Journal of Computer Applications ›› 2022, Vol. 42 ›› Issue (3): 874-882.DOI: 10.11772/j.issn.1001-9081.2021030395
Special Issue: 人工智能
• Artificial intelligence • Previous Articles Next Articles
Fangxin NIE, Yujia WANG(), Xin JIA
Received:
2021-03-18
Revised:
2021-06-15
Accepted:
2021-06-17
Online:
2022-04-09
Published:
2022-03-10
Contact:
Yujia WANG
About author:
NIE Fangxin, born in 1996, M. S. candidate. His research interests include evolutionary algorithms.Supported by:
通讯作者:
王宇嘉
作者简介:
聂方鑫(1996—),男,安徽和县人,硕士研究生,主要研究方向:进化算法基金资助:
CLC Number:
Fangxin NIE, Yujia WANG, Xin JIA. Teaching and learning information interactive particle swarm optimization algorithm[J]. Journal of Computer Applications, 2022, 42(3): 874-882.
聂方鑫, 王宇嘉, 贾欣. 教与学信息交互粒子群优化算法[J]. 《计算机应用》唯一官方网站, 2022, 42(3): 874-882.
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URL: https://www.joca.cn/EN/10.11772/j.issn.1001-9081.2021030395
算法 | 参数设置 |
---|---|
TLPSO | |
PSO | |
CMA-ES | |
PPSO | |
PSOGWO | |
PSOGSA | |
EGWO |
Tab. 1 Parameter settings for contrast algorithms
算法 | 参数设置 |
---|---|
TLPSO | |
PSO | |
CMA-ES | |
PPSO | |
PSOGWO | |
PSOGSA | |
EGWO |
函数 | 性能指标 | PSO | CMA-ES | PPSO | PSOGWO | PSOGSA | EGWO | TLPSO |
---|---|---|---|---|---|---|---|---|
F1 | Ave | 7.31E-06 | 1.34E-23 | 5.47E-08 | 9.42E-31 | 2.90E-19 | 3.77E-103 | 2.39E-167 |
Std | 1.24E-05 | 3.66E-24 | 3.51E-08 | 1.20E-30 | 1.50E-20 | 6.84E-103 | 0 | |
F2 | Ave | 2.61E-02 | 3.99E-10 | 1.68E-02 | 1.97E-18 | 2.18E-09 | 5.39E-61 | 3.92E-83 |
Std | 3.51E-02 | 4.52E-11 | 7.43E-03 | 1.63E-18 | 1.34E-10 | 5.48E-61 | 1.93E-83 | |
F3 | Ave | 5.92E+01 | 3.26E+00 | 7.57E-03 | 2.13E-02 | 1.47E+02 | 5.28E-31 | 8.31E-34 |
Std | 6.83E+01 | 2.01E+00 | 1.53E-02 | 4.32E-02 | 1.12E+02 | 1.36E-30 | 1.04E-33 | |
F4 | Ave | 7.77E+01 | 2.70E-09 | 2.64E-04 | 2.23E-08 | 3.18E+01 | 3.10E-28 | 5.30E-67 |
Std | 2.58E+00 | 9.09E-10 | 1.71E-04 | 1.46E-08 | 1.35E+01 | 2.48E-28 | 2.12E-67 | |
F5 | Ave | 3.58E+02 | 5.18E+00 | 2.29E+01 | 3.37E+01 | 2.77E+01 | 2.73E+01 | 5.75E+00 |
Std | 2.52E+02 | 1.97E-01 | 3.88E-01 | 1.24E+01 | 1.30E+01 | 3.71E+00 | 8.98E-01 | |
