一种基于自适应模糊支配的高维多目标粒子群算法

余伟伟; 谢承旺; 闭应洲; 夏学文; 李雄; 任柯燕; 赵怀瑞; 王少锋

doi:10.16383/j.aas.2018.c170573

一种基于自适应模糊支配的高维多目标粒子群算法

doi: 10.16383/j.aas.2018.c170573

余伟伟^1,,
谢承旺^2, ,,
闭应洲^2,,
夏学文^3,,
李雄^3,,
任柯燕^1,,
赵怀瑞^4,,
王少锋^5,

1.
北京工业大学信息学部软件学院北京 100124
2.
广西师范学院科学计算与智能信息处理广西高校重点实验室南宁 530023
3.
华东交通大学软件学院南昌 330013
4.
华东交通大学机械与车辆工程学院南昌 330013
5.
华东交通大学土建学院南昌 330013

基金项目:

国家自然科学基金 61602174

国家自然科学基金 61663009

国家自然科学基金 51708221

国家自然科学基金 51465018

航空科学基金 20161375002

国家自然科学基金 61763010

科学计算与智能信息处理广西高校重点实验室开放课题 GXSCIIP201604

详细信息

作者简介:
余伟伟   北京工业大学信息学部软件学院硕士研究生.2012年获得华东交通大学软件学院学士学位.主要研究方向为智能计算与多目标优化E-mail:ecjtu_yuweiwei@163.com

闭应洲   广西师范学院计算机与信息工程学院教授.2008年获得武汉大学计算机软件与理论专业博士学位.主要研究方向为智能计算与自然语言处理.E-mail:byzhou@163.com

夏学文  华东交通大学软件学院副教授.2009年获得武汉大学计算机软件与理论专业博士学位.主要研究方向为计算智能及其应用.E-mail:xwxia@whu.edu.cn

李雄  华东交通大学软件学院讲师.2015年获得湖南大学计算机科学与技术专业博士学位.主要研究方向为数据挖掘, 机器学习, 生物信息处理.E-mail:lx_hncs@163.com

任柯燕   北京工业大学信息学部讲师.2011年获得北京邮电大学电气工程专业博士学位.主要研究方向为大规模场景目标检测, 跟踪与识别.E-mail:keyanren@bjut.edu.cn

赵怀瑞   华东交通大学机电与车辆工程学院讲师.2012年获得北京交通大学车辆工程专业博士学位.主要研究方向为空气动力学, 多学科设计优化和结构疲劳.E-mail:shiren@ecjtu.jx.cn

王少锋   华东交通大学土建学院讲师.2014年获得同济大学道路与铁道工程专业博士学位.主要研究方向为轮轨关系, 轨道损伤机理及维护.E-mail:hexieshehui@foxmail.com

通讯作者:
谢承旺广西师范学院计算机与信息工程学院副教授.2010年获得武汉大学计算机软件与理论专业博士学位.主要研究方向为智能计算, 多目标和高维多目标优化.本文通信作者.E-mail:chengwangxie@163.com

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出版历程
- 收稿日期: 2017-10-10
- 录用日期: 2018-03-06
- 刊出日期: 2018-12-20

Many-objective Particle Swarm Optimization Based on Adaptive Fuzzy Dominance

1.
School of Software Engineering, Beijing University of Technology, Beijing 100124
2.
Guangxi Colleges and Universities Key Laboratory Scientific Computing and Intelligent Information Processing, Guangxi Teachers Education University, Nanning 530023
3.
School of Software, East China Jiaotong University, Nanchang 330013
4.
School of Mechatronics & Vehicle Engineering, East China Jiaotong University, Nanchang 330013
5.
School of Civil Engineering and Architecture, East China Jiaotong University, Nanchang 330013

Funds:

National Natural Science Foundation of China 61602174

National Natural Science Foundation of China 61663009

National Natural Science Foundation of China 51708221

National Natural Science Foundation of China 51465018

Aeronautical Science Foundation of China 20161375002

National Natural Science Foundation of China 61763010

Science Computing and Intelligent Information Processing of Guangxi Higher Education Key Laboratory GXSCIIP201604

More Information

Author Bio:
Master student at the College of Computer Science and Technology, Dalian University of Technology. Her research interest covers computational intelligence and machine learning methods

   Professor at the School of Computer and Information Engineering, Guangxi Teachers Education University. He received his Ph. D. degree in computer software and theory from Wuhan University in 2008. His research interest covers intelligence computing and natural language processing

