摘要
群体智能优化算法是一种近年来新兴的优化方法,是受到关注最多的优化研究领域之一,其模拟社会性动物的各种群体行为,利用群体中的个体之间的信息交互和合作来实现寻优的目的。与其它类型的优化方法相比,其实现较为简单、效率较高。
粒子群优化算法(Particle Swarm Optimization,PSO算法)源于鸟群和鱼群群体运动行为的研究,是一种新的群体智能优化算法,是演化计算领域中的一个新的分支。它的主要特点是原理简单、参数少、收敛速度较快,所需领域知识少。具有量子行为的粒子群优化(Quantum-behaved Particle Swarm Optimization,QPSO)算法是在深入研究PSO算法单个粒子收敛行为的基础上,受量子物理学的启发而提出,QPSO算法具有控制参数更少,收敛速度快,全局搜索能力强等特点。
本文以PSO算法与QPSO算法的理论分析及改进方法研究为重点,系统的研究了QPSO算法及其改进算法在相关方面的应用,具体内容如下:
(1)从最优化问题概念及其求解方法入手,阐述了智能智能优化算法研究背景,详细介绍了几种常见的智能优化算法;通过阐述了没有免费午餐定理,说明了本文研究的基础;针对PSO算法的缺陷,提出了本课题的立题依据、研究目标、研究内容以及研究思路与方法。
(2)首先介绍了PSO算法的基本原理与基本流程,详细讨论了两种重要的改进算法:带权重的PSO算法和带压缩因子的PSO算法;阐述了QPSO算法的思想来源,给出了QPSO算法的设计思路。分析了随机算法收敛的两个判断准则,即全局搜索算法的收敛准则与局部搜索算法的收敛准则,利用这两个收敛准则作为依据,证明了QPSO算法是一个全局搜索的随机算法;对QPSO算法和PSO算法从算法本身的角度做了比较,说明QPSO的特点;最后尝试在QPSO算法中引入一种新的变异机制,提出了基于云模型变异的量子粒子群优化算法(QPSO-NCM),从而增加种群的多样性,提高算法跳出陷入局部寻优的能力,进一步增强全局搜索能力。变异操作能够增加群体的多样性,使得算法具有突跳的能力,进入新的搜索区域。
(3)针对QPSO算法在解决多峰优化问题中也可能出现局部收敛的现象,分析了出局部收敛的主要原因在于群体多样性较低而使得群体失去了在大范围内进行搜索的能力,通过使用物种形成策略的概念,结合QPSO算法提出了一种SQPSO(The Species-Based QPSO)算法,将粒子群系统中的粒子根据相似度进行划分,用来实现对多峰函数的优化。通过对静态多峰环境和动态多峰环境的测试仿真证明,改进后的算法全局搜索能力和局部搜索能力均得到很大提升。
(4)为了可以克服最小二乘法难于处理的时滞在线辨识,在QPSO算法中引入单神经元结构,提高算法的局部搜索能力,实现线性离散系统的在线辨识。改进QPSO算法收敛速度快,窗口长度更小,更适用于实时要求比较高的在线辨识应用。在时变时滞系统在线辨识的仿真结果也验证了改进QPSO算法具有很好的跟踪能力和稳定性,更适合实际的工程。通过引入接纳时间比控制机制,提出并设计了一种基于QPSO算法在线辨识的自适应反馈控制方法,实现了动态调整QoS的性能控制。
(5)将QPSO算法分别用于混沌系统、周期系统和稳定系统中的参数辨识研究,通过仿真实验验证了QPSO算法在系统参数辨识中比PSO算法和GA算法具有更好的性能。对于存在噪声的混沌系统,提出基于QPSO算法的在线参数辨识并证明了该方法的有效性。
(6) QPSO算法在故障诊断方面的研究。智能故障诊断技术是人工智能和故障诊断相结合的产物,通过人工的方法使用计算机模拟人类专家对复杂系统进行诊断。单一径向基(RBF)神经网络是一种性能良好的前向网络,其既有生物背景,又与函数逼近理论相配,适合于多变量函数逼近。用遗传算法优化RBF神经网络结构和权重等参数的方法具有一定的有效性,但遗传算法复杂的遗传操作(如选择、交叉、变异)使神经网络的训练时间随问题规模及复杂程度的增大而呈指数级增长。针对这些问题采用基于QPSO算法优化的RBF神经网络,进行故障进行诊断,可以有效地提高故障的正辩率。
论文最后对所做工作与主要研究成果进行了总结,并提出了进一步的研究方向。
Swarm Intelligent (SI) algorithm is an algorithmic approach, which has gradually attracted more attention. To achieve the purpose of optimizing, SI simulated social behavior of various groups of animals and the individuals in the groups exchange information and cooperate each other. Compared with other optimization algorithms SI is easier to performe and more efficient.
