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一种正交反向学习萤火虫算法

周凌云 丁立新 马懋德 唐菀

引用本文: 周凌云, 丁立新, 马懋德, 唐菀. 一种正交反向学习萤火虫算法[J]. 电子与信息学报, 2019, 41(1): 202-209. doi: 10.11999/JEIT180187 shu
Citation:  Lingyun ZHOU, Lixin DING, Maode MA, Wan TANG. Orthogonal Opposition Based Firefly Algorithm[J]. Journal of Electronics and Information Technology, 2019, 41(1): 202-209. doi: 10.11999/JEIT180187 shu

一种正交反向学习萤火虫算法

    作者简介: 周凌云: 女,1979年生,讲师,研究方向为计算智能;
    丁立新: 男,1967年生,教授,研究方向为计算智能与机器学习;
    马懋德: 男,1957年生,教授,研究方向主要为无线网络;
    唐菀: 女,1974年生,教授,研究方向主要为数据中心网络
    通讯作者: 丁立新,lxding@whu.edu.cn
  • 基金项目: 国家自然科学基金(61379059),中南民族大学中央高校基本科研业务费专项资金(CZY18012)

摘要: 针对萤火虫算法求解复杂优化问题时收敛精度较低的问题,该文提出一种正交反向学习策略,嵌入萤火虫算法,得到一种正交反向学习萤火虫算法。正交反向学习策略中,采用重心反向计算,利用群体搜索经验的同时避免搜索依赖坐标;采用正交试验设计,构建部分维上取反向值的正交反向候选解,充分挖掘个体和反向个体在不同维度上的有利信息。在标准测试集上进行验证,实验结果说明了正交反向学习策略的有效性。与多种新近的改进萤火虫算法相比,该算法在大多数函数上获得更高的求解精度。

English

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  • 图 1  试验解的构建

    图 2  FA与OOFA在函数f1, f4, f9f12上的收敛曲线

    表 1  算法1:OOBL策略

     输入:种群X,一个个体的索引ind和正交表L
     输出:新种群X
     步骤:
     (1) 根据式(5)计算当前种群重心G
     (2) 根据式(6)计算指定个体的反向个体ox
     (3) 根据式(7)更新群体边界;根据式(8)对ox进行边界检查;
     (4) for i=1: L的行数M
     (5)  for j=1: 问题维数D
     (6)   if L(i, j)==1
     (7)    oox(i, j)=X(ind, j);
     (8)   else
     (9)    oox(i, j)=ox( j);
     (10)  end if
     (11) end for
     (12) end for
     (13) 评估正交反向候选解,评估次数FEs=FEs+M–1;
     (14) 从X和正交反向候选解中选出适应值最优的N个个体。
    下载: 导出CSV

    表 2  算法2:OOFA算法

     输入:目标函数;
     输出:全局最优位置及适应值。
     步骤:
     (1) 随机初始化有N个个体的种群X
     (2) 评估初始种群f(X),当前函数评估次数FEs=N
     (3) 根据种群适应值排序;
     (4) 根据函数维数D,生成2水平D因素的正交表L
     (5) while 未达迭代终止条件
     (6)   for i=1:N
     (7)    for j=1: i
     (8)     根据式(1)和式(2),第i个个体向第j个个体移位;
     (9)    end for
     (10)  end for
     (11)  对种群进行边界检查;
     (12)  评估种群,函数评估次数FEs=FEs+N
     (13)  随机选择群体中一个个体,执行OOBL;
     (14)  根据式(3)更新步长因子;
     (15) end while
    下载: 导出CSV