   Associate professor at the School of Software, East China Jiaotong University. He received his Ph. D. degree in computer software and theory from Wuhan University in 2009. His research interest covers computational intelligence techniques and their applications

Lecturer at the School of Software, East China Jiaotong University. He received his Ph. D. degree in computer science and technology from Hunan University in 2015. His research interest covers data mining, machine learning, and bioinformatics

Lecturer at the faculty of Information Technology, Beijing University of Technology. She received her Ph. D. degree in electrical engineering from the Beijing University of Posts and Telecommunications in 2011. Her research interest covers detection, tracking and recognition in a large scene

   Lecturer at the School of Mechatronics & Vechicle Engineering, East China Jiaotong University. He received his Ph. D. degree in vehicle engineering from Beijing Jiaotong University in 2012. His research interest covers aerodynamic, MDO, and structural fatigue

   Lecturer at the School of Civil Engineering and Architecture, East China Jiaotong University. He received his Ph. D. degree in highway & railway engineering from Tongji University in 2014. His research interest covers wheel-rail interaction damagement theory and maintenance of rail and track

Corresponding author: XIE Cheng-Wang Associate professor at the School of Computer and Information Engineering, Guangxi Teachers Education University. He received his Ph. D. degree in computer software and theory from Wuhan University in 2010. His research interest covers intelligence computing, multi-objective optimization, and many-objective optimization. Corresponding author of this paper

摘要

摘要: 高维多目标优化问题由于具有巨大的目标空间使得一些经典的多目标优化算法面临挑战.提出一种基于自适应模糊支配的高维多目标粒子群算法MAPSOAF，该算法定义了一种自适应的模糊支配关系，通过对模糊支配的阈值自适应变化若干步长，在加强个体间支配能力的同时实现对种群选择压力的精细化控制，以改善算法的收敛性；其次，通过从外部档案集中选取扰动粒子，并在粒子速度更新公式中新增一扰动项以克服粒子群早熟收敛并改善个体分布的均匀性；另外，算法利用简化的Harmonic归一化距离评估个体的密度，在改善种群分布性的同时降低算法的计算代价.该算法与另外五种高性能的多目标进化算法在标准测试函数集DTLZ{1，2，4，5}上进行对比实验，结果表明该算法在收敛性和多样性方面总体上具有较显著的性能优势.
- 自适应模糊支配 /
- 精英个体扰动 /
- 粒子群算法 /
- 高维多目标优化问题 /
- 高维多目标粒子群优化算法
Abstract: The huge objective space makes some representative multiobjective optimization algorithms face challenges. A many-objective particle swarm optimization based on adaptive fuzzy dominance (MAPSOAF) is proposed. An adaptive fuzzy dominance relation is defined to adjust the threshold of fuzzy dominance adaptively to improve the convergence of MAPSOAF. Second, a perturbation term is added to the particle's velocity formula by selecting an elite member from the external archive to conquer premature convergence and to enhance the diversity of population. In addition, a method of simplified Harmonic normalized distance is utilized to evaluate the density of individuals and reduce the computational cost when while improving the population diversity. MAPSOAF is compared with other five high-performance multiobjective evolutionary algorithms on the benchmark test set DTLZ {1, 2, 4, 5}, and the results show that the proposed MAPSOAF has more significant performance advantages in convergence and diversity over the peering algorithms.
- Adaptive fuzzy dominance /
- particle swarm optimization (PSO) /
- disturbance derived from elite individual /
- many-objective optimization problem /
- many-objective particle swarm optimization
注释:

1) 本文责任编委魏庆来

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图 1 多目标粒子群算法中粒子的速度更新示意图

Fig. 1 Velocity updation of particles in MOPSO

下载: 全尺寸图片幻灯片

图 2 增加扰动项之后算法中粒子的速度更新示意图

Fig. 2 Velocity updation of particles after adding turbulence item in MOSPO

下载: 全尺寸图片幻灯片

表 1 5种对比算法的参数设置

Table 1 Parameter settings of all the algorithms compared

Algorithm	Parameter settings
NSGA-II	${N}=100, P_{c}=0.9, P_{m}=1/n, \eta_{c}=20, \eta_{m}=20$
SPEA2	${N}=100, P_{c}=0.9, P_{m}=1/n, \eta_{c}=20, \eta_{m}=20$
SMPSO	${C}_1\in[1.5, 2.5], C_2\in[1.5, 2.5], P_{m}=1/n, \eta_{m}=20$
AbYSS	${N}=100, N_{RefSet1}=10, N_{RefSet2}=10, P_{c}=0.9, P_{m}=1/n, \eta_{c}=20, \eta_{m}=20$
MOEA/D-ACD	${N}=100, CR=1.0, F=0.5, P_{m}=1/n, \eta_{m}=20, \delta=0.9, n_{r}=2$