F6 | Ave | 4.15E-08 | 1.47E-23 | 1.41E-07 | 2.94E-04 | 2.86E-19 | 1.64E-04 | 4.55E-31 |
Std | 6.60E-08 | 6.44E-24 | 6.65E-08 | 3.93E-04 | 2.27E-20 | 2.49E-04 | 1.90E-31 | |
F7 | Ave | 2.41E+00 | 4.76E-03 | 6.76E-04 | 3.81E-03 | 2.21E-02 | 8.49E-04 | 2.45E-04 |
Std | 2.42E+00 | 6.98E-04 | 3.67E-04 | 1.58E-03 | 3.88E-03 | 2.72E-04 | 7.36E-05 | |
F8 | Ave | 1.33E+02 | 1.41E+02 | 1.45E-07 | 3.16E+01 | 1.05E+02 | 5.68E-14 | 0 |
Std | 3.41E+01 | 2.62E+01 | 1.52E-07 | 1.31E+01 | 1.70E+01 | 6.31E-30 | 0 | |
F9 | Ave | 6.90E+00 | 1.01E+00 | 3.76E-05 | 4.02E-13 | 3.63E-10 | 1.51E-14 | 4.44E-15 |
Std | 3.33E+00 | 1.8E+00 | 8.36E-06 | 4.62E-13 | 1.70E-11 | 3.15E-30 | 0 | |
F10 | Ave | 8.63E-02 | 0 | 1.51E-06 | 0 | 0 | 0 | 0 |
Std | 4.24E-02 | 0 | 7.73E-07 | 0 | 0 | 0 | 0 | |
F11 | Ave | -1.031 6 | -9.66E-01 | -1.031 6 | -1.031 6 | -1.031 6 | -1.031 6 | -1.031 6 |
Std | 0 | 6.34E-02 | 2.22E-16 | 3.12E-16 | 2.22E-16 | 2.22E-16 | 0 | |
F12 | Ave | 1.03E-03 | 1.14E-03 | 1.01E-03 | 2.58E-03 | 6.80E-04 | 2.64E-03 | 3.30E-03 |
Std | 1.22E-06 | 5.29E-05 | 3.50E-04 | 5.94E-03 | 4.61E-04 | 5.92E-03 | 5.39E-05 | |
F13 | Ave | -3.86E+00 | -3.86E+00 | -3.85E+00 | -3.85E+00 | -3.86E+00 | -3.85E+00 | -3.86E+00 |
Std | 0 | 7.51E-15 | 2.79E-03 | 3.63E-03 | 0 | 2.79E-03 | 0 | |
F14 | Ave | -3.27E+00 | -3.19E+00 | -3.09E+00 | -2.94E+00 | -3.20E+00 | -3.17E+00 | -3.32E+00 |
Std | 5.83E-02 | 6.52E-01 | 5.10E-02 | 5.99E-01 | 1.83E-02 | 1.11E-01 | 0 | |
F15 | Ave | 1.24E-02 | 6.22E-02 | 3.65E-01 | 1.39E-03 | 1.52E+00 | 1.21E-01 | 4.04E-07 |
Std | 3.12E-02 | 1.24E-01 | 6.09E-02 | 2.62E-03 | 2.62E+00 | 1.71E-01 | 7.56E-07 |
Tab. 2 Experimental results comparison of low dimensional benchmark functions
函数 | 性能指标 | PSO | CMA-ES | PPSO | PSOGWO | PSOGSA | EGWO | TLPSO |
---|---|---|---|---|---|---|---|---|
F1 | Ave | 7.31E-06 | 1.34E-23 | 5.47E-08 | 9.42E-31 | 2.90E-19 | 3.77E-103 | 2.39E-167 |
Std | 1.24E-05 | 3.66E-24 | 3.51E-08 | 1.20E-30 | 1.50E-20 | 6.84E-103 | 0 | |
F2 | Ave | 2.61E-02 | 3.99E-10 | 1.68E-02 | 1.97E-18 | 2.18E-09 | 5.39E-61 | 3.92E-83 |
