Journal of Computer Applications ›› 2022, Vol. 42 ›› Issue (6): 1852-1861.DOI: 10.11772/j.issn.1001-9081.2021040555
Special Issue: 人工智能
• Artificial intelligence • Previous Articles Next Articles
Received:
2021-04-12
Revised:
2021-07-12
Accepted:
2021-07-20
Online:
2022-06-22
Published:
2022-06-10
Contact:
Xianfeng TANG
About author:
CHEN Liang,born in 1980,M. S.,engineer. His research interests include artificial intelligence.
Supported by:
通讯作者:
汤显峰
作者简介:
陈亮(1980—),男,四川遂宁人,工程师,硕士,主要研究方向:人工智能
基金资助:
CLC Number:
Liang CHEN, Xianfeng TANG. Improved sine cosine algorithm for optimizing feature selection and data classification[J]. Journal of Computer Applications, 2022, 42(6): 1852-1861.
陈亮, 汤显峰. 改进正余弦算法优化特征选择及数据分类[J]. 《计算机应用》唯一官方网站, 2022, 42(6): 1852-1861.
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URL: https://www.joca.cn/EN/10.11772/j.issn.1001-9081.2021040555
基准函数 | 函数表达式 | 搜索空间 | 收敛精度 | 最优解fmin |
---|---|---|---|---|
f1(x)=Sphere | [-100,100] | 0 | ||
f2(x)=Schwefel2.22 | [-10,10] | 0 | ||
f3(x)=Schwefel1.2 | [-100,100] | 0 | ||
f4(x)=Schwefel2.21 | [-100,100] | 0 | ||
f5(x)=Quartic | [-1.28,1.28] | 0 | ||
f6(x)=Rastigin | [-5.12,5.12] | 0 | ||
f7(x)=Griewank | [-600,600] | 0 | ||
f8(x)=Ackley | [-32,32] | 0 |
Tab.1 Benchmark functions
基准函数 | 函数表达式 | 搜索空间 | 收敛精度 | 最优解fmin |
---|---|---|---|---|
f1(x)=Sphere | [-100,100] | 0 | ||
f2(x)=Schwefel2.22 | [-10,10] | 0 | ||
f3(x)=Schwefel1.2 | [-100,100] | 0 | ||
f4(x)=Schwefel2.21 | [-100,100] | 0 | ||
f5(x)=Quartic | [-1.28,1.28] | 0 | ||
f6(x)=Rastigin | [-5.12,5.12] | 0 | ||
f7(x)=Griewank | [-600,600] | 0 | ||
f8(x)=Ackley | [-32,32] | 0 |
基准 函数 | 统计指标 | SCA | PSCA | LSSCA | IWCCSCA | 基准 函数 | 统计指标 | SCA | PSCA | LSSCA | IWCCSCA |
---|---|---|---|---|---|---|---|---|---|---|---|
f1(x) | 平均值 | 3.54E-06 | 6.63E-09 | 8.25E-12 | 5.57E-15 | f5(x) | 平均值 | -2.53E+03 | -2.57E+03 | -6.56E+06 | -6.57E+09 |
标准方差 | 3.89E-06 | 5.51E-09 | 7.26E-12 | 7.46E-15 | 标准方差 | -2.64E+03 | -2.90E+03 | -6.09E+06 | -8.46E+09 | ||
最小值 | 6.36E-07 | 7.45E-11 | 5.09E-13 | 2.32E-18 | 最小值 | -3.22E+05 | -4.29E+06 | -4.27E+09 | -1.34E+11 | ||
最大值 | 1.32E-04 | 3.59E-07 | 4.78E-09 | 3.29E-11 | 最大值 | -1.19E+01 | -6.28E+02 | -5.29E+04 | -2.08E+07 | ||
f2(x) | 平均值 | 2.13E-03 | 7.47E-05 | 6.35E-09 | 5.47E-11 | f6(x) | 平均值 | 4.94E-06 | 3.15E-07 | 4.04E-11 | 0 |