下载: 导出CSV

表 2 各算法在DTLZ1函数上获得IGD值的比较

Table 2 Results of IGD for algorithms compared based on DTLZ1

		各项指标	算法
		各项指标	NSGA-II	AbYSS	SPEA2	SMPSO	MOEA$/$D-ACD	MAPSOAF
目标个数	4目标	mean	2.0458E-01	9.5918E-02	1.7712E-01	7.8417E-02	3.4736E-01	8.2288E-02
		std	5.6012E-04	5.5421E-04	1.1871E-04	4.0001E-04	5.8170E-05	8.4901E-04
		rank	5 $-$	3 $-$	4 $-$	1 +	6 $-$	2
	10目标	mean	6.7936E-01	5.9651E-01	6.1816E-01	5.0051E-01	6.9881E-01	4.9810E-01
		std	4.9647E-04	7.5481E-04	3.6454E-04	4.7007E-04	4.4327E-05	7.5541E-04
		rank	5 $-$	3 $-$	4 $-$	2 $\approx$	6 $-$	1
	30目标	mean	7.9579E-01	7.8171E-01	7.7545E-01	7.4014E-01	8.0986E-01	6.5187E-01
		std	2.1294E-04	4.5699E-03	6.5441E-04	0.00E+00	2.9857E-04	5.3458E-03
		rank	5 $-$	3 $-$	4 $-$	2 $\approx$	6 $-$	1
rank sum			15	10	11	5	18	4
final rank			5	3	4	2	6	1
better$/$worst$/$similar			0$/3/$0	0$/3/$0	0$/3/$0	1$/1/$1	0$/3/$0	$/$

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表 3 各算法在DTLZ2函数上获得IGD值的比较

Table 3 Results of IGD for algorithms compared based on DTLZ2

		各项指标	算法
		各项指标	NSGA-II	AbYSS	SPEA2	SMPSO	MOEA$/$D-ACD	MAPSOAF
目标个数	4目标	mean	7.0109E-02	2.8412E-01	3.5341E-01	1.5415E-01	4.1627E-01	8.9241E-02
		std	5.1015E-04	7.1918E-04	6.8418E-04	4.5159E-04	1.8748E-04	4.6174E-04
		rank	1+	4 $-$	5 $-$	3 $-$	6 $-$	2
	10目标	mean	5.2851E-01	5.6171E-01	6.0151E-01	5.5241E-01	6.9741E-01	4.8169E-01
		std	5.6740E-04	6.9151E-04	5.9871E-04	5.1762E-04	3.5061E-04	5.5651E-04
		rank	2 $\approx$	4 $-$	5 $-$	3 $-$	6 $-$	1
	30目标	mean	7.5548E-01	7.8851E-01	7.8158E-01	7.7941E-01	7.9967E-01	6.9181E-01
		std	6.5141E-03	5.9210E-04	4.2225E-04	6.2131E-03	5.1101E-04	3.6518E-03
		rank	2 $-$	5 $-$	4 $-$	3 $-$	6 $-$	1
rank sum			5	13	14	9	18	4
final rank			2	4	5	3	6	1
better$/$worst$/$similar			1$/1/$1	0$/3/$0	0$/3/$0	0$/0/$0	0$/3/$0	$/$

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表 4 各算法在DTLZ4函数上获得IGD值的比较

Table 4 Results of IGD for algorithms compared based on DTLZ4

		各项指标	算法
		各项指标	NSGA-II	AbYSS	SPEA2	SMPSO	MOEA$/$D-ACD	MAPSOAF
目标个数	4目标	mean	8.3841E-02	2.1541E-01	2.6114E-01	1.5116E-01	7.1981E-02	7.9141E-02
		std	3.2987E-04	4.1123E-04	5.6101E-04	6.8917E-04	3.3176E-04	4.5005E-04
		rank	3 $\approx$	5 $-$	6 $-$	4 $-$	1+	2
	10目标	mean	5.8584E-01	6.5141E-01	6.9184E-01	6.6810E-01	5.4214E-01	5.9515E-01
		std	5.8771E-04	4.4414E-04	6.6516E-04	7.0151E-04	3.6011E-04	4.6001E-04
		rank	2 $\approx$	4 $-$	6 $-$	5 $-$	1+	3
	30目标	mean	7.5541E-01	8.2994E-01	8.0441E-01	8.1945E-01	7.0713E-01	7.9541E-01
		std	8.8151E-03	8.5104E-04	2.9414E-03	4.6054E-03	5.6807E-03	5.1112E-03
		rank	2 $-$	6 $-$	4 $-$	5 $-$	1+	3
rank sum			7	15	16	14	3	8
final rank			2	5	6	4	1	3
better$/$worst$/$similar			0$/2/$1	0$/3/$0	0$/3/$0	0$/3/$0	3$/0/$0	$/$

