Journal of Computer Applications ›› 2021, Vol. 41 ›› Issue (11): 3097-3103.DOI: 10.11772/j.issn.1001-9081.2020121895
• Artificial intelligence • Next Articles
Gangzhu QIAO1,2, Rui WANG1, Chaoli SUN1()
Received:
2020-12-04
Revised:
2021-08-07
Accepted:
2021-08-18
Online:
2021-11-20
Published:
2021-11-10
Contact:
Chaoli SUN
About author:
QIAO Gangzhu,born in 1975,Ph. D.,professor.His researchinterests include computational intelligence, deep learningSupported by:
通讯作者:
孙超利
作者简介:
乔钢柱(1975一),男,陕西汉阴人,教授,博士,CCF会员,主要研究方向:计算智能、深度学习基金资助:
CLC Number:
Gangzhu QIAO, Rui WANG, Chaoli SUN. Improved high-dimensional many-objective evolutionary algorithm based on decomposition[J]. Journal of Computer Applications, 2021, 41(11): 3097-3103.
乔钢柱, 王瑞, 孙超利. 基于分解的高维多目标改进进化算法[J]. 《计算机应用》唯一官方网站, 2021, 41(11): 3097-3103.
Add to citation manager EndNote|Ris|BibTeX
URL: http://www.joca.cn/EN/10.11772/j.issn.1001-9081.2020121895
问题 | 目标数 | RVEA | SPEA/R | RPDNSGA-II | |||
---|---|---|---|---|---|---|---|
平均值 | 标准差 | 平均值 | 标准差 | 平均值 | 标准差 | ||
MaF1 | 10 | 5.835 4E | 5.96E | 5.055 9E | 4.48E | 3.855 5E | 2.19E |
15 | 6.752 7E | 8.50E | 4.604 0E | 6.34E | 4.737 0E | 3.91E | |
MaF2 | 10 | 2.441 1E | 6.22E | 2.048 7E | 4.14E | 2.068 1E | 7.62E |
15 | 7.760 9E | 9.20E | 2.832 7E | 6.14E | 2.138 4E | 6.31E | |
MaF3 | 10 | 9.470 5E-2(-) | 3.08E | 7.354 8E+4(+) | 1.45E+5 | 4.137 0E | 1.69E |
15 | 9.943 6E-2(-) | 7.45E | 5.671 0E+5(+) | 8.42E+5 | 1.356 8E | 3.61E | |
MaF4 | 10 | 1.978 1E+2(≈) | 5.54E+1 | 2.040 4E+2(≈) | 1.08E+2 | 1.235 8E+2(-) | 1.34E+1 |
15 | 7.857 6E+3(≈) | 2.02E+3 | 7.422 6E+3( | 3.43E+3 | 4.925 8E+3(-) | 9.77E+2 | |
MaF5 | 10 | 9.673 3E+1( | 1.15E+1 | 8.019 6E+1( | 1.17E+0 | 6.658 2E+1(-) | 3.24E+0 |
15 | 3.612 8E+3( | 4.09E+2 | 2.851 6E+3( | 2.38E+2 | 2.887 9E+3( | 2.04E+2 | |
MaF6 | 10 | 1.111 3E | 2.25E | 1.962 7E+0(+) | 7.64E+0 | 2.602 7E | 1.09E |
15 | 2.254 8E | 1.67E | 4.813 2E+1(+) | 3.96E+1 | 4.409 3E | 1.83E | |
MaF7 | 10 | 2.540 1E+0(+) | 3.44E | 1.960 4E+0(+) | 2.42E | 1.463 8E+0(≈) | 1.40E |
15 | 2.661 5E+0(+) | 3.31E | 8.690 5E+0(+) | 5.66E | 6.691 7E+0(+) | 1.33E+0 | |
MaF8 | 10 | 9.453 5E | 1.32E | 1.800 6E+2(+) | 6.96E+2 | 6.728 9E | 1.13E |
15 | 1.180 2E+0(+) | 2.09E | 9.141 6E+2(+) | 1.98E+3 | 8.958 0E | 9.28E | |
MaF9 | 10 | 9.014 8E | 1.84E | 1.316 8E+0(+) | 3.65E | 5.572 2E | 8.93E |
15 | 1.676 4E+0(+) | 4.19E | 1.069 1E+1(+) | 9.16E+0 | 2.065 8E+0(+) | 3.41E+0 | |
MaF10 | 10 | 1.190 3E+0(≈) | 6.07E | 1.299 0E+0(≈) | 5.81E | 1.273 1E+0(≈) | 8.54E |
15 | 1.910 2E+0(-) | 1.66E | 2.532 6E+0(≈) | 1.63E | 2.260 2E+0( | 2.03E | |
MaF11 | 10 | 7.978 3E+0( | 2.82E+0 | 2.089 9E+0(-) | 3.80E | 3.035 1E+0( | 4.89E |
15 | 1.742 6E+1( | 4.02E+0 | 2.361 3E-1(-) | 3.28E | 7.775 6E | 1.30E+0 | |
