Journal of Computer Applications ›› 2024, Vol. 44 ›› Issue (5): 1415-1422.DOI: 10.11772/j.issn.1001-9081.2023050696
Special Issue: 人工智能; 2023年中国计算机学会人工智能会议(CCFAI 2023)
• 2023 CCF Conference on Artificial Intelligence (CCFAI 2023) • Previous Articles Next Articles
Kaiwen ZHAO, Peng WANG(), Xiangrong TONG
Received:
2023-05-08
Revised:
2023-06-06
Accepted:
2023-06-08
Online:
2023-08-01
Published:
2024-05-10
Contact:
Peng WANG
About author:
ZHAO Kaiwen, born in 1997, M. S. candidate. His research interests include evolutionary computation, swarm intelligence algorithm.Supported by:
通讯作者:
王鹏
作者简介:
赵楷文(1997—),男,山东菏泽人,硕士研究生,主要研究方向:进化计算、群体智能算法基金资助:
CLC Number:
Kaiwen ZHAO, Peng WANG, Xiangrong TONG. Two-stage search-based constrained evolutionary multitasking optimization algorithm[J]. Journal of Computer Applications, 2024, 44(5): 1415-1422.
赵楷文, 王鹏, 童向荣. 基于双阶段搜索的约束进化多任务优化算法[J]. 《计算机应用》唯一官方网站, 2024, 44(5): 1415-1422.
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URL: https://www.joca.cn/EN/10.11772/j.issn.1001-9081.2023050696
测试问题 | C-TAEA | CMOEA-MS | MOEADDAE | ToP | EMCMO | TEMA | ||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|
平均值 | 标准差 | 平均值 | 标准差 | 平均值 | 标准差 | 平均值 | 标准差 | 平均值 | 标准差 | 平均值 | 标准差 | |
+/-/= | 0/8/1 | 2/5/2 | 0/9/0 | 0/8/1 | 3/4/2 | |||||||
DASCMOP1 | 1.42E-2 | 1.71E-2 | 7.79E-2 | 1.31E-1 | 5.94E-2 | 1.28E-1 | 2.53E-2 | 1.21E-1 | 1.24E-2 | 2.75E-2 | 3.27E-3 | 3.79E-4 |
DASCMOP2 | 7.48E-3 | 4.47E-4 | 8.11E-3 | 4.28E-3 | 5.52E-2 | 4.50E-2 | 5.00E-3 | 1.59E-4 | 1.33E-2 | 1.37E-2 | 3.95E-3 | 5.88E-5 |
DASCMOP3 | 2.90E-2 | 6.56E-3 | 1.12E-1 | 6.67E-2 | 6.76E-2 | 5.41E-2 | 1.15E-1 | 9.62E-2 | 4.28E-2 | 2.78E-2 | 2.85E-2 | 2.30E-2 |
DASCMOP4 | 1.16E-2 | 1.90E-3 | 2.52E-2 | 7.34E-2 | 1.30E-3 | 3.55E-5 | 6.24E-1 | 1.71E-1 | 9.85E-6 | 1.43E-5 | ||
DASCMOP5 | 7.61E-3 | 5.32E-4 | 3.64E-2 | 2.92E-2 | 3.08E-3 | 1.04E-4 | 5.92E-1 | 2.21E-1 | 2.92E-3 | 1.15E-4 | 2.77E-3 | 5.81E-5 |
DASCMOP6 | 2.57E-2 | 2.58E-3 | 2.03E-2 | 1.43E-2 | 1.96E-2 | 4.78E-3 | 6.89E-1 | 1.20E-1 | 1.77E-2 | 3.12E-3 | 1.66E-2 | 3.42E-3 |
DASCMOP7 | 5.93E-2 | 6.06E-3 | 7.47E-2 | 1.37E-1 | 3.50E-2 | 1.77E-3 | 4.61E-1 | 2.01E-1 | 3.13E-2 | 6.37E-4 | 3.19E-2 | 6.22E-4 |
DASCMOP8 | 9.38E-2 | 7.39E-3 | 3.96E-2 | 8.82E-4 | 4.58E-2 | 2.06E-3 | 5.88E-1 | 2.35E-1 | 3.94E-2 | 7.30E-4 | 4.11E-2 | 9.17E-4 |
DASCMOP9 | 9.52E-2 | 6.67E-3 | 4.06E-2 | 7.17E-4 | 6.61E-2 | 1.35E-2 | 6.22E-2 | 3.55E-3 | 4.02E-2 | 8.51E-4 | 4.20E-2 | 1.07E-3 |
Tab. 1 IGD results of TEMA and five comparison algorithms on DASCMOP
测试问题 | C-TAEA | CMOEA-MS | MOEADDAE | ToP | EMCMO | TEMA | ||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|
平均值 | 标准差 | 平均值 | 标准差 | 平均值 | 标准差 | 平均值 | 标准差 | 平均值 | 标准差 | 平均值 | 标准差 | |
+/-/= | 0/8/1 | 2/5/2 | 0/9/0 | 0/8/1 | 3/4/2 | |||||||
DASCMOP1 | 1.42E-2 | 1.71E-2 | 7.79E-2 | 1.31E-1 | 5.94E-2 | 1.28E-1 | 2.53E-2 | 1.21E-1 | 1.24E-2 | 2.75E-2 | 3.27E-3 | 3.79E-4 |
DASCMOP2 | 7.48E-3 | 4.47E-4 | 8.11E-3 | 4.28E-3 | 5.52E-2 | 4.50E-2 | 5.00E-3 | 1.59E-4 | 1.33E-2 | 1.37E-2 | 3.95E-3 | 5.88E-5 |
DASCMOP3 | 2.90E-2 | 6.56E-3 | 1.12E-1 | 6.67E-2 | 6.76E-2 | 5.41E-2 | 1.15E-1 | 9.62E-2 | 4.28E-2 | 2.78E-2 | 2.85E-2 | 2.30E-2 |
DASCMOP4 | 1.16E-2 | 1.90E-3 | 2.52E-2 | 7.34E-2 | 1.30E-3 | 3.55E-5 | 6.24E-1 | 1.71E-1 | 9.85E-6 | 1.43E-5 | ||
DASCMOP5 | 7.61E-3 | 5.32E-4 | 3.64E-2 | 2.92E-2 | 3.08E-3 | 1.04E-4 | 5.92E-1 | 2.21E-1 | 2.92E-3 | 1.15E-4 | 2.77E-3 | 5.81E-5 |
DASCMOP6 | 2.57E-2 | 2.58E-3 | 2.03E-2 | 1.43E-2 | 1.96E-2 | 4.78E-3 | 6.89E-1 | 1.20E-1 | 1.77E-2 | 3.12E-3 | 1.66E-2 | 3.42E-3 |
DASCMOP7 | 5.93E-2 | 6.06E-3 | 7.47E-2 | 1.37E-1 | 3.50E-2 | 1.77E-3 | 4.61E-1 | 2.01E-1 | 3.13E-2 | 6.37E-4 | 3.19E-2 | 6.22E-4 |