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表 5 各算法在DTLZ5函数上获得IGD值的比较

Table 5 Results of IGD for algorithms compared based on DTLZ5

		各项指标	算法
		各项指标	NSGA-II	AbYSS	SPEA2	SMPSO	MOEA$/$D-ACD	MAPSOAF
目标个数	4目标	mean	1.38121E-01	1.6051E-01	1.7717E-01	9.5651E-02	1.8678E-01	9.1410E-02
		std	5.6012E-04	5.5421E-04	1.1871E-04	4.0001E-04	5.8170E-05	8.4901E-04
		rank	3 $-$	4 $-$	5 $-$	2 $\approx$	6 $-$	1
	10目标	mean	6.5172E-01	7.1141E-01	7.0914E-01	6.9241E-01	7.2661E-01	5.0941E-01
		std	7.5615E-04	5.5551E-04	4.1191E-04	6.4101E-04	5.5827E-04	5.9151E-04
		rank	2 $\approx$	5 $-$	4 $-$	3 $-$	6 $-$	1
	30目标	mean	7.7141E-01	7.8810E-01	7.6585E-01	7.6151E-01	7.9841E-01	6.9510E-01
		std	3.4287E-03	8.8140E-04	3.9410E-03	4.6415E-03	8.2662E-04	4.6519E-03
		rank	4 $-$	5 $-$	3 $-$	2 $-$	6 $-$	1
rank sum			9	14	13	7	18	3
final rank			3	5	4	2	6	1
better$/$worst$/$similar			0$/2/$1	0$/3/$0	0$/3/$0	0$/3/$1	0$/3/$0	$/$

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参考文献(22)