Std | 3.51E-02 | 4.52E-11 | 7.43E-03 | 1.63E-18 | 1.34E-10 | 5.48E-61 | 1.93E-83 | |
F3 | Ave | 5.92E+01 | 3.26E+00 | 7.57E-03 | 2.13E-02 | 1.47E+02 | 5.28E-31 | 8.31E-34 |
Std | 6.83E+01 | 2.01E+00 | 1.53E-02 | 4.32E-02 | 1.12E+02 | 1.36E-30 | 1.04E-33 | |
F4 | Ave | 7.77E+01 | 2.70E-09 | 2.64E-04 | 2.23E-08 | 3.18E+01 | 3.10E-28 | 5.30E-67 |
Std | 2.58E+00 | 9.09E-10 | 1.71E-04 | 1.46E-08 | 1.35E+01 | 2.48E-28 | 2.12E-67 | |
F5 | Ave | 3.58E+02 | 5.18E+00 | 2.29E+01 | 3.37E+01 | 2.77E+01 | 2.73E+01 | 5.75E+00 |
Std | 2.52E+02 | 1.97E-01 | 3.88E-01 | 1.24E+01 | 1.30E+01 | 3.71E+00 | 8.98E-01 | |
F6 | Ave | 4.15E-08 | 1.47E-23 | 1.41E-07 | 2.94E-04 | 2.86E-19 | 1.64E-04 | 4.55E-31 |
Std | 6.60E-08 | 6.44E-24 | 6.65E-08 | 3.93E-04 | 2.27E-20 | 2.49E-04 | 1.90E-31 | |
F7 | Ave | 2.41E+00 | 4.76E-03 | 6.76E-04 | 3.81E-03 | 2.21E-02 | 8.49E-04 | 2.45E-04 |
Std | 2.42E+00 | 6.98E-04 | 3.67E-04 | 1.58E-03 | 3.88E-03 | 2.72E-04 | 7.36E-05 | |
F8 | Ave | 1.33E+02 | 1.41E+02 | 1.45E-07 | 3.16E+01 | 1.05E+02 | 5.68E-14 | 0 |
Std | 3.41E+01 | 2.62E+01 | 1.52E-07 | 1.31E+01 | 1.70E+01 | 6.31E-30 | 0 | |
F9 | Ave | 6.90E+00 | 1.01E+00 | 3.76E-05 | 4.02E-13 | 3.63E-10 | 1.51E-14 | 4.44E-15 |
Std | 3.33E+00 | 1.8E+00 | 8.36E-06 | 4.62E-13 | 1.70E-11 | 3.15E-30 | 0 | |
F10 | Ave | 8.63E-02 | 0 | 1.51E-06 | 0 | 0 | 0 | 0 |
Std | 4.24E-02 | 0 | 7.73E-07 | 0 | 0 | 0 | 0 | |
F11 | Ave | -1.031 6 | -9.66E-01 | -1.031 6 | -1.031 6 | -1.031 6 | -1.031 6 | -1.031 6 |
Std | 0 | 6.34E-02 | 2.22E-16 | 3.12E-16 | 2.22E-16 | 2.22E-16 | 0 | |
F12 | Ave | 1.03E-03 | 1.14E-03 | 1.01E-03 | 2.58E-03 | 6.80E-04 | 2.64E-03 | 3.30E-03 |
Std | 1.22E-06 | 5.29E-05 | 3.50E-04 | 5.94E-03 | 4.61E-04 | 5.92E-03 | 5.39E-05 | |
F13 | Ave | -3.86E+00 | -3.86E+00 | -3.85E+00 | -3.85E+00 | -3.86E+00 | -3.85E+00 | -3.86E+00 |
Std | 0 | 7.51E-15 | 2.79E-03 | 3.63E-03 | 0 | 2.79E-03 | 0 | |
F14 | Ave | -3.27E+00 | -3.19E+00 | -3.09E+00 | -2.94E+00 | -3.20E+00 | -3.17E+00 | -3.32E+00 |
Std | 5.83E-02 | 6.52E-01 | 5.10E-02 | 5.99E-01 | 1.83E-02 | 1.11E-01 | 0 | |
F15 | Ave | 1.24E-02 | 6.22E-02 | 3.65E-01 | 1.39E-03 | 1.52E+00 | 1.21E-01 | 4.04E-07 |