标准方差 | 4.42E-03 | 5.18E-05 | 6.36E-09 | 4.74E-11 | 标准方差 | 0 | 0 | 6.46E-11 | 0 | ||
最小值 | 5.39E-05 | 3.90E-08 | 1.19E-11 | 4.81E-14 | 最小值 | 0 | 0 | 2.34E-13 | 0 | ||
最大值 | 3.98E-02 | 4.08E-03 | 1.45E-08 | 5.21E-10 | 最大值 | 6.39E-04 | 5.45E-05 | 3.28E-08 | 2.10E-01 | ||
f3(x) | 平均值 | 4.38E-02 | 1.35E-04 | 3.90E-10 | 6.57E-12 | f7(x) | 平均值 | 1.34E-03 | 6.54E-07 | 0 | 0 |
标准方差 | 5.09E-02 | 4.45E-04 | 2.56E-10 | 7.44E-12 | 标准方差 | 1.52E-03 | 3.78E-07 | 0 | 0 | ||
最小值 | 6.37E-05 | 4.87E-07 | 7.81E-13 | 5.17E-15 | 最小值 | 3.06E-05 | 2.86E-10 | 0 | 0 | ||
最大值 | 4.37E-01 | 2.87E-02 | 6.87E-09 | 3.84E-11 | 最大值 | 2.86E-01 | 7.81E-06 | 0 | 0 | ||
f4(x) | 平均值 | 1.12E-02 | 5.46E-03 | 4.95E-07 | 6.74E-09 | f8(x) | 平均值 | 2.121E-01 | 3.36E-02 | 0 | 0 |
标准方差 | 3.42E-02 | 2.74E-03 | 0 | 0 | 标准方差 | 0 | 0 | 0 | 0 | ||
最小值 | 6.37E-04 | 4.65E-06 | 3.01E-10 | 4.75E-12 | 最小值 | 0 | 0 | 0 | 0 | ||
最大值 | 5.35E+00 | 3.76E-01 | 2.19E-05 | 3.67E-08 | 最大值 | 3.13E-01 | 6.43E-03 | 0 | 0 |
Tab.2 Statistical results comparison of different algorithms on benchmark functions
基准 函数 | 统计指标 | SCA | PSCA | LSSCA | IWCCSCA | 基准 函数 | 统计指标 | SCA | PSCA | LSSCA | IWCCSCA |
---|---|---|---|---|---|---|---|---|---|---|---|
f1(x) | 平均值 | 3.54E-06 | 6.63E-09 | 8.25E-12 | 5.57E-15 | f5(x) | 平均值 | -2.53E+03 | -2.57E+03 | -6.56E+06 | -6.57E+09 |
标准方差 | 3.89E-06 | 5.51E-09 | 7.26E-12 | 7.46E-15 | 标准方差 | -2.64E+03 | -2.90E+03 | -6.09E+06 | -8.46E+09 | ||
最小值 | 6.36E-07 | 7.45E-11 | 5.09E-13 | 2.32E-18 | 最小值 | -3.22E+05 | -4.29E+06 | -4.27E+09 | -1.34E+11 | ||
最大值 | 1.32E-04 | 3.59E-07 | 4.78E-09 | 3.29E-11 | 最大值 | -1.19E+01 | -6.28E+02 | -5.29E+04 | -2.08E+07 | ||
f2(x) | 平均值 | 2.13E-03 | 7.47E-05 | 6.35E-09 | 5.47E-11 | f6(x) | 平均值 | 4.94E-06 | 3.15E-07 | 4.04E-11 | 0 |
标准方差 | 4.42E-03 | 5.18E-05 | 6.36E-09 | 4.74E-11 | 标准方差 | 0 | 0 | 6.46E-11 | 0 | ||
最小值 | 5.39E-05 | 3.90E-08 | 1.19E-11 | 4.81E-14 | 最小值 | 0 | 0 | 2.34E-13 | 0 | ||
最大值 | 3.98E-02 | 4.08E-03 | 1.45E-08 | 5.21E-10 | 最大值 | 6.39E-04 | 5.45E-05 | 3.28E-08 | 2.10E-01 | ||
f3(x) | 平均值 | 4.38E-02 | 1.35E-04 | 3.90E-10 | 6.57E-12 | f7(x) | 平均值 | 1.34E-03 | 6.54E-07 | 0 | 0 |
标准方差 | 5.09E-02 | 4.45E-04 | 2.56E-10 | 7.44E-12 | 标准方差 | 1.52E-03 | 3.78E-07 | 0 | 0 | ||
最小值 | 6.37E-05 | 4.87E-07 | 7.81E-13 | 5.17E-15 | 最小值 | 3.06E-05 | 2.86E-10 | 0 | 0 | ||