Particle swarm optimization (PSO) is an evolutionary computation technique developed by Dr. Kennedy and Dr. Eberhart in1995, inspired by social behavior of bird flocking or fish schooling. PSO is simple in concept, few in parameters, and easy in implementation. It was proved to be an efficient method to solve optimization problems. Based on the deep study of PSO algorithm and inspired by quantum physics, Quantum-behaved Particle Swarm Optimization (QPSO) algorithm is proposed. QPSO algorithm has much less parameters and much stronger global search ability than the PSO algorithm.
Theoretical analyses and algorithm improving on PSO algorithm and QPSO algorithm are mainly discussed in our work and the application of QPSO algorithm are also studied in this work. The main contents of this dissertation are as follows:
1. The concept of optimization problem and its solution are introduced to explain the research background of the swarm intelligence algorithm and several common intelligent optimization algorithms are described in detail. The basis of our study is illustrated by the no free lunch theorem. Against the defects of PSO algorithm, the research objectives, research content, research ideas and methods in the work are proposed.
2. After the principle and procedure of PSO algorithm is presented, two important versions, PSO with inertia weight and PSO with contraction coefficient, are discussed. Some improved PSO methods are also mentioned for reference. The thought of QPSO algorithm is discussed. Convergence criteria of random search algorithms are introduced, including global convergence criteria and local convergence criteria. Based on these two convergence criteria, QPSO algorithm is proven to be a global search stochastic algorithm. By comparing QPSO algorithm and PSO algorithm, the characteristics of QPSO are indicated. Finally try to introduce a new mutation mechanism in the QPSO algorithm and the quantum-behaved particle swarm optimization based on cloud model mutation (QPSO-NCM) is proposed to increase the diversity of the population and improve the ability of the algorithm to fall into local optimization so as to enhance the global search capability.
3. Premature convergence is also appeared in QPSO algorithm when solving multimodal problems. The reason for premature convergence lies in the collections of swarm which makes the swarm diversity decline and the particles lose the ability of searching in a wide space. An improved Quantum-behaved Particle Swarm Optimization using the notion of species for solving multi-peaks functions optimization problems is proposed. In the proposed Species-based QPSO (SQPSO), the swarm population is divided into paralleled species subpopulations based on their similarity and each peaks are ensure to be searched equally, regardless if they are global or local optima. Our experiments for static and dynamic multi-peaks environments demonstrate that global search ability and local search capabilities of the improved algorithm have been greatly enhanced.
4. In order to overcome the difficulty that the least-squares method cannot deal with time-delay-line identification, QPSO algorithm combined with the single neuron is proposed to improve the local search capabilities and identification accuracy. Then the improved QPSO is applied to online identify parameters of a system described by differential equations. The improve QPSO algorithm has faster convergence speed and smaller length of the identification window, so it is more suitable for real-time online identification in practice. Time-delay and parameter changes for the simulation experiment illustrates the stability and tracking capability of improved QPSO algorithm are better. By introducing a session-based admission time-ratio feedback control mechanism an adaptive control of Web QoS based on system model online identification using QPSO algorithm is designed and implemented which dynamically adjust parameters of proportional-integral (PI) controller according to the changes of system model.