MaF12 | 10 | 4.325 1E+0(-) | 2.56E | 4.521 3E+0(+) | 7.70E | 4.523 1E+0(+) | 8.45E |
15 | 9.166 4E+0( | 9.96E | 9.173 4E+0( | 2.04E | 9.149 2E+0(-) | 4.78E | |
MaF13 | 10 | 9.350 0E | 3.91E | 7.532 2E | 2.85E | 5.730 2E | 5.26E |
15 | 1.241 5E+0(+) | 4.39E | 8.297 3E | 3.43E | 7.571 9E | 2.01E | |
MaF14 | 10 | 9.919 0E | 4.43E | 1.169 9E+1(+) | 3.16E+0 | 3.067 6E+0(+) | 1.82E+0 |
15 | 2.137 1E+0(≈) | 2.37E+0 | 1.981 6E+1(+) | 5.57E+0 | 2.297 7E+0(≈) | 1.87E+0 | |
MaF15 | 10 | 1.012 9E+0( | 5.24E | 6.869 6E+0(≈) | 1.66E+0 | 1.037 7E+0( | 5.70E |
15 | 1.228 6E+0(-) | 5.55E | 1.844 8E+1(+) | 6.49E+0 | 3.032 8E+0(≈) | 1.17E+0 | |
+/≈/ | 14/4/12 | 18/6/6 | 16/5/9 | ||||
问题 | 目标数 | MOEA/DD | IMaOEA/D | ||||
平均值 | 标准差 | 平均值 | 标准差 | ||||
MaF1 | 10 | 4.592 0E | 2.98E | 3.486 3E-01 | 2.33E | ||
15 | 6.308 5E | 4.02E | 4.474 7E-1 | 2.47E | |||
MaF2 | 10 | 2.442 4E | 3.02E | 1.690 2E-1 | 3.46E | ||
15 | 3.358 9E | 2.58E | 2.088 7E-1 | 9.21E | |||
MaF3 | 10 | 1.180 8E | 7.48E | 9.511 1E | 4.88E | ||
15 | 2.936 2E | 8.07E | 1.244 5E | 7.96E | |||
MaF4 | 10 | 3.900 2E+2(+) | 1.29E+1 | 1.810 2E+2 | 3.02E+1 | ||
15 | 1.604 8E+4(+) | 2.31E+3 | 8.917 7E+3 | 1.94E+3 | |||
MaF5 | 10 | 2.885 9E+2(+) | 1.32E+1 | 2.709 4E+2 | 2.15E | ||
15 | 7.296 7E+3(+) | 5.24E+1 | 6.988 7E+3 | 1.94E+0 | |||
MaF6 | 10 | 1.033 6E | 2.27E | 8.932 2E-2 | 1.92E | ||
15 | 1.472 3E-1(≈) | 2.25E | 1.585 2E-1 | 9.49E | |||
MaF7 | 10 | 2.655 6E+0(+) | 4.61E | 1.459 2E+0 | 1.90E | ||
15 | 3.434 8E+0(+) | 1.02E | 2.543 1E+0 | 6.98E | |||
MaF8 | 10 | 9.074 8E | 2.53E | 4.439 9E-1 | 1.10E | ||
15 | 1.548 9E+0(+) | 1.56E | 5.256 9E-1 | 6.89E | |||
MaF9 | 10 | 5.936 5E | 3.58E | 4.088 5E-1 | 3.77E | ||
15 | 7.354 8E | 4.33E | 7.091 2E-1 | 1.28E | |||
MaF10 | 10 | 1.900 7E+0(+) | 4.76E | 1.317 4E+0 | 1.99E | ||
15 | 2.548 7E+0(≈) | 6.56E | 2.535 1E+0 | 2.49E | |||
MaF11 | 10 | 1.519 4E+1(+) | 5.18E | 1.358 3E+1 | 6.79E | ||
15 | 2.598 9E+1(+) | 4.06E | 2.454 8E+1 | 1.25E+0 | |||
MaF12 | 10 | 6.169 4E+0(+) | 3.41E | 4.374 7E+0 | 2.45E | ||
15 | 1.117 8E+1(+) | 5.74E | 9.623 3E+0 | 8.54E | |||
MaF13 | 10 | 3.776 4E-1(-) | 3.22E | 4.983 1E | 5.76E | ||
15 | 6.100 9E-1(-) | 1.12E | 4.04E | ||||
MaF14 | 10 | 9.525 2E-1(-) | 1.04E | 8.192 4E | 2.21E | ||
15 | 1.380 8E+0(≈) | 1.73E | 1.019 2E+0 | 7.88E | |||
MaF15 | 10 | 9.896 3E-1(-) | 3.65E | 1.718 3E+0 | 2.66E+00 | ||
15 | 1.292 4E+0( | 6.98E | 7.479 0E+0 | 6.34E+0 | |||
+/≈/ | 22/3/5 |
Tab. 1 IGD mean values and standard deviations obtained by different algorithms on MaF test problems with different dimensions of objectives
问题 | 目标数 | RVEA | SPEA/R | RPDNSGA-II | |||
---|---|---|---|---|---|---|---|
平均值 | 标准差 | 平均值 | 标准差 | 平均值 | 标准差 | ||
MaF1 | 10 | 5.835 4E | 5.96E | 5.055 9E | 4.48E | 3.855 5E | 2.19E |
15 | 6.752 7E | 8.50E | 4.604 0E | 6.34E | 4.737 0E | 3.91E | |
