Journal of Computer Applications ›› 2024, Vol. 44 ›› Issue (10): 3021-3031.DOI: 10.11772/j.issn.1001-9081.2023091313
• Artificial intelligence • Previous Articles Next Articles
Rui ZHANG1(), Junming PAN1, Xiaolu BAI2, Jing HU1, Rongguo ZHANG1, Pengyun ZHANG1
Received:
2023-09-25
Revised:
2024-03-07
Accepted:
2024-03-19
Online:
2024-04-01
Published:
2024-10-10
Contact:
Rui ZHANG
About author:
PAN Junming, born in 1996, M. S. candidate. His research interests include intelligent information processing.Supported by:
张睿1(), 潘俊铭1, 白晓露2, 胡静1, 张荣国1, 张鹏云1
通讯作者:
张睿
作者简介:
张睿(1987—),男,山西太原人,副教授,博士,CCF高级会员,主要研究方向:自动机器学习、智能信息处理 zhangrui@tyust.edu.cn基金资助:
CLC Number:
Rui ZHANG, Junming PAN, Xiaolu BAI, Jing HU, Rongguo ZHANG, Pengyun ZHANG. Agent model for hyperparameter self-optimization of deep classification model[J]. Journal of Computer Applications, 2024, 44(10): 3021-3031.
张睿, 潘俊铭, 白晓露, 胡静, 张荣国, 张鹏云. 面向深度分类模型超参数自优化的代理模型[J]. 《计算机应用》唯一官方网站, 2024, 44(10): 3021-3031.
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URL: https://www.joca.cn/EN/10.11772/j.issn.1001-9081.2023091313
问题 | 维度 | Dropout | Kriging | FEDA |
---|---|---|---|---|
DTLZ1 | 20 | 3.24E+2 (3.22E+1)+ | 3.50E+2 (3.78E+1)+ | 3.01E+2 (3.40E+1) |
40 | 8.54E+2 (5.40E+1)= | 8.79E+2 (6.16E+1)= | 8.73E+2 (5.83E+1) | |
60 | 1.43E+3 (5.32E+1)+ | 1.46E+3 (6.04E+1)+ | 1.40E+3 (4.81E+1) | |
100 | 2.58E+3 (6.83E+1)+ | 2.62E+3 (6.14E+1)+ | 2.49E+3 (7.24E+1) | |
DTLZ2 | 20 | 6.74E-1 (6.57E-2)- | 7.14E-1 (7.84E-2)= | 7.04E-1 (6.32E-2) |
40 | 1.95E+0 (1.24E-1)= | 2.01E+0 (1.36E-1)= | 1.86E+0 (1.18E-1) | |
60 | 3.29E+0 (1.27E-1)= | 3.31E+0 (1.82E-1)= | 3.17E+0 (1.32E-1) | |
100 | 5.85E+0 (1.41E-1)= | 5.88E+0 (1.55E-1)= | 5.75E+0 (1.47E-1) | |
DTLZ3 | 20 | 1.06E+3 (1.44E+2)+ | 1.07E+3 (1.40E+2)+ | 8.66E+2 (1.36E+2) |
40 | 2.77E+3 (1.53E+2)+ | 2.78E+3 (1.61E+2)+ | 2.58E+3 (6.70E+1) | |
60 | 4.53E+3 (2.04E+2)+ | 4.51E+3 (2.13E+2)+ | 4.31E+3 (1.14E+2) | |
100 | 8.27E+3 (2.14E+2)+ | 8.27E+3 (2.02E+2)+ | 7.89E+3 (1.81E+2) | |
DTLZ4 | 20 | 8.37E-1 (1.76E-1)- | 9.54E-1 (7.49E-2)+ | 1.10E+0 (8.72E-1) |
40 | 2.20E+0 (1.58E-1)= | 2.33E+0 (1.96E-1)+ | 2.22E+0 (1.84E-1) | |
60 | 3.45E+0 (2.27E-1)+ | 3.68E+0 (1.75E-1)+ | 3.36E+0 (1.99E-1) | |
100 | 6.34E+0 (2.17E-1)+ | 6.33E+0 (2.26E-1)+ | 6.07E+0 (1.84E-1) | |
DTLZ5 | 20 | 4.71E-1 (7.82E-2)+ | 5.31E-1 (7.49E-2)+ | 3.21E-1 (5.22E-2) |
40 | 1.92E+0 (1.24E-1)+ | 1.95E+0 (1.31E-1)+ | 1.79E+0 (9.44E-2) | |
60 | 3.22E+0 (1.62E-1)= | 3.24E+0 (1.87E-1)= | 3.02E+0 (1.74E-1) | |
100 | 6.14E+0 (1.47E-1)+ | 6.04E+0 (1.66E-1)+ | 5.61E+0 (1.16E-1) | |
DTLZ6 | 20 | 1.37E+1 (7.96E-1)= | 1.30E+1 (5.44E-1)- | 1.39E+1 (7.06E-1) |
40 | 3.15E+1 (4.52E-1)+ | 3.22E+1 (5.97E-1)+ | 3.15E+1 (4.17E-1) | |
60 | 4.95E+1 (7.33E-1)+ | 4.78E+1 (5.11E-1)= | 4.79E+1 (6.55E-1) | |
100 | 4.84E+1 (7.17E-1)- | 8.56E+1 (5.94E-1)= | 8.44E+1 (6.24E-1) | |
DTLZ7 | 20 | 2.95E+0 (7.02E-1)+ | 2.18E+0 (3.83E-1)- | 2.66E+0 (3.71E-1) |