Std | 3.12E-02 | 1.24E-01 | 6.09E-02 | 2.62E-03 | 2.62E+00 | 1.71E-01 | 7.56E-07 |
函数 | 性能指标 | PSO | CMA-ES | PPSO | PSOGWO | PSOGSA | EGWO | TLPSO |
---|---|---|---|---|---|---|---|---|
F1 | Ave | 1.94E+04 | 3.79E-08 | 2.29E-02 | 1.31E-07 | 3.00E+03 | 2.23E-68 | 4.41E-151 |
Std | 4.29E+03 | 1.12E-08 | 3.63E-02 | 4.11E-08 | 4.31E+03 | 3.66E-68 | 4.57E-151 | |
F2 | Ave | 2.01E+02 | 4.36E-02 | 2.41E+00 | 5.46E-04 | 2.01E+02 | 2.95E-41 | 1.04E-75 |
Std | 3.82E+01 | 6.11E-02 | 2.72E+00 | 8.15E-04 | 1.36E+02 | 1.74E-41 | 4.40E-76 | |
F3 | Ave | 1.19E+05 | 9.19E+02 | 1.90E+00 | 1.37E+01 | 8.55E+04 | 1.51E-16 | 5.04E-24 |
Std | 1.44E+04 | 2.62E+02 | 2.43E+00 | 2.78E+01 | 1.58E+04 | 2.55E-16 | 8.42E-24 | |
F4 | Ave | 5.42E+02 | 1.90E-02 | 1.94E-02 | 2.93E+01 | 8.45E+01 | 2.71E-16 | 1.74E-59 |
Std | 5.45E+01 | 4.83E-03 | 2.87E-02 | 3.94E+01 | 1.43E+01 | 2.20E-16 | 7.13E-60 | |
F5 | Ave | 3.77E+03 | 1.45E+03 | 9.93E+01 | 9.49E+02 | 2.52E+02 | 9.68E+01 | 8.82E+01 |
Std | 2.05E+03 | 3.66E+03 | 1.17E+00 | 2.12E+01 | 6.49E+01 | 6.84E-01 | 2.21E+00 | |
F6 | Ave | 4.01E+01 | 3.47E-08 | 2.13E-01 | 3.97E+00 | 2.47E+03 | 1.08E+01 | 1.31E-04 |
Std | 3.16E+01 | 1.16E-08 | 7.26E-02 | 7.95E+00 | 3.99E+03 | 6.68E-01 | 3.79E-04 | |
F7 | Ave | 3.87E+01 | 2.72E-02 | 5.27E-02 | 1.80E+02 | 4.40E-01 | 1.14E-03 | 5.02E-04 |
Std | 1.65E+01 | 7.75E-03 | 5.89E-02 | 4.00E+02 | 9.12E-02 | 1.22E-04 | 1.22E-04 | |
F8 | Ave | 5.64E+02 | 4.28E+02 | 1.78E+01 | 4.85E+02 | 4.73E+02 | 2.33E-07 | 0 |
Std | 4.71E+01 | 2.96E+02 | 3.30E+01 | 5.90E+02 | 8.53E+01 | 8.51E-07 | 0 | |
F9 | Ave | 1.60E+01 | 2.13E+01 | 1.20E+00 | 4.10E+00 | 1.88E+01 | 9.48E-11 | 7.99E-15 |
Std | 7.27E-01 | 1.83E-02 | 1.03E+01 | 5.75E+00 | 6.01E-01 | 4.62E-11 | 0 | |
F10 | Ave | 2.03E+02 | 4.37E-07 | 7.91E-04 | 2.22E-16 | 2.65E-02 | 0 | 0 |
Std | 5.97E+01 | 1.78E-07 | 7.72E-04 | 7.43E-16 | 2.17E-02 | 0 | 0 | |
F15 | Ave | 8.40E+02 | 4.01E+01 | 6.21E+01 | 8.59E+00 | 3.32E+01 | 7.91E-01 | 1.79E-06 |
Std | 3.81E+01 | 5.29E+00 | 2.59E+00 | 1.20E+01 | 1.92E+01 | 6.29E-01 | 7.08E-06 |