DASCMOP8 | 9.38E-2 | 7.39E-3 | 3.96E-2 | 8.82E-4 | 4.58E-2 | 2.06E-3 | 5.88E-1 | 2.35E-1 | 3.94E-2 | 7.30E-4 | 4.11E-2 | 9.17E-4 |
DASCMOP9 | 9.52E-2 | 6.67E-3 | 4.06E-2 | 7.17E-4 | 6.61E-2 | 1.35E-2 | 6.22E-2 | 3.55E-3 | 4.02E-2 | 8.51E-4 | 4.20E-2 | 1.07E-3 |
测试问题 | C-TAEA | CMOEA-MS | MOEADDAE | ToP | EMCMO | TEMA | ||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|
平均值 | 标准差 | 平均值 | 标准差 | 平均值 | 标准差 | 平均值 | 标准差 | 平均值 | 标准差 | 平均值 | 标准差 | |
+/-/= | 0/8/1 | 2/5/2 | 0/9/0 | 0/7/2 | 1/5/3 | |||||||
DASCMOP1 | 2.06E-1 | 7.06E-3 | 1.92E-1 | 2.77E-2 | 1.93E-1 | 4.29E-2 | 2.08E-1 | 2.53E-2 | 2.07E-1 | 7.06E-3 | 2.13E-1 | 3.82E-4 |
DASCMOP2 | 3.53E-1 | 3.53E-4 | 3.50E-1 | 4.82E-3 | 3.34E-1 | 1.76E-2 | 3.55E-1 | 9.41E-5 | 3.49E-1 | 6.19E-3 | 3.56E-1 | 4.20E-5 |
DASCMOP3 | 3.08E-1 | 3.77E-3 | 2.90E-1 | 1.33E-2 | 2.83E-1 | 1.63E-2 | 2.92E-1 | 2.36E-2 | 2.94E-1 | 1.02E-2 | 3.02E-1 | 1.13E-2 |
DASCMOP4 | 1.94E-1 | 4.25E-3 | 2.00E-1 | 1.21E-2 | 2.04E-1 | 4.80E-5 | 2.63E-2 | 3.96E-2 | 2.04E-1 | 2.09E-5 | 2.04E-1 | 2.29E-5 |
DASCMOP5 | 3.48E-1 | 4.17E-4 | 3.36E-1 | 1.58E-2 | 3.52E-1 | 1.14E-4 | 7.83E-2 | 7.95E-2 | 3.51E-1 | 2.38E-4 | 3.52E-1 | 1.04E-4 |
DASCMOP6 | 3.08E-1 | 1.20E-3 | 3.11E-1 | 4.04E-3 | 3.12E-1 | 3.46E-3 | 3.37E-2 | 4.69E-2 | 3.12E-1 | 2.96E-4 | 3.12E-1 | 2.14E-4 |
DASCMOP7 | 2.80E-1 | 1.33E-3 | 2.74E-1 | 4.19E-2 | 2.87E-1 | 6.55E-4 | 1.13E-1 | 6.51E-2 | 2.88E-1 | 3.44E-4 | 2.88E-1 | 5.27E-4 |
DASCMOP8 | 1.94E-1 | 1.75E-3 | 2.08E-1 | 3.69E-4 | 2.00E-1 | 7.21E-4 | 1.98E-1 | 4.58E-2 | 2.07E-1 | 4.92E-4 | 2.06E-1 | 5.51E-4 |
DASCMOP9 | 1.94E-1 | 1.44E-3 | 2.08E-1 | 3.85E-4 | 2.00E-1 | 3.95E-3 | 1.98E-1 | 1.21E-3 | 2.07E-1 | 2.54E-4 | 2.06E-1 | 2.61E-4 |
Tab. 2 HV results of TEMA and five comparison algorithms on DASCMOP
测试问题 | C-TAEA | CMOEA-MS | MOEADDAE | ToP | EMCMO | TEMA | ||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|
平均值 | 标准差 | 平均值 | 标准差 | 平均值 | 标准差 | 平均值 | 标准差 | 平均值 | 标准差 | 平均值 | 标准差 | |
+/-/= | 0/8/1 | 2/5/2 | 0/9/0 | 0/7/2 | 1/5/3 | |||||||
DASCMOP1 | 2.06E-1 | 7.06E-3 | 1.92E-1 | 2.77E-2 | 1.93E-1 | 4.29E-2 | 2.08E-1 | 2.53E-2 | 2.07E-1 | 7.06E-3 | 2.13E-1 | 3.82E-4 |
DASCMOP2 | 3.53E-1 | 3.53E-4 | 3.50E-1 | 4.82E-3 | 3.34E-1 | 1.76E-2 | 3.55E-1 | 9.41E-5 | 3.49E-1 | 6.19E-3 | 3.56E-1 | 4.20E-5 |
DASCMOP3 | 3.08E-1 | 3.77E-3 | 2.90E-1 | 1.33E-2 | 2.83E-1 | 1.63E-2 | 2.92E-1 | 2.36E-2 | 2.94E-1 | 1.02E-2 | 3.02E-1 | 1.13E-2 |
DASCMOP4 | 1.94E-1 | 4.25E-3 | 2.00E-1 | 1.21E-2 | 2.04E-1 | 4.80E-5 | 2.63E-2 | 3.96E-2 | 2.04E-1 | 2.09E-5 | 2.04E-1 | 2.29E-5 |
DASCMOP5 | 3.48E-1 | 4.17E-4 | 3.36E-1 | 1.58E-2 | 3.52E-1 | 1.14E-4 | 7.83E-2 | 7.95E-2 | 3.51E-1 | 2.38E-4 | 3.52E-1 | 1.04E-4 |
DASCMOP6 | 3.08E-1 | 1.20E-3 | 3.11E-1 | 4.04E-3 | 3.12E-1 | 3.46E-3 | 3.37E-2 | 4.69E-2 | 3.12E-1 | 2.96E-4 | 3.12E-1 | 2.14E-4 |
DASCMOP7 | 2.80E-1 | 1.33E-3 | 2.74E-1 | 4.19E-2 | 2.87E-1 | 6.55E-4 | 1.13E-1 | 6.51E-2 | 2.88E-1 | 3.44E-4 | 2.88E-1 | 5.27E-4 |
DASCMOP8 | 1.94E-1 | 1.75E-3 | 2.08E-1 | 3.69E-4 | 2.00E-1 | 7.21E-4 | 1.98E-1 | 4.58E-2 | 2.07E-1 | 4.92E-4 | 2.06E-1 | 5.51E-4 |
DASCMOP9 | 1.94E-1 | 1.44E-3 | 2.08E-1 | 3.85E-4 | 2.00E-1 | 3.95E-3 | 1.98E-1 | 1.21E-3 | 2.07E-1 | 2.54E-4 | 2.06E-1 | 2.61E-4 |
测试问题 | C-TAEA | CMOEA-MS | MOEADDAE | ToP | EMCMO | TEMA | ||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|
平均值 | 标准差 | 平均值 | 标准差 | 平均值 | 标准差 | 平均值 | 标准差 | 平均值 | 标准差 | 平均值 | 标准差 | |
+/-/= | 1/13/0 | 2/8/4 | 5/9/0 | 1/12/1 | 4/7/3 | |||||||
LIRCMOP1 | 2.46E-1 | 1.27E-1 | 4.08E-1 | 1.37E-1 | 2.37E-1 | 1.65E-1 | 1.07E-1 | 1.05E-1 | 1.28E-1 | 6.38E-2 | 2.28E-2 | 6.02E-3 |
LIRCMOP2 | 7.03E-2 | 2.40E-2 | 2.72E-1 | 8.98E-2 | 1.61E-1 | 1.24E-1 | 1.48E-1 | 1.03E-1 | 7.28E-2 | 3.75E-2 | 2.16E-2 | 4.95E-3 |