5. QPSO algorithm is used to identify parameters of chaotic systems, periodic systems and stability systems. The simulation results of QPSO compared with PSO and GA demonstrate that in the system parameter identification QPSO algorithm has best performance. For the existence of noise in chaotic systems, the online parameter identification based on QPSO is proposed and the effectiveness of the method is proved.
6. The study of QPSO algorithm in fault diagnosis research. Intelligent fault diagnosis technology is a combination of artificial intelligence and fault diagnosis, which use a computer to simulate human expert through artificial methods so as to diagnosis complex systems. A single radial basis function neural network (RBF NN) is a good performance feed forward network which not only has biological context, but also match with the function approximation theory and is suitable for multi-variable function approximation. It is validity to use GA to optimize the structure and weight parameters of RBF neural network. However the complexity genetic manipulation (such as selection, crossover, and mutation) of GA causes training time of the neural network increasing exponentially with the increase of the scale and complexity of the problem. To solve these problems, a RBF network algorithm based on QPSO is presented to effectively improve faults diagnosis.
The main contributions in this work are summarized at last and further research considerations are put forward.
引文
[1] Rao, S.S. Optimization Theory and Application (Second Edition). New Delhi: Wiley Eastem Limited 1984.
[2] Fogel L J, Owens A J and Walsch M J. Artificial Intelligence Through Simulated Evolution [M], New York: John Wiley,1996
[3] Holland J H. Adaptation in Nature and Artificial System [M], University of Michigan Ann Arbor, 1975
[4] Farmer J D, Packed N H, Perelson A S. The immune system, adaptation, and machine learning [J], Physica, 1986, 22(2):187-204.
[5] Dorigo M, Maniezzo V, Colorni A. The ant system: optimization by a colony of cooperating agents [J], IEEE Trans. On Systems, Man and Cybernetics Part B, 1996, 26(1):29-41.
[6] Kennedy J. and Ebethart R.C. Particle swarm optimization [A]. Proc. IEEE International Conference on Neural Networks[C], Piscataway NJ: IEEE Service Center, 1995, 1942-1948.
[7] R.C. Ebehtart and J.Kennedy. A new optimizer using particle swarm theory [A]. Proc. on the Sixth Imitational Symposium on Micromachine and Human Science [C], Nagoya, Japan, 1995, 39-43.
[8] Kennedy J. The particle Swarm: Social Adaptation of Knowledge [A], IEEE International Conference on Evolutionary Computation [C], Piscataway NJ: IEEE Service Center, 1997, 303-308.
[9] Hopfield, J.J., Tank, D.W.‘Neural’computation of decisions in optimization problems. Biological Cybernetics, 1985, 52:141-152
[10] Hopfield, J.J., Tank, D.W. Computing with neural circuits: A model. .Science, 1986, 233:625-633.
[11] Kirkrpartick S., Gelatt J.C.D., and Vecchi, M.P. Optimization by simulated annealing. Science, 1983, 220:671-680.
[12] Glover, F. Tabu search-Part 1.ORSA Journal Computing, 1989, l (3):190-206.
[13] Glover, F. Tabu search-Part II.ORSA Journal Computing, .1990, 2(l):4-32.
[14]黄席樾,向长城,殷礼胜现代智能算法理论及应用[M]科学出版社2009-3
[15] Bezedek J C. Fuzzy Models-What Are They, and Why? IEEE Transactions on Fuzzy Systems, 1993,2(l):l-6
[16] Rechenberg I. Evolution strategies: optimiering technischer system nach prinzipien der biolgischen evolution. Stuttgart:Formmann-HolzboogVerlag, 1973
[17] Schwefel H P. Numerical optimization of computer models.Chichster,U.K.:Wiley,1981
[18] Schwefel H P, Evolution and Optimum Seeking.NewYork: Wiley, 1995.