最大值 | 4.37E-01 | 2.87E-02 | 6.87E-09 | 3.84E-11 | 最大值 | 2.86E-01 | 7.81E-06 | 0 | 0 | ||
f4(x) | 平均值 | 1.12E-02 | 5.46E-03 | 4.95E-07 | 6.74E-09 | f8(x) | 平均值 | 2.121E-01 | 3.36E-02 | 0 | 0 |
标准方差 | 3.42E-02 | 2.74E-03 | 0 | 0 | 标准方差 | 0 | 0 | 0 | 0 | ||
最小值 | 6.37E-04 | 4.65E-06 | 3.01E-10 | 4.75E-12 | 最小值 | 0 | 0 | 0 | 0 | ||
最大值 | 5.35E+00 | 3.76E-01 | 2.19E-05 | 3.67E-08 | 最大值 | 3.13E-01 | 6.43E-03 | 0 | 0 |
基准函数 | 算法 | 平均值 | 标准方差 | 基准函数 | 算法 | 平均值 | 标准方差 |
---|---|---|---|---|---|---|---|
f1(x) | C-SCA | 3.12E-07 | 4.05E-07 | f5(x) | C-SCA | -2.01E+04 | -3.45E+04 |
I-SCA | 5.37E-08 | 5.92E-08 | I-SCA | -6.01E+04 | -5.16E+04 | ||
CC-SCA | 1.02E-11 | 2.67E-11 | CC-SCA | -3.47E+05 | -6.22E+05 | ||
IWCCSCA | 5.57E-15 | 7.46E-15 | IWCCSCA | -6.57E+09 | -8.46E+09 | ||
f2(x) | C-SCA | 2.27E-04 | 3.02E-04 | f6(x) | C-SCA | 3.00E-08 | 2.91E-08 |
I-SCA | 6.81E-06 | 5.72E-06 | I-SCA | 4.12E-09 | 0 | ||
CC-SCA | 3.81E-07 | 3.24E-07 | CC-SCA | 0 | 0 | ||
IWCCSCA | 5.47E-11 | 4.74E-11 | IWCCSCA | 0 | 0 | ||
f3(x) | C-SCA | 4.92E-03 | 3.77E-03 | f7(x) | C-SCA | 5.51E-07 | 4.92E-07 |
I-SCA | 4.04E-03 | 5.19E-03 | I-SCA | 3.26E-10 | 3.11E-10 | ||
CC-SCA | 1.15E-07 | 2.75E-07 | CC-SCA | 0 | 0 | ||
IWCCSCA | 6.57E-12 | 7.44E-12 | IWCCSCA | 0 | 0 | ||
f4(x) | C-SCA | 2.26E-03 | 2.34E-03 | f8(x) | C-SCA | 3.36E-02 | 3.02E-02 |
I-SCA | 4.19E-04 | 6.91E-04 | I-SCA | 4.07E-05 | 0 | ||
CC-SCA | 7.18E-06 | 7.18E-06 | CC-SCA | 0 | 0 | ||
IWCCSCA | 6.74E-09 | 0 | IWCCSCA | 0 | 0 |
Tab.3 Influence of different improvement strategies
基准函数 | 算法 | 平均值 | 标准方差 | 基准函数 | 算法 | 平均值 | 标准方差 |
---|---|---|---|---|---|---|---|
f1(x) | C-SCA | 3.12E-07 | 4.05E-07 | f5(x) | C-SCA | -2.01E+04 | -3.45E+04 |
I-SCA | 5.37E-08 | 5.92E-08 | I-SCA | -6.01E+04 | -5.16E+04 | ||
CC-SCA | 1.02E-11 | 2.67E-11 | CC-SCA | -3.47E+05 | -6.22E+05 | ||
IWCCSCA | 5.57E-15 | 7.46E-15 | IWCCSCA | -6.57E+09 | -8.46E+09 | ||
f2(x) | C-SCA | 2.27E-04 | 3.02E-04 | f6(x) | C-SCA | 3.00E-08 | 2.91E-08 |
I-SCA | 6.81E-06 | 5.72E-06 | I-SCA | 4.12E-09 | 0 | ||
CC-SCA | 3.81E-07 | 3.24E-07 | CC-SCA | 0 | 0 | ||
IWCCSCA | 5.47E-11 | 4.74E-11 | IWCCSCA | 0 | 0 | ||
f3(x) | C-SCA | 4.92E-03 | 3.77E-03 | f7(x) | C-SCA | 5.51E-07 | 4.92E-07 |
I-SCA | 4.04E-03 | 5.19E-03 | I-SCA | 3.26E-10 | 3.11E-10 | ||
CC-SCA | 1.15E-07 | 2.75E-07 | CC-SCA | 0 | 0 | ||
IWCCSCA | 6.57E-12 | 7.44E-12 | IWCCSCA | 0 | 0 | ||