LIRCMOP3 | 2.45E-1 | 1.47E-1 | 3.18E-1 | 6.86E-2 | 1.08E-1 | 8.97E-2 | 3.62E-1 | 5.35E-2 | 1.31E-1 | 3.84E-2 | 3.24E-2 | 9.71E-3 |
LIRCMOP4 | 1.58E-1 | 9.87E-2 | 3.26E-1 | 1.08E-1 | 4.69E-2 | 2.64E-2 | 3.23E-1 | 3.78E-2 | 1.46E-1 | 5.59E-2 | 2.65E-2 | 1.09E-2 |
LIRCMOP5 | 8.46E-2 | 2.15E-2 | 1.29E-2 | 1.36E-2 | 5.57E-2 | 1.92E-2 | 1.69E-1 | 3.96E-1 | 7.00E-3 | 1.83E-3 | 1.08E-2 | 1.04E-2 |
LIRCMOP6 | 1.42E-1 | 1.23E-1 | 1.51E-2 | 2.76E-2 | 4.96E-2 | 3.56E-2 | 5.36E-2 | 1.01E-1 | 6.10E-3 | 3.60E-4 | 5.70E-3 | 2.96E-4 |
LIRCMOP7 | 2.12E-2 | 8.42E-3 | 2.02E-2 | 3.38E-2 | 7.32E-2 | 1.88E-2 | 8.66E-3 | 3.18E-4 | 7.60E-3 | 6.33E-4 | 7.31E-3 | 3.81E-4 |
LIRCMOP8 | 1.79E-2 | 5.04E-3 | 1.21E-2 | 2.68E-2 | 8.64E-2 | 4.58E-2 | 8.75E-3 | 3.17E-4 | 7.20E-3 | 2.13E-4 | 7.12E-3 | 5.95E-4 |
LIRCMOP9 | 6.74E-2 | 2.67E-2 | 2.42E-1 | 1.46E-1 | 3.27E-3 | 1.17E-4 | 3.08E-1 | 1.37E-1 | 5.49E-3 | 2.21E-3 | 1.45E-1 | 7.35E-2 |
LIRCMOP10 | 7.63E-2 | 7.94E-2 | 7.54E-2 | 6.46E-2 | 4.77E-3 | 1.90E-4 | 5.54E-3 | 2.63E-4 | 4.81E-3 | 2.39E-4 | 9.80E-3 | 2.05E-2 |
LIRCMOP11 | 1.36E-1 | 3.59E-2 | 8.29E-2 | 8.49E-2 | 2.51E-3 | 2.18E-4 | 1.39E-1 | 8.46E-2 | 2.39E-3 | 6.87E-5 | 2.38E-3 | 5.43E-5 |
LIRCMOP12 | 1.65E-2 | 6.10E-3 | 4.20E-2 | 5.35E-2 | 3.21E-3 | 1.61E-4 | 5.35E-2 | 6.29E-2 | 3.08E-3 | 8.69E-5 | 6.15E-3 | 1.23E-2 |
LIRCMOP13 | 1.09E-1 | 1.87E-3 | 9.25E-2 | 8.47E-4 | 9.75E-2 | 9.91E-4 | 1.27E-1 | 3.75E-3 | 9.10E-2 | 5.14E-4 | 9.94E-2 | 1.33E-3 |
LIRCMOP14 | 1.11E-1 | 7.89E-4 | 9.49E-2 | 9.17E-4 | 9.92E-2 | 5.83E-4 | 1.20E-1 | 3.57E-3 | 9.57E-2 | 8.73E-4 | 1.01E-1 | 9.89E-4 |
Tab. 3 IGD results of TEMA and four comparison algorithms on LIRCMOP
测试问题 | C-TAEA | CMOEA-MS | MOEADDAE | ToP | EMCMO | TEMA | ||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|
平均值 | 标准差 | 平均值 | 标准差 | 平均值 | 标准差 | 平均值 | 标准差 | 平均值 | 标准差 | 平均值 | 标准差 | |
+/-/= | 1/13/0 | 2/8/4 | 5/9/0 | 1/12/1 | 4/7/3 | |||||||
LIRCMOP1 | 2.46E-1 | 1.27E-1 | 4.08E-1 | 1.37E-1 | 2.37E-1 | 1.65E-1 | 1.07E-1 | 1.05E-1 | 1.28E-1 | 6.38E-2 | 2.28E-2 | 6.02E-3 |
LIRCMOP2 | 7.03E-2 | 2.40E-2 | 2.72E-1 | 8.98E-2 | 1.61E-1 | 1.24E-1 | 1.48E-1 | 1.03E-1 | 7.28E-2 | 3.75E-2 | 2.16E-2 | 4.95E-3 |
LIRCMOP3 | 2.45E-1 | 1.47E-1 | 3.18E-1 | 6.86E-2 | 1.08E-1 | 8.97E-2 | 3.62E-1 | 5.35E-2 | 1.31E-1 | 3.84E-2 | 3.24E-2 | 9.71E-3 |
LIRCMOP4 | 1.58E-1 | 9.87E-2 | 3.26E-1 | 1.08E-1 | 4.69E-2 | 2.64E-2 | 3.23E-1 | 3.78E-2 | 1.46E-1 | 5.59E-2 | 2.65E-2 | 1.09E-2 |
LIRCMOP5 | 8.46E-2 | 2.15E-2 | 1.29E-2 | 1.36E-2 | 5.57E-2 | 1.92E-2 | 1.69E-1 | 3.96E-1 | 7.00E-3 | 1.83E-3 | 1.08E-2 | 1.04E-2 |
LIRCMOP6 | 1.42E-1 | 1.23E-1 | 1.51E-2 | 2.76E-2 | 4.96E-2 | 3.56E-2 | 5.36E-2 | 1.01E-1 | 6.10E-3 | 3.60E-4 | 5.70E-3 | 2.96E-4 |
LIRCMOP7 | 2.12E-2 | 8.42E-3 | 2.02E-2 | 3.38E-2 | 7.32E-2 | 1.88E-2 | 8.66E-3 | 3.18E-4 | 7.60E-3 | 6.33E-4 | 7.31E-3 | 3.81E-4 |
LIRCMOP8 | 1.79E-2 | 5.04E-3 | 1.21E-2 | 2.68E-2 | 8.64E-2 | 4.58E-2 | 8.75E-3 | 3.17E-4 | 7.20E-3 | 2.13E-4 | 7.12E-3 | 5.95E-4 |
LIRCMOP9 | 6.74E-2 | 2.67E-2 | 2.42E-1 | 1.46E-1 | 3.27E-3 | 1.17E-4 | 3.08E-1 | 1.37E-1 | 5.49E-3 | 2.21E-3 | 1.45E-1 | 7.35E-2 |
LIRCMOP10 | 7.63E-2 | 7.94E-2 | 7.54E-2 | 6.46E-2 | 4.77E-3 | 1.90E-4 | 5.54E-3 | 2.63E-4 | 4.81E-3 | 2.39E-4 | 9.80E-3 | 2.05E-2 |
LIRCMOP11 | 1.36E-1 | 3.59E-2 | 8.29E-2 | 8.49E-2 | 2.51E-3 | 2.18E-4 | 1.39E-1 | 8.46E-2 | 2.39E-3 | 6.87E-5 | 2.38E-3 | 5.43E-5 |
LIRCMOP12 | 1.65E-2 | 6.10E-3 | 4.20E-2 | 5.35E-2 | 3.21E-3 | 1.61E-4 | 5.35E-2 | 6.29E-2 | 3.08E-3 | 8.69E-5 | 6.15E-3 | 1.23E-2 |
LIRCMOP13 | 1.09E-1 | 1.87E-3 | 9.25E-2 | 8.47E-4 | 9.75E-2 | 9.91E-4 | 1.27E-1 | 3.75E-3 | 9.10E-2 | 5.14E-4 | 9.94E-2 | 1.33E-3 |
LIRCMOP14 | 1.11E-1 | 7.89E-4 | 9.49E-2 | 9.17E-4 | 9.92E-2 | 5.83E-4 | 1.20E-1 | 3.57E-3 | 9.57E-2 | 8.73E-4 | 1.01E-1 | 9.89E-4 |