[1]	Adra S F, Fleming P J. A diversity management operator for evolutionary many-objective optimisation. In: International Conference on Evolutionary Multi-Criterion Optimization. Berlin, Heidelberg, Germany: Springer-Verlag, 2009. 81-94
[2]	Wagner T, Beume N, Naujoks B. Pareto-, aggregation-, and indicator-based methods in many-objective optimization. In: International Conference on Evolutionary Multi-Criterion Optimization. Berlin, Heidelberg, Germany: Springer-Verlag, 2007. 742-756
[3]	Li M Q, Yang S X, Liu X H. Shift-based density estimation for Pareto-based algorithms in many-objective optimization. IEEE Transactions on Evolutionary Computation, 2014, 18(3):348-365 doi: 10.1109/TEVC.2013.2262178
[4]	陈振兴, 严宣辉, 吴坤安, 白猛.融合张角拥挤控制策略的高维多目标优化.自动化学报, 2015, 41(6):1145-1158 http://www.aas.net.cn/CN/abstract/abstract18689.shtml Chen Zhen-Xing, Yan Xuan-Hui, Wu Kun-An, Bai Meng. Many-objective optimization integrating open angle based congestion control strategy. Acta Automatica Sinica, 2015, 41(6):1145-1158 http://www.aas.net.cn/CN/abstract/abstract18689.shtml
[5]	巩敦卫, 刘益萍, 孙晓燕, 韩玉艳.基于目标分解的高维多目标并行进化优化方法.自动化学报, 2015, 41(8):1438-1451 http://www.aas.net.cn/CN/Y2015/V41/I8/1438 Gong Dun-Wei, Liu Yi-Ping, Sun Xiao-Yan, Han Yu-Yan. Parallel many-objective evolutionary optimization using objectives decomposition. Acta Automatica Sinica, 2015, 41(8):1438-1451 http://www.aas.net.cn/CN/Y2015/V41/I8/1438
[6]	Drechsler D, Drechsler R, Becker B. Multi-objective optimisation based on relation favour. In: Proceedings of the 1st International Conference on Evolutionary Multi-Criterion Optimization. London, UK: Springer-Verlag, 2001. 154-166
[7]	Di Pierro F, Djordjević S, Kapelan Z, Khu S T, Savić D, Walters G A. Automatic calibration of urban drainage model using a novel multi-objective genetic algorithm. Water Science and Technology, 2005, 52(5):43-52 doi: 10.2166/wst.2005.0105
[8]	Sato H, Aguirre H E, Tanaka K. Controlling dominance area of solutions and its impact on the performance of MOEAs. In: International Conference on Evolutionary Multi-Criterion Optimization, Lecture Notes in Computer Science, Vol.4403. Berlin, Germany: Springer, 2007. 5-20
[9]	Hernández-Díaz A, Santana-Quintero L, Coello-Coello C, Molina J. Pareto-adaptive ε-dominance. Evolutionary Computation, 2007, 15(4):493-517 doi: 10.1162/evco.2007.15.4.493
[10]	Kang Z, Kang L S, Zou X F, Liu M Z, Li C H, Yang M, et al. A new evolutionary decision theory for many-objective optimization problems. In: Advances in Computation and Intelligence. Berlin, Heidelberg, Germany: Springer, 2007. 1-11
[11]	Zou X F, Chen Y, Liu M Z, Kang L S. A new evolutionary algorithm for solving many-objective optimization problems. IEEE Transactions on Systems, Man, and Cybernetics-Part B:Cybernetics, 2008, 38(5):1402-1412 doi: 10.1109/TSMCB.2008.926329
[12]	Farina M, Amato P. A fuzzy definition of "optimality" for many-criterion optimization problems. IEEE Transactions on Systems, Man, and Cybernetics-Part A:Systems and Humans, 2004, 34(3):315-326 doi: 10.1109/TSMCA.2004.824873
[13]	毕晓君, 张永建, 陈春雨.基于模糊支配的高维多目标进化算法MFEA.电子学报, 2014, 42(8):1653-1659 doi: 10.3969/j.issn.0372-2112.2014.08.031 Bi Xiao-Jun, Zhang Yong-Jian, Chen Chun-Yu. A many-objective evolutionary algorithm based on fuzzy dominance:MFEA. Acta Electronica Sinica, 2014, 42(8):1653-1659 doi: 10.3969/j.issn.0372-2112.2014.08.031
[14]	Kennedy J, Eberhart R C. Particle swarm optimization. In: Proceedings of the 1995 IEEE International Conference on Neural Networks. Perth, WA, Australia: IEEE, 1995. 1942-1948
[15]	肖婧, 毕晓君, 王科俊.基于全局排序的高维多目标优化研究.软件学报, 2015, 26(7):1574-1583 http://d.old.wanfangdata.com.cn/Periodical/rjxb201507002 Xiao Jing, Bi Xiao-Jun, Wang Ke-Jun. Research of global ranking based many-objective optimization. Journal of Software, 2015, 26(7):1574-1583 http://d.old.wanfangdata.com.cn/Periodical/rjxb201507002
[16]	Deb K, Pratap A, Agarwal S, Meyarivan T. A fast and elitist multiobjective genetic algorithm:NSGA-Ⅱ. IEEE Transactions on Evolutionary Computation, 2002, 6(2):182-197 doi: 10.1109/4235.996017
[17]	Nebro A J, Luna F, Alba E, Dorronsoro B, Durillo J J, Beham A. AbYSS:adapting scatter search to multiobjective optimization. IEEE Transactions on Evolutionary Computation, 2008, 12(4):439-457 doi: 10.1109/TEVC.2007.913109
[18]	Zitzler E, Laumanns M, Thiele L. SPEA2: Improving the Strength Pareto Evolutionary Algorithm, TIK-Report 103, 2001.
[19]	Nebro A J, Durillo J J, Garcia-Nieto J, Coello Coello C A, Luna F, Alba E. SMPSO: a new PSO-based metaheuristic for multi-objective optimization. In: Proceedings of the 2009 IEEE Symposium on Computational Intelligence in Multi-Criteria Decision-Making (MCDM). Nashville, TN, USA, 2009, 66-73
[20]	Wang L P, Zhang Q F, Zhou A M, Gong M G, Jiao L C. Constrained subproblems in a decomposition-based multiobjective evolutionary algorithm. IEEE Transactions on Evolutionary Computation, 2016, 20(3):475-480 doi: 10.1109/TEVC.2015.2457616
[21]	Deb K, Thiele L, Laumanns M, Zitzler E. Scalable multi-objective optimization test problems. In: Proceedings of the 2002 IEEE Congress on Evolutionary Computation. Honolulu, HI, USA: IEEE, 2002. 825-830
[22]	Zhang Q F, Zhou A M, Zhao S Z, Suganthan P N, Liu W D, Tiwari S. Multiobjective Optimization Test Instances for the CEC 2009 Special Session and Competition, Technical Report CES-487, 2009.