Journal of Computer Applications ›› 2024, Vol. 44 ›› Issue (12): 3844-3853.DOI: 10.11772/j.issn.1001-9081.2023121744
• Advanced computing • Previous Articles Next Articles
Yawei HUANG(), Xuezhong QIAN, Wei SONG
Received:
2023-12-18
Revised:
2024-02-06
Accepted:
2024-02-28
Online:
2024-03-11
Published:
2024-12-10
Contact:
Yawei HUANG
About author:
QIAN Xuezhong, born in 1967, M. S, associate professor. His research interests include data mining, artificial intelligence.Supported by:
通讯作者:
黄亚伟
作者简介:
黄亚伟(1999—),男,安徽六安人,硕士研究生,主要研究方向:智能计算、人工智能基金资助:
CLC Number:
Yawei HUANG, Xuezhong QIAN, Wei SONG. Improved differential evolution algorithm based on dual-archive population size adaptive method[J]. Journal of Computer Applications, 2024, 44(12): 3844-3853.
黄亚伟, 钱雪忠, 宋威. 基于双档案种群大小自适应方法的改进差分进化算法[J]. 《计算机应用》唯一官方网站, 2024, 44(12): 3844-3853.
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URL: https://www.joca.cn/EN/10.11772/j.issn.1001-9081.2023121744
测试函数 | 指标 | JADE | SHADE | LSHADE | DPSHADE | MPEDE | APDE |
---|---|---|---|---|---|---|---|
F1 | 平均值 | 0.00E+00 | 0.00E+00 | 0.00E+00 | 0.00E+00 | 0.00E+00 | 0.00E+00 |
标准差 | 0.00E+00 | 0.00E+00 | 0.00E+00 | 0.00E+00 | 0.00E+00 | 0.00E+00 | |
F2 | 平均值 | 0.00E+00 | 0.00E+00 | 0.00E+00 | 0.00E+00 | 0.00E+00 | 0.00E+00 |
标准差 | 0.00E+00 | 0.00E+00 | 0.00E+00 | 0.00E+00 | 0.00E+00 | 0.00E+00 | |
F3 | 平均值 | 9.92E+03 | 0.00E+00 | 0.00E+00 | 0.00E+00 | 0.00E+00 | 0.00E+00 |
标准差 | 1.61E+04 | 0.00E+00 | 0.00E+00 | 0.00E+00 | 0.00E+00 | 0.00E+00 | |
F4 | 平均值 | 4.79E+01 | 5.77E+01 | 5.86E+01 | 5.86E+01 | 5.35E+01 | 5.86E+01 |
标准差 | 2.38E+01 | 8.35E+00 | 3.00E-14 | 2.80E-14 | 1.77E+01 | 2.56E-14 | |
F5 | 平均值 | 2.94E+01 | 1.55E+01 | 6.60E+00 | 6.07E+00 | 2.74E+01 | 6.59E+00 |
标准差 | 3.91E+00 | 2.62E+00 | 1.40E+00 | 1.75E+00 | 7.32E+00 | 1.48E+00 | |
F6 | 平均值 | 0.00E+00 | 3.86E-07 | 1.21E-08 | 3.76E-08 | 0.00E+00 | 1.02E-08 |
标准差 | 0.00E+00 | 1.24E-06 | 3.75E-08 | 8.96E-08 | 0.00E+00 | 3.32E-08 | |
F7 | 平均值 | 5.84E+01 | 4.61E+01 | 3.76E+01 | 3.74E+01 | 5.62E+01 | 3.78E+01 |
标准差 | 3.97E+00 | 2.68E+00 | 1.19E+00 | 1.45E+00 | 7.25E+00 | 1.18E+00 | |
F8 | 平均值 | 2.77E+01 | 1.65E+01 | 7.36E+00 | 7.28E+00 | 2.72E+01 | 7.36E+00 |
标准差 | 4.10E+00 | 2.83E+00 | 1.62E+00 | 1.54E+00 | 7.26E+00 | 1.52E+00 | |
F9 | 平均值 | 0.00E+00 | 0.00E+00 | 0.00E+00 | 0.00E+00 | 1.42E-02 | 0.00E+00 |
标准差 | 0.00E+00 | 0.00E+00 | 0.00E+00 | 0.00E+00 | 6.64E-02 | 0.00E+00 | |
F10 | 平均值 | 2.09E+03 | 1.68E+03 | 1.40E+03 | 1.40E+03 | 2.63E+03 | 1.30E+03 |
标准差 | 2.00E+02 | 2.12E+02 | 2.08E+02 | 2.52E+02 | 3.58E+02 | 1.96E+02 | |
F11 | 平均值 | 3.40E+01 | 2.17E+01 | 3.56E+01 | 3.20E+01 | 2.30E+01 | 3.28E+01 |
标准差 | 2.78E+01 | 2.30E+01 | 2.83E+01 | 2.89E+01 | 1.77E+01 | 2.80E+01 | |
F12 | 平均值 | 1.15E+03 | 1.22E+03 | 1.18E+03 | 1.03E+03 | 8.99E+02 | 1.10E+03 |
标准差 | 4.65E+02 | 4.68E+02 | 4.15E+02 | 3.58E+02 | 4.01E+02 | 3.29E+02 | |
F13 | 平均值 | 1.94E+02 | 4.09E+01 | 1.72E+01 | 1.76E+01 | 2.17E+01 | 1.58E+01 |
标准差 | 1.12E+03 | 2.33E+01 | 7.14E+00 | 5.99E+00 | 8.49E+00 | 7.25E+00 | |
F14 | 平均值 | 5.81E+03 | 3.09E+01 | 2.19E+01 | 2.16E+01 | 1.66E+01 | 2.17E+01 |
标准差 | 7.96E+03 | 6.85E+00 | 1.22E+00 | 1.08E+00 | 1.05E+01 | 9.44E-01 | |
F15 | 平均值 | 1.21E+03 | 1.87E+01 | 3.73E+00 | 3.57E+00 | 8.86E+00 | 3.51E+00 |
标准差 | 3.36E+03 | 1.02E+01 | 1.72E+00 | 2.01E+00 | 3.28E+00 | 1.78E+00 | |
F16 | 平均值 | 4.33E+02 | 2.88E+02 | 3.57E+01 | 3.49E+01 | 4.01E+02 | 3.14E+01 |
标准差 | 1.21E+02 | 1.40E+02 | 1.90E+01 | 2.43E+01 | 1.76E+02 | 1.97E+01 | |
F17 | 平均值 | 8.83E+01 | 4.44E+01 | 3.29E+01 | 3.21E+01 | 5.38E+01 | 3.11E+01 |
标准差 | 3.17E+01 | 1.11E+01 | 5.55E+00 | 7.99E+00 | 1.46E+01 | 6.00E+00 | |
F18 | 平均值 | 2.49E+04 | 1.11E+02 | 2.28E+01 | 2.21E+01 | 2.24E+01 | 2.23E+01 |
标准差 | 5.91E+04 | 6.78E+01 | 1.66E+00 | 1.17E+00 | 8.71E+00 | 1.27E+00 | |
F19 | 平均值 | 1.81E+03 | 1.26E+01 | 5.94E+00 | 6.09E+00 | 7.13E+00 | 5.75E+00 |