[19] Fogel L J, Owens A J, Walsh M J.Artificial Intelligence through Simulated Evolution. NewYork: Wiley,1966
[20] Fogel D B, System Identifieation through Simulated Evolution: A Machine Learning Approach to Modeling. Needham Heights, MA:Ginn,1991
[21] Yao X, Evolutionary Computation: Toward a New Philosophy of Machine Intelligence. NewYork: IEEEPress,1995
[22] Millonas M. Swarm, phase transitions and collective intelligence. In Langton CG, Ed., Artificial LifeIII. Addison Wesley, Reading,MA.1994
[23]王玫,朱云龙,何小贤.群体智能研究综述.计算机工程,2005,31(ll): 194-196
[24]李晓磊,邵之江,钱积新一种基于动物自治体的寻优模式:鱼群算法.系统工程理论与实践,2002,22(1l):32-38
[25] Holland J H. Adaptation in Natural and Artificial Systems. Cambridge: MIT Press, 1992
[26] Dorigo M, Sehnepf U. Genetics-based machine learning and behavior based robotics: a new synthesis. IEEE Transactions on Systems, Man and Cybernetics, 1985, 23(l):141-154
[27] Grefenstette J J. Optimization of Control Parameters for Genetic Algorithms. IEEE Transactions on Systems, Man and Cybernetics, 1986, 16(l):122-128
[28]彭喜元,彭宇,戴毓丰.群智能理论及应用研究.电子学报,2003,31(l2):1982-1988
[29]冯静,舒宁.群智能理论及应用研究.计算机工程与应用,2006,17(6):31-34
[30] Dorigo M, Gambardella L M. Ant colony system: a cooperative learning approach to the traveling salesman problem.IEEE Transactions on Evolutionary Computation,1997,1(1):53-66
[31] Wo1Pert, D.H. and Macready, W.G. No free lunch theorems of search.Technical Report SFI-TR-95-02-010, Santa Fe Inst., Sante Fe, New Mexico,1995.[online]:Availbale:citeseer. nj.nec.com/wolPert95no.hmtl.
[32] Wolpert, D.H.and Macready, W.G. No free lunch theorems for optimization.IEEE Transactions on Evolutional Computation, 1997, l (l):67-82.
[33] Christensen, S. and Oppacher, F. What can we learn from No Free Lunch A first attempt to characterize the concept of a searchable function.Porceednig of GECCO, Morgan Kaufmann, 2001.1219-1226.
[34] Bergh F V d. An Analysis of Particle Swarm Optimizers [D]: University of Pretoria, 2001
[35] Sun J, Feng B, Xu W. Particle Swarm Optimization with Particles Having Quantum Behavior[C] IEEE Congresson Evolutionary Computation,2004:325-331
[36] Sun J, Feng B, Xu W. A Global search strategy of Quantum-behaved Particle Swarm Optimization [C]. IEEE Conference on Cybernetics and Intelligent Systems,2004:111-116
[37]刘静.粒子群优化算法研究及其在优化理论中的应用[D]:[博士学位论文].无锡:江南大学,2007
[38]冯斌.群体智能优化算法及其在生化过程控制中的应用研究[D]:[博十学位论文].无锡:江南大学,2005
[39]方伟群体智能算法及其在数字滤波器优化设计中的研究[D]: [博士学位论文].无锡:江南大学,2008
[40]孙俊.量子行为粒子群优化算法研究[D]: [博士学位论文].无锡:江南大学,2009
[41] Kenndey, J. and Mendes, R. Neighborhood topologies in fully-informed and best-of-neighborhood particle swarms, Proceedings of the 2003 IEEE Imitational Workshop on Soft Computing in Indusrtial Applications 2003(SMCia/03), 2003, 45-50.