测试问题 | C-TAEA | CMOEA-MS | MOEADDAE | ToP | EMCMO | TEMA | ||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|
平均值 | 标准差 | 平均值 | 标准差 | 平均值 | 标准差 | 平均值 | 标准差 | 平均值 | 标准差 | 平均值 | 标准差 | |
+/-/= | 0/13/1 | 2/9/3 | 5/9/0 | 1/12/1 | 5/6/3 | |||||||
LIRCMOP1 | 1.37E-1 | 4.01E-2 | 1.08E-1 | 2.04E-2 | 1.49E-1 | 4.78E-2 | 1.90E-1 | 3.14E-2 | 1.74E-1 | 2.19E-2 | 2.31E-1 | 2.26E-3 |
LIRCMOP2 | 3.22E-1 | 1.46E-2 | 2.36E-1 | 3.60E-2 | 2.82E-1 | 5.85E-2 | 2.85E-1 | 5.02E-2 | 3.20E-1 | 2.06E-2 | 3.52E-1 | 2.56E-3 |
LIRCMOP3 | 1.27E-1 | 3.07E-2 | 1.01E-1 | 2.11E-2 | 1.75E-1 | 2.60E-2 | 9.29E-2 | 1.22E-2 | 1.54E-1 | 1.58E-2 | 1.99E-1 | 3.82E-3 |
LIRCMOP4 | 2.37E-1 | 4.92E-2 | 1.86E-1 | 4.28E-2 | 2.95E-1 | 1.34E-2 | 1.78E-1 | 2.30E-2 | 2.51E-1 | 2.38E-2 | 3.06E-1 | 4.26E-3 |
LIRCMOP5 | 2.62E-1 | 8.45E-3 | 2.88E-1 | 4.56E-3 | 2.61E-1 | 1.02E-2 | 2.50E-1 | 1.01E-1 | 2.91E-1 | 1.11E-3 | 2.89E-1 | 3.69E-3 |
LIRCMOP6 | 1.54E-1 | 3.27E-2 | 1.94E-1 | 7.41E-3 | 1.82E-1 | 8.60E-3 | 1.78E-1 | 3.85E-2 | 1.87E-4 | 2.31E-4 | ||
LIRCMOP7 | 2.87E-1 | 4.35E-3 | 2.89E-1 | 1.30E-2 | 2.62E-1 | 6.68E-3 | 2.94E-1 | 1.40E-4 | 2.94E-1 | 6.21E-4 | 2.93E-1 | 5.40E-4 |
LIRCMOP8 | 2.90E-1 | 3.44E-3 | 2.93E-1 | 1.02E-2 | 2.61E-1 | 1.13E-2 | 2.94E-1 | 1.85E-4 | 2.95E-1 | 9.43E-5 | 2.94E-1 | 1.01E-3 |
LIRCMOP9 | 5.28E-1 | 1.06E-2 | 4.75E-1 | 6.24E-2 | 5.68E-1 | 1.00E-4 | 4.76E-1 | 4.06E-2 | 5.65E-1 | 1.47E-3 | 5.28E-1 | 2.18E-2 |
LIRCMOP10 | 6.67E-1 | 3.35E-2 | 6.78E-1 | 3.10E-2 | 7.08E-1 | 7.60E-5 | 7.07E-1 | 1.34E-4 | 7.08E-1 | 1.68E-4 | 7.06E-1 | 7.70E-3 |
LIRCMOP11 | 6.42E-1 | 1.58E-2 | 6.54E-1 | 5.68E-2 | 6.94E-1 | 1.21E-4 | 6.06E-1 | 5.46E-2 | 6.94E-1 | 2.21E-5 | 6.94E-1 | 9.29E-6 |
LIRCMOP12 | 6.13E-1 | 1.80E-3 | 6.06E-1 | 2.60E-2 | 6.20E-1 | 2.65E-5 | 5.97E-1 | 2.93E-2 | 6.20E-1 | 1.70E-5 | 6.19E-1 | 3.93E-3 |
LIRCMOP13 | 5.47E-1 | 1.26E-3 | 5.56E-1 | 1.41E-3 | 5.55E-1 | 1.53E-3 | 5.13E-1 | 3.26E-3 | 5.59E-1 | 1.18E-3 | 5.48E-1 | 1.94E-3 |
LIRCMOP14 | 5.47E-1 | 6.47E-4 | 5.55E-1 | 1.23E-3 | 5.54E-1 | 1.52E-3 | 5.27E-1 | 3.89E-3 | 5.54E-1 | 1.65E-3 | 5.50E-1 | 1.62E-3 |
Tab. 4 HV results of TEMA and four comparison algorithms on LIRCMOP
测试问题 | C-TAEA | CMOEA-MS | MOEADDAE | ToP | EMCMO | TEMA | ||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|
平均值 | 标准差 | 平均值 | 标准差 | 平均值 | 标准差 | 平均值 | 标准差 | 平均值 | 标准差 | 平均值 | 标准差 | |
+/-/= | 0/13/1 | 2/9/3 | 5/9/0 | 1/12/1 | 5/6/3 | |||||||
LIRCMOP1 | 1.37E-1 | 4.01E-2 | 1.08E-1 | 2.04E-2 | 1.49E-1 | 4.78E-2 | 1.90E-1 | 3.14E-2 | 1.74E-1 | 2.19E-2 | 2.31E-1 | 2.26E-3 |
LIRCMOP2 | 3.22E-1 | 1.46E-2 | 2.36E-1 | 3.60E-2 | 2.82E-1 | 5.85E-2 | 2.85E-1 | 5.02E-2 | 3.20E-1 | 2.06E-2 | 3.52E-1 | 2.56E-3 |
LIRCMOP3 | 1.27E-1 | 3.07E-2 | 1.01E-1 | 2.11E-2 | 1.75E-1 | 2.60E-2 | 9.29E-2 | 1.22E-2 | 1.54E-1 | 1.58E-2 | 1.99E-1 | 3.82E-3 |
LIRCMOP4 | 2.37E-1 | 4.92E-2 | 1.86E-1 | 4.28E-2 | 2.95E-1 | 1.34E-2 | 1.78E-1 | 2.30E-2 | 2.51E-1 | 2.38E-2 | 3.06E-1 | 4.26E-3 |
LIRCMOP5 | 2.62E-1 | 8.45E-3 | 2.88E-1 | 4.56E-3 | 2.61E-1 | 1.02E-2 | 2.50E-1 | 1.01E-1 | 2.91E-1 | 1.11E-3 | 2.89E-1 | 3.69E-3 |
LIRCMOP6 | 1.54E-1 | 3.27E-2 | 1.94E-1 | 7.41E-3 | 1.82E-1 | 8.60E-3 | 1.78E-1 | 3.85E-2 | 1.87E-4 | 2.31E-4 | ||
LIRCMOP7 | 2.87E-1 | 4.35E-3 | 2.89E-1 | 1.30E-2 | 2.62E-1 | 6.68E-3 | 2.94E-1 | 1.40E-4 | 2.94E-1 | 6.21E-4 | 2.93E-1 | 5.40E-4 |
LIRCMOP8 | 2.90E-1 | 3.44E-3 | 2.93E-1 | 1.02E-2 | 2.61E-1 | 1.13E-2 | 2.94E-1 | 1.85E-4 | 2.95E-1 | 9.43E-5 | 2.94E-1 | 1.01E-3 |
LIRCMOP9 | 5.28E-1 | 1.06E-2 | 4.75E-1 | 6.24E-2 | 5.68E-1 | 1.00E-4 | 4.76E-1 | 4.06E-2 | 5.65E-1 | 1.47E-3 | 5.28E-1 | 2.18E-2 |
LIRCMOP10 | 6.67E-1 | 3.35E-2 | 6.78E-1 | 3.10E-2 | 7.08E-1 | 7.60E-5 | 7.07E-1 | 1.34E-4 | 7.08E-1 | 1.68E-4 | 7.06E-1 | 7.70E-3 |
