Journal of Computer Applications ›› 2023, Vol. 43 ›› Issue (9): 2868-2876.DOI: 10.11772/j.issn.1001-9081.2022060813
• Advanced computing • Previous Articles Next Articles
Bo WANG, Hao WANG, Xiaoxin DU, Xiaodong ZHENG, Wei ZHOU
Received:
2022-06-06
Revised:
2022-08-17
Accepted:
2022-08-22
Online:
2022-09-22
Published:
2023-09-10
Contact:
Bo WANG
About author:
WANG Hao, born in 1996, M. S. candidate. His research interests include intelligent optimization algorithm.Supported by:
王波, 王浩, 杜晓昕, 郑晓东, 周薇
通讯作者:
王波
作者简介:
王浩(1996—),男,河南商丘人,硕士研究生,主要研究方向:智能优化算法基金资助:
CLC Number:
Bo WANG, Hao WANG, Xiaoxin DU, Xiaodong ZHENG, Wei ZHOU. Hybrid dragonfly algorithm based on subpopulation and differential evolution[J]. Journal of Computer Applications, 2023, 43(9): 2868-2876.
王波, 王浩, 杜晓昕, 郑晓东, 周薇. 基于亚群和差分进化的混合蜻蜓算法[J]. 《计算机应用》唯一官方网站, 2023, 43(9): 2868-2876.
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URL: https://www.joca.cn/EN/10.11772/j.issn.1001-9081.2022060813
函数表达式 | 维度d | 搜索区域 | 全局最优 |
---|---|---|---|
30 | [-100,100] | 0 | |
30 | [-10,10] | 0 | |
30 | [-100,100] | 0 | |
30 | [-100,100] | 0 | |
30 | [-30,30] | 0 | |
30 | [-100,100] | 0 | |
30 | [-1.28,1.28] | 0 | |
30 | [-500,500] | -418.98d | |
30 | [-5.12,5.12] | 0 | |
30 | [-32,32] | 0 | |
30 | [-600,600] | 0 | |
30 | [-50,50] | 0 | |
30 | [-50,50] | 0 |
Tab.1 Test functions
函数表达式 | 维度d | 搜索区域 | 全局最优 |
---|---|---|---|
30 | [-100,100] | 0 | |
30 | [-10,10] | 0 | |
30 | [-100,100] | 0 | |
30 | [-100,100] | 0 | |
30 | [-30,30] | 0 | |
30 | [-100,100] | 0 | |
30 | [-1.28,1.28] | 0 | |
30 | [-500,500] | -418.98d | |
30 | [-5.12,5.12] | 0 | |
30 | [-32,32] | 0 | |
30 | [-600,600] | 0 | |
30 | [-50,50] | 0 | |
30 | [-50,50] | 0 |
函数类型 | 测试函数 | 指标 | HDASDE | DA | DE | PSO | ABC | GWO |
---|---|---|---|---|---|---|---|---|
单 峰 函 数 | F1 | 最优值 | 0.00E+00 | 4.38E+01 | 2.39E-12 | 5.77E-01 | 3.18E-03 | 3.63E-68 |
平均值 | 0.00E+00 | 4.44E+02 | 7.35E-12 | 1.81E+00 | 1.50E-02 | 4.72E-65 | ||
标准差 | 0.00E+00 | 2.71E+02 | 4.09E-12 | 1.09E+00 | 7.81E-03 | 1.59E-64 | ||
F2 | 最优值 | 0.00E+00 | 1.68E+00 | 5.41E-08 | 0.00E+00 | 8.74E-04 | 1.58E-39 | |