    表 3  FA与OOFA的比较结果

    函数FAOOFA加速比R
    MeanSDFEsT (s)MeanSDFEsT (s)
    f15.16E+046.35E+03802323.851.70E–108.44E–1010910.0373.54
    f27.30E+082.15E+08723143.823.39E+071.04E+0717040.0642.44
    f34.74E+161.43E+17166620.941.61E+098.63E+086160.0227.05
    f49.36E+041.29E+04379731.947.25E+041.22E+0456690.176.70
    f51.58E+043.90E+03445442.251.06E+023.32E+0114210.0431.35
    f68.71E+032.01E+03364631.856.90E+012.47E+019040.0340.34
    f71.08E+051.13E+05323222.114.11E+011.12E+0110820.0529.87
    f82.10E+015.29E–02827414.872.10E+016.09E–02859773.230.96
    f94.28E+011.42E+006464318.072.14E+014.18E+0041781.0815.47
    f106.79E+031.12E+03723733.951.67E+011.19E+0110940.0466.15
    f118.38E+029.77E+01524072.851.13E+013.35E+009890.0352.99
    f128.43E+029.43E+01565173.511.05E+023.38E+0111330.0549.88
    f138.17E+029.91E+01605953.898.64E+013.04E+0113040.0646.47
    f148.10E+033.23E+02804184.481.55E+035.45E+0253590.1915.01
    f158.07E+033.59E+02728594.244.41E+037.63E+0255980.2113.02
    f163.19E+005.04E–015779311.011.79E+005.38E–01109981.865.25
    f171.40E+031.91E+02566222.954.09E+013.16E+0019550.0628.96
    f181.44E+031.68E+02526123.011.06E+022.98E+0114840.0535.45
    f191.04E+064.38E+05524222.753.34E+007.17E–0112300.0442.62
    f201.50E+011.43E–0588880.511.50E+013.14E–059620.049.24
    f213.57E+031.80E+02643955.242.92E+022.75E+0119010.1233.87
    f228.87E+033.07E+02610694.751.91E+031.25E+0346290.2713.19
    f239.05E+034.02E+02491344.215.61E+031.21E+0344370.2911.07
    f244.15E+022.78E+013229510.012.17E+026.37E+006520.1949.53
    f254.09E+021.66E+014440413.742.70E+021.38E+017280.2160.99
    f263.08E+024.83E+016435920.942.95E+022.03E+014166712.631.54
    f271.64E+035.93E+013276210.504.51E+026.27E+019550.2934.31
    f286.25E+035.82E+02485514.943.00E+026.06E–0314990.1232.39
    下载: 导出CSV

    表 4  各FA变种算法结果的比较(Mean±SD)