标准差 | 4.81E+03 | 6.71E+00 | 1.80E+00 | 1.75E+00 | 1.94E+00 | 1.39E+00 | |
F20 | 平均值 | 1.18E+02 | 5.99E+01 | 3.06E+01 | 3.20E+01 | 7.82E+01 | 3.02E+01 |
标准差 | 5.39E+01 | 3.89E+01 | 5.46E+00 | 5.11E+00 | 5.66E+01 | 5.66E+00 | |
F21 | 平均值 | 2.29E+02 | 2.18E+02 | 2.08E+02 | 2.08E+02 | 2.28E+02 | 2.08E+02 |
标准差 | 4.33E+00 | 2.69E+00 | 1.53E+00 | 1.48E+00 | 7.39E+00 | 1.50E+00 | |
F22 | 平均值 | 1.00E+02 | 1.00E+02 | 1.00E+02 | 1.00E+02 | 1.00E+02 | 1.00E+02 |
标准差 | 1.44E-14 | 1.44E-14 | 1.44E-14 | 1.44E-14 | 1.44E-14 | 1.44E-14 | |
F23 | 平均值 | 3.76E+02 | 3.66E+02 | 3.53E+02 | 3.53E+02 | 3.76E+02 | 3.54E+02 |
标准差 | 5.76E+00 | 5.33E+00 | 3.09E+00 | 2.86E+00 | 1.02E+01 | 3.09E+00 | |
F24 | 平均值 | 4.42E+02 | 4.37E+02 | 4.28E+02 | 4.28E+02 | 4.43E+02 | 4.28E+02 |
标准差 | 4.88E+00 | 4.26E+00 | 2.01E+00 | 1.63E+00 | 8.17E+00 | 1.55E+00 | |
F25 | 平均值 | 3.87E+02 | 3.87E+02 | 3.87E+02 | 3.87E+02 | 3.80E+02 | 3.87E+02 |
标准差 | 1.29E-01 | 6.79E-02 | 2.20E-02 | 1.97E-02 | 1.32E+00 | 2.12E-02 | |
F26 | 平均值 | 1.19E+03 | 1.13E+03 | 9.80E+02 | 9.75E+02 | 1.23E+03 | 9.71E+02 |
标准差 | 7.87E+01 | 5.91E+01 | 3.32E+01 | 3.35E+01 | 1.07E+02 | 3.76E+01 | |
F27 | 平均值 | 5.03E+02 | 5.04E+02 | 5.07E+02 | 5.07E+02 | 5.01E+02 | 5.06E+02 |
标准差 | 7.08E+00 | 7.31E+00 | 4.67E+00 | 4.78E+00 | 6.27E+00 | 4.07E+00 | |
F28 | 平均值 | 3.46E+02 | 3.46E+02 | 3.58E+02 | 3.21E+02 | 3.31E+02 | 3.41E+02 |
标准差 | 5.58E+01 | 5.89E+01 | 5.88E+01 | 4.66E+01 | 4.92E+01 | 5.68E+01 | |
F29 | 平均值 | 4.82E+02 | 4.71E+02 | 4.38E+02 | 4.36E+02 | 4.54E+02 | 4.36E+02 |
标准差 | 3.26E+01 | 3.34E+01 | 7.93E+00 | 7.80E+00 | 2.77E+01 | 7.16E+00 | |
F30 | 平均值 | 2.12E+03 | 2.12E+03 | 2.01E+03 | 2.00E+03 | 2.02E+03 | 2.01E+03 |
标准差 | 1.47E+02 | 1.56E+02 | 6.55E+01 | 7.88E+01 | 8.62E+01 | 8.18E+01 | |
+ | 21 | 20 | 3 | 3 | 18 | ||
- | 2 | 2 | 0 | 0 | 5 | ||
= | 7 | 8 | 27 | 27 | 7 |
Tab.1 Results of 6 DE variants on CEC2017 test set (dimension = 30)
测试函数 | 指标 | JADE | SHADE | LSHADE | DPSHADE | MPEDE | APDE |
---|---|---|---|---|---|---|---|
F1 | 平均值 | 0.00E+00 | 0.00E+00 | 0.00E+00 | 0.00E+00 | 0.00E+00 | 0.00E+00 |
标准差 | 0.00E+00 | 0.00E+00 | 0.00E+00 | 0.00E+00 | 0.00E+00 | 0.00E+00 | |
F2 | 平均值 | 0.00E+00 | 0.00E+00 | 0.00E+00 | 0.00E+00 | 0.00E+00 | 0.00E+00 |
标准差 | 0.00E+00 | 0.00E+00 | 0.00E+00 | 0.00E+00 | 0.00E+00 | 0.00E+00 | |
F3 | 平均值 | 9.92E+03 | 0.00E+00 | 0.00E+00 | 0.00E+00 | 0.00E+00 | 0.00E+00 |
标准差 | 1.61E+04 | 0.00E+00 | 0.00E+00 | 0.00E+00 | 0.00E+00 | 0.00E+00 | |
F4 | 平均值 | 4.79E+01 | 5.77E+01 | 5.86E+01 | 5.86E+01 | 5.35E+01 | 5.86E+01 |
标准差 | 2.38E+01 | 8.35E+00 | 3.00E-14 | 2.80E-14 | 1.77E+01 | 2.56E-14 | |
F5 | 平均值 | 2.94E+01 | 1.55E+01 | 6.60E+00 | 6.07E+00 | 2.74E+01 | 6.59E+00 |
标准差 | 3.91E+00 | 2.62E+00 | 1.40E+00 | 1.75E+00 | 7.32E+00 | 1.48E+00 | |
F6 | 平均值 | 0.00E+00 | 3.86E-07 | 1.21E-08 | 3.76E-08 | 0.00E+00 | 1.02E-08 |
标准差 | 0.00E+00 | 1.24E-06 | 3.75E-08 | 8.96E-08 | 0.00E+00 | 3.32E-08 | |
F7 | 平均值 | 5.84E+01 | 4.61E+01 | 3.76E+01 | 3.74E+01 | 5.62E+01 | 3.78E+01 |
标准差 | 3.97E+00 | 2.68E+00 | 1.19E+00 | 1.45E+00 | 7.25E+00 | 1.18E+00 | |
F8 | 平均值 | 2.77E+01 | 1.65E+01 | 7.36E+00 | 7.28E+00 | 2.72E+01 | 7.36E+00 |
标准差 | 4.10E+00 | 2.83E+00 | 1.62E+00 | 1.54E+00 | 7.26E+00 | 1.52E+00 | |
F9 | 平均值 | 0.00E+00 | 0.00E+00 | 0.00E+00 | 0.00E+00 | 1.42E-02 | 0.00E+00 |
标准差 | 0.00E+00 | 0.00E+00 | 0.00E+00 | 0.00E+00 | 6.64E-02 | 0.00E+00 | |
F10 | 平均值 | 2.09E+03 | 1.68E+03 | 1.40E+03 | 1.40E+03 | 2.63E+03 | 1.30E+03 |
标准差 | 2.00E+02 | 2.12E+02 | 2.08E+02 | 2.52E+02 | 3.58E+02 | 1.96E+02 | |
F11 | 平均值 | 3.40E+01 | 2.17E+01 | 3.56E+01 | 3.20E+01 | 2.30E+01 | 3.28E+01 |
标准差 | 2.78E+01 | 2.30E+01 | 2.83E+01 | 2.89E+01 | 1.77E+01 | 2.80E+01 | |
F12 | 平均值 | 1.15E+03 | 1.22E+03 | 1.18E+03 | 1.03E+03 | 8.99E+02 | 1.10E+03 |
标准差 | 4.65E+02 | 4.68E+02 | 4.15E+02 | 3.58E+02 | 4.01E+02 | 3.29E+02 | |
F13 | 平均值 | 1.94E+02 | 4.09E+01 | 1.72E+01 | 1.76E+01 | 2.17E+01 | 1.58E+01 |