MaF2 | 10 | 2.441 1E | 6.22E | 2.048 7E | 4.14E | 2.068 1E | 7.62E |
15 | 7.760 9E | 9.20E | 2.832 7E | 6.14E | 2.138 4E | 6.31E | |
MaF3 | 10 | 9.470 5E-2(-) | 3.08E | 7.354 8E+4(+) | 1.45E+5 | 4.137 0E | 1.69E |
15 | 9.943 6E-2(-) | 7.45E | 5.671 0E+5(+) | 8.42E+5 | 1.356 8E | 3.61E | |
MaF4 | 10 | 1.978 1E+2(≈) | 5.54E+1 | 2.040 4E+2(≈) | 1.08E+2 | 1.235 8E+2(-) | 1.34E+1 |
15 | 7.857 6E+3(≈) | 2.02E+3 | 7.422 6E+3( | 3.43E+3 | 4.925 8E+3(-) | 9.77E+2 | |
MaF5 | 10 | 9.673 3E+1( | 1.15E+1 | 8.019 6E+1( | 1.17E+0 | 6.658 2E+1(-) | 3.24E+0 |
15 | 3.612 8E+3( | 4.09E+2 | 2.851 6E+3( | 2.38E+2 | 2.887 9E+3( | 2.04E+2 | |
MaF6 | 10 | 1.111 3E | 2.25E | 1.962 7E+0(+) | 7.64E+0 | 2.602 7E | 1.09E |
15 | 2.254 8E | 1.67E | 4.813 2E+1(+) | 3.96E+1 | 4.409 3E | 1.83E | |
MaF7 | 10 | 2.540 1E+0(+) | 3.44E | 1.960 4E+0(+) | 2.42E | 1.463 8E+0(≈) | 1.40E |
15 | 2.661 5E+0(+) | 3.31E | 8.690 5E+0(+) | 5.66E | 6.691 7E+0(+) | 1.33E+0 | |
MaF8 | 10 | 9.453 5E | 1.32E | 1.800 6E+2(+) | 6.96E+2 | 6.728 9E | 1.13E |
15 | 1.180 2E+0(+) | 2.09E | 9.141 6E+2(+) | 1.98E+3 | 8.958 0E | 9.28E | |
MaF9 | 10 | 9.014 8E | 1.84E | 1.316 8E+0(+) | 3.65E | 5.572 2E | 8.93E |
15 | 1.676 4E+0(+) | 4.19E | 1.069 1E+1(+) | 9.16E+0 | 2.065 8E+0(+) | 3.41E+0 | |
MaF10 | 10 | 1.190 3E+0(≈) | 6.07E | 1.299 0E+0(≈) | 5.81E | 1.273 1E+0(≈) | 8.54E |
15 | 1.910 2E+0(-) | 1.66E | 2.532 6E+0(≈) | 1.63E | 2.260 2E+0( | 2.03E | |
MaF11 | 10 | 7.978 3E+0( | 2.82E+0 | 2.089 9E+0(-) | 3.80E | 3.035 1E+0( | 4.89E |
15 | 1.742 6E+1( | 4.02E+0 | 2.361 3E-1(-) | 3.28E | 7.775 6E | 1.30E+0 | |
MaF12 | 10 | 4.325 1E+0(-) | 2.56E | 4.521 3E+0(+) | 7.70E | 4.523 1E+0(+) | 8.45E |
15 | 9.166 4E+0( | 9.96E | 9.173 4E+0( | 2.04E | 9.149 2E+0(-) | 4.78E | |
MaF13 | 10 | 9.350 0E | 3.91E | 7.532 2E | 2.85E | 5.730 2E | 5.26E |
15 | 1.241 5E+0(+) | 4.39E | 8.297 3E | 3.43E | 7.571 9E | 2.01E | |
MaF14 | 10 | 9.919 0E | 4.43E | 1.169 9E+1(+) | 3.16E+0 | 3.067 6E+0(+) | 1.82E+0 |
15 | 2.137 1E+0(≈) | 2.37E+0 | 1.981 6E+1(+) | 5.57E+0 | 2.297 7E+0(≈) | 1.87E+0 | |
MaF15 | 10 | 1.012 9E+0( | 5.24E | 6.869 6E+0(≈) | 1.66E+0 | 1.037 7E+0( | 5.70E |
15 | 1.228 6E+0(-) | 5.55E | 1.844 8E+1(+) | 6.49E+0 | 3.032 8E+0(≈) | 1.17E+0 | |
+/≈/ | 14/4/12 | 18/6/6 | 16/5/9 | ||||
问题 | 目标数 | MOEA/DD | IMaOEA/D | ||||
平均值 | 标准差 | 平均值 | 标准差 | ||||
MaF1 | 10 | 4.592 0E | 2.98E | 3.486 3E-01 | 2.33E | ||
15 | 6.308 5E | 4.02E | 4.474 7E-1 | 2.47E | |||
MaF2 | 10 | 2.442 4E | 3.02E | 1.690 2E-1 | 3.46E | ||
15 | 3.358 9E | 2.58E | 2.088 7E-1 | 9.21E | |||
MaF3 | 10 | 1.180 8E | 7.48E | 9.511 1E | 4.88E | ||
15 | 2.936 2E | 8.07E | 1.244 5E | 7.96E | |||
MaF4 | 10 | 3.900 2E+2(+) | 1.29E+1 | 1.810 2E+2 | 3.02E+1 | ||
15 | 1.604 8E+4(+) | 2.31E+3 | 8.917 7E+3 | 1.94E+3 | |||