平均值 | 3.87E-35 | 9.07E+00 | 9.33E-08 | 1.00E+00 | 1.81E-03 | 3.34E-38 | ||
标准差 | 2.45E-34 | 2.88E+00 | 2.61E-08 | 3.04E+00 | 8.67E-04 | 3.61E-38 | ||
F3 | 最优值 | 9.00E-19 | 1.04E+02 | 1.90E+04 | 5.49E+01 | 2.09E+04 | 1.45E-22 | |
平均值 | 8.03E-12 | 1.61E+03 | 2.87E+04 | 1.40E+02 | 2.84E+04 | 2.10E-17 | ||
标准差 | 3.79E-11 | 1.09E+03 | 4.49E+03 | 6.91E+01 | 3.67E+03 | 6.83E-17 | ||
F4 | 最优值 | 0.00E+00 | 2.99E+00 | 1.94E-01 | 2.43E+00 | 4.78E+01 | 5.57E-18 | |
平均值 | 0.00E+00 | 9.22E+00 | 3.07E-01 | 5.83E+00 | 5.73E+01 | 2.24E-16 | ||
标准差 | 0.00E+00 | 2.98E+00 | 5.75E-02 | 2.06E+00 | 3.99E+00 | 3.15E-16 | ||
F5 | 最优值 | 0.00E+00 | 2.06E+02 | 2.47E+01 | 4.65E+01 | 8.89E+02 | 2.53E+01 | |
平均值 | 3.00E+00 | 1.02E+04 | 2.95E+01 | 5.41E+02 | 2.05E+03 | 2.67E+01 | ||
标准差 | 8.28E+00 | 1.06E+04 | 1.29E+01 | 3.48E+02 | 8.52E+02 | 7.66E-01 | ||
F6 | 最优值 | 0.00E+00 | 1.87E+00 | 2.19E-12 | 4.77E-01 | 3.66E-03 | 8.91E-06 | |
平均值 | 0.00E+00 | 3.46E+02 | 6.94E-12 | 1.46E+00 | 1.29E-02 | 4.96E-01 | ||
标准差 | 0.00E+00 | 2.11E+02 | 4.26E-12 | 6.54E-01 | 5.92E-03 | 2.86E-01 | ||
多 峰 函 数 | F7 | 最优值 | 1.24E-03 | 1.13E-02 | 1.48E-01 | 9.14E-04 | 7.89E-02 | 1.40E-04 |
平均值 | 5.90E-03 | 1.03E-01 | 3.77E-01 | 3.70E+00 | 1.27E-01 | 5.69E-04 | ||
标准差 | 2.26E-03 | 6.41E-02 | 1.03E-01 | 6.32E+00 | 2.65E-02 | 3.35E-04 | ||
F8 | 最优值 | -1.26E+04 | -8.02E+03 | -1.17E+04 | -8.99E+03 | -6.13E+03 | -7.87E+03 | |
平均值 | -1.26E+04 | -3.19E+03 | -8.93E+03 | -5.01E+03 | -4.77E+03 | -3.43E+03 | ||
标准差 | 1.84E-12 | 1.14E+03 | 6.98E+02 | 8.77E+02 | 3.12E+02 | 9.01E+02 | ||
F9 | 最优值 | 0.00E+00 | 1.56E+01 | 7.00E+01 | 6.94E+01 | 1.89E+02 | 0.00E+00 | |
平均值 | 0.00E+00 | 4.17E+01 | 8.65E+01 | 1.26E+02 | 2.19E+02 | 1.39E-01 | ||
标准差 | 0.00E+00 | 1.27E+01 | 6.67E+00 | 3.21E+01 | 1.11E+01 | 8.80E-01 | ||
F10 | 最优值 | 4.44E-15 | 4.12E+00 | 3.54E-07 | 3.07E-01 | 1.11E-01 | 7.99E-15 | |
平均值 | 4.44E-15 | 5.69E+00 | 6.35E-07 | 3.36E+00 | 6.31E-01 | 1.43E-14 | ||
标准差 | 0.00E+00 | 1.10E+00 | 1.36E-07 | 9.09E-01 | 5.12E-01 | 2.61E-15 | ||
F11 | 最优值 | 0.00E+00 | 1.13E+00 | 6.72E-12 | 5.59E-02 | 2.33E-01 | 0.00E+00 | |