标准差 | 1.12E+03 | 2.33E+01 | 7.14E+00 | 5.99E+00 | 8.49E+00 | 7.25E+00 | |
F14 | 平均值 | 5.81E+03 | 3.09E+01 | 2.19E+01 | 2.16E+01 | 1.66E+01 | 2.17E+01 |
标准差 | 7.96E+03 | 6.85E+00 | 1.22E+00 | 1.08E+00 | 1.05E+01 | 9.44E-01 | |
F15 | 平均值 | 1.21E+03 | 1.87E+01 | 3.73E+00 | 3.57E+00 | 8.86E+00 | 3.51E+00 |
标准差 | 3.36E+03 | 1.02E+01 | 1.72E+00 | 2.01E+00 | 3.28E+00 | 1.78E+00 | |
F16 | 平均值 | 4.33E+02 | 2.88E+02 | 3.57E+01 | 3.49E+01 | 4.01E+02 | 3.14E+01 |
标准差 | 1.21E+02 | 1.40E+02 | 1.90E+01 | 2.43E+01 | 1.76E+02 | 1.97E+01 | |
F17 | 平均值 | 8.83E+01 | 4.44E+01 | 3.29E+01 | 3.21E+01 | 5.38E+01 | 3.11E+01 |
标准差 | 3.17E+01 | 1.11E+01 | 5.55E+00 | 7.99E+00 | 1.46E+01 | 6.00E+00 | |
F18 | 平均值 | 2.49E+04 | 1.11E+02 | 2.28E+01 | 2.21E+01 | 2.24E+01 | 2.23E+01 |
标准差 | 5.91E+04 | 6.78E+01 | 1.66E+00 | 1.17E+00 | 8.71E+00 | 1.27E+00 | |
F19 | 平均值 | 1.81E+03 | 1.26E+01 | 5.94E+00 | 6.09E+00 | 7.13E+00 | 5.75E+00 |
标准差 | 4.81E+03 | 6.71E+00 | 1.80E+00 | 1.75E+00 | 1.94E+00 | 1.39E+00 | |
F20 | 平均值 | 1.18E+02 | 5.99E+01 | 3.06E+01 | 3.20E+01 | 7.82E+01 | 3.02E+01 |
标准差 | 5.39E+01 | 3.89E+01 | 5.46E+00 | 5.11E+00 | 5.66E+01 | 5.66E+00 | |
F21 | 平均值 | 2.29E+02 | 2.18E+02 | 2.08E+02 | 2.08E+02 | 2.28E+02 | 2.08E+02 |
标准差 | 4.33E+00 | 2.69E+00 | 1.53E+00 | 1.48E+00 | 7.39E+00 | 1.50E+00 | |
F22 | 平均值 | 1.00E+02 | 1.00E+02 | 1.00E+02 | 1.00E+02 | 1.00E+02 | 1.00E+02 |
标准差 | 1.44E-14 | 1.44E-14 | 1.44E-14 | 1.44E-14 | 1.44E-14 | 1.44E-14 | |
F23 | 平均值 | 3.76E+02 | 3.66E+02 | 3.53E+02 | 3.53E+02 | 3.76E+02 | 3.54E+02 |
标准差 | 5.76E+00 | 5.33E+00 | 3.09E+00 | 2.86E+00 | 1.02E+01 | 3.09E+00 | |
F24 | 平均值 | 4.42E+02 | 4.37E+02 | 4.28E+02 | 4.28E+02 | 4.43E+02 | 4.28E+02 |
标准差 | 4.88E+00 | 4.26E+00 | 2.01E+00 | 1.63E+00 | 8.17E+00 | 1.55E+00 | |
F25 | 平均值 | 3.87E+02 | 3.87E+02 | 3.87E+02 | 3.87E+02 | 3.80E+02 | 3.87E+02 |
标准差 | 1.29E-01 | 6.79E-02 | 2.20E-02 | 1.97E-02 | 1.32E+00 | 2.12E-02 | |
F26 | 平均值 | 1.19E+03 | 1.13E+03 | 9.80E+02 | 9.75E+02 | 1.23E+03 | 9.71E+02 |
标准差 | 7.87E+01 | 5.91E+01 | 3.32E+01 | 3.35E+01 | 1.07E+02 | 3.76E+01 | |
F27 | 平均值 | 5.03E+02 | 5.04E+02 | 5.07E+02 | 5.07E+02 | 5.01E+02 | 5.06E+02 |
标准差 | 7.08E+00 | 7.31E+00 | 4.67E+00 | 4.78E+00 | 6.27E+00 | 4.07E+00 | |
F28 | 平均值 | 3.46E+02 | 3.46E+02 | 3.58E+02 | 3.21E+02 | 3.31E+02 | 3.41E+02 |
标准差 | 5.58E+01 | 5.89E+01 | 5.88E+01 | 4.66E+01 | 4.92E+01 | 5.68E+01 | |
F29 | 平均值 | 4.82E+02 | 4.71E+02 | 4.38E+02 | 4.36E+02 | 4.54E+02 | 4.36E+02 |
标准差 | 3.26E+01 | 3.34E+01 | 7.93E+00 | 7.80E+00 | 2.77E+01 | 7.16E+00 | |
F30 | 平均值 | 2.12E+03 | 2.12E+03 | 2.01E+03 | 2.00E+03 | 2.02E+03 | 2.01E+03 |
标准差 | 1.47E+02 | 1.56E+02 | 6.55E+01 | 7.88E+01 | 8.62E+01 | 8.18E+01 | |
+ | 21 | 20 | 3 | 3 | 18 | ||
- | 2 | 2 | 0 | 0 | 5 | ||
= | 7 | 8 | 27 | 27 | 7 |
测试函数 | 指标 | JADE | SHADE | LSHADE | DPSHADE | MPEDE | APDE |
---|---|---|---|---|---|---|---|
F1 | 平均值 | 0.00E+00 | 0.00E+00 | 0.00E+00 | 0.00E+00 | 0.00E+00 | 0.00E+00 |
标准差 | 0.00E+00 | 0.00E+00 | 0.00E+00 | 0.00E+00 | 0.00E+00 | 0.00E+00 | |
F2 | 平均值 | 0.00E+00 | 0.00E+00 | 0.00E+00 | 0.00E+00 | 0.00E+00 | 0.00E+00 |
标准差 | 0.00E+00 | 0.00E+00 | 0.00E+00 | 0.00E+00 | 0.00E+00 | 0.00E+00 | |
F3 | 平均值 | 2.15E+04 | 0.00E+00 | 0.00E+00 | 0.00E+00 | 7.77E-04 | 0.00E+00 |
标准差 | 4.24E+04 | 0.00E+00 | 0.00E+00 | 0.00E+00 | 3.38E-03 | 0.00E+00 | |
F4 | 平均值 | 5.79E+01 | 6.81E+01 | 6.24E+01 | 8.38E+01 | 5.97E+01 | 5.79E+01 |
标准差 | 4.60E+01 | 4.87E+01 | 5.02E+01 | 5.05E+01 | 4.47E+01 | 5.44E+01 | |
F5 | 平均值 | 6.40E+01 | 3.17E+01 | 1.17E+01 | 1.08E+01 | 5.37E+01 | 1.08E+01 |
标准差 | 8.49E+00 | 3.97E+00 | 2.35E+00 | 2.19E+00 | 1.21E+01 | 2.02E+00 | |
F6 | 平均值 | 5.50E-08 | 5.15E-05 | 8.42E-06 | 5.79E-08 | 6.97E-04 | 2.31E-08 |
标准差 | 1.26E-07 | 7.16E-05 | 5.98E-05 | 9.90E-08 | 2.09E-03 | 3.85E-08 | |
F7 | 平均值 | 1.15E+02 | 8.35E+01 | 6.42E+01 | 6.33E+01 | 1.07E+02 | 6.32E+01 |
