Page 189 - 《软件学报》2021年第10期

肖辉辉 等:基于多策略的改进花授粉算法 3161

实验误差,本文对每种比较算法在每个测试函数上都分别独立执行 30 次,计算其 Mean_error(平均值误差)、
Std.Dev(标准方差).实验的其他参数设置为:种群个数 n=50;函数维数 D=30 或 4;最大评估次数为 10000D;转换
概率 p=0.8 [5,2629] .
为了对所有算法的优化能力做出公平公正的评估,本文对所有测试函数的测试结果分别利用 Wilcoxon(威
尔科克森)秩和检验(а=0.05)进行实验分析,测试结果见表 3.其中,符号“†”“”“‡”分别表示 MIFPA 算法解的质量
好于、相当于或差于对比算法,符号“w/t/l”分别表示 MIFPA 算法解的质量有 w 个函数优于对比算法、t 个函数
与对比算法相当、l 个函数差于对比算法.
Table 3 Optimal mean error values and standard deviations of the six algorithms (D=30,4)
表 3 6 种算法的优化均值误差和标准差(D=30,4)
Mean_errorStd.Dev
测试函数
HCLPSO MPEDE EOFPA
f 1 2.70E484.43E48† 3.41E421.10E41† 0.00E+000.00E+00
f 2 8.18E059.63E05† 8.05E283.71E27† 0.00E+000.00E+00
f 3 7.44E+004.23E+00† 1.33E017.28E01† 1.51E+011.07E+00†
f 4 2.60E031.00E03† 8.92E043.09E04† 2.37E042.14E04†
f 5 9.66E148.33E14† 0.00E+000.00E+00≈ 0.00E+000.00E+00
f 6 2.11E145.04E15† 4.44E150.00E+00† 8.88E160.00E+00
f 7 8.22E042.50E03† 3.29E041.80E03† 0.00E+000.00E+00
f 8 1.57E325.57E48‡ 1.57E325.57E48‡ 9.17E284.17E27†
f 9 1.35E325.57E48‡ 1.35E325.57E48‡ 3.50E031.89E02†
f 10 1.40E083.31E18‡ 1.50E042.76E04† 9.94E052.78E04†
f 11 3.21E073.24E16 3.21E070.00E+00 1.36E+002.29E+00†
f 12 4.06E055.42E16 4.06E050.00E+00 5.32E011.62E+00†
f 13 9.82E067.23E16† 9.82E064.51E16 3.61E011.37E+00†
f 14 4.70E+022.18E+02‡ 7.18E243.93E23‡ 8.43E+021.62E+02†
f 15 1.61E+021.42E+01† 1.40E+021.07E+01† 0.00E+000.00E+00
f 16 5.60E032.36E02† 0.00E+000.00E+00 0.00E+000.00E+00
f 17 7.01E142.45E14† 0.00E+000.00E+00 0.00E+000.00E+00
f 18 5.34E+004.32E+00† 3.13E+001.27E+01† 2.65E+015.50E+01†
f 19 2.08E+019.64E02‡ 2.09E+015.22E02 2.02E+012.71E01‡
w/t/l 12/2/5 9/7/3 10/8/1
Table 3 Optimal mean error values and standard deviations of the six algorithms (D=30,4) (Continued)
表 3 6 种算法的优化均值误差和标准差(D=30,4)(续)
Mean_errorStd.Dev
测试函数
MGOFPA FPA MIFPA
f 1 1.12E1232.98E123† 5.54E084.01E08† 0.00E+000.00E+00
f 2 1.48E394.95E39† 2.85E043.29E04† 0.00E+000.00E+00
f 3 2.42E+015.97E01† 2.08E+014.41E+00† 7.53E049.86E04
f 4 9.04E056.47E05† 1.86E027.00E03† 4.87E064.14E06
f 5 7.94E011.88E+01† 6.12E+019.70E+00† 0.00E+000.00E+00
f 6 4.44E150.00E+00† 1.50E+007.25E01† 8.88E160.00E+00
f 7 0.00E+000.00E+00 8.49E051.29E04† 0.00E+000.00E+00
f 8 6.18E054.33E05† 1.34E023.74E02† 1.69E327.26E34
f 9 5.26E053.60E05† 2.09E052.72E05† 2.79E321.20E32
f 10 1.40E085.31E14‡ 1.40E081.24E19† 1.40E087.22E20
f 11 3.21E078.85E16† 3.21E070.00E+00 3.21E070.00E+00
f 12 4.06E058.54E16‡ 4.06E055.42E16 4.06E054.51E16
f 13 9.82E061.00E15‡ 9.82E060.00E+00 9.82E060.00E+00
f 14 6.49E+028.58E+01† 1.17E+032.28E+02† 5.74E+029.53E+01
f 15 0.00E+000.00E+00 1.74E+021.04E+01† 0.00E+000.00E+00
f 16 0.00E+000.00E+00 7.67E011.07E01† 0.00E+000.00E+00
f 17 5.19E+004.57E+00† 3.60E073.26E-07† 0.00E+000.00E+00
f 18 1.38E+042.59E+04† 1.52E+024.52E+02† 1.75E012.58E01
f 19 2.10E+014.90E02 2.10E+014.40E02 2.09E+012.77E01
w/t/l 12/4/3 15/4/0 //
表 3 中给出了 6 种对比算法的优化均值误差及标准差,其中,加粗的数值表示该算法在该测试函数上取得