[42] Y. Shi, R. C. Eberhart, A modified particle swarm optimizer, in Proc. IEEE Int. Conf. Evolutionary Computation, 1998, pp. 69-73
[43] M. Clerc, The swarm and the queen: towards a deterministic and adaptive particle swarm optimization, Proc. Congress on Evolutionary Computation, 1999, vol. 3, pp. 1951-1957
[44] P. J. Angeline, Using selection to improve particle swarm optimization, in Proc. IEEE Int. Conf. Evolutionary Computation, 1998, pp. 84-89
[45] P. N. Suganthan, Particle swarm optimizer with neighborhood operator, in Proc. 1999 Congr. Evolutionary Computation, vol. 3, pp. 1962-1967
[46] J. Kennedy, Small worlds and mega-minds: effects of neighborhood topology on particle swarm performance, Proc. Congr. Evolutionary Computation, 1999, vol. 3, pp. 1931-1938
[47] J. Kennedy, Stereotyping: Improving particle swarm performance with cluster analysis, in Proc. 2000 Congr. Computational Intelligence, Honolulu, HI, May 2000, pp. 1671-1676
[48] J.J. Liang and P.N. Suganthan, Dynamic multiswarm particle swarm optimizer (DMS-PSO), in Proc. 2005 IEEE Swarm Intelligence Symp., Pasadena, CA, pp. 124-129
[49] A. Mohais, R. Mendes, C. Ward and C. Postoff, Neighborhood re-structuring in particle swarm optimization, in Proc. 18th Australian Joint Conf. Artificial Intelligence, Sydney, 2005
[50] R. Mendes, J. Kennedy and J. Neves, The fully informed particle swarm: simpler, maybe better, IEEE Trans. Evol. Comput., vol. 8, no. 3, pp. 204-210, Jun. 2004
[51] E. Ozcan and C. K. Mohan, Particle swami optimization: Surfing the waves, in Proc. IEEE Congr. Evol. Comput., Washington, DC, Jul. 1999, pp. 1939-1944
[52] M. Clerc and J. Kennedy, The particle swarm-explosion, stability and convergence in a multidimensional complex space, IEEE Trans. Evol. Comput, vol. 6, no. 2, Feb. 2002 ,pp. 58-73
[53] R. C. Eberhart and Y. Shi, Parameter selection in particle swarm optimization, in Proc. 7th Conf. Evol. Program, vol. 1447, Mar. 1998, pp. 591-600.
[54] I. C. Trelea, The particle swarm optimization algorithm: Convergence analysis and parameter selection, Inf. Process. Lett, vol. 85, Mar. 2003, pp 317-325
[55] H. M. Emara and H. A. A. Fattah, Continuous swarm optimization technique with stability analysis, in Proc. Amer. Control Conf., Boston, MA, 2004, pp 2811-2817
[56] V. Gavi and K. M. Passino, Stability analysis of social foraging swarms, IEEE Trans. Syst. Man Cybern., vol. 34, no. 1, Jan. 2003,pp 539-557
[57] V. Kadirkamanathan, K. Selvarajah and P. J. Fleming, Stability analysis of the particle dynamics in particle swarm optimizer, IEEE Trans. Evol. Comput., vol. 10, No. 3, 2006, pp245-255
[58]崔志华,曾建潮.基于微分模型的改进微粒群算法[J].计算机研究与发展. 2006, 04: 646-653
[59]王丽芳,曾建潮.基于微粒群算法与模拟退火算法的协同进化方法[J].自动化学报.2006,04: 630-635
[60]高海兵,周驰,高亮.广义粒子群优化模型[J] .计算机学报.2005,12:1980-1987
[61]丛琳,焦李成,沙宇恒.正交免疫克隆粒子群多目标优化算法[J].电子与信息学报, 2008,10:2320-2324
[62]窦全胜,周春光,马铭.粒子群优化的两种改进策略[J].计算机研究与发展.2005,05:897-904