标准差 | 7.99E+00 | 3.90E+00 | 1.97E+00 | 1.71E+00 | 1.13E+01 | 1.93E+00 | |
F8 | 平均值 | 6.63E+01 | 3.15E+01 | 1.12E+01 | 1.10E+01 | 5.53E+01 | 1.07E+01 |
标准差 | 6.88E+00 | 4.81E+00 | 1.94E+00 | 2.39E+00 | 1.23E+01 | 2.66E+00 | |
F9 | 平均值 | 2.25E-01 | 2.84E-01 | 0.00E+00 | 0.00E+00 | 9.35E-01 | 1.76E-03 |
标准差 | 3.03E-01 | 2.98E-01 | 0.00E+00 | 0.00E+00 | 8.92E-01 | 1.25E-02 | |
F10 | 平均值 | 4.61E+03 | 3.27E+03 | 3.12E+03 | 3.15E+03 | 4.85E+03 | 2.95E+03 |
标准差 | 3.24E+02 | 3.20E+02 | 2.87E+02 | 3.11E+02 | 7.28E+02 | 3.00E+02 | |
F11 | 平均值 | 1.29E+02 | 9.87E+01 | 4.69E+01 | 4.70E+01 | 1.04E+02 | 4.96E+01 |
标准差 | 5.90E+01 | 2.41E+01 | 1.09E+01 | 8.16E+00 | 2.51E+01 | 8.06E+00 | |
F12 | 平均值 | 4.93E+03 | 5.62E+03 | 2.22E+03 | 2.18E+03 | 9.81E+03 | 2.33E+03 |
标准差 | 3.93E+03 | 4.07E+03 | 5.00E+02 | 6.14E+02 | 7.02E+03 | 4.62E+02 | |
F13 | 平均值 | 1.51E+02 | 3.73E+02 | 6.78E+01 | 6.46E+01 | 9.52E+01 | 5.97E+01 |
标准差 | 8.70E+01 | 3.33E+02 | 2.90E+01 | 2.94E+01 | 3.51E+01 | 2.93E+01 | |
F14 | 平均值 | 1.66E+04 | 2.24E+02 | 3.16E+01 | 2.96E+01 | 6.14E+01 | 2.96E+01 |
标准差 | 4.46E+04 | 6.44E+01 | 3.97E+00 | 3.44E+00 | 1.64E+01 | 2.64E+00 | |
F15 | 平均值 | 2.19E+02 | 3.01E+02 | 4.59E+01 | 4.41E+01 | 7.83E+01 | 4.70E+01 |
标准差 | 1.02E+02 | 1.06E+02 | 1.33E+01 | 1.06E+01 | 4.32E+01 | 1.27E+01 | |
F16 | 平均值 | 9.10E+02 | 7.01E+02 | 3.27E+02 | 3.49E+02 | 9.67E+02 | 3.56E+02 |
标准差 | 1.88E+02 | 2.13E+02 | 1.14E+02 | 1.20E+02 | 2.91E+02 | 1.36E+02 | |
F17 | 平均值 | 6.91E+02 | 5.09E+02 | 2.13E+02 | 2.28E+02 | 5.88E+02 | 2.26E+02 |
标准差 | 1.44E+02 | 1.32E+02 | 8.22E+01 | 6.64E+01 | 1.99E+02 | 7.54E+01 | |
F18 | 平均值 | 3.02E+03 | 1.68E+02 | 5.53E+01 | 4.49E+01 | 1.21E+02 | 5.12E+01 |
标准差 | 1.99E+04 | 9.07E+01 | 2.26E+01 | 1.30E+01 | 9.31E+01 | 2.18E+01 | |
F19 | 平均值 | 1.31E+02 | 1.44E+02 | 3.09E+01 | 2.98E+01 | 4.44E+01 | 3.43E+01 |
标准差 | 3.77E+01 | 4.76E+01 | 1.01E+01 | 8.99E+00 | 1.86E+01 | 1.31E+01 | |
F20 | 平均值 | 5.10E+02 | 3.02E+02 | 1.64E+02 | 1.70E+02 | 3.50E+02 | 1.55E+02 |
标准差 | 1.25E+02 | 1.06E+02 | 6.57E+01 | 6.70E+01 | 1.74E+02 | 6.61E+01 | |
F21 | 平均值 | 2.66E+02 | 2.35E+02 | 2.14E+02 | 2.13E+02 | 2.53E+02 | 2.14E+02 |
标准差 | 7.79E+00 | 4.72E+00 | 2.35E+00 | 2.29E+00 | 1.37E+01 | 2.16E+00 | |
F22 | 平均值 | 4.12E+03 | 3.07E+03 | 1.98E+03 | 2.69E+03 | 3.68E+03 | 2.72E+03 |
标准差 | 2.09E+03 | 1.68E+03 | 1.74E+03 | 1.49E+03 | 2.67E+03 | 1.26E+03 | |
F23 | 平均值 | 4.92E+02 | 4.63E+02 | 4.32E+02 | 4.30E+02 | 4.81E+02 | 4.31E+02 |
标准差 | 1.10E+01 | 9.07E+00 | 3.76E+00 | 3.85E+00 | 1.39E+01 | 3.95E+00 | |
F24 | 平均值 | 5.45E+02 | 5.34E+02 | 5.11E+02 | 5.11E+02 | 5.43E+02 | 5.11E+02 |
标准差 | 8.88E+00 | 5.91E+00 | 2.59E+00 | 2.39E+00 | 1.34E+01 | 2.57E+00 | |
F25 | 平均值 | 5.14E+02 | 5.01E+02 | 4.81E+02 | 4.81E+02 | 4.98E+02 | 4.81E+02 |
标准差 | 3.37E+01 | 3.31E+01 | 2.33E+00 | 2.75E+00 | 3.44E+01 | 3.93E+00 | |
F26 | 平均值 | 1.66E+03 | 1.46E+03 | 1.21E+03 | 1.19E+03 | 1.56E+03 | 1.21E+03 |
标准差 | 9.89E+01 | 8.45E+01 | 3.86E+01 | 4.87E+01 | 1.68E+02 | 4.24E+01 | |
F27 | 平均值 | 5.38E+02 | 5.49E+02 | 5.39E+02 | 5.42E+02 | 5.43E+02 | 5.44E+02 |
标准差 | 1.97E+01 | 3.42E+01 | 1.47E+01 | 1.78E+01 | 2.41E+01 | 2.09E+01 | |
F28 | 平均值 | 4.87E+02 | 4.82E+02 | 4.65E+02 | 4.63E+02 | 4.89E+02 | 4.71E+02 |
标准差 | 2.39E+01 | 2.34E+01 | 1.66E+01 | 1.27E+01 | 2.34E+01 | 2.07E+01 | |
F29 | 平均值 | 4.89E+02 | 4.65E+02 | 3.48E+02 | 3.48E+02 | 4.39E+02 | 3.41E+02 |
标准差 | 5.95E+01 | 9.44E+01 | 1.25E+01 | 8.56E+00 | 1.26E+02 | 9.59E+00 | |
F30 | 平均值 | 6.84E+05 | 6.78E+05 | 6.69E+05 | 6.68E+05 | 6.80E+05 | 6.71E+05 |
标准差 | 7.35E+04 | 8.47E+04 | 9.54E+04 | 7.50E+04 | 9.69E+04 | 7.70E+04 | |
+ | 24 | 24 | 5 | 4 | 24 | ||
- | 0 | 0 | 1 | 1 | 0 | ||
= | 6 | 6 | 24 | 25 | 6 |
Tab.2 Results of 6 DE variants on CEC2017 test set (dimension = 50)
测试函数 | 指标 | JADE | SHADE | LSHADE | DPSHADE | MPEDE | APDE |
---|---|---|---|---|---|---|---|
F1 | 平均值 | 0.00E+00 | 0.00E+00 | 0.00E+00 | 0.00E+00 | 0.00E+00 | 0.00E+00 |