Tab. 3 Experimental results comparison of high dimensional benchmark functions
函数 | 性能指标 | PSO | CMA-ES | PPSO | PSOGWO | PSOGSA | EGWO | TLPSO |
---|---|---|---|---|---|---|---|---|
F1 | Ave | 1.94E+04 | 3.79E-08 | 2.29E-02 | 1.31E-07 | 3.00E+03 | 2.23E-68 | 4.41E-151 |
Std | 4.29E+03 | 1.12E-08 | 3.63E-02 | 4.11E-08 | 4.31E+03 | 3.66E-68 | 4.57E-151 | |
F2 | Ave | 2.01E+02 | 4.36E-02 | 2.41E+00 | 5.46E-04 | 2.01E+02 | 2.95E-41 | 1.04E-75 |
Std | 3.82E+01 | 6.11E-02 | 2.72E+00 | 8.15E-04 | 1.36E+02 | 1.74E-41 | 4.40E-76 | |
F3 | Ave | 1.19E+05 | 9.19E+02 | 1.90E+00 | 1.37E+01 | 8.55E+04 | 1.51E-16 | 5.04E-24 |
Std | 1.44E+04 | 2.62E+02 | 2.43E+00 | 2.78E+01 | 1.58E+04 | 2.55E-16 | 8.42E-24 | |
F4 | Ave | 5.42E+02 | 1.90E-02 | 1.94E-02 | 2.93E+01 | 8.45E+01 | 2.71E-16 | 1.74E-59 |
Std | 5.45E+01 | 4.83E-03 | 2.87E-02 | 3.94E+01 | 1.43E+01 | 2.20E-16 | 7.13E-60 | |
F5 | Ave | 3.77E+03 | 1.45E+03 | 9.93E+01 | 9.49E+02 | 2.52E+02 | 9.68E+01 | 8.82E+01 |
Std | 2.05E+03 | 3.66E+03 | 1.17E+00 | 2.12E+01 | 6.49E+01 | 6.84E-01 | 2.21E+00 | |
F6 | Ave | 4.01E+01 | 3.47E-08 | 2.13E-01 | 3.97E+00 | 2.47E+03 | 1.08E+01 | 1.31E-04 |
Std | 3.16E+01 | 1.16E-08 | 7.26E-02 | 7.95E+00 | 3.99E+03 | 6.68E-01 | 3.79E-04 | |
F7 | Ave | 3.87E+01 | 2.72E-02 | 5.27E-02 | 1.80E+02 | 4.40E-01 | 1.14E-03 | 5.02E-04 |
Std | 1.65E+01 | 7.75E-03 | 5.89E-02 | 4.00E+02 | 9.12E-02 | 1.22E-04 | 1.22E-04 | |
F8 | Ave | 5.64E+02 | 4.28E+02 | 1.78E+01 | 4.85E+02 | 4.73E+02 | 2.33E-07 | 0 |
Std | 4.71E+01 | 2.96E+02 | 3.30E+01 | 5.90E+02 | 8.53E+01 | 8.51E-07 | 0 | |
F9 | Ave | 1.60E+01 | 2.13E+01 | 1.20E+00 | 4.10E+00 | 1.88E+01 | 9.48E-11 | 7.99E-15 |
Std | 7.27E-01 | 1.83E-02 | 1.03E+01 | 5.75E+00 | 6.01E-01 | 4.62E-11 | 0 | |
F10 | Ave | 2.03E+02 | 4.37E-07 | 7.91E-04 | 2.22E-16 | 2.65E-02 | 0 | 0 |
Std | 5.97E+01 | 1.78E-07 | 7.72E-04 | 7.43E-16 | 2.17E-02 | 0 | 0 | |
F15 | Ave | 8.40E+02 | 4.01E+01 | 6.21E+01 | 8.59E+00 | 3.32E+01 | 7.91E-01 | 1.79E-06 |
Std | 3.81E+01 | 5.29E+00 | 2.59E+00 | 1.20E+01 | 1.92E+01 | 6.29E-01 | 7.08E-06 |
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