LIRCMOP11 | 6.42E-1 | 1.58E-2 | 6.54E-1 | 5.68E-2 | 6.94E-1 | 1.21E-4 | 6.06E-1 | 5.46E-2 | 6.94E-1 | 2.21E-5 | 6.94E-1 | 9.29E-6 |
LIRCMOP12 | 6.13E-1 | 1.80E-3 | 6.06E-1 | 2.60E-2 | 6.20E-1 | 2.65E-5 | 5.97E-1 | 2.93E-2 | 6.20E-1 | 1.70E-5 | 6.19E-1 | 3.93E-3 |
LIRCMOP13 | 5.47E-1 | 1.26E-3 | 5.56E-1 | 1.41E-3 | 5.55E-1 | 1.53E-3 | 5.13E-1 | 3.26E-3 | 5.59E-1 | 1.18E-3 | 5.48E-1 | 1.94E-3 |
LIRCMOP14 | 5.47E-1 | 6.47E-4 | 5.55E-1 | 1.23E-3 | 5.54E-1 | 1.52E-3 | 5.27E-1 | 3.89E-3 | 5.54E-1 | 1.65E-3 | 5.50E-1 | 1.62E-3 |
与TEMA对比 的算法 | IGD | HV | ||
---|---|---|---|---|
Wilcoxon检验(-/+/=) | Friedman检验平均排名 | Wilcoxon检验(-/+/=) | Friedman检验平均排名 | |
TEMA | — | 1.891 3 | — | 2.195 7 |
C-TAEA | 21/1/1 | 4.347 8 | 21/0/2 | 4.413 0 |
CMOEA-MS | 13/4/6 | 4.217 4 | 14/4/5 | 4.087 0 |
MOEADDAE | 18/5/0 | 3.565 2 | 18/5/0 | 3.434 8 |
ToP | 20/1/2 | 4.913 0 | 19/1/3 | 4.652 2 |
EMCMO | 11/7/5 | 2.065 2 | 11/6/6 | 2.217 4 |
Tab. 5 Wilcoxon’s test results and Friedman test mean ranks on two benchmark test suites
与TEMA对比 的算法 | IGD | HV | ||
---|---|---|---|---|
Wilcoxon检验(-/+/=) | Friedman检验平均排名 | Wilcoxon检验(-/+/=) | Friedman检验平均排名 | |
TEMA | — | 1.891 3 | — | 2.195 7 |
C-TAEA | 21/1/1 | 4.347 8 | 21/0/2 | 4.413 0 |
CMOEA-MS | 13/4/6 | 4.217 4 | 14/4/5 | 4.087 0 |
MOEADDAE | 18/5/0 | 3.565 2 | 18/5/0 | 3.434 8 |
ToP | 20/1/2 | 4.913 0 | 19/1/3 | 4.652 2 |
EMCMO | 11/7/5 | 2.065 2 | 11/6/6 | 2.217 4 |
与TEMA对比 的算法 | IGD | HV | ||||
---|---|---|---|---|---|---|
R+ | R- | P值 | R+ | R- | P值 | |
C-TAEA | 258.0 | 18.0 | 0.000 25 | 245.0 | 8.0 | 0.000 06 |
CMOEA-MS | 258.0 | 18.0 | 0.005 39 | 247.0 | 29.0 | 0.000 69 |
MOEADDAE | 229.0 | 47.0 | 0.000 04 | 218.5 | 57.5 | 0.013 05 |
ToP | 272.0 | 4.0 | 0.000 04 | 249.0 | 4.0 | 0.000 05 |
EMCMO | 148.0 | 105.0 | 0.475 08 | 138.5 | 114.5 | 0.634 60 |
Tab. 6 Multi-problem Wilcoxon’s test results on two benchmark test suites
与TEMA对比 的算法 | IGD | HV | ||||
---|---|---|---|---|---|---|
R+ | R- | P值 | R+ | R- | P值 | |
C-TAEA | 258.0 | 18.0 | 0.000 25 | 245.0 | 8.0 | 0.000 06 |
CMOEA-MS | 258.0 | 18.0 | 0.005 39 | 247.0 | 29.0 | 0.000 69 |
MOEADDAE | 229.0 | 47.0 | 0.000 04 | 218.5 | 57.5 | 0.013 05 |
ToP | 272.0 | 4.0 | 0.000 04 | 249.0 | 4.0 | 0.000 05 |
EMCMO | 148.0 | 105.0 | 0.475 08 | 138.5 | 114.5 | 0.634 60 |
测试问题 | TEMA-1 | TEMA-2 | TEMA | |||
---|---|---|---|---|---|---|
平均值 | 标准差 | 平均值 | 标准差 | 平均值 | 标准差 | |
+/-/= | 3/6/5 | 3/7/4 | ||||
LIRCMOP1 | 1.89E-1 | 9.33E-2 | 3.38E-1 | 2.14E-1 | 2.28E-2 | 6.02E-3 |
LIRCMOP2 | 6.96E-2 | 3.47E-2 | 7.97E-2 | 3.26E-2 | 2.16E-2 | 4.95E-3 |
LIRCMOP3 | 1.72E-1 | 6.91E-2 | 1.66E-1 | 8.88E-2 | 3.24E-2 | 9.71E-3 |
LIRCMOP4 | 1.43E-1 | 6.37E-2 | 1.20E-1 | 8.47E-2 | 2.65E-2 | 1.09E-2 |
LIRCMOP5 | 6.92E-3 | 1.94E-3 | 8.35E-3 | 3.74E-3 | 1.08E-2 | 1.04E-2 |
LIRCMOP6 | 6.06E-3 | 3.66E-4 | 7.21E-3 | 2.82E-3 | 5.70E-3 | 2.96E-4 |
LIRCMOP7 | 7.51E-3 | 5.64E-4 | 8.00E-3 | 1.88E-3 | 7.31E-3 | 3.81E-4 |
LIRCMOP8 | 7.19E-3 | 1.91E-4 | 7.27E-3 | 3.30E-4 | 7.12E-3 | 5.95E-4 |
LIRCMOP9 | 5.02E-3 | 1.79E-3 | 3.12E-2 | 3.48E-2 | 1.45E-1 | 7.35E-2 |
LIRCMOP10 | 4.69E-3 | 2.04E-4 | 4.60E-3 | 1.36E-4 | 9.80E-3 | 2.05E-2 |
LIRCMOP11 | 2.38E-3 | 5.27E-5 | 2.38E-3 | 5.41E-5 | 2.38E-3 | 5.43E-5 |
LIRCMOP12 | 3.05E-3 | 7.16E-5 | 3.01E-3 | 7.00E-5 | 6.15E-3 | 1.23E-2 |
LIRCMOP13 | 9.80E-2 | 1.01E-3 | 9.82E-2 | 1.03E-3 | 9.94E-2 | 1.33E-3 |
LIRCMOP14 | 1.01E-1 | 1.04E-3 | 1.01E-1 | 1.19E-3 | 1.01E-1 | 9.89E-4 |
Tab. 7 IGD results for TEMA and two variant algorithms on LIRCMOP
测试问题 | TEMA-1 | TEMA-2 | TEMA | |||
---|---|---|---|---|---|---|
平均值 | 标准差 | 平均值 | 标准差 | 平均值 | 标准差 | |
+/-/= | 3/6/5 | 3/7/4 | ||||
LIRCMOP1 | 1.89E-1 | 9.33E-2 | 3.38E-1 | 2.14E-1 | 2.28E-2 | 6.02E-3 |
LIRCMOP2 | 6.96E-2 | 3.47E-2 | 7.97E-2 | 3.26E-2 | 2.16E-2 | 4.95E-3 |