40 | 4.49E+0 (9.37E-1)- | 8.85E+0 (2.17E-0)+ | 4.31E+0 (8.94E-1) | |
60 | 5.22E+0 (5.76E-1)- | 9.25E+0 (5.83E-1)= | 8.26E+0 (6.55E-1) | |
100 | 6.56E+0 (5.16E-1)+ | 1.24E+1 (5.08E-1)+ | 5.76E+0 (4.37E-1) |
Tab. 1 Average IGD values obtained by three proxy methods on DTLZ test problems
问题 | 维度 | Dropout | Kriging | FEDA |
---|---|---|---|---|
DTLZ1 | 20 | 3.24E+2 (3.22E+1)+ | 3.50E+2 (3.78E+1)+ | 3.01E+2 (3.40E+1) |
40 | 8.54E+2 (5.40E+1)= | 8.79E+2 (6.16E+1)= | 8.73E+2 (5.83E+1) | |
60 | 1.43E+3 (5.32E+1)+ | 1.46E+3 (6.04E+1)+ | 1.40E+3 (4.81E+1) | |
100 | 2.58E+3 (6.83E+1)+ | 2.62E+3 (6.14E+1)+ | 2.49E+3 (7.24E+1) | |
DTLZ2 | 20 | 6.74E-1 (6.57E-2)- | 7.14E-1 (7.84E-2)= | 7.04E-1 (6.32E-2) |
40 | 1.95E+0 (1.24E-1)= | 2.01E+0 (1.36E-1)= | 1.86E+0 (1.18E-1) | |
60 | 3.29E+0 (1.27E-1)= | 3.31E+0 (1.82E-1)= | 3.17E+0 (1.32E-1) | |
100 | 5.85E+0 (1.41E-1)= | 5.88E+0 (1.55E-1)= | 5.75E+0 (1.47E-1) | |
DTLZ3 | 20 | 1.06E+3 (1.44E+2)+ | 1.07E+3 (1.40E+2)+ | 8.66E+2 (1.36E+2) |
40 | 2.77E+3 (1.53E+2)+ | 2.78E+3 (1.61E+2)+ | 2.58E+3 (6.70E+1) | |
60 | 4.53E+3 (2.04E+2)+ | 4.51E+3 (2.13E+2)+ | 4.31E+3 (1.14E+2) | |
100 | 8.27E+3 (2.14E+2)+ | 8.27E+3 (2.02E+2)+ | 7.89E+3 (1.81E+2) | |
DTLZ4 | 20 | 8.37E-1 (1.76E-1)- | 9.54E-1 (7.49E-2)+ | 1.10E+0 (8.72E-1) |
40 | 2.20E+0 (1.58E-1)= | 2.33E+0 (1.96E-1)+ | 2.22E+0 (1.84E-1) | |
60 | 3.45E+0 (2.27E-1)+ | 3.68E+0 (1.75E-1)+ | 3.36E+0 (1.99E-1) | |
100 | 6.34E+0 (2.17E-1)+ | 6.33E+0 (2.26E-1)+ | 6.07E+0 (1.84E-1) | |
DTLZ5 | 20 | 4.71E-1 (7.82E-2)+ | 5.31E-1 (7.49E-2)+ | 3.21E-1 (5.22E-2) |
40 | 1.92E+0 (1.24E-1)+ | 1.95E+0 (1.31E-1)+ | 1.79E+0 (9.44E-2) | |
60 | 3.22E+0 (1.62E-1)= | 3.24E+0 (1.87E-1)= | 3.02E+0 (1.74E-1) | |
100 | 6.14E+0 (1.47E-1)+ | 6.04E+0 (1.66E-1)+ | 5.61E+0 (1.16E-1) | |
DTLZ6 | 20 | 1.37E+1 (7.96E-1)= | 1.30E+1 (5.44E-1)- | 1.39E+1 (7.06E-1) |
40 | 3.15E+1 (4.52E-1)+ | 3.22E+1 (5.97E-1)+ | 3.15E+1 (4.17E-1) | |
60 | 4.95E+1 (7.33E-1)+ | 4.78E+1 (5.11E-1)= | 4.79E+1 (6.55E-1) | |
100 | 4.84E+1 (7.17E-1)- | 8.56E+1 (5.94E-1)= | 8.44E+1 (6.24E-1) | |
DTLZ7 | 20 | 2.95E+0 (7.02E-1)+ | 2.18E+0 (3.83E-1)- | 2.66E+0 (3.71E-1) |
40 | 4.49E+0 (9.37E-1)- | 8.85E+0 (2.17E-0)+ | 4.31E+0 (8.94E-1) | |
60 | 5.22E+0 (5.76E-1)- | 9.25E+0 (5.83E-1)= | 8.26E+0 (6.55E-1) | |
100 | 6.56E+0 (5.16E-1)+ | 1.24E+1 (5.08E-1)+ | 5.76E+0 (4.37E-1) |
问题 | 维度 | N-ARMOEA | K-ARMOEA | FEDA |
---|---|---|---|---|
WFG1 | 20 | 4.67E+2 (3.22E+1)+ | 3.83E+2 (3.78E+1)+ | 3.01E+2 (3.40E+1) |
40 | 8.54E+2 (5.40E+1)= | 8.79E+2 (6.16E+1)= | 8.73E+2 (5.83E+1) | |
60 | 1.43E+3 (5.32E+1)+ | 1.46E+3 (6.04E+1)+ | 1.40E+3 (4.81E+1) | |
100 | 2.58E+3 (6.83E+1)+ | 2.62E+3 (6.14E+1)+ | 2.49E+3 (7.24E+1) | |
WFG2 | 20 | 6.74E-1 (6.57E-2)- | 7.14E-1 (7.84E-2)= | 7.04E-1 (6.32E-2) |
40 | 1.95E+0 (1.24E-1)= | 2.01E+0 (1.36E-1)= | 1.86E+0 (1.18E-1) | |
60 | 3.29E+0 (1.27E-1)= | 3.31E+0 (1.82E-1)= | 3.17E+0 (1.32E-1) | |