标准差 | 0.00E+00 | 0.00E+00 | 0.00E+00 | 0.00E+00 | 0.00E+00 | 0.00E+00 | |
F2 | 平均值 | 0.00E+00 | 0.00E+00 | 0.00E+00 | 0.00E+00 | 0.00E+00 | 0.00E+00 |
标准差 | 0.00E+00 | 0.00E+00 | 0.00E+00 | 0.00E+00 | 0.00E+00 | 0.00E+00 | |
F3 | 平均值 | 2.15E+04 | 0.00E+00 | 0.00E+00 | 0.00E+00 | 7.77E-04 | 0.00E+00 |
标准差 | 4.24E+04 | 0.00E+00 | 0.00E+00 | 0.00E+00 | 3.38E-03 | 0.00E+00 | |
F4 | 平均值 | 5.79E+01 | 6.81E+01 | 6.24E+01 | 8.38E+01 | 5.97E+01 | 5.79E+01 |
标准差 | 4.60E+01 | 4.87E+01 | 5.02E+01 | 5.05E+01 | 4.47E+01 | 5.44E+01 | |
F5 | 平均值 | 6.40E+01 | 3.17E+01 | 1.17E+01 | 1.08E+01 | 5.37E+01 | 1.08E+01 |
标准差 | 8.49E+00 | 3.97E+00 | 2.35E+00 | 2.19E+00 | 1.21E+01 | 2.02E+00 | |
F6 | 平均值 | 5.50E-08 | 5.15E-05 | 8.42E-06 | 5.79E-08 | 6.97E-04 | 2.31E-08 |
标准差 | 1.26E-07 | 7.16E-05 | 5.98E-05 | 9.90E-08 | 2.09E-03 | 3.85E-08 | |
F7 | 平均值 | 1.15E+02 | 8.35E+01 | 6.42E+01 | 6.33E+01 | 1.07E+02 | 6.32E+01 |
标准差 | 7.99E+00 | 3.90E+00 | 1.97E+00 | 1.71E+00 | 1.13E+01 | 1.93E+00 | |
F8 | 平均值 | 6.63E+01 | 3.15E+01 | 1.12E+01 | 1.10E+01 | 5.53E+01 | 1.07E+01 |
标准差 | 6.88E+00 | 4.81E+00 | 1.94E+00 | 2.39E+00 | 1.23E+01 | 2.66E+00 | |
F9 | 平均值 | 2.25E-01 | 2.84E-01 | 0.00E+00 | 0.00E+00 | 9.35E-01 | 1.76E-03 |
标准差 | 3.03E-01 | 2.98E-01 | 0.00E+00 | 0.00E+00 | 8.92E-01 | 1.25E-02 | |
F10 | 平均值 | 4.61E+03 | 3.27E+03 | 3.12E+03 | 3.15E+03 | 4.85E+03 | 2.95E+03 |
标准差 | 3.24E+02 | 3.20E+02 | 2.87E+02 | 3.11E+02 | 7.28E+02 | 3.00E+02 | |
F11 | 平均值 | 1.29E+02 | 9.87E+01 | 4.69E+01 | 4.70E+01 | 1.04E+02 | 4.96E+01 |
标准差 | 5.90E+01 | 2.41E+01 | 1.09E+01 | 8.16E+00 | 2.51E+01 | 8.06E+00 | |
F12 | 平均值 | 4.93E+03 | 5.62E+03 | 2.22E+03 | 2.18E+03 | 9.81E+03 | 2.33E+03 |
标准差 | 3.93E+03 | 4.07E+03 | 5.00E+02 | 6.14E+02 | 7.02E+03 | 4.62E+02 | |
F13 | 平均值 | 1.51E+02 | 3.73E+02 | 6.78E+01 | 6.46E+01 | 9.52E+01 | 5.97E+01 |
标准差 | 8.70E+01 | 3.33E+02 | 2.90E+01 | 2.94E+01 | 3.51E+01 | 2.93E+01 | |
F14 | 平均值 | 1.66E+04 | 2.24E+02 | 3.16E+01 | 2.96E+01 | 6.14E+01 | 2.96E+01 |
标准差 | 4.46E+04 | 6.44E+01 | 3.97E+00 | 3.44E+00 | 1.64E+01 | 2.64E+00 | |
F15 | 平均值 | 2.19E+02 | 3.01E+02 | 4.59E+01 | 4.41E+01 | 7.83E+01 | 4.70E+01 |
标准差 | 1.02E+02 | 1.06E+02 | 1.33E+01 | 1.06E+01 | 4.32E+01 | 1.27E+01 | |
F16 | 平均值 | 9.10E+02 | 7.01E+02 | 3.27E+02 | 3.49E+02 | 9.67E+02 | 3.56E+02 |
标准差 | 1.88E+02 | 2.13E+02 | 1.14E+02 | 1.20E+02 | 2.91E+02 | 1.36E+02 | |
F17 | 平均值 | 6.91E+02 | 5.09E+02 | 2.13E+02 | 2.28E+02 | 5.88E+02 | 2.26E+02 |
标准差 | 1.44E+02 | 1.32E+02 | 8.22E+01 | 6.64E+01 | 1.99E+02 | 7.54E+01 | |
F18 | 平均值 | 3.02E+03 | 1.68E+02 | 5.53E+01 | 4.49E+01 | 1.21E+02 | 5.12E+01 |
标准差 | 1.99E+04 | 9.07E+01 | 2.26E+01 | 1.30E+01 | 9.31E+01 | 2.18E+01 | |
F19 | 平均值 | 1.31E+02 | 1.44E+02 | 3.09E+01 | 2.98E+01 | 4.44E+01 | 3.43E+01 |
标准差 | 3.77E+01 | 4.76E+01 | 1.01E+01 | 8.99E+00 | 1.86E+01 | 1.31E+01 | |
F20 | 平均值 | 5.10E+02 | 3.02E+02 | 1.64E+02 | 1.70E+02 | 3.50E+02 | 1.55E+02 |
标准差 | 1.25E+02 | 1.06E+02 | 6.57E+01 | 6.70E+01 | 1.74E+02 | 6.61E+01 | |
F21 | 平均值 | 2.66E+02 | 2.35E+02 | 2.14E+02 | 2.13E+02 | 2.53E+02 | 2.14E+02 |
标准差 | 7.79E+00 | 4.72E+00 | 2.35E+00 | 2.29E+00 | 1.37E+01 | 2.16E+00 | |
F22 | 平均值 | 4.12E+03 | 3.07E+03 | 1.98E+03 | 2.69E+03 | 3.68E+03 | 2.72E+03 |
标准差 | 2.09E+03 | 1.68E+03 | 1.74E+03 | 1.49E+03 | 2.67E+03 | 1.26E+03 | |
F23 | 平均值 | 4.92E+02 | 4.63E+02 | 4.32E+02 | 4.30E+02 | 4.81E+02 | 4.31E+02 |
标准差 | 1.10E+01 | 9.07E+00 | 3.76E+00 | 3.85E+00 | 1.39E+01 | 3.95E+00 | |
F24 | 平均值 | 5.45E+02 | 5.34E+02 | 5.11E+02 | 5.11E+02 | 5.43E+02 | 5.11E+02 |
标准差 | 8.88E+00 | 5.91E+00 | 2.59E+00 | 2.39E+00 | 1.34E+01 | 2.57E+00 | |
F25 | 平均值 | 5.14E+02 | 5.01E+02 | 4.81E+02 | 4.81E+02 | 4.98E+02 | 4.81E+02 |
标准差 | 3.37E+01 | 3.31E+01 | 2.33E+00 | 2.75E+00 | 3.44E+01 | 3.93E+00 | |
F26 | 平均值 | 1.66E+03 | 1.46E+03 | 1.21E+03 | 1.19E+03 | 1.56E+03 | 1.21E+03 |
标准差 | 9.89E+01 | 8.45E+01 | 3.86E+01 | 4.87E+01 | 1.68E+02 | 4.24E+01 | |