[63]刘宇,覃征,卢江,史哲文.多模态粒子群集成神经网络[J].计算机研究与发展. 2005,42(9):1519-1526
[64]刘宇,覃征,史哲文.简约粒子群优化算法[J],西安交通大学学报.2006,08:883-887
[65]俞欢军,张丽平,陈德钊等.基于反馈策略的自适应粒子群优化算法[J],浙江大学学报(工学版).2005,09:12-17
[66]巩敦卫,张勇,张建化,周勇.新型粒子群优化算法[J]..控制理论与应用,2008,01:111-115
[67]高尚,韩斌,吴小俊,杨静宇.求解旅行商问题的混合粒子群优化算法[J].控制与决策, 2004, 11:1286-1290
[68]滕居特,陈国初,顾幸生.分段式微粒群优化算法[J].华东理工大学学报(自然科学版),2006,04: 462-465
[69]魏静萱,王宇平.一种解决约束优化问题的模糊粒子群算法[J].电子与信息学报.2008,05: 1218-1222
[70] Jiang M, Luo Y P, Yang S Y. Stochastic Convergence Analysis and Parameter Selection of the Standard Particle Swarm Optimization Algorithm. Information Processing Letters.2007,102:8-16
[71]崔志华,曾建潮.基于控制理论的微粒群算法分析与改进[J].小型微型计算机系统.2006,05: 849-853
[72]曾建潮,崔志华,微粒群算法的统一模型及分析[J].计算机研究与发展.2006,43(1):96-100
[73]潘峰,陈杰,甘明刚等.粒子群优化算法模型分析[J],自动化学报.2006,03:368-377
[74]刘洪波,王秀坤,谭国真.粒子群优化算法的收敛性分析及其混沌改进算法[J].控制与决策.2006,06: 636-640
[75]陈贵敏,贾建援,韩琪.粒子群优化算法的惯性权值递减策略研究[J],西安交通大学学报,2006,01:53-57
[76] Shi Y, Ebehtart R C., Empirical study of Particle swarm optimization. Proceedings of the World Multiconference on Systemics, Cybernetics and Informatics, Orlando, FL, 2000, 1945-1950.
[77] Shi Y, Ebehtart R C. Fuzzy Adaptive Particle Swarm Optimization. Proceedings of the 2001 Congerss on Evolutionyar ComPutation.Piseataway,NJ:IEEEPress,2001,101-106
[78] Jacques Riget and Jakob S. Vesterstr. A diversity-guided particle swarm optimizer-the ARPSO
[79] Van den Bergh, F. and Engelbrecht, A.P. A new locally convergent particle swarm optimizer. Proceedings of IEEE International Conefernce on Systems, Man, and Cybermetics (SMC), 2002, 96-101.
[80] Van den Bergh, F. and Engelbrecht, A.P. Particle swarm weight initialization in multi-layer perception artificial neural networks. Development and Practice of Artificial Intelligence Techniques. Durban,South Africa,1999,41-45
[81] Van den Bergh, F., and Engelbrecht, A.P. Using neighborhoods with the guaranteed convergence PSO. Proceedings of the IEEE Swarm Intelligence Symposium (SIS), Indianapolis Indiana, USA, 2003, 235-242.
[82] Clerc M, Kennedy J. The Particle Swarm: Explosion, Stability and Convergence in a Multi-Dimensional Complex Space [J]. IEEE Transactions on Evolutionary Computation.2002,6:58-73
[83] Stacey A, Janeie M, Grundy I. Particle swarm optimization with mutation[C].The 2003 Congess on Evolutionary Computation, 2003,2:1425-1430
[84] Higashi N, Iba H. Particle swarm optimization with Gaussian mutation[C]. Proceedings of the 2003 IEEE Swarm Intelligence Symposium,2003:72-79
[85] Kennedy J. Bare bones particle swarms[C]. Proceedings of the 2003 IEEE Swarm IntelligenceSymposium,2003:80-87
[86] Tiew-On T, Rao M V C, Loo C K, etc. A new class of operators to accelerate particle swarm optimization[C]. The 2003 Congress on Evolutionary Computation,2003,4:2406-2410
[87] Liu J, Sun J, Xu W. Quantum-behaved particle swarm optimization with adaptive mutation operator[C]. ICNC,2006,4221:959-967
[88]李德毅,孟海军,史雪梅,隶属云和隶属云发生器[J]计算机研究与发展,1995, 32 (6):15-20.