100 | 5.85E+0 (1.41E-1)= | 5.88E+0 (1.55E-1)= | 5.75E+0 (1.47E-1) | |
WFG3 | 20 | 1.06E+3 (1.44E+2)+ | 1.07E+3 (1.40E+2)+ | 8.66E+2 (1.36E+2) |
40 | 2.77E+3 (1.53E+2)+ | 2.78E+3 (1.61E+2)+ | 2.58E+3 (6.70E+1) | |
60 | 4.54E+3 (2.04E+2)+ | 4.51E+3 (2.13E+2)+ | 4.31E+3 (1.14E+2) | |
100 | 8.28E+3 (2.14E+2)+ | 8.27E+3 (2.02E+2)+ | 7.89E+3 (1.81E+2) | |
WFG4 | 20 | 8.38E-1 (1.76E-1)- | 9.54E-1 (7.49E-2)+ | 1.10E+0 (8.72E-1) |
40 | 2.20E+0 (1.58E-1)= | 2.33E+0 (1.96E-1)+ | 2.22E+0 (1.84E-1) | |
60 | 3.45E+0 (2.27E-1)+ | 3.68E+0 (1.75E-1)+ | 3.36E+0 (1.99E-1) | |
100 | 6.34E+0 (2.17E-1)+ | 6.33E+0 (2.26E-1)+ | 6.07E+0 (1.84E-1) | |
WFG5 | 20 | 4.71E-1 (7.82E-2)+ | 5.31E-1 (7.49E-2)+ | 3.21E-1 (5.22E-2) |
40 | 1.92E+0 (1.24E-1)+ | 1.95E+0 (1.31E-1)+ | 1.79E+0 (9.44E-2) | |
60 | 3.22E+0 (1.62E-1)= | 3.24E+0 (1.87E-1)= | 3.02E+0 (1.74E-1) | |
100 | 6.14E+0 (1.47E-1)+ | 6.04E+0 (1.66E-1)+ | 5.61E+0 (1.16E-1) | |
WFG6 | 20 | 1.37E+1 (7.96E-1)= | 1.30E+1 (5.44E-1)- | 1.39E+1 (7.06E-1) |
40 | 3.15E+1 (4.52E-1)= | 3.23E+1 (5.97E-1)+ | 3.15E+1 (4.17E-1) | |
60 | 4.95E+1 (7.33E-1)+ | 4.78E+1 (5.11E-1)= | 4.79E+1 (6.55E-1) | |
100 | 4.84E+1 (7.17E-1)- | 8.56E+1 (5.94E-1)= | 8.44E+1 (6.24E-1) | |
WFG7 | 20 | 2.95E+0 (7.02E-1)+ | 2.18E+0 (3.83E-1)- | 2.66E+0 (3.71E-1) |
40 | 4.49E+0 (9.37E-1)+ | 8.85E+0 (2.17E-0)+ | 5.61E+0 (8.94E-1) | |
60 | 5.22E+0 (5.76E-1)- | 9.25E+0 (5.83E-1)= | 8.26E+0 (6.55E-1) | |
100 | 6.56E+0 (5.16E-1)+ | 1.24E+1 (5.08E-1)+ | 5.76E+0 (4.37E-1) |
Tab.2 IGD values obtained by proxy models with different selection methods on WFG test problems
问题 | 维度 | N-ARMOEA | K-ARMOEA | FEDA |
---|---|---|---|---|
WFG1 | 20 | 4.67E+2 (3.22E+1)+ | 3.83E+2 (3.78E+1)+ | 3.01E+2 (3.40E+1) |
40 | 8.54E+2 (5.40E+1)= | 8.79E+2 (6.16E+1)= | 8.73E+2 (5.83E+1) | |
60 | 1.43E+3 (5.32E+1)+ | 1.46E+3 (6.04E+1)+ | 1.40E+3 (4.81E+1) | |
100 | 2.58E+3 (6.83E+1)+ | 2.62E+3 (6.14E+1)+ | 2.49E+3 (7.24E+1) | |
WFG2 | 20 | 6.74E-1 (6.57E-2)- | 7.14E-1 (7.84E-2)= | 7.04E-1 (6.32E-2) |
40 | 1.95E+0 (1.24E-1)= | 2.01E+0 (1.36E-1)= | 1.86E+0 (1.18E-1) | |
60 | 3.29E+0 (1.27E-1)= | 3.31E+0 (1.82E-1)= | 3.17E+0 (1.32E-1) | |
100 | 5.85E+0 (1.41E-1)= | 5.88E+0 (1.55E-1)= | 5.75E+0 (1.47E-1) | |
WFG3 | 20 | 1.06E+3 (1.44E+2)+ | 1.07E+3 (1.40E+2)+ | 8.66E+2 (1.36E+2) |
40 | 2.77E+3 (1.53E+2)+ | 2.78E+3 (1.61E+2)+ | 2.58E+3 (6.70E+1) | |
60 | 4.54E+3 (2.04E+2)+ | 4.51E+3 (2.13E+2)+ | 4.31E+3 (1.14E+2) | |
100 | 8.28E+3 (2.14E+2)+ | 8.27E+3 (2.02E+2)+ | 7.89E+3 (1.81E+2) | |
WFG4 | 20 | 8.38E-1 (1.76E-1)- | 9.54E-1 (7.49E-2)+ | 1.10E+0 (8.72E-1) |
40 | 2.20E+0 (1.58E-1)= | 2.33E+0 (1.96E-1)+ | 2.22E+0 (1.84E-1) | |
60 | 3.45E+0 (2.27E-1)+ | 3.68E+0 (1.75E-1)+ | 3.36E+0 (1.99E-1) | |
100 | 6.34E+0 (2.17E-1)+ | 6.33E+0 (2.26E-1)+ | 6.07E+0 (1.84E-1) | |
WFG5 | 20 | 4.71E-1 (7.82E-2)+ | 5.31E-1 (7.49E-2)+ | 3.21E-1 (5.22E-2) |
40 | 1.92E+0 (1.24E-1)+ | 1.95E+0 (1.31E-1)+ | 1.79E+0 (9.44E-2) | |
60 | 3.22E+0 (1.62E-1)= | 3.24E+0 (1.87E-1)= | 3.02E+0 (1.74E-1) | |