F27 | 平均值 | 5.38E+02 | 5.49E+02 | 5.39E+02 | 5.42E+02 | 5.43E+02 | 5.44E+02 |
标准差 | 1.97E+01 | 3.42E+01 | 1.47E+01 | 1.78E+01 | 2.41E+01 | 2.09E+01 | |
F28 | 平均值 | 4.87E+02 | 4.82E+02 | 4.65E+02 | 4.63E+02 | 4.89E+02 | 4.71E+02 |
标准差 | 2.39E+01 | 2.34E+01 | 1.66E+01 | 1.27E+01 | 2.34E+01 | 2.07E+01 | |
F29 | 平均值 | 4.89E+02 | 4.65E+02 | 3.48E+02 | 3.48E+02 | 4.39E+02 | 3.41E+02 |
标准差 | 5.95E+01 | 9.44E+01 | 1.25E+01 | 8.56E+00 | 1.26E+02 | 9.59E+00 | |
F30 | 平均值 | 6.84E+05 | 6.78E+05 | 6.69E+05 | 6.68E+05 | 6.80E+05 | 6.71E+05 |
标准差 | 7.35E+04 | 8.47E+04 | 9.54E+04 | 7.50E+04 | 9.69E+04 | 7.70E+04 | |
+ | 24 | 24 | 5 | 4 | 24 | ||
- | 0 | 0 | 1 | 1 | 0 | ||
= | 6 | 6 | 24 | 25 | 6 |
测试函数 | 指标 | JADE | SHADE | LSHADE | DPSHADE | MPEDE | APDE |
---|---|---|---|---|---|---|---|
F1 | 平均值 | 0.00E+00 | 0.00E+00 | 0.00E+00 | 0.00E+00 | 0.00E+00 | 0.00E+00 |
标准差 | 0.00E+00 | 0.00E+00 | 0.00E+00 | 0.00E+00 | 0.00E+00 | 0.00E+00 | |
F2 | 平均值 | 2.30E+04 | 8.80E+17 | 2.17E+05 | 3.00E+06 | 9.32E+14 | 4.58E+02 |
标准差 | 1.46E+05 | 6.28E+18 | 1.39E+06 | 2.08E+07 | 6.66E+15 | 1.42E+03 | |
F3 | 平均值 | 1.41E+05 | 1.72E-06 | 2.65E-06 | 4.38E-06 | 1.73E+01 | 2.23E-07 |
标准差 | 1.86E+05 | 4.17E-06 | 3.08E-06 | 6.27E-06 | 5.49E+01 | 2.22E-07 | |
F4 | 平均值 | 8.59E+01 | 1.51E+02 | 1.95E+02 | 2.01E+02 | 8.84E+01 | 1.98E+02 |
标准差 | 6.65E+01 | 6.57E+01 | 2.85E+01 | 8.98E+00 | 6.43E+01 | 6.10E+00 | |
F5 | 平均值 | 1.73E+02 | 9.55E+01 | 2.67E+01 | 2.60E+01 | 1.57E+02 | 2.33E+01 |
标准差 | 1.75E+01 | 1.15E+01 | 6.94E+00 | 6.84E+00 | 2.75E+01 | 4.99E+00 | |
F6 | 平均值 | 1.45E-04 | 7.96E-02 | 1.88E-03 | 1.55E-03 | 1.69E-01 | 1.71E-03 |
标准差 | 5.51E-04 | 6.43E-02 | 1.42E-03 | 1.23E-03 | 1.40E-01 | 1.24E-03 | |
F7 | 平均值 | 2.86E+02 | 2.03E+02 | 1.34E+02 | 1.36E+02 | 2.98E+02 | 1.33E+02 |
标准差 | 1.66E+01 | 1.16E+01 | 1.94E+01 | 4.13E+00 | 3.50E+01 | 3.51E+00 | |
F8 | 平均值 | 1.76E+02 | 9.41E+01 | 2.75E+01 | 2.43E+01 | 1.46E+02 | 2.45E+01 |
标准差 | 1.91E+01 | 1.10E+01 | 5.84E+00 | 5.67E+00 | 2.33E+01 | 5.61E+00 | |
F9 | 平均值 | 1.11E+01 | 2.19E+01 | 1.81E-01 | 1.35E-01 | 3.59E+01 | 1.04E-01 |
标准差 | 1.17E+01 | 1.13E+01 | 2.84E-01 | 1.94E-01 | 2.36E+01 | 1.57E-01 | |
F10 | 平均值 | 1.38E+04 | 9.28E+03 | 1.01E+04 | 1.04E+04 | 1.11E+04 | 9.80E+03 |
标准差 | 4.56E+02 | 4.58E+02 | 1.53E+03 | 4.87E+02 | 1.05E+03 | 4.77E+02 | |
F11 | 平均值 | 9.66E+03 | 1.18E+03 | 3.81E+02 | 3.47E+02 | 7.82E+02 | 3.87E+02 |
标准差 | 7.24E+03 | 2.61E+02 | 1.16E+02 | 1.01E+02 | 2.24E+02 | 9.91E+01 | |
F12 | 平均值 | 1.70E+04 | 2.29E+04 | 2.29E+04 | 2.90E+04 | 3.43E+04 | 2.15E+04 |
标准差 | 8.61E+03 | 1.85E+04 | 1.01E+04 | 9.30E+03 | 2.26E+04 | 8.55E+03 | |
F13 | 平均值 | 2.00E+03 | 1.32E+03 | 1.21E+03 | 1.34E+03 | 6.46E+02 | 1.01E+03 |
标准差 | 1.97E+03 | 3.20E+03 | 7.53E+02 | 8.97E+02 | 7.56E+02 | 6.35E+02 | |
F14 | 平均值 | 5.36E+02 | 6.37E+02 | 2.51E+02 | 2.51E+02 | 4.83E+02 | 2.63E+02 |
标准差 | 1.15E+02 | 1.96E+02 | 4.59E+01 | 2.74E+01 | 1.26E+02 | 3.53E+01 | |
F15 | 平均值 | 3.45E+02 | 3.83E+02 | 2.42E+02 | 2.44E+02 | 3.32E+02 | 2.53E+02 |
标准差 | 1.57E+02 | 1.03E+02 | 6.36E+01 | 3.90E+01 | 1.25E+02 | 4.81E+01 | |
F16 | 平均值 | 2.98E+03 | 2.38E+03 | 1.57E+03 | 1.54E+03 | 2.83E+03 | 1.47E+03 |
标准差 | 3.13E+02 | 3.43E+02 | 3.17E+02 | 2.21E+02 | 5.86E+02 | 2.46E+02 | |
F17 | 平均值 | 2.27E+03 | 1.95E+03 | 1.04E+03 | 1.05E+03 | 1.92E+03 | 1.01E+03 |
标准差 | 2.64E+02 | 2.54E+02 | 2.78E+02 | 1.76E+02 | 4.57E+02 | 1.90E+02 | |
F18 | 平均值 | 5.12E+02 | 2.10E+03 | 2.22E+02 | 2.21E+02 | 1.41E+03 | 2.05E+02 |
标准差 | 2.47E+02 | 1.98E+03 | 5.29E+01 | 4.96E+01 | 1.23E+03 | 5.05E+01 | |
F19 | 平均值 | 2.32E+02 | 2.68E+02 | 1.72E+02 | 1.80E+02 | 2.39E+02 | 1.74E+02 |
标准差 | 5.05E+01 | 5.76E+01 | 3.75E+01 | 2.63E+01 | 6.49E+01 | 2.42E+01 | |
F20 | 平均值 | 2.27E+03 | 1.71E+03 | 1.43E+03 | 1.47E+03 | 1.85E+03 | 1.35E+03 |
标准差 | 2.19E+02 | 2.11E+02 | 2.77E+02 | 1.96E+02 | 3.75E+02 | 2.25E+02 | |