MaF5 | 10 | 2.885 9E+2(+) | 1.32E+1 | 2.709 4E+2 | 2.15E | ||
15 | 7.296 7E+3(+) | 5.24E+1 | 6.988 7E+3 | 1.94E+0 | |||
MaF6 | 10 | 1.033 6E | 2.27E | 8.932 2E-2 | 1.92E | ||
15 | 1.472 3E-1(≈) | 2.25E | 1.585 2E-1 | 9.49E | |||
MaF7 | 10 | 2.655 6E+0(+) | 4.61E | 1.459 2E+0 | 1.90E | ||
15 | 3.434 8E+0(+) | 1.02E | 2.543 1E+0 | 6.98E | |||
MaF8 | 10 | 9.074 8E | 2.53E | 4.439 9E-1 | 1.10E | ||
15 | 1.548 9E+0(+) | 1.56E | 5.256 9E-1 | 6.89E | |||
MaF9 | 10 | 5.936 5E | 3.58E | 4.088 5E-1 | 3.77E | ||
15 | 7.354 8E | 4.33E | 7.091 2E-1 | 1.28E | |||
MaF10 | 10 | 1.900 7E+0(+) | 4.76E | 1.317 4E+0 | 1.99E | ||
15 | 2.548 7E+0(≈) | 6.56E | 2.535 1E+0 | 2.49E | |||
MaF11 | 10 | 1.519 4E+1(+) | 5.18E | 1.358 3E+1 | 6.79E | ||
15 | 2.598 9E+1(+) | 4.06E | 2.454 8E+1 | 1.25E+0 | |||
MaF12 | 10 | 6.169 4E+0(+) | 3.41E | 4.374 7E+0 | 2.45E | ||
15 | 1.117 8E+1(+) | 5.74E | 9.623 3E+0 | 8.54E | |||
MaF13 | 10 | 3.776 4E-1(-) | 3.22E | 4.983 1E | 5.76E | ||
15 | 6.100 9E-1(-) | 1.12E | 4.04E | ||||
MaF14 | 10 | 9.525 2E-1(-) | 1.04E | 8.192 4E | 2.21E | ||
15 | 1.380 8E+0(≈) | 1.73E | 1.019 2E+0 | 7.88E | |||
MaF15 | 10 | 9.896 3E-1(-) | 3.65E | 1.718 3E+0 | 2.66E+00 | ||
15 | 1.292 4E+0( | 6.98E | 7.479 0E+0 | 6.34E+0 | |||
+/≈/ | 22/3/5 |
1 | HAN Y Y, GONG D W, SUN X Y, et al. An improved NSGA-II algorithm for multi-objective lot-streaming flow shop scheduling problem [J]. International Journal of Production Research, 2014, 52(8): 2211-2231. 10.1080/00207543.2013.848492 |
2 | ZHANG Y, GONG D W, DING Z H. A bare-bones multi-objective particle swarm optimization algorithm for environmental/economic dispatch [J]. Information Sciences, 2012, 192: 213-227. 10.1016/j.ins.2011.06.004 |
3 | FARINA M, AMATO P. On the optimal solution definition for many-criteria optimization problems [C]// Proceedings of the 2002 Annual Meeting of the North American Fuzzy Information Processing Society. Piscataway: IEEE, 2002: 233-238. 10.1109/nafips.2002.1018061 |
4 | DEB K, PRATAP A, AGARWAL S, et al. A fast and elitist multiobjective genetic algorithm: NSGA-II [J]. IEEE Transactions on Evolutionary Computation, 2002, 6(2): 182-197. 10.1109/4235.996017 |
5 | WANG H, LIANG M N, SUN C L, et al. Multiple-strategy learning particle swarm optimization for large-scale optimization problems [J]. Complex and Intelligent Systems, 2020, 7(1): 1-16. 10.1007/s40747-020-00148-1 |
6 | ZHANG Q F, 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 |
7 | ZITZLER E, KÜNZLI S. Indicator-based selection in multiobjective search [C]// Proceedings of the 2004 International Conference on Parallel Problem Solving from Nature, LNCS3242. Berlin: Springer, 2004: 832-842. |