100 | 6.14E+0 (1.47E-1)+ | 6.04E+0 (1.66E-1)+ | 5.61E+0 (1.16E-1) | |
WFG6 | 20 | 1.37E+1 (7.96E-1)= | 1.30E+1 (5.44E-1)- | 1.39E+1 (7.06E-1) |
40 | 3.15E+1 (4.52E-1)= | 3.23E+1 (5.97E-1)+ | 3.15E+1 (4.17E-1) | |
60 | 4.95E+1 (7.33E-1)+ | 4.78E+1 (5.11E-1)= | 4.79E+1 (6.55E-1) | |
100 | 4.84E+1 (7.17E-1)- | 8.56E+1 (5.94E-1)= | 8.44E+1 (6.24E-1) | |
WFG7 | 20 | 2.95E+0 (7.02E-1)+ | 2.18E+0 (3.83E-1)- | 2.66E+0 (3.71E-1) |
40 | 4.49E+0 (9.37E-1)+ | 8.85E+0 (2.17E-0)+ | 5.61E+0 (8.94E-1) | |
60 | 5.22E+0 (5.76E-1)- | 9.25E+0 (5.83E-1)= | 8.26E+0 (6.55E-1) | |
100 | 6.56E+0 (5.16E-1)+ | 1.24E+1 (5.08E-1)+ | 5.76E+0 (4.37E-1) |
问题 | 维度 | FEDA-AROMEA | FEDA-DS | FEDA-AE |
---|---|---|---|---|
WFG1 | 20 | 3.01E+2 (3.40E+1) | 3.83E+2 (3.78E+1)+ | 4.67E+2 (3.22E+1)+ |
WFG2 | 20 | 7.04E-1 (6.32E-2) | 7.14E-1 (7.84E-2)= | 6.74E-1 (6.57E-2)- |
WFG3 | 20 | 8.66E+2 (1.36E+2) | 1.07E+3 (1.40E+2)+ | 1.06E+3 (1.44E+2)+ |
WFG4 | 20 | 1.10E+0 (8.72E-1) | 9.54E-1 (7.49E-2)+ | 8.38E-1 (1.76E-1)- |
WFG5 | 20 | 3.21E-1 (5.22E-2) | 5.31E-1 (7.49E-2)+ | 4.71E-1 (7.82E-2)+ |
WFG6 | 20 | 1.29E+1 (7.06E-1) | 1.30E+1 (5.44E-1)+ | 1.37E+1 (7.96E-1)= |
WFG7 | 20 | 2.66E+0 (3.71E-1) | 2.18E+0 (3.83E-1)- | 2.95E+0 (7.02E-1)+ |
WFG8 | 20 | 8.66E+2 (1.36E+2) | 1.07E+3 (1.40E+2)+ | 1.06E+3 (1.44E+2)+ |
WFG9 | 20 | 3.01E+2 (3.40E+1) | 3.83E+2 (3.78E+1)+ | 4.67E+2 (3.22E+1)+ |
Tab. 3 Average IGD values obtained by proxy models with different model management strategies on WFG test problems
问题 | 维度 | FEDA-AROMEA | FEDA-DS | FEDA-AE |
---|---|---|---|---|
WFG1 | 20 | 3.01E+2 (3.40E+1) | 3.83E+2 (3.78E+1)+ | 4.67E+2 (3.22E+1)+ |
WFG2 | 20 | 7.04E-1 (6.32E-2) | 7.14E-1 (7.84E-2)= | 6.74E-1 (6.57E-2)- |
WFG3 | 20 | 8.66E+2 (1.36E+2) | 1.07E+3 (1.40E+2)+ | 1.06E+3 (1.44E+2)+ |
WFG4 | 20 | 1.10E+0 (8.72E-1) | 9.54E-1 (7.49E-2)+ | 8.38E-1 (1.76E-1)- |
WFG5 | 20 | 3.21E-1 (5.22E-2) | 5.31E-1 (7.49E-2)+ | 4.71E-1 (7.82E-2)+ |
WFG6 | 20 | 1.29E+1 (7.06E-1) | 1.30E+1 (5.44E-1)+ | 1.37E+1 (7.96E-1)= |
WFG7 | 20 | 2.66E+0 (3.71E-1) | 2.18E+0 (3.83E-1)- | 2.95E+0 (7.02E-1)+ |
WFG8 | 20 | 8.66E+2 (1.36E+2) | 1.07E+3 (1.40E+2)+ | 1.06E+3 (1.44E+2)+ |
WFG9 | 20 | 3.01E+2 (3.40E+1) | 3.83E+2 (3.78E+1)+ | 4.67E+2 (3.22E+1)+ |
问题 | M | FEDA-ARMOEA | EDN-ARMOEA | HeE-MOEA | CMOEA-MS |
---|---|---|---|---|---|
DTLZ1 | 3 | 3.74E+2 (3.73E+1) | 3.76E+2 (3.98E+1)- | 3.75E+2 (4.69E+1)- | 3.80E+2 (6.05E+1)- |
5 | 2.74E+2 (2.50E+1) | 2.91E+2 (2.82E+1)- | 2.86E+2 (3.18E+1)- | 2.93E+2 (4.19E+1)- | |
8 | 2.00E+2 (2.89E+1) | 2.16E+2 (2.23E+1)- | 2.01E+2 (3.79E+1)- | 2.23E+2 (7.12E+1)- | |
10 | 1.60E+2 (2.35E+1) | 1.64E+2 (2.02E+1)- | 1.58E+2 (2.61E+1)+ | 1.60E+2 (3.25E+1)- | |
DTLZ2 | 3 | 9.01E-1 (4.65E-2) | 9.00E-1 (3.99E-2)+ | 9.11E-1 (4.84E-2)- | 9.04E-1 (5.26E-2)- |
5 | 9.74E-1 (5.27E-2) | 9.82E-1 (3.85E-2)- | 9.79E-1 (4.50E-2)- | 9.79E-1 (7.65E-2)- | |
8 | 1.05E+0 (3.23E-2) | 1.06E+0 (3.74E-2)- | 1.06E+0 (3.49E-2)- | 1.10E+0 (4.98E-2)- | |