[89]刘桂花,宋承祥,刘弘,云发生器的软件实现[J],计算机应用研究2007(1),46-48
[90]刘常昱,李德毅等,正态云模型的统计分析[J]信息与控制,2005, 34(2), pp.236-239.
[91] Castro L, Zuben L. Learning and optimization using the clonal selection principle evolutionary computation [J]. IEEE Trans , 2002, 6 (3) : 34-50
[92] Li, J., Balazs, M.E., Parks, G.T., Clarkson, P.J.: A Species Conserving Genetic Algorithm for Multimodal Function Optimization. Evolutionary Computation 10(3):207-234, (2002)
[93] T. M. Blackwell,“Swarms in dynamic environments,”in Lecture Notes in Computer Science Chicago, IL, 2003, vol. 2723, Proc. Genetic Evol.Comput. Conf., pp. 1-12.
[94] T. M. Blackwell and J. Branke,“Multi-swarm optimization in dynamic environments,”in Proc. Appl. Evol. Comput.: EvoWorkshops 2004: EvoBIO, EvoCOMNET, EvoHOT, EvoISAP, EvoMUSART, and EvoSTOC, vol. 3005, LNCS, Coimbra, Portugal, 2004, pp. 489-500.
[95] J. Branke, T. Kaubler, C. Schmidt, and H. Schmeck,“A multi-population approach to dynamic optimization problems,”in Adaptive Computing in Design and Manufacture 2000. Berlin, Germany: Springer-Verlag, 2000, pp. 299-308.
[96] Y. Jin and J. Branke,“Evolutionary optimization in uncertain environments-A survey,”IEEE Trans. Evol. Comput, vol. 9, no. 3, Jun. 2005, pp. 303-317.
[97] R. K. Ursem,“Multinational GAs: Multimodal optimization techniques in dynamic environments,”in Proc. 2nd Genetic Evol. Comput. Conf., 2000, pp. 19-26.
[98] D. Beasley, D. R. Bull, and R. R. Martin, A sequential niche technique for multimodal function optimization, Evol. Comput, vol. 1, no. 2, pp. 101-125, 1993.
[99] J. P. Li, M. E. Balazs, G. Parks, and P. J. Clarkson, A species conserving genetic algorithm for multimodal function optimization, Evol. Comput, vol. 10, no. 3, 2002, pp. 207-234.
[100] Brits et al.,“Solving systems of unconstrained equations using particle swarm optimization,”in Proc. IEEE Conf. Syst., Man, Cybern., Hammamet, Tunisa, 2002, pp. 102-107.
[101] K. E. Parsopoulos and M. N. Vrahatis, Modification of the particle swarm optimizer for locating all the global minima, in Proc. Int. Conf. Artif. Neural Netw. Genetic Algorithms, Prague, Czech Republic, 2001, pp. 324-327.
[102] K. E. Parsopoulos and M. N. Vrahatis, On the computation of all global minimizers through particle swarm optimization, IEEE Trans. Evol. Comput, vol. 8, no. 3, pp. 211-224, Jun. 2004.
[103] D. Beasley, D. R. Bull, and R. R. Martin, A sequential niche technique for multimodal function optimization, Evol. Comput, vol. 1, no. 2, pp. 101-125, 1993.
[104] R. Brits, A. P. Engelbrecht, and F. van den Bergh,“A niching particle swarm optimizer,”in