Program Funding Project (1611422002)
  • 摘要: 種群多樣性與交叉算子在差分進化(DE)算法求解全局優(yōu)化問題中具有重要作用,該文提出一種多種群協(xié)方差學(xué)習(xí)差分進化(MCDE)算法。首先,采用多種群機制的種群結(jié)構(gòu),利用每一子種群結(jié)合相應(yīng)的變異策略保證進化過程個體多樣性。然后,通過種群間的協(xié)方差學(xué)習(xí),為交叉操作建立一個適當旋轉(zhuǎn)的坐標系統(tǒng);同時,使用自適應(yīng)控制參數(shù)來平衡種群的勘測與收斂能力。最后,在單峰函數(shù)、多峰函數(shù)、偏移函數(shù)和高維函數(shù)的25個基準測試函數(shù)上進行測試,并同其他先進的進化算法對比,實驗結(jié)果表明該文算法相較于其他算法在求解全局優(yōu)化問題上達到最優(yōu)效果。
  • 圖  1  種群進化過程坐標系

    圖  2  4種演化算法在8個測試函數(shù)上的平均函數(shù)誤差

    表  1  D=30下3種算法與MCDE的Wilcoxon’s檢測結(jié)果比較

    比較算法R+RP$\alpha $=0.05$\alpha $=0.10
    JADE240.559.50.007012
    CoDE264.560.50.005181
    CoBiDE251.074.00.016633
    下載: 導(dǎo)出CSV

    表  2  D=30下各算法的Friedman平均排名

    算法顯著值最終排名
    JADE3.783
    CoDE3.804
    CoBiDE3.342
    MCDE2.741
    下載: 導(dǎo)出CSV

    表  3  30次獨立運行在4種算法的最優(yōu)解平均值及標準差

    函數(shù)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
    下載: 導(dǎo)出CSV

    表  4  30次獨立運行在CLPSO, CMA-ES, GL-25, MCDE最優(yōu)解平均值及標準差

    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
    下載: 導(dǎo)出CSV
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  • 收稿日期:  2018-07-06
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