f4(x) | C-SCA | 2.26E-03 | 2.34E-03 | f8(x) | C-SCA | 3.36E-02 | 3.02E-02 |
I-SCA | 4.19E-04 | 6.91E-04 | I-SCA | 4.07E-05 | 0 | ||
CC-SCA | 7.18E-06 | 7.18E-06 | CC-SCA | 0 | 0 | ||
IWCCSCA | 6.74E-09 | 0 | IWCCSCA | 0 | 0 |
基准函数 | k=2 | k =3 | k =3.5 | k =4 | ||||
---|---|---|---|---|---|---|---|---|
平均值 | 标准方差 | 平均值 | 标准方差 | 平均值 | 标准方差 | 平均值 | 标准方差 | |
f1(x) | 5.39E-11 | 6.73E-11 | 5.57E-15 | 7.46E-15 | 5.09E-15 | 6.38E-15 | 4.39E-13 | 6.12E-13 |
f2(x) | 3.19E-07 | 4.89E-07 | 5.47E-11 | 4.74E-11 | 1.10E-09 | 2.75E-09 | 2.48E-09 | 3.67E-09 |
f3(x) | 3.75E-09 | 2.57E-09 | 6.57E-12 | 7.44E-12 | 3.91E-14 | 4.56E-14 | 2.90E-13 | 3.82E-13 |
f4(x) | 5.54E-08 | 6.12E-08 | 6.74E-09 | 0 | 8.15E-08 | 0 | 5.38E-05 | 0 |
f5(x) | -3.67E+05 | -6.59E+05 | -6.57E+09 | -8.46E+09 | -2.45E+04 | -3.82E+04 | -3.86E+04 | -3.18E+04 |
f6(x) | 0 | 0 | 0 | 0 | 6.23E-09 | 0 | 5.72E-09 | 0 |
f7(x) | 3.18E-10 | 4.21E-10 | 0 | 0 | 5.02E-08 | 4.58E-08 | 5.11E-08 | 6.28E-08 |
f8(x) | 0 | 0 | 0 | 0 | 4.29E-05 | 0 | 5.38E-05 | 0 |
Tab.4 Influence of adjustment factor k on performance of IWCCSCA
基准函数 | k=2 | k =3 | k =3.5 | k =4 | ||||
---|---|---|---|---|---|---|---|---|
平均值 | 标准方差 | 平均值 | 标准方差 | 平均值 | 标准方差 | 平均值 | 标准方差 | |
f1(x) | 5.39E-11 | 6.73E-11 | 5.57E-15 | 7.46E-15 | 5.09E-15 | 6.38E-15 | 4.39E-13 | 6.12E-13 |
f2(x) | 3.19E-07 | 4.89E-07 | 5.47E-11 | 4.74E-11 | 1.10E-09 | 2.75E-09 | 2.48E-09 | 3.67E-09 |
f3(x) | 3.75E-09 | 2.57E-09 | 6.57E-12 | 7.44E-12 | 3.91E-14 | 4.56E-14 | 2.90E-13 | 3.82E-13 |
f4(x) | 5.54E-08 | 6.12E-08 | 6.74E-09 | 0 | 8.15E-08 | 0 | 5.38E-05 | 0 |
f5(x) | -3.67E+05 | -6.59E+05 | -6.57E+09 | -8.46E+09 | -2.45E+04 | -3.82E+04 | -3.86E+04 | -3.18E+04 |
f6(x) | 0 | 0 | 0 | 0 | 6.23E-09 | 0 | 5.72E-09 | 0 |
f7(x) | 3.18E-10 | 4.21E-10 | 0 | 0 | 5.02E-08 | 4.58E-08 | 5.11E-08 | 6.28E-08 |
f8(x) | 0 | 0 | 0 | 0 | 4.29E-05 | 0 | 5.38E-05 | 0 |
基准函数 | ||||||||
---|---|---|---|---|---|---|---|---|
平均值 | 标准方差 | 平均值 | 标准方差 | 平均值 | 标准方差 | 平均值 | 标准方差 | |
f1(x) | 6.39E-15 | 6.92E-15 | 5.57E-15 | 7.46E-15 | 6.33E-15 | 5.07E-15 | 5.04E-14 | 4.39E-14 |
f2(x) | 4.18E-11 | 4.15E-11 | 5.47E-11 | 4.74E-11 | 2.57E-11 | 2.66E-11 | 3.31E-10 | 4.45E-10 |
f3(x) | 4.09E-12 | 3.08E-12 | 6.57E-12 | 7.44E-12 | 4.34E-13 | 4.00E-13 | 2.88E-12 | 2.26E-12 |