LIRCMOP3 | 1.72E-1 | 6.91E-2 | 1.66E-1 | 8.88E-2 | 3.24E-2 | 9.71E-3 |
LIRCMOP4 | 1.43E-1 | 6.37E-2 | 1.20E-1 | 8.47E-2 | 2.65E-2 | 1.09E-2 |
LIRCMOP5 | 6.92E-3 | 1.94E-3 | 8.35E-3 | 3.74E-3 | 1.08E-2 | 1.04E-2 |
LIRCMOP6 | 6.06E-3 | 3.66E-4 | 7.21E-3 | 2.82E-3 | 5.70E-3 | 2.96E-4 |
LIRCMOP7 | 7.51E-3 | 5.64E-4 | 8.00E-3 | 1.88E-3 | 7.31E-3 | 3.81E-4 |
LIRCMOP8 | 7.19E-3 | 1.91E-4 | 7.27E-3 | 3.30E-4 | 7.12E-3 | 5.95E-4 |
LIRCMOP9 | 5.02E-3 | 1.79E-3 | 3.12E-2 | 3.48E-2 | 1.45E-1 | 7.35E-2 |
LIRCMOP10 | 4.69E-3 | 2.04E-4 | 4.60E-3 | 1.36E-4 | 9.80E-3 | 2.05E-2 |
LIRCMOP11 | 2.38E-3 | 5.27E-5 | 2.38E-3 | 5.41E-5 | 2.38E-3 | 5.43E-5 |
LIRCMOP12 | 3.05E-3 | 7.16E-5 | 3.01E-3 | 7.00E-5 | 6.15E-3 | 1.23E-2 |
LIRCMOP13 | 9.80E-2 | 1.01E-3 | 9.82E-2 | 1.03E-3 | 9.94E-2 | 1.33E-3 |
LIRCMOP14 | 1.01E-1 | 1.04E-3 | 1.01E-1 | 1.19E-3 | 1.01E-1 | 9.89E-4 |
测试问题 | TEMA-1 | TEMA-2 | TEMA | |||
---|---|---|---|---|---|---|
平均值 | 标准差 | 平均值 | 标准差 | 平均值 | 标准差 | |
+/-/= | 0/4/5 | 0/4/5 | ||||
DASCMOP1 | 6.99E-3 | 4.53E-3 | 6.57E-3 | 4.45E-3 | 3.27E-3 | 3.79E-4 |
DASCMOP2 | 1.82E-2 | 2.03E-2 | 2.01E-2 | 2.61E-2 | 3.95E-3 | 5.88E-5 |
DASCMOP3 | 4.63E-2 | 3.39E-2 | 7.95E-2 | 5.14E-2 | 2.85E-2 | 2.30E-2 |
DASCMOP4 | 1.14E-3 | 9.38E-6 | 1.14E-3 | 8.85E-6 | 1.14E-3 | 1.43E-5 |
DASCMOP5 | 2.80E-3 | 1.07E-4 | 2.77E-3 | 8.70E-5 | 2.77E-3 | 5.81E-5 |
DASCMOP6 | 1.83E-2 | 2.73E-3 | 1.89E-2 | 5.34E-3 | 1.66E-2 | 3.42E-3 |
DASCMOP7 | 3.17E-2 | 8.90E-4 | 3.17E-2 | 6.25E-4 | 3.19E-2 | 6.22E-4 |
DASCMOP8 | 4.10E-2 | 1.00E-3 | 4.11E-2 | 1.03E-3 | 4.11E-2 | 9.17E-4 |
DASCMOP9 | 4.15E-2 | 8.11E-4 | 4.18E-2 | 9.14E-4 | 4.20E-2 | 1.07E-3 |
Tab. 8 IGD results for TEMA and two variant algorithms on DASCMOP
测试问题 | TEMA-1 | TEMA-2 | TEMA | |||
---|---|---|---|---|---|---|
平均值 | 标准差 | 平均值 | 标准差 | 平均值 | 标准差 | |
+/-/= | 0/4/5 | 0/4/5 | ||||
DASCMOP1 | 6.99E-3 | 4.53E-3 | 6.57E-3 | 4.45E-3 | 3.27E-3 | 3.79E-4 |
DASCMOP2 | 1.82E-2 | 2.03E-2 | 2.01E-2 | 2.61E-2 | 3.95E-3 | 5.88E-5 |
DASCMOP3 | 4.63E-2 | 3.39E-2 | 7.95E-2 | 5.14E-2 | 2.85E-2 | 2.30E-2 |
DASCMOP4 | 1.14E-3 | 9.38E-6 | 1.14E-3 | 8.85E-6 | 1.14E-3 | 1.43E-5 |
DASCMOP5 | 2.80E-3 | 1.07E-4 | 2.77E-3 | 8.70E-5 | 2.77E-3 | 5.81E-5 |
DASCMOP6 | 1.83E-2 | 2.73E-3 | 1.89E-2 | 5.34E-3 | 1.66E-2 | 3.42E-3 |
DASCMOP7 | 3.17E-2 | 8.90E-4 | 3.17E-2 | 6.25E-4 | 3.19E-2 | 6.22E-4 |
DASCMOP8 | 4.10E-2 | 1.00E-3 | 4.11E-2 | 1.03E-3 | 4.11E-2 | 9.17E-4 |
DASCMOP9 | 4.15E-2 | 8.11E-4 | 4.18E-2 | 9.14E-4 | 4.20E-2 | 1.07E-3 |
1 | LIN H. Multi‐objective optimization of cordon sanitaire with vehicle waiting time constraint[J]. IET Intelligent Transport Systems, 2021, 15(7): 929-940. 10.1049/itr2.12072 |
2 | LEVI Y, BEKHOR S, ROSENFELD Y. A multi-objective optimization model for urban planning: the case of a very large floating structure[J]. Transportation Research Part C: Emerging Technologies, 2019, 98: 85-100. 10.1016/j.trc.2018.11.013 |
3 | M-F LEUNG, WANG J. Cardinality-constrained portfolio selection based on collaborative neurodynamic optimization[J]. Neural Networks, 2022, 145: 68-79. 10.1016/j.neunet.2021.10.007 |
4 | HASANZADEH R, MOJAVER P, CHITSAZ A, et al. Analysis of variance and multi-objective optimization of efficiencies and emission in air/steam rigid and flexible polyurethane foam wastes gasification[J]. Chemical Engineering and Processing — Process Intensification, 2022, 176: 108961. 10.1016/j.cep.2022.108961 |
5 | LIANG J, BAN X, YU K, et al. A survey on evolutionary constrained multiobjective optimization[J]. IEEE Transactions on Evolutionary Computation, 2023, 27(2): 201-221. 10.1109/tevc.2022.3155533 |
6 | 王峰,张衡,韩孟臣,等.基于协同进化的混合变量多目标粒子群优化算法求解无人机协同多任务分配问题[J].计算机学报, 2021,44(10):1967-1983. 10.11897/SP.J.1016.2021.01967 |