10 | 1.06E+0 (3.20E-2) | 1.07E+0 (3.51E-2)- | 1.06E+0 (2.47E-2)- | 1.08E+0 (3.47E-2)- | |
DTLZ3 | 3 | 1.10E+3 (1.08E+2) | 1.12E+3 (1.17E+2)- | 1.14E+3 (9.21E+1)- | 1.14E+3 (4.13E+1)- |
5 | 9.57E+2 (9.89E+1) | 9.69E+2 (1.17E+2)- | 9.93E+2 (1.01E+2)- | 9.87E+2 (2.35E+2)- | |
8 | 7.12E+2 (7.88E+1) | 7.01E+3 (9.78E+1)- | 7.10E+2 (1.06E+2)- | 6.98E+2 (3.12E+2)+ | |
10 | 5.44E+3 (7.32E+2) | 5.64E+3 (8.39E+1)- | 5.56E+2 (9.17E+1)- | 5.73E+2 (8.16E+1)- | |
DTLZ4 | 3 | 1.28E+0 (8.88E-2) | 1.28E+0 (8.50E-2)- | 1.28E+0 (8.68E-2)- | 1.29E+0 (3.45E-2)- |
5 | 1.30E+0 (7.88E-2) | 1.35E+0 (7.70E-2)- | 1.31E+0 (7.82E-2)- | 1.33E+0 (6.18E-2)- | |
8 | 1.24E+0 (6.63E-2) | 1.27E+0 (6.57E-2)- | 1.26E+0 (6.33E-2)- | 1.28E+0 (4.66E-2)- | |
10 | 1.19E+0 (4.24E-2) | 1.20E+0 (5.61E-2)- | 1.19E+0 (4.31E-2)- | 1.20E+0 (1.98E-2)- | |
DTLZ5 | 3 | 8.40E-1 (5.59E-2) | 8.30E-1 (5.65E-2)+ | 8.44E-1 (5.86E-2)- | 8.34E-1(7.71E-2)- |
5 | 7.24E-1 (7.52E-2) | 7.18E-1 (5.96E-2)- | 7.37E-1 (4.97E-2)- | 7.13E-1(5.25E-2)+ | |
8 | 5.45E-1 (4.48E-2) | 5.59E-1 (4.89E-2)- | 5.58E-1 (4.18E-2)- | 5.50E-1(5.62E-2)- | |
10 | 4.20E+0 (4.91E-2) | 4.44E-1 (4.17E-2)- | 4.30E-1 (3.82E-2)- | 4.30E-1(4.32E-2)- | |
DTLZ6 | 3 | 1.54E+1 (1.78E-1) | 1.54E+1 (1.31E-1) - | 1.54E+1 (1.07E-1)- | 1.60E+1 (7.22E-1)- |
5 | 1.36E+1 (1.54E-1) | 1.37E+1 (1.29E-1) - | 1.36E+1 (1.47E-1)- | 1.39E+1 (2.21E-1)- | |
8 | 1.11E+1 (1.34E-1) | 1.10E+1 (1.48E-1) - | 1.10E+1 (1.36E-1)+ | 1.13E+1 (1.78E-1)= | |
10 | 9.13E+0 (1.05E-1) | 9.29E+0 (1.06E-1) - | 9.30E+0 (8.60E-2)- | 9.30E+0 (7.41E-2)- | |
DTLZ7 | 3 | 8.07E+0 (7.85E-1) | 8.18E+0 (7.17E-1) - | 8.39E+0 (6.60E-1)- | 8.21E+0 (9.61E-1)- |
5 | 1.31E+1 (1.30E+0) | 1.33E+1 (1.24E+0) - | 1.36E+1 (1.39E+0)- | 1.37E+1 (2.10E+0)- | |
8 | 2.00E+1 (2.30E+0) | 2.02E+1 (2.00E+0) - | 2.00E+1 (2.11E+0)- | 2.01E+1 (2.03E+0)- | |
10 | 2.38E+1 (2.59E+0) | 2.35E+1(3.10E+0) + | 2.43E+1 (3.75E+0)- | 2.40E+1 (7.62E+0)- |
Tab. 4 IGD values on 20 dimensions for different algorithms with different target numbers
问题 | M | FEDA-ARMOEA | EDN-ARMOEA | HeE-MOEA | CMOEA-MS |
---|---|---|---|---|---|
DTLZ1 | 3 | 3.74E+2 (3.73E+1) | 3.76E+2 (3.98E+1)- | 3.75E+2 (4.69E+1)- | 3.80E+2 (6.05E+1)- |
5 | 2.74E+2 (2.50E+1) | 2.91E+2 (2.82E+1)- | 2.86E+2 (3.18E+1)- | 2.93E+2 (4.19E+1)- | |
8 | 2.00E+2 (2.89E+1) | 2.16E+2 (2.23E+1)- | 2.01E+2 (3.79E+1)- | 2.23E+2 (7.12E+1)- | |
10 | 1.60E+2 (2.35E+1) | 1.64E+2 (2.02E+1)- | 1.58E+2 (2.61E+1)+ | 1.60E+2 (3.25E+1)- | |
DTLZ2 | 3 | 9.01E-1 (4.65E-2) | 9.00E-1 (3.99E-2)+ | 9.11E-1 (4.84E-2)- | 9.04E-1 (5.26E-2)- |
5 | 9.74E-1 (5.27E-2) | 9.82E-1 (3.85E-2)- | 9.79E-1 (4.50E-2)- | 9.79E-1 (7.65E-2)- | |
8 | 1.05E+0 (3.23E-2) | 1.06E+0 (3.74E-2)- | 1.06E+0 (3.49E-2)- | 1.10E+0 (4.98E-2)- | |
10 | 1.06E+0 (3.20E-2) | 1.07E+0 (3.51E-2)- | 1.06E+0 (2.47E-2)- | 1.08E+0 (3.47E-2)- | |
DTLZ3 | 3 | 1.10E+3 (1.08E+2) | 1.12E+3 (1.17E+2)- | 1.14E+3 (9.21E+1)- | 1.14E+3 (4.13E+1)- |