F21 | 平均值 | 3.94E+02 | 3.29E+02 | 2.52E+02 | 2.55E+02 | 3.64E+02 | 2.54E+02 |
标准差 | 1.97E+01 | 1.68E+01 | 3.61E+01 | 4.60E+00 | 2.45E+01 | 4.51E+00 | |
F22 | 平均值 | 1.49E+04 | 1.05E+04 | 1.07E+04 | 1.10E+04 | 1.22E+04 | 1.06E+04 |
标准差 | 4.81E+02 | 4.70E+02 | 1.60E+03 | 5.43E+02 | 1.11E+03 | 4.52E+02 | |
F23 | 平均值 | 6.81E+02 | 6.14E+02 | 5.60E+02 | 5.62E+02 | 6.94E+02 | 5.58E+02 |
标准差 | 1.08E+01 | 1.41E+01 | 6.34E+00 | 7.98E+00 | 2.85E+01 | 8.39E+00 | |
F24 | 平均值 | 1.03E+03 | 9.96E+02 | 9.19E+02 | 9.15E+02 | 1.03E+03 | 9.15E+02 |
标准差 | 1.98E+01 | 2.14E+01 | 6.88E+00 | 7.17E+00 | 2.67E+01 | 7.40E+00 | |
F25 | 平均值 | 7.52E+02 | 7.43E+02 | 7.50E+02 | 7.40E+02 | 7.41E+02 | 7.49E+02 |
标准差 | 4.14E+01 | 3.98E+01 | 2.81E+01 | 3.29E+01 | 6.04E+01 | 3.05E+01 | |
F26 | 平均值 | 4.46E+03 | 4.37E+03 | 3.42E+03 | 3.38E+03 | 4.51E+03 | 3.40E+03 |
标准差 | 2.53E+02 | 2.59E+02 | 9.06E+01 | 1.00E+02 | 2.89E+02 | 9.49E+01 | |
F27 | 平均值 | 6.87E+02 | 6.73E+02 | 6.54E+02 | 6.50E+02 | 7.00E+02 | 6.52E+02 |
标准差 | 2.85E+01 | 2.74E+01 | 1.55E+01 | 1.51E+01 | 3.69E+01 | 1.83E+01 | |
F28 | 平均值 | 5.25E+02 | 5.28E+02 | 5.29E+02 | 5.24E+02 | 5.26E+02 | 5.28E+02 |
标准差 | 3.93E+01 | 3.73E+01 | 1.95E+01 | 2.04E+01 | 3.59E+01 | 2.06E+01 | |
F29 | 平均值 | 2.21E+03 | 2.04E+03 | 1.43E+03 | 1.44E+03 | 2.43E+03 | 1.30E+03 |
标准差 | 2.43E+02 | 2.95E+02 | 1.72E+02 | 1.54E+02 | 4.55E+02 | 1.95E+02 | |
F30 | 平均值 | 3.33E+03 | 2.86E+03 | 2.40E+03 | 2.39E+03 | 2.55E+03 | 2.39E+03 |
标准差 | 1.43E+03 | 1.14E+03 | 1.52E+02 | 1.40E+02 | 1.93E+02 | 1.41E+02 | |
+ | 23 | 22 | 13 | 11 | 25 | ||
- | 3 | 2 | 0 | 1 | 2 | ||
= | 4 | 6 | 17 | 18 | 3 |
Tab.3 Results of 6 DE variants on CEC2017 test set (dimension = 100)
测试函数 | 指标 | JADE | SHADE | LSHADE | DPSHADE | MPEDE | APDE |
---|---|---|---|---|---|---|---|
F1 | 平均值 | 0.00E+00 | 0.00E+00 | 0.00E+00 | 0.00E+00 | 0.00E+00 | 0.00E+00 |
标准差 | 0.00E+00 | 0.00E+00 | 0.00E+00 | 0.00E+00 | 0.00E+00 | 0.00E+00 | |
F2 | 平均值 | 2.30E+04 | 8.80E+17 | 2.17E+05 | 3.00E+06 | 9.32E+14 | 4.58E+02 |
标准差 | 1.46E+05 | 6.28E+18 | 1.39E+06 | 2.08E+07 | 6.66E+15 | 1.42E+03 | |
F3 | 平均值 | 1.41E+05 | 1.72E-06 | 2.65E-06 | 4.38E-06 | 1.73E+01 | 2.23E-07 |
标准差 | 1.86E+05 | 4.17E-06 | 3.08E-06 | 6.27E-06 | 5.49E+01 | 2.22E-07 | |
F4 | 平均值 | 8.59E+01 | 1.51E+02 | 1.95E+02 | 2.01E+02 | 8.84E+01 | 1.98E+02 |
标准差 | 6.65E+01 | 6.57E+01 | 2.85E+01 | 8.98E+00 | 6.43E+01 | 6.10E+00 | |
F5 | 平均值 | 1.73E+02 | 9.55E+01 | 2.67E+01 | 2.60E+01 | 1.57E+02 | 2.33E+01 |
标准差 | 1.75E+01 | 1.15E+01 | 6.94E+00 | 6.84E+00 | 2.75E+01 | 4.99E+00 | |
F6 | 平均值 | 1.45E-04 | 7.96E-02 | 1.88E-03 | 1.55E-03 | 1.69E-01 | 1.71E-03 |
标准差 | 5.51E-04 | 6.43E-02 | 1.42E-03 | 1.23E-03 | 1.40E-01 | 1.24E-03 | |
F7 | 平均值 | 2.86E+02 | 2.03E+02 | 1.34E+02 | 1.36E+02 | 2.98E+02 | 1.33E+02 |
标准差 | 1.66E+01 | 1.16E+01 | 1.94E+01 | 4.13E+00 | 3.50E+01 | 3.51E+00 | |
F8 | 平均值 | 1.76E+02 | 9.41E+01 | 2.75E+01 | 2.43E+01 | 1.46E+02 | 2.45E+01 |
标准差 | 1.91E+01 | 1.10E+01 | 5.84E+00 | 5.67E+00 | 2.33E+01 | 5.61E+00 | |
F9 | 平均值 | 1.11E+01 | 2.19E+01 | 1.81E-01 | 1.35E-01 | 3.59E+01 | 1.04E-01 |
标准差 | 1.17E+01 | 1.13E+01 | 2.84E-01 | 1.94E-01 | 2.36E+01 | 1.57E-01 | |
F10 | 平均值 | 1.38E+04 | 9.28E+03 | 1.01E+04 | 1.04E+04 | 1.11E+04 | 9.80E+03 |
标准差 | 4.56E+02 | 4.58E+02 | 1.53E+03 | 4.87E+02 | 1.05E+03 | 4.77E+02 | |
F11 | 平均值 | 9.66E+03 | 1.18E+03 | 3.81E+02 | 3.47E+02 | 7.82E+02 | 3.87E+02 |
标准差 | 7.24E+03 | 2.61E+02 | 1.16E+02 | 1.01E+02 | 2.24E+02 | 9.91E+01 | |
F12 | 平均值 | 1.70E+04 | 2.29E+04 | 2.29E+04 | 2.90E+04 | 3.43E+04 | 2.15E+04 |
标准差 | 8.61E+03 | 1.85E+04 | 1.01E+04 | 9.30E+03 | 2.26E+04 | 8.55E+03 | |
F13 | 平均值 | 2.00E+03 | 1.32E+03 | 1.21E+03 | 1.34E+03 | 6.46E+02 | 1.01E+03 |
标准差 | 1.97E+03 | 3.20E+03 | 7.53E+02 | 8.97E+02 | 7.56E+02 | 6.35E+02 | |
F14 | 平均值 | 5.36E+02 | 6.37E+02 | 2.51E+02 | 2.51E+02 | 4.83E+02 | 2.63E+02 |
标准差 | 1.15E+02 | 1.96E+02 | 4.59E+01 | 2.74E+01 | 1.26E+02 | 3.53E+01 | |