    函数MFAVSSFAOFARaFAODFAOOFA
    f13.58E+04±5.83E+033.45E+04±4.31E+032.42E+04±5.28E+034.03E+02±7.35E+021.32E+04±5.63E+031.70E–10±8.44E–10
    f25.03E+08±1.67E+083.73E+08±7.44E+073.34E+08±1.65E+083.71E+07±2.17E+072.19E+08±8.17E+073.39E+07±1.04E+07
    f31.47E+15±2.87E+151.68E+13±2.15E+132.01E+14±5.77E+142.62E+10±1.55E+106.04E+14±2.98E+151.61E+09±8.63E+08
    f49.27E+04±1.08E+048.04E+04±8.81E+038.68E+04±1.27E+041.04E+05±3.33E+048.21E+04±2.27E+047.25E+04±1.22E+04
    f59.85E+03±4.47E+038.56E+03±1.64E+035.70E+03±1.94E+034.99E+02±1.01E+031.14E+03±6.20E+021.06E+02±3.32E+01
    f65.84E+03±1.72E+034.49E+03±5.99E+023.48E+03±1.19E+031.71E+02±7.17E+011.64E+03±1.07E+036.90E+01±2.47E+01
    f72.52E+04±2.64E+042.61E+03±1.28E+036.42E+03±1.09E+043.03E+04±4.31E+042.40E+04±5.81E+044.11E+01±1.12E+01
    f82.10E+01±6.57E–022.10E+01±5.85E–022.10E+01±6.54E–022.11E+01±5.93E–022.10E+01±5.39E–022.10E+01±6.09E–02
    f94.16E+01±1.81E+004.05E+01±9.64E–013.83E+01±3.17E+003.96E+01±2.48E+003.72E+01±3.35E+002.14E+01±4.18E+00
    f105.14E+03±1.10E+034.59E+03±5.23E+023.29E+03±8.44E+021.49E+02±1.23E+021.97E+03±9.37E+021.67E+01±1.19E+01
    f116.54E+02±1.11E+026.50E+02±4.33E+014.60E+02±9.00E+011.52E+02±5.41E+014.65E+02±9.63E+011.13E+01±3.35E+00
    f127.40E+02±8.81E+016.52E+02±4.22E+015.13E+02±9.01E+018.69E+02±1.54E+026.73E+02±1.39E+021.05E+02±3.38E+01
    f137.42E+02±9.14E+016.50E+02±5.49E+015.48E+02±7.61E+018.81E+02±1.31E+026.86E+02±9.57E+018.64E+01±3.04E+01
    f147.44E+03±4.96E+027.66E+03±2.56E+025.83E+03±6.32E+021.62E+03±3.60E+027.27E+03±6.99E+021.55E+03±5.45E+02
    f157.56E+03±5.92E+027.65E+03±3.13E+025.72E+03±7.14E+024.89E+03±1.01E+037.26E+03±4.44E+024.41E+03±7.63E+02
    f162.70E+00±4.78E–012.76E+00±3.05E–011.47E+00±4.45E–011.95E+00±5.61E–012.46E+00±4.73E–011.79E+00±5.38E–01
    f171.26E+03±1.41E+021.18E+03±8.23E+016.52E+02±1.04E+029.87E+01±4.59E+018.98E+02±1.68E+024.09E+01±3.16E+00
    f181.28E+03±2.00E+021.16E+03±9.17E+017.18E+02±1.52E+021.55E+03±2.47E+021.03E+03±1.92E+021.06E+02±2.98E+01
    f192.75E+05±2.01E+052.39E+05±6.70E+045.00E+04±3.86E+047.96E+01±1.68E+022.68E+04±5.41E+043.34E+00±7.17E–01
    f201.50E+01±3.72E–021.50E+01±2.29E–021.50E+01±6.32E–081.49E+01±1.78E–011.37E+01±8.18E–011.50E+01±3.14E–05
    f213.03E+03±2.98E+023.10E+03±1.43E+022.47E+03±1.64E+024.57E+02±1.71E+022.16E+03±3.59E+022.92E+02±2.75E+01
    f228.43E+03±4.74E+028.29E+03±2.74E+026.77E+03±1.01E+032.07E+03±5.70E+027.63E+03±9.75E+021.91E+03±1.25E+03
    f238.16E+03±4.96E+028.28E+03±2.43E+026.82E+03±8.01E+026.38E+03±9.46E+027.58E+03±6.23E+025.61E+03±1.21E+03
    f243.83E+02±2.26E+013.57E+02±8.70E+003.45E+02±1.59E+013.69E+02±2.90E+013.48E+02±1.61E+012.17E+02±6.37E+00
    f254.02E+02±1.31E+013.76E+02±6.32E+003.85E+02±1.81E+013.94E+02±1.78E+013.74E+02±1.73E+012.70E+02±1.38E+01
    f262.73E+02±4.82E+012.50E+02±1.53E+012.62E+02±5.77E+013.31E+02±1.08E+023.04E+02±9.55E+012.95E+02±2.03E+01
    f271.56E+03±6.16E+011.47E+03±3.89E+011.41E+03±4.78E+011.60E+03±1.07E+021.46E+03±9.06E+014.51E+02±6.27E+01
    f285.60E+03±5.24E+024.96E+03±2.87E+024.56E+03±5.53E+026.00E+03±1.08E+034.45E+03±6.04E+023.00E+02±6.06E–03
    –/≈/+25/2/125/2/124/2/227/0/126/1/1
    P-value1.18E–51.18E–51.33E–54.46E–67.03E–6
    Friedman5.304.303.133.613.321.34
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文章相关
  • 通讯作者:  丁立新, lxding@whu.edu.cn
  • 收稿日期:  2018-02-10
  • 录用日期:  2018-08-23
  • 网络出版日期:  2018-08-29
  • 刊出日期:  2019-01-01
通讯作者: 陈斌, bchen63@163.com
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