5 | 9.57E+2 (9.89E+1) | 9.69E+2 (1.17E+2)- | 9.93E+2 (1.01E+2)- | 9.87E+2 (2.35E+2)- | |
8 | 7.12E+2 (7.88E+1) | 7.01E+3 (9.78E+1)- | 7.10E+2 (1.06E+2)- | 6.98E+2 (3.12E+2)+ | |
10 | 5.44E+3 (7.32E+2) | 5.64E+3 (8.39E+1)- | 5.56E+2 (9.17E+1)- | 5.73E+2 (8.16E+1)- | |
DTLZ4 | 3 | 1.28E+0 (8.88E-2) | 1.28E+0 (8.50E-2)- | 1.28E+0 (8.68E-2)- | 1.29E+0 (3.45E-2)- |
5 | 1.30E+0 (7.88E-2) | 1.35E+0 (7.70E-2)- | 1.31E+0 (7.82E-2)- | 1.33E+0 (6.18E-2)- | |
8 | 1.24E+0 (6.63E-2) | 1.27E+0 (6.57E-2)- | 1.26E+0 (6.33E-2)- | 1.28E+0 (4.66E-2)- | |
10 | 1.19E+0 (4.24E-2) | 1.20E+0 (5.61E-2)- | 1.19E+0 (4.31E-2)- | 1.20E+0 (1.98E-2)- | |
DTLZ5 | 3 | 8.40E-1 (5.59E-2) | 8.30E-1 (5.65E-2)+ | 8.44E-1 (5.86E-2)- | 8.34E-1(7.71E-2)- |
5 | 7.24E-1 (7.52E-2) | 7.18E-1 (5.96E-2)- | 7.37E-1 (4.97E-2)- | 7.13E-1(5.25E-2)+ | |
8 | 5.45E-1 (4.48E-2) | 5.59E-1 (4.89E-2)- | 5.58E-1 (4.18E-2)- | 5.50E-1(5.62E-2)- | |
10 | 4.20E+0 (4.91E-2) | 4.44E-1 (4.17E-2)- | 4.30E-1 (3.82E-2)- | 4.30E-1(4.32E-2)- | |
DTLZ6 | 3 | 1.54E+1 (1.78E-1) | 1.54E+1 (1.31E-1) - | 1.54E+1 (1.07E-1)- | 1.60E+1 (7.22E-1)- |
5 | 1.36E+1 (1.54E-1) | 1.37E+1 (1.29E-1) - | 1.36E+1 (1.47E-1)- | 1.39E+1 (2.21E-1)- | |
8 | 1.11E+1 (1.34E-1) | 1.10E+1 (1.48E-1) - | 1.10E+1 (1.36E-1)+ | 1.13E+1 (1.78E-1)= | |
10 | 9.13E+0 (1.05E-1) | 9.29E+0 (1.06E-1) - | 9.30E+0 (8.60E-2)- | 9.30E+0 (7.41E-2)- | |
DTLZ7 | 3 | 8.07E+0 (7.85E-1) | 8.18E+0 (7.17E-1) - | 8.39E+0 (6.60E-1)- | 8.21E+0 (9.61E-1)- |
5 | 1.31E+1 (1.30E+0) | 1.33E+1 (1.24E+0) - | 1.36E+1 (1.39E+0)- | 1.37E+1 (2.10E+0)- | |
8 | 2.00E+1 (2.30E+0) | 2.02E+1 (2.00E+0) - | 2.00E+1 (2.11E+0)- | 2.01E+1 (2.03E+0)- | |
10 | 2.38E+1 (2.59E+0) | 2.35E+1(3.10E+0) + | 2.43E+1 (3.75E+0)- | 2.40E+1 (7.62E+0)- |
问题 | M | FEDA-ARMOEA | EDN-ARMOEA | HeE-MOREA | CMOEA-MS |
---|---|---|---|---|---|
DTLZ1 | 3 | 9.05E+2 (5.62E+1) | 9.08E+2 (5.16E+1) - | 9.17E+2 (4.95E+1)- | 9.10E+2 (4.60E+1)- |
5 | 7.45E+2 (2.86E+1) | 7.39E+2 (4.78E+1) - | 7.22E+2 (4.64E+1)+ | 7.26E+2 (4.69E+1)- | |
8 | 6.07E+2 (4.90E+1) | 6.08E+2 (4.76E+1) - | 6.16E+2 (4.16E+1)- | 6.12E+2 (4.59E+1)- | |
10 | 5.47E+2 (4.16E+1) | 5.57E+2 (5.47E+1) - | 5.63E+2 (5.86E+1)- | 5.76E+2 (4.97E+1)- | |
DTLZ2 | 3 | 2.06E+0 (9.75E-2) | 2.05E+0 (1.19E-1) + | 2.06E+0 (1.14E-1)- | 2.07E+0 (9.58E-2)- |
5 | 2.11E+0 (1.23E-1) | 2.14E+0 (1.03E-1) - | 2.13E+0 (8.83E-2)- | 2.16E+0 (8.36E-2)- | |
8 | 2.15E+0 (8.58E-2) | 2.18E+0 (9.52E-2) - | 2.17E+0 (6.68E-2)- | 2.17E+0 (9.69E-2)- | |
10 | 2.10E+0 (8.08E-2) | 2.12E+0 (8.35E-2) - | 2.10E+0 (9.01E-2)- | 2.11E+0 (1.08E-1)- | |
DTLZ3 | 3 | 2.76E+3 (1.34E+2) | 2.87E+3 (1.44E+2) - | 2.78E+3 (1.48E+2)- | 2.83E+3(1.49E+2)- |
5 | 2.61E+3 (1.81E+2) | 2.60E+3 (1.73E+2) - | 2.59E+3 (1.60E+2)+ | 2.63E+3(1.50E+2)- | |
8 | 2.34E+3 (1.59E+2) | 2.36E+3 (1.26E+2) - | 2.36E+3 (1.46E+2)- | 2.34E+3(1.12E+2)- | |
10 | 2.11E+3 (1.59E+2) | 2.11E+3 (1.68E+2) - | 2.20E+3 (1.53E+2)- | 2.19E+3(1.44E+2)- | |