8 | ZHANG X Y, TIAN Y, JIN Y C. A knee point-driven evolutionary algorithm for many-objective optimization [J]. IEEE Transactions on Evolutionary Computation, 2015, 19(6): 761-776. 10.1109/tevc.2014.2378512 |
9 | LI M Q, YANG S X, LIU X H. Shift-based density estimation for Pareto-based algorithms in many-objective optimization [J]. IEEE Transactions on Evolutionary Computation, 2014, 18(3): 348-365. 10.1109/tevc.2013.2262178 |
10 | QASIM S Z, ISMAIL M A. RODE: ranking-dominance-based algorithm for many-objective optimization with opposition-based differential evolution [J]. Arabian Journal for Science and Engineering, 2020, 45(12): 10079-10096. 10.1007/s13369-020-04536-0 |
11 | 肖婧,毕晓君,王科俊.基于全局排序的高维多目标优化研究[J].软件学报,2015,26(7):1574-1583. 10.13328/j.cnki.jos.004612 |
XIAO J, BI X J, WANG K J. Research of global ranking based many-objective optimization [J]. Journal of Software, 2015, 26(7): 1574-1583. 10.13328/j.cnki.jos.004612 | |
12 | 谭阳,唐德权,曹守富.基于超球形模糊支配的高维多目标粒子群优化算法[J].计算机应用,2019,39(11):3233-3241. |
TAN Y, TANG D Q, CAO S F. Many-objective particle swarm optimization algorithm based on hyper-spherical fuzzy dominance [J]. Journal of Computer Applications, 2019, 39(11): 3233-3241. | |
13 | CHIANG T C, LAI Y P. MOEA/D-AMS: improving MOEA/D by an adaptive mating selection mechanism [C]// Proceedings of the 2011 IEEE Congress on Evolutionary Computation. Piscataway: IEEE, 2011: 1473-1480. 10.1109/cec.2011.5949789 |
14 | LIU H L, GU F Q, ZHANG Q F. Decomposition of a multiobjective optimization problem into a number of simple multiobjective subproblems [J]. IEEE Transactions on Evolutionary Computation, 2014, 18(3): 450-455. 10.1109/tevc.2013.2281533 |
15 | HE X Y, ZHOU Y R, CHEN Z F, et al. Evolutionary many-objective optimization based on dynamical decomposition [J]. IEEE Transactions on Evolutionary Computation, 2019, 23(3): 361-375. 10.1109/tevc.2018.2865590 |
16 | CHENG R, JIN Y C, OLHOFER M, et al. A reference vector guided evolutionary algorithm for many-objective optimization [J]. IEEE Transactions on Evolutionary Computation, 2016, 20(5): 773-791. 10.1109/tevc.2016.2519378 |
17 | QIN S F, SUN C L, ZHANG G C, et al. A modified particle swarm optimization based on decomposition with different ideal points for many-objective optimization problems [J]. Complex and Intelligent Systems, 2020, 6(2): 261-274. 10.1007/s40747-020-00134-7 |
18 | 巩敦卫,刘益萍,孙晓燕,等.基于目标分解的高维多目标并行进化优化方法[J].自动化学报,2015,41(8):1438-1451. 10.16383/j.aas.2015.c140832 |
GONG D W, LIU Y P, SUN X Y, et al. Parallel many-objective evolutionary optimization using objectives decomposition [J]. Acta Automatica Sinica, 2015, 41(8): 1438-1451. 10.16383/j.aas.2015.c140832 | |
19 | WHILE L, BRADSTREET L, BARONE L. A fast way of calculating exact hypervolumes [J]. IEEE Transactions on Evolutionary Computation, 2012, 16(1): 86-95. 10.1109/tevc.2010.2077298 |