f4(x) | 6.43E-09 | 5.56E-09 | 6.74E-09 | 0 | 7.38E-08 | 0 | 5.46E-08 | 0 |
f5(x) | -4.27E+08 | -7.01E+08 | -6.57E+09 | -8.46E+09 | -2.11E+09 | -3.75E+09 | -3.26E+08 | -3.02E+08 |
f6(x) | 0 | 0 | 0 | 0 | 6.74E-09 | 000E+00 | 5.61E-09 | 000E+00 |
f7(x) | 3.11E-11 | 4.37E-11 | 0 | 0 | 5.86E-09 | 3.38E-09 | 5.25E-09 | 5.38E-09 |
f8(x) | 0 | 0 | 0 | 0 | 5.37E-05 | 0 | 6.24E-05 | 0 |
Tab.4 Influence of inertia weights wmax、wmin on performance of IWCCSCA
基准函数 | ||||||||
---|---|---|---|---|---|---|---|---|
平均值 | 标准方差 | 平均值 | 标准方差 | 平均值 | 标准方差 | 平均值 | 标准方差 | |
f1(x) | 6.39E-15 | 6.92E-15 | 5.57E-15 | 7.46E-15 | 6.33E-15 | 5.07E-15 | 5.04E-14 | 4.39E-14 |
f2(x) | 4.18E-11 | 4.15E-11 | 5.47E-11 | 4.74E-11 | 2.57E-11 | 2.66E-11 | 3.31E-10 | 4.45E-10 |
f3(x) | 4.09E-12 | 3.08E-12 | 6.57E-12 | 7.44E-12 | 4.34E-13 | 4.00E-13 | 2.88E-12 | 2.26E-12 |
f4(x) | 6.43E-09 | 5.56E-09 | 6.74E-09 | 0 | 7.38E-08 | 0 | 5.46E-08 | 0 |
f5(x) | -4.27E+08 | -7.01E+08 | -6.57E+09 | -8.46E+09 | -2.11E+09 | -3.75E+09 | -3.26E+08 | -3.02E+08 |
f6(x) | 0 | 0 | 0 | 0 | 6.74E-09 | 000E+00 | 5.61E-09 | 000E+00 |
f7(x) | 3.11E-11 | 4.37E-11 | 0 | 0 | 5.86E-09 | 3.38E-09 | 5.25E-09 | 5.38E-09 |
f8(x) | 0 | 0 | 0 | 0 | 5.37E-05 | 0 | 6.24E-05 | 0 |
算法 | p-value | |
---|---|---|
IWCCSCA vs LSSCA | 1.612 3E-05 | Yes |
IWCCSCA vs PSCA | 1.503 8E-05 | Yes |
IWCCSCA vs SCA | 3.289 1E-05 | Yes |
Tab.6 Wilcoxon rank sum test results
算法 | p-value | |
---|---|---|
IWCCSCA vs LSSCA | 1.612 3E-05 | Yes |
IWCCSCA vs PSCA | 1.503 8E-05 | Yes |
IWCCSCA vs SCA | 3.289 1E-05 | Yes |
数据集序号 | 数据集名称 | 特征数 | 样本数 | 分类数 |
---|---|---|---|---|
1 | Arrhythmia | 297 | 452 | 6 |
2 | Breastcancer | 9 | 699 | 4 |
3 | BreastEW | 30 | 476 | 7 |
4 | Clean1 | 166 | 62 | 2 |
5 | Colon | 1 000 | 1 000 | 15 |
6 | German | 24 | 270 | 4 |
7 | HeartEW | 13 | 351 | 2 |
8 | Lonosphere | 34 | 72 | 6 |
9 | Leukemia | 7 129 | 360 | 17 |
10 | Libras | 90 | 4 400 | 24 |
Tab.7 Test datasets
数据集序号 | 数据集名称 | 特征数 | 样本数 | 分类数 |
---|---|---|---|---|
1 | Arrhythmia | 297 | 452 | 6 |
2 | Breastcancer | 9 | 699 | 4 |
3 | BreastEW | 30 | 476 | 7 |
4 | Clean1 | 166 | 62 | 2 |
5 | Colon | 1 000 | 1 000 | 15 |
6 | German | 24 | 270 | 4 |
7 | HeartEW | 13 | 351 | 2 |
8 | Lonosphere | 34 | 72 | 6 |
9 | Leukemia | 7 129 | 360 | 17 |
10 | Libras | 90 | 4 400 | 24 |
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