平均值 | 0.00E+00 | 4.00E+00 | 5.80E-10 | 1.57E-01 | 5.07E-01 | 2.45E-03 | ||
标准差 | 0.00E+00 | 1.93E+00 | 1.66E-09 | 4.99E-02 | 1.23E-01 | 6.24E-03 | ||
F12 | 最优值 | 1.57E-32 | 5.42E-01 | 5.94E-13 | 9.54E-01 | 2.42E+01 | 2.45E-06 | |
平均值 | 1.57E-32 | 4.11E+00 | 2.04E-12 | 6.06E+00 | 1.03E+03 | 3.48E-02 | ||
标准差 | 5.54E-48 | 2.38E+00 | 1.37E-12 | 4.07E+00 | 5.57E+03 | 2.33E-02 | ||
F13 | 最优值 | 1.35E-32 | 4.95E+00 | 1.45E-12 | 4.04E-01 | 3.30E+01 | 2.80E-05 | |
平均值 | 1.35E-32 | 6.32E+01 | 8.04E-12 | 5.54E+00 | 2.92E+03 | 3.91E-01 | ||
标准差 | 5.54E-48 | 2.23E+02 | 5.11E-12 | 8.55E+00 | 4.71E+03 | 1.85E-01 |
Tab. 2 Comparison of results of different algorithms on test functions
函数类型 | 测试函数 | 指标 | HDASDE | DA | DE | PSO | ABC | GWO |
---|---|---|---|---|---|---|---|---|
单 峰 函 数 | F1 | 最优值 | 0.00E+00 | 4.38E+01 | 2.39E-12 | 5.77E-01 | 3.18E-03 | 3.63E-68 |
平均值 | 0.00E+00 | 4.44E+02 | 7.35E-12 | 1.81E+00 | 1.50E-02 | 4.72E-65 | ||
标准差 | 0.00E+00 | 2.71E+02 | 4.09E-12 | 1.09E+00 | 7.81E-03 | 1.59E-64 | ||
F2 | 最优值 | 0.00E+00 | 1.68E+00 | 5.41E-08 | 0.00E+00 | 8.74E-04 | 1.58E-39 | |
平均值 | 3.87E-35 | 9.07E+00 | 9.33E-08 | 1.00E+00 | 1.81E-03 | 3.34E-38 | ||
标准差 | 2.45E-34 | 2.88E+00 | 2.61E-08 | 3.04E+00 | 8.67E-04 | 3.61E-38 | ||
F3 | 最优值 | 9.00E-19 | 1.04E+02 | 1.90E+04 | 5.49E+01 | 2.09E+04 | 1.45E-22 | |
平均值 | 8.03E-12 | 1.61E+03 | 2.87E+04 | 1.40E+02 | 2.84E+04 | 2.10E-17 | ||
标准差 | 3.79E-11 | 1.09E+03 | 4.49E+03 | 6.91E+01 | 3.67E+03 | 6.83E-17 | ||
F4 | 最优值 | 0.00E+00 | 2.99E+00 | 1.94E-01 | 2.43E+00 | 4.78E+01 | 5.57E-18 | |
平均值 | 0.00E+00 | 9.22E+00 | 3.07E-01 | 5.83E+00 | 5.73E+01 | 2.24E-16 | ||
标准差 | 0.00E+00 | 2.98E+00 | 5.75E-02 | 2.06E+00 | 3.99E+00 | 3.15E-16 | ||
F5 | 最优值 | 0.00E+00 | 2.06E+02 | 2.47E+01 | 4.65E+01 | 8.89E+02 | 2.53E+01 | |
平均值 | 3.00E+00 | 1.02E+04 | 2.95E+01 | 5.41E+02 | 2.05E+03 | 2.67E+01 | ||
标准差 | 8.28E+00 | 1.06E+04 | 1.29E+01 | 3.48E+02 | 8.52E+02 | 7.66E-01 | ||
F6 | 最优值 | 0.00E+00 | 1.87E+00 | 2.19E-12 | 4.77E-01 | 3.66E-03 | 8.91E-06 | |
平均值 | 0.00E+00 | 3.46E+02 | 6.94E-12 | 1.46E+00 | 1.29E-02 | 4.96E-01 | ||
标准差 | 0.00E+00 | 2.11E+02 | 4.26E-12 | 6.54E-01 | 5.92E-03 | 2.86E-01 | ||