F15 | 平均值 | 3.45E+02 | 3.83E+02 | 2.42E+02 | 2.44E+02 | 3.32E+02 | 2.53E+02 |
标准差 | 1.57E+02 | 1.03E+02 | 6.36E+01 | 3.90E+01 | 1.25E+02 | 4.81E+01 | |
F16 | 平均值 | 2.98E+03 | 2.38E+03 | 1.57E+03 | 1.54E+03 | 2.83E+03 | 1.47E+03 |
标准差 | 3.13E+02 | 3.43E+02 | 3.17E+02 | 2.21E+02 | 5.86E+02 | 2.46E+02 | |
F17 | 平均值 | 2.27E+03 | 1.95E+03 | 1.04E+03 | 1.05E+03 | 1.92E+03 | 1.01E+03 |
标准差 | 2.64E+02 | 2.54E+02 | 2.78E+02 | 1.76E+02 | 4.57E+02 | 1.90E+02 | |
F18 | 平均值 | 5.12E+02 | 2.10E+03 | 2.22E+02 | 2.21E+02 | 1.41E+03 | 2.05E+02 |
标准差 | 2.47E+02 | 1.98E+03 | 5.29E+01 | 4.96E+01 | 1.23E+03 | 5.05E+01 | |
F19 | 平均值 | 2.32E+02 | 2.68E+02 | 1.72E+02 | 1.80E+02 | 2.39E+02 | 1.74E+02 |
标准差 | 5.05E+01 | 5.76E+01 | 3.75E+01 | 2.63E+01 | 6.49E+01 | 2.42E+01 | |
F20 | 平均值 | 2.27E+03 | 1.71E+03 | 1.43E+03 | 1.47E+03 | 1.85E+03 | 1.35E+03 |
标准差 | 2.19E+02 | 2.11E+02 | 2.77E+02 | 1.96E+02 | 3.75E+02 | 2.25E+02 | |
F21 | 平均值 | 3.94E+02 | 3.29E+02 | 2.52E+02 | 2.55E+02 | 3.64E+02 | 2.54E+02 |
标准差 | 1.97E+01 | 1.68E+01 | 3.61E+01 | 4.60E+00 | 2.45E+01 | 4.51E+00 | |
F22 | 平均值 | 1.49E+04 | 1.05E+04 | 1.07E+04 | 1.10E+04 | 1.22E+04 | 1.06E+04 |
标准差 | 4.81E+02 | 4.70E+02 | 1.60E+03 | 5.43E+02 | 1.11E+03 | 4.52E+02 | |
F23 | 平均值 | 6.81E+02 | 6.14E+02 | 5.60E+02 | 5.62E+02 | 6.94E+02 | 5.58E+02 |
标准差 | 1.08E+01 | 1.41E+01 | 6.34E+00 | 7.98E+00 | 2.85E+01 | 8.39E+00 | |
F24 | 平均值 | 1.03E+03 | 9.96E+02 | 9.19E+02 | 9.15E+02 | 1.03E+03 | 9.15E+02 |
标准差 | 1.98E+01 | 2.14E+01 | 6.88E+00 | 7.17E+00 | 2.67E+01 | 7.40E+00 | |
F25 | 平均值 | 7.52E+02 | 7.43E+02 | 7.50E+02 | 7.40E+02 | 7.41E+02 | 7.49E+02 |
标准差 | 4.14E+01 | 3.98E+01 | 2.81E+01 | 3.29E+01 | 6.04E+01 | 3.05E+01 | |
F26 | 平均值 | 4.46E+03 | 4.37E+03 | 3.42E+03 | 3.38E+03 | 4.51E+03 | 3.40E+03 |
标准差 | 2.53E+02 | 2.59E+02 | 9.06E+01 | 1.00E+02 | 2.89E+02 | 9.49E+01 | |
F27 | 平均值 | 6.87E+02 | 6.73E+02 | 6.54E+02 | 6.50E+02 | 7.00E+02 | 6.52E+02 |
标准差 | 2.85E+01 | 2.74E+01 | 1.55E+01 | 1.51E+01 | 3.69E+01 | 1.83E+01 | |
F28 | 平均值 | 5.25E+02 | 5.28E+02 | 5.29E+02 | 5.24E+02 | 5.26E+02 | 5.28E+02 |
标准差 | 3.93E+01 | 3.73E+01 | 1.95E+01 | 2.04E+01 | 3.59E+01 | 2.06E+01 | |
F29 | 平均值 | 2.21E+03 | 2.04E+03 | 1.43E+03 | 1.44E+03 | 2.43E+03 | 1.30E+03 |
标准差 | 2.43E+02 | 2.95E+02 | 1.72E+02 | 1.54E+02 | 4.55E+02 | 1.95E+02 | |
F30 | 平均值 | 3.33E+03 | 2.86E+03 | 2.40E+03 | 2.39E+03 | 2.55E+03 | 2.39E+03 |
标准差 | 1.43E+03 | 1.14E+03 | 1.52E+02 | 1.40E+02 | 1.93E+02 | 1.41E+02 | |
+ | 23 | 22 | 13 | 11 | 25 | ||
- | 3 | 2 | 0 | 1 | 2 | ||
= | 4 | 6 | 17 | 18 | 3 |
算法 | 30维 | 50维 | 100维 |
---|---|---|---|
APDE | 2.35 | 2.25 | 1.95 |
JADE | 4.87 | 5.03 | 4.72 |
SHADE | 4.18 | 4.45 | 4.12 |
LSHADE | 3.42 | 2.33 | 3.12 |
DPSHADE | 2.42 | 2.17 | 2.45 |
MPEDE | 3.77 | 4.77 | 4.65 |
Tab. 4 Average ranks based on Friedman test
算法 | 30维 | 50维 | 100维 |
---|---|---|---|
APDE | 2.35 | 2.25 | 1.95 |
JADE | 4.87 | 5.03 | 4.72 |
SHADE | 4.18 | 4.45 | 4.12 |
LSHADE | 3.42 | 2.33 | 3.12 |
DPSHADE | 2.42 | 2.17 | 2.45 |
MPEDE | 3.77 | 4.77 | 4.65 |
α值 | 30维 | 50维 | 100维 |
---|---|---|---|
1.0 | 2.00 | 1.88 | 1.93 |
0.8 | 1.90 | 2.17 | 2.00 |
0.9 | 2.10 | 1.95 | 2.07 |
Tab. 5 Average ranks based on Friedman test under different parameters
α值 | 30维 | 50维 | 100维 |
---|---|---|---|
1.0 | 2.00 | 1.88 | 1.93 |
0.8 | 1.90 | 2.17 | 2.00 |
0.9 | 2.10 | 1.95 | 2.07 |
算法 | 平均值 | 标准差 |
---|---|---|
JADE | -2.34E+01 | 6.15E-01 |
SHADE | -2.26E+01 | 1.22E+00 |
LSHADE | -2.55E+01 | 5.66E-01 |
DPSHADE | -2.61E+01 | 4.88E-01 |
MPEDE | -2.17E+01 | 1.49E+00 |
APDE | -2.65E+01 | 6.39E-01 |
Tab. 4 Test results on Lennard-Jones potential problem
算法 | 平均值 | 标准差 |
---|---|---|
JADE | -2.34E+01 | 6.15E-01 |
SHADE | -2.26E+01 | 1.22E+00 |
LSHADE | -2.55E+01 | 5.66E-01 |
DPSHADE | -2.61E+01 | 4.88E-01 |
MPEDE | -2.17E+01 | 1.49E+00 |
APDE | -2.65E+01 | 6.39E-01 |
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