WANG F, ZHANG H, HAN M C, et al. Co-evolution based mixed-variable multi-objective particle swarm optimization for UAV cooperative multi-task allocation problem[J]. Chinese Journal of Computers, 2021, 44(10): 1967-1983. 10.11897/SP.J.1016.2021.01967 | |
7 | 陈晓纪,石川,周爱民,等.混合个体选择机制的多目标进化算法[J].软件学报,2019,30(12):3651-3664. |
CHEN X J, SHI C, ZHOU A M, et al. Multiobjective evolutionary algorithm based on hybrid individual selection mechanism[J]. Journal of Software, 2019, 30(12): 3651-3664. | |
8 | LI W, ZHANG T, WANG R, et al. Weighted indicator-based evolutionary algorithm for multimodal multiobjective optimization[J]. IEEE Transactions on Evolutionary Computation, 2021, 25(6): 1064-1078. 10.1109/tevc.2021.3078441 |
9 | YUAN J, LIU H-L, Y-S ONG, et al. Indicator-based evolutionary algorithm for solving constrained multiobjective optimization problems[J]. IEEE Transactions on Evolutionary Computation, 2022, 26(2): 379-391. 10.1109/tevc.2021.3089155 |
10 | WANG C, XU R. An angle based evolutionary algorithm with infeasibility information for constrained many-objective optimization[J]. Applied Soft Computing, 2020, 86: 105911. 10.1016/j.asoc.2019.105911 |
11 | 张磊,毕晓君,王艳娇.基于重新匹配策略的ε约束多目标分解优化算法[J].电子学报,2018,46(5):1032-1040. 10.3969/j.issn.0372-2112.2018.05.002 |
ZHANG L, BI X J, WANG Y J. The ε constrained multi-objective decomposition optimization algorithm based on re-matching strategy[J]. Acta Electronica Sinica, 2018, 46(5): 1032-1040. 10.3969/j.issn.0372-2112.2018.05.002 | |
12 | MING M, TRIVEDI A, WANG R, et al. A dual-population-based evolutionary algorithm for constrained multiobjective optimization[J]. IEEE Transactions on Evolutionary Computation, 2021, 25(4): 739-753. 10.1109/tevc.2021.3066301 |
13 | 陈少淼,陈瑞,梁伟,等.面向复杂约束优化问题的进化算法综述[J].软件学报,2023,34(2):565-581. |
CHEN S M, CHEN R, LIANG W, et al. Overview of evolutionary algorithms for complex constrained optimization problems[J]. Journal of Software, 2023, 34(2): 565-581. | |
14 | 李豪,汪磊,张元侨,等.演化多任务优化研究综述[J].软件学报,2023,34(2):509-538. 10.1109/tevc.2022.3141819 |
LI H, WANG L, ZHANG Y Q, et al. Survey of evolutionary multitasking optimization[J]. Journal of Software, 2023, 34(2): 509-538. 10.1109/tevc.2022.3141819 | |
15 | DEB K. Multi-objective optimisation using evolutionary algorithms: an introduction[M]// Multi-objective Optimisation for Product Design and Manufacturing. London: Springer, 2011: 3-34. 10.1007/978-0-85729-652-8_1 |
16 | SANTANA-QUINTERO L V, HERNÁNDEZ-DÍAZ A G, MOLINA J, et al. DEMORS: a hybrid multi-objective optimization algorithm using differential evolution and rough set theory for constrained problems[J]. Computers & Operations Research, 2010, 37(3): 470-480. 10.1016/j.cor.2009.02.006 |
17 | LIU Z-Z, WANG Y. Handling constrained multiobjective optimization problems with constraints in both the decision and objective spaces[J]. IEEE Transactions on Evolutionary Computation, 2019, 23(5): 870-884. 10.1109/tevc.2019.2894743 |
18 | FAN Z, LI W, CAI X, et al. Push and pull search for solving constrained multi-objective optimization problems[J]. Swarm and Evolutionary Computation, 2019, 44: 665-679. 10.1016/j.swevo.2018.08.017 |
19 | YU K, LIANG J, QU B, et al. Purpose-directed two-phase multiobjective differential evolution for constrained multiobjective optimization[J]. Swarm and Evolutionary Computation, 2021, 60: 100799. 10.1016/j.swevo.2020.100799 |
20 | TIAN Y, ZHANG Y, SU Y, et al. Balancing objective optimization and constraint satisfaction in constrained evolutionary multiobjective optimization[J]. IEEE Transactions on Cybernetics, 2022, 52(9): 9559-9572. 10.1109/tcyb.2020.3021138 |