多 峰 函 数 | F7 | 最优值 | 1.24E-03 | 1.13E-02 | 1.48E-01 | 9.14E-04 | 7.89E-02 | 1.40E-04 |
平均值 | 5.90E-03 | 1.03E-01 | 3.77E-01 | 3.70E+00 | 1.27E-01 | 5.69E-04 | ||
标准差 | 2.26E-03 | 6.41E-02 | 1.03E-01 | 6.32E+00 | 2.65E-02 | 3.35E-04 | ||
F8 | 最优值 | -1.26E+04 | -8.02E+03 | -1.17E+04 | -8.99E+03 | -6.13E+03 | -7.87E+03 | |
平均值 | -1.26E+04 | -3.19E+03 | -8.93E+03 | -5.01E+03 | -4.77E+03 | -3.43E+03 | ||
标准差 | 1.84E-12 | 1.14E+03 | 6.98E+02 | 8.77E+02 | 3.12E+02 | 9.01E+02 | ||
F9 | 最优值 | 0.00E+00 | 1.56E+01 | 7.00E+01 | 6.94E+01 | 1.89E+02 | 0.00E+00 | |
平均值 | 0.00E+00 | 4.17E+01 | 8.65E+01 | 1.26E+02 | 2.19E+02 | 1.39E-01 | ||
标准差 | 0.00E+00 | 1.27E+01 | 6.67E+00 | 3.21E+01 | 1.11E+01 | 8.80E-01 | ||
F10 | 最优值 | 4.44E-15 | 4.12E+00 | 3.54E-07 | 3.07E-01 | 1.11E-01 | 7.99E-15 | |
平均值 | 4.44E-15 | 5.69E+00 | 6.35E-07 | 3.36E+00 | 6.31E-01 | 1.43E-14 | ||
标准差 | 0.00E+00 | 1.10E+00 | 1.36E-07 | 9.09E-01 | 5.12E-01 | 2.61E-15 | ||
F11 | 最优值 | 0.00E+00 | 1.13E+00 | 6.72E-12 | 5.59E-02 | 2.33E-01 | 0.00E+00 | |
平均值 | 0.00E+00 | 4.00E+00 | 5.80E-10 | 1.57E-01 | 5.07E-01 | 2.45E-03 | ||
标准差 | 0.00E+00 | 1.93E+00 | 1.66E-09 | 4.99E-02 | 1.23E-01 | 6.24E-03 | ||
F12 | 最优值 | 1.57E-32 | 5.42E-01 | 5.94E-13 | 9.54E-01 | 2.42E+01 | 2.45E-06 | |
平均值 | 1.57E-32 | 4.11E+00 | 2.04E-12 | 6.06E+00 | 1.03E+03 | 3.48E-02 | ||
标准差 | 5.54E-48 | 2.38E+00 | 1.37E-12 | 4.07E+00 | 5.57E+03 | 2.33E-02 | ||
F13 | 最优值 | 1.35E-32 | 4.95E+00 | 1.45E-12 | 4.04E-01 | 3.30E+01 | 2.80E-05 | |
平均值 | 1.35E-32 | 6.32E+01 | 8.04E-12 | 5.54E+00 | 2.92E+03 | 3.91E-01 | ||
标准差 | 5.54E-48 | 2.23E+02 | 5.11E-12 | 8.55E+00 | 4.71E+03 | 1.85E-01 |
测试函数 | DA | DE | PSO | ABC | GWO |
---|---|---|---|---|---|
(-/+/=) | 13/0/0 | 13/0/0 | 12/1/0 | 13/0/0 | 10/2/1 |
F1 | - | - | - | - | - |
F2 | - | - | + | - | - |
F3 | - | - | - | - | + |
F4 | - | - | - | - | - |
F5 | - | - | - | - | - |
F6 | - | - | - | - | - |
F7 | - | - | - | - | + |
F8 | - | - | - | - | - |
F9 | - | - | - | - | - |
F10 | - | - | - | - | - |
F11 | - | - | - | - | = |
F12 | - | - | - | - | - |
F13 | - | - | - | - | - |
Tab.3 Wilcoxon signed-rank test