20 | SUN Y N, YEN G G, YI Z. IGD indicator-based evolutionary algorithm for many-objective optimization problems [J]. IEEE Transactions on Evolutionary Computation, 2019, 23(2): 173-187. 10.1109/tevc.2018.2791283 |
21 | LIU Y P, GONG D W, SUN J, et al. A many-objective evolutionary algorithm using a one-by-one selection strategy [J]. IEEE Transactions on Cybernetics, 2017, 47(9): 2689-2702. 10.1109/tcyb.2016.2638902 |
22 | LI K, DEB K, ZHANG Q F, et al. An evolutionary many-objective optimization algorithm based on dominance and decomposition [J]. IEEE Transactions on Evolutionary Computation, 2015, 19(5): 694-716. 10.1109/tevc.2014.2373386 |
23 | DEB K, JAIN H. An evolutionary many-objective optimization algorithm using reference-point-based nondominated sorting approach, part I: solving problems with box constraints [J]. IEEE Transactions on Evolutionary Computation, 2014, 18(4): 577-601. 10.1109/tevc.2013.2281535 |
24 | LI M Q, YANG S X, LIU X H. Bi-goal evolution for many-objective optimization problems [J]. Artificial Intelligence, 2015, 228: 45-65. 10.1016/j.artint.2015.06.007 |
25 | 朱占磊,李征,赵瑞莲.基于线性权重最优支配的高维多目标优化算法[J].计算机应用,2017,37(10):2823-2827, 2865. 10.11772/j.issn.1001-9081.2017.10.2823 |
ZHU Z L, LI Z, ZHAO R L. Many-objective optimization algorithm based on linear weighted minimal/maximal dominance [J]. Journal of Computer Applications, 2017, 37(10): 2823-2827, 2865. 10.11772/j.issn.1001-9081.2017.10.2823 | |
26 | DEB K, AGRAWAL R B. Simulated binary crossover for continuous search space [J]. Complex Systems, 1995, 9(2): 115-148. 10.7135/upo9781843318118.005 |
27 | DEB K, GOYAL M. A combined Genetic Adaptive Search (GeneAS) for engineering design[J]. Computer Science and Informatics, 1996, 26(4):30-45. 10.1007/978-3-662-03423-1_27 |
28 | CHENG R, LI M Q, TIAN Y, et al. A benchmark test suite for evolutionary many-objective optimization [J]. Complex and Intelligent Systems, 2017, 3(1): 67-81. 10.1007/s40747-017-0039-7 |
29 | JIANG S Y, YANG S X. A strength Pareto evolutionary algorithm based on reference direction for multiobjective and many-objective optimization [J]. IEEE Transactions on Evolutionary Computation, 2017, 21(3): 329-346. 10.1109/tevc.2016.2592479 |
30 | ELARBI M, BECHIKH S, GUPTA A, et al. A new decomposition-based NSGA-II for many-objective optimization [J]. IEEE Transactions on Systems, Man, and Cybernetics: Systems, 2018, 48(7): 1191-1210. 10.1109/tsmc.2017.2654301 |
[1] | MAO Mingze, CAO Ruihao, YAN Chungang. Semi-supervised classification algorithm based on weight diversity [J]. Journal of Computer Applications, 2021, 41(9): 2473-2480. |
[2] | ZHU Liang, XU Hua, CUI Xin. Improved AdaBoost algorithm based on base classifier coefficients and diversity [J]. Journal of Computer Applications, 2021, 41(8): 2225-2231. |