DTLZ4 | 3 | 2.46E+0 (1.24E-1) | 2.46E+0 (1.21E-1) - | 2.48E+0 (9.96E-2)- | 2.46E+0 (1.17E-1)- |
5 | 2.46E+0 (1.05E-1) | 2.46E+0 (1.25E-1) - | 2.50E+0 (1.01E-1)- | 2.48E+0 (1.16E-1)- | |
8 | 2.39E+0 (8.52E-2) | 2.36E+0 (9.23E-2) - | 2.40E+0 (6.16E-2)- | 2.35E+0 (1.17E-1)+ | |
10 | 2.28E+0 (7.91E-2) | 2.30E+0 (6.65E-2) - | 2.31E+0 (7.22E-2)- | 2.29E+0 (8.47E-2)- | |
DTLZ5 | 3 | 2.02E+0 (1.09E-1) | 2.03E+0 (1.44E-1) - | 2.04E+0 (9.52E-2)- | 2.02E+0 (1.27E-1)- |
5 | 1.90E+0 (9.59E-2) | 1.91E+0 (9.94E-2) - | 1.91E+0 (1.21E-1)- | 1.94E+0 (1.14E-1)- | |
8 | 1.69E+0 (1.23E-1) | 1.71E+0 (1.34E-1) - | 1.72E+0 (8.92E-2)- | 1.70E+0 (9.51E-2)- | |
10 | 1.55E+0 (1.21E-1) | 1.62E+0 (1.03E-1) - | 1.60E+0 (7.85E-2)- | 1.57E+0 (9.85E-2)- | |
DTLZ6 | 3 | 3.30E+1 (2.12E-1) | 3.30E+1 (2.12E-1) - | 3.31E+1 (1.56E-1)- | 3.30E+1 (1.98E-1)- |
5 | 3.12E+1 (2.68E-1) | 3.13E+1 (1.97E-1) - | 3.13E+1 (1.99E-1)- | 3.13E+1 (2.11E-1)- | |
8 | 2.86E+1 (1.81E-1) | 2.86E+1 (2.22E-1) - | 2.85E+1 (2.33E-1)+ | 2.86E+1 (2.01E-1)= | |
10 | 2.69E+1 (1.77E-1) | 2.68E+1 (1.71E-1) + | 2.69E+1 (1.87E-1)- | 2.68E+1 (2.15E-1)= | |
DTLZ7 | 3 | 9.02E+0 (6.00E-1) | 9.09E+0 (6.19E-1) - | 9.04E+0 (5.10E-1)- | 9.07E+0 (5.46E-1)= |
5 | 1.53E+1 (8.33E-1) | 1.56E+1 (7.46E-1) - | 1.56E+1 (9.09E-1)- | 1.54E+1 (8.05E-1)- | |
8 | 2.47E+1 (1.72E+0) | 2.54E+1 (1.23E+0) - | 2.52E+1 (1.72E+0)- | 2.50E+1 (1.52E+0)- | |
10 | 3.14E+1 (1.81E+0) | 3.07E+1 (2.15E+0) + | 3.08E+1 (1.62E+0)- | 3.09E+1 (2.09E+0)- |
Tab. 5 IGD values on dimension 40 for different algorithms with different target numbers
问题 | M | FEDA-ARMOEA | EDN-ARMOEA | HeE-MOREA | CMOEA-MS |
---|---|---|---|---|---|
DTLZ1 | 3 | 9.05E+2 (5.62E+1) | 9.08E+2 (5.16E+1) - | 9.17E+2 (4.95E+1)- | 9.10E+2 (4.60E+1)- |
5 | 7.45E+2 (2.86E+1) | 7.39E+2 (4.78E+1) - | 7.22E+2 (4.64E+1)+ | 7.26E+2 (4.69E+1)- | |
8 | 6.07E+2 (4.90E+1) | 6.08E+2 (4.76E+1) - | 6.16E+2 (4.16E+1)- | 6.12E+2 (4.59E+1)- | |
10 | 5.47E+2 (4.16E+1) | 5.57E+2 (5.47E+1) - | 5.63E+2 (5.86E+1)- | 5.76E+2 (4.97E+1)- | |
DTLZ2 | 3 | 2.06E+0 (9.75E-2) | 2.05E+0 (1.19E-1) + | 2.06E+0 (1.14E-1)- | 2.07E+0 (9.58E-2)- |
5 | 2.11E+0 (1.23E-1) | 2.14E+0 (1.03E-1) - | 2.13E+0 (8.83E-2)- | 2.16E+0 (8.36E-2)- | |
8 | 2.15E+0 (8.58E-2) | 2.18E+0 (9.52E-2) - | 2.17E+0 (6.68E-2)- | 2.17E+0 (9.69E-2)- | |
10 | 2.10E+0 (8.08E-2) | 2.12E+0 (8.35E-2) - | 2.10E+0 (9.01E-2)- | 2.11E+0 (1.08E-1)- | |
DTLZ3 | 3 | 2.76E+3 (1.34E+2) | 2.87E+3 (1.44E+2) - | 2.78E+3 (1.48E+2)- | 2.83E+3(1.49E+2)- |
5 | 2.61E+3 (1.81E+2) | 2.60E+3 (1.73E+2) - | 2.59E+3 (1.60E+2)+ | 2.63E+3(1.50E+2)- | |
8 | 2.34E+3 (1.59E+2) | 2.36E+3 (1.26E+2) - | 2.36E+3 (1.46E+2)- | 2.34E+3(1.12E+2)- | |
10 | 2.11E+3 (1.59E+2) | 2.11E+3 (1.68E+2) - | 2.20E+3 (1.53E+2)- | 2.19E+3(1.44E+2)- | |
DTLZ4 | 3 | 2.46E+0 (1.24E-1) | 2.46E+0 (1.21E-1) - | 2.48E+0 (9.96E-2)- | 2.46E+0 (1.17E-1)- |
5 | 2.46E+0 (1.05E-1) | 2.46E+0 (1.25E-1) - | 2.50E+0 (1.01E-1)- | 2.48E+0 (1.16E-1)- | |