21 | MING F, GONG W, ZHEN H, et al. A simple two-stage evolutionary algorithm for constrained multi-objective optimization[J]. Knowledge-Based Systems, 2021, 228: 107263. 10.1016/j.knosys.2021.107263 |
22 | WANG J, LIANG G, ZHANG J. Cooperative differential evolution framework for constrained multiobjective optimization[J]. IEEE Transactions on Cybernetics, 2019, 49(6): 2060-2072. 10.1109/tcyb.2018.2819208 |
23 | YANG Y, LIU J, TAN S. A partition-based constrained multi-objective evolutionary algorithm[J]. Swarm and Evolutionary Computation, 2021, 66: 100940. 10.1016/j.swevo.2021.100940 |
24 | LI K, CHEN R, FU G, et al. Two-archive evolutionary algorithm for constrained multiobjective optimization[J]. IEEE Transactions on Evolutionary Computation, 2019, 23(2): 303-315. 10.1109/tevc.2018.2855411 |
25 | TIAN Y, ZHANG T, XIAO J, et al. A coevolutionary framework for constrained multiobjective optimization problems[J]. IEEE Transactions on Evolutionary Computation, 2021, 25(1): 102-116. 10.1109/tevc.2020.3004012 |
26 | LIU Z-Z, WANG B-C, TANG K. Handling constrained multiobjective optimization problems via bidirectional coevolution[J]. IEEE Transactions on Cybernetics, 2022, 52(10): 10163-10176. 10.1109/tcyb.2021.3056176 |
27 | ZITZLER E, LAUMANNS M, THIELE L. SPEA2: improving the strength Pareto evolutionary algorithm: TIK Report 103[R/OL]. [2023-05-01]. . |
28 | ZHANG Q, LI H. MOEA/D: a multiobjective evolutionary algorithm based on decomposition[J]. IEEE Transactions on Evolutionary Computation, 2007, 11(6): 712-731. 10.1109/tevc.2007.892759 |
29 | FAN Z, LI W, CAI X, et al. Difficulty adjustable and scalable constrained multiobjective test problem toolkit[J]. Evolutionary Computation, 2020, 28(3): 339-378. 10.1162/evco_a_00259 |
30 | FAN Z, LI W, CAI X, et al. An improved epsilon constraint-handling method in MOEA/D for CMOPs with large infeasible regions[J]. Soft Computing, 2019, 23: 12491-12510. 10.1007/s00500-019-03794-x |
31 | BOSMAN P A N, THIERENS D. The balance between proximity and diversity in multiobjective evolutionary algorithms[J]. IEEE Transactions on Evolutionary Computation, 2003, 7(2): 174-188. 10.1109/tevc.2003.810761 |
32 | ZITZLER E, THIELE L. Multiobjective evolutionary algorithms: a comparative case study and the strength Pareto approach[J]. IEEE Transactions on Evolutionary Computation, 1999, 3(4): 257-271. 10.1109/4235.797969 |
33 | ZHU Q, ZHANG Q, LIN Q. A constrained multiobjective evolutionary algorithm with detect-and-escape strategy[J]. IEEE Transactions on Evolutionary Computation, 2020, 24(5): 938-947. 10.1109/tevc.2020.2981949 |
34 | QIAO K, YU K, QU B, et al. An evolutionary multitasking optimization framework for constrained multiobjective optimization problems[J]. IEEE Transactions on Evolutionary Computation, 2022, 26(2): 263-277. 10.1109/tevc.2022.3145582 |
35 | TIAN Y, CHENG R, ZHANG X, et al. PlatEMO: a Matlab platform for evolutionary multi-objective optimization [educational forum] [J]. IEEE Computational Intelligence Magazine, 2017, 12(4): 73-87. 10.1109/mci.2017.2742868 |
36 | PRICE K V, STORN R M, LAMPINEN J A. Differential Evolution: A Practical Approach to Global Optimization[M]. Heidelberg: Springer, 2005. 10.1007/978-3-540-39930-8_6 |
37 | DEB K, AGRAWAL R. Simulated binary crossover for continuous search space[J]. Complex Systems, 1995, 9(2): 115-148. |
38 | DEB K, GOYAL M. A combined Genetic Adaptive Search (GeneAS) for engineering design[J]. Journal of Computer Science and Informatics, 1996, 26: 30-45. |
39 | ALCALÁ-FDEZ J, SÁNCHEZ L, GARCÍA S, et al. KEEL: a software tool to assess evolutionary algorithms for data mining problems[J]. Soft Computing, 2009, 13: 307-318. 10.1007/s00500-008-0323-y |
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