[3] | WEI Bo, YANG Rong, SHU Sihao, WAN Yong, MIAO Jianguo. Path planning of mobile robots based on ion motion-artificial bee colony algorithm [J]. Journal of Computer Applications, 2021, 41(2): 379-383. |
[4] | LI Erchao, LI Kangwei. Decomposition based many-objective evolutionary algorithm based on minimum distance and aggregation strategy [J]. Journal of Computer Applications, 2021, 41(1): 22-28. |
[5] | LI Erchao, YANG Rongrong. Multi-objective estimation of distribution algorithm with adaptive opposition-based learning [J]. Journal of Computer Applications, 2021, 41(1): 15-21. |
[6] | LIU Jingshu, WANG Li, LIU Jinglei. Fast spectral clustering algorithm without eigen-decomposition [J]. Journal of Computer Applications, 2020, 40(12): 3413-3422. |
[7] | CHEN Weixing, LIU Qingtao, SUN Xixi, CHEN Bin. Fast convergence average TimeSynch algorithm for apron sensor network [J]. Journal of Computer Applications, 2020, 40(11): 3407-3412. |
[8] | FU Yu, WANG Hong. Virtual trajectory filling algorithm for location privacy protection [J]. Journal of Computer Applications, 2019, 39(8): 2318-2325. |
[9] | WEI Shanshan, HU Shengbo, YAN Tingting, MO Jinrong. Radio wave propagation characteristics and analysis software in troposphere based on split step wavelet method [J]. Journal of Computer Applications, 2019, 39(6): 1792-1798. |
[10] | TAN Yang, TANG Dequan, CAO Shoufu. Many-objective particle swarm optimization algorithm based on hyper-spherical fuzzy dominance [J]. Journal of Computer Applications, 2019, 39(11): 3233-3241. |
[11] | YUAN Xiaoping, JIANG Shuo. Improved particle swarm optimization algorithm based on hierarchical autonomous learning [J]. Journal of Computer Applications, 2019, 39(1): 148-153. |
[12] | LI Renmin, HUANG Jinsong, CHEN Chen, WU Junqin. Hybrid precoding scheme based on improved particle swarm optimization algorithm in mmWave massive MIMO system [J]. Journal of Computer Applications, 2018, 38(8): 2365-2369. |
[13] | GAO Huiyun, LU Huijuan, YAN Ke, YE Minchao. Selective ensemble algorithm for gene expression data based on diversity and accuracy of weighted harmonic average measure [J]. Journal of Computer Applications, 2018, 38(5): 1512-1516. |
[14] | WANG Yonggui, HU Caiyun, LI Xin. Perturbation particle swarm optimization algorithm based on local far-neighbor differential enhancement [J]. Journal of Computer Applications, 2018, 38(5): 1239-1244. |
[15] | ZHOU Haipeng, GAO Qin, JIANG Fengqian, YU Dawei, QIAO Yan, LI Yang. Application of self-adaptive chaotic quantum particle swarm algorithm in coverage optimization of wireless sensor network [J]. Journal of Computer Applications, 2018, 38(4): 1064-1071. |
Viewed | ||||||
Full text |
|
|||||
Abstract |
|
|||||