8 | 2.39E+0 (8.52E-2) | 2.36E+0 (9.23E-2) - | 2.40E+0 (6.16E-2)- | 2.35E+0 (1.17E-1)+ | |
10 | 2.28E+0 (7.91E-2) | 2.30E+0 (6.65E-2) - | 2.31E+0 (7.22E-2)- | 2.29E+0 (8.47E-2)- | |
DTLZ5 | 3 | 2.02E+0 (1.09E-1) | 2.03E+0 (1.44E-1) - | 2.04E+0 (9.52E-2)- | 2.02E+0 (1.27E-1)- |
5 | 1.90E+0 (9.59E-2) | 1.91E+0 (9.94E-2) - | 1.91E+0 (1.21E-1)- | 1.94E+0 (1.14E-1)- | |
8 | 1.69E+0 (1.23E-1) | 1.71E+0 (1.34E-1) - | 1.72E+0 (8.92E-2)- | 1.70E+0 (9.51E-2)- | |
10 | 1.55E+0 (1.21E-1) | 1.62E+0 (1.03E-1) - | 1.60E+0 (7.85E-2)- | 1.57E+0 (9.85E-2)- | |
DTLZ6 | 3 | 3.30E+1 (2.12E-1) | 3.30E+1 (2.12E-1) - | 3.31E+1 (1.56E-1)- | 3.30E+1 (1.98E-1)- |
5 | 3.12E+1 (2.68E-1) | 3.13E+1 (1.97E-1) - | 3.13E+1 (1.99E-1)- | 3.13E+1 (2.11E-1)- | |
8 | 2.86E+1 (1.81E-1) | 2.86E+1 (2.22E-1) - | 2.85E+1 (2.33E-1)+ | 2.86E+1 (2.01E-1)= | |
10 | 2.69E+1 (1.77E-1) | 2.68E+1 (1.71E-1) + | 2.69E+1 (1.87E-1)- | 2.68E+1 (2.15E-1)= | |
DTLZ7 | 3 | 9.02E+0 (6.00E-1) | 9.09E+0 (6.19E-1) - | 9.04E+0 (5.10E-1)- | 9.07E+0 (5.46E-1)= |
5 | 1.53E+1 (8.33E-1) | 1.56E+1 (7.46E-1) - | 1.56E+1 (9.09E-1)- | 1.54E+1 (8.05E-1)- | |
8 | 2.47E+1 (1.72E+0) | 2.54E+1 (1.23E+0) - | 2.52E+1 (1.72E+0)- | 2.50E+1 (1.52E+0)- | |
10 | 3.14E+1 (1.81E+0) | 3.07E+1 (2.15E+0) + | 3.08E+1 (1.62E+0)- | 3.09E+1 (2.09E+0)- |
待优化参数 | 搜索范围 |
---|---|
卷积核大小 | (1×1)、(3×3)、(5×5)、(7×7) |
卷积层激活函数 | ReLU、sigmoid、ReLU6、tanh、Softsign、LReLU |
梯度下降函数 | Adam、SGD、Adamx、Adadelta、 AdamW、ASGD、RMSprop |
学习率 | [10-5,10-1] |
批次大小 | [ |
Tab. 6 MobileNetV3 parameters to be optimized and their search scopes
待优化参数 | 搜索范围 |
---|---|
卷积核大小 | (1×1)、(3×3)、(5×5)、(7×7) |
卷积层激活函数 | ReLU、sigmoid、ReLU6、tanh、Softsign、LReLU |
梯度下降函数 | Adam、SGD、Adamx、Adadelta、 AdamW、ASGD、RMSprop |
学习率 | [10-5,10-1] |
批次大小 | [ |
待优化参数 | 搜索范围 |
---|---|
卷积核通道数 | [32,512] |
池化方式 | Maxpool、Avgpool |
全连接层节点数 | [16,1 024] |
学习率 | [10-5,10-1] |
批次大小 | [ |
梯度下降函数 | Adam、Adamx、SGD、ASGD |
Tab. 7 VGG-16 parameters to be optimized and their search scopes
待优化参数 | 搜索范围 |
---|---|
卷积核通道数 | [32,512] |
池化方式 | Maxpool、Avgpool |
全连接层节点数 | [16,1 024] |
学习率 | [10-5,10-1] |
批次大小 | [ |
梯度下降函数 | Adam、Adamx、SGD、ASGD |
基线模型 | MobileNetV3(MTF任务) | VGG-16(CIFAR-10任务) | ||
---|---|---|---|---|
训练时间/h | 最高精度/% | 训练时间/h | 最高精度/% | |
ARMOEA[ | 7.59 | 94.72 | 26.85 | 92.32 |
CMOEA-MS[ | 6.80 | 94.32 | 23.80 | 93.12 |
HeE-MOEA[ | 5.76 | 95.58 | 20.13 | 93.28 |
EDN- ARMOEA[ | 4.32 | 94.50 | 17.12 | 92.20 |
FEDA-ARMOEA | 4.02 | 96.16 | 16.36 | 93.79 |
Tab. 8 Training time and highest accuracy for different classification models
基线模型 | MobileNetV3(MTF任务) | VGG-16(CIFAR-10任务) | ||
---|---|---|---|---|
训练时间/h | 最高精度/% | 训练时间/h | 最高精度/% | |
ARMOEA[ | 7.59 | 94.72 | 26.85 | 92.32 |
CMOEA-MS[ | 6.80 | 94.32 | 23.80 | 93.12 |
HeE-MOEA[ | 5.76 | 95.58 | 20.13 | 93.28 |
EDN- ARMOEA[ | 4.32 | 94.50 | 17.12 | 92.20 |
FEDA-ARMOEA | 4.02 | 96.16 | 16.36 | 93.79 |
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