测试函数 | DA | DE | PSO | ABC | GWO |
---|---|---|---|---|---|
(-/+/=) | 13/0/0 | 13/0/0 | 12/1/0 | 13/0/0 | 10/2/1 |
F1 | - | - | - | - | - |
F2 | - | - | + | - | - |
F3 | - | - | - | - | + |
F4 | - | - | - | - | - |
F5 | - | - | - | - | - |
F6 | - | - | - | - | - |
F7 | - | - | - | - | + |
F8 | - | - | - | - | - |
F9 | - | - | - | - | - |
F10 | - | - | - | - | - |
F11 | - | - | - | - | = |
F12 | - | - | - | - | - |
F13 | - | - | - | - | - |
算法 | 优化变量 | 最优值 | |
---|---|---|---|
A1 | A2 | ||
DA | 0.784 043 | 0.421 509 | 263.911 867 |
DE | 0.784 405 | 0.420 460 | 263.909 439 |
ABC | 0.788 689 | 0.408 325 | 263.907 749 |
GWO | 0.787 470 | 0.411 678 | 263.898 126 |
PSO | 0.788 714 | 0.408 137 | 263.895 843 |
GOA | 0.788 897 | 0.407 619 | 263.895 881 |
ALO | 0.788 662 | 0.408 283 | 263.895 843 |
MGWO-Ⅲ | 0.788 693 | 0.408 199 | 263.895 860 |
MGWO-Ⅱ | 0.788 861 | 0.407 724 | 263.895 880 |
GWO-Ⅰ | 0.788 561 | 0.408 571 | 263.895 890 |
SCA | 0.789 068 | 0.407 162 | 263.898 380 |
MVO | 0.788 993 | 0.407 351 | 263.895 940 |
GSA | 0.777 622 | 0.448 853 | 264.829 960 |
CS | 0.788 670 | 0.409 020 | 263.971 600 |
ERDSSA | 0.795 000 | 0.395 000 | 264.300 000 |
HDASDE | 0.788 668 | 0.408 265 | 263.895 843 |
Tab.4 Optimal values obtained by different algorithms in solving three-bar truss design problem
算法 | 优化变量 | 最优值 | |
---|---|---|---|
A1 | A2 | ||
DA | 0.784 043 | 0.421 509 | 263.911 867 |
DE | 0.784 405 | 0.420 460 | 263.909 439 |
ABC | 0.788 689 | 0.408 325 | 263.907 749 |
GWO | 0.787 470 | 0.411 678 | 263.898 126 |
PSO | 0.788 714 | 0.408 137 | 263.895 843 |
GOA | 0.788 897 | 0.407 619 | 263.895 881 |
ALO | 0.788 662 | 0.408 283 | 263.895 843 |
MGWO-Ⅲ | 0.788 693 | 0.408 199 | 263.895 860 |
MGWO-Ⅱ | 0.788 861 | 0.407 724 | 263.895 880 |
GWO-Ⅰ | 0.788 561 | 0.408 571 | 263.895 890 |
SCA | 0.789 068 | 0.407 162 | 263.898 380 |
MVO | 0.788 993 | 0.407 351 | 263.895 940 |
GSA | 0.777 622 | 0.448 853 | 264.829 960 |
CS | 0.788 670 | 0.409 020 | 263.971 600 |
ERDSSA | 0.795 000 | 0.395 000 | 264.300 000 |
HDASDE | 0.788 668 | 0.408 265 | 263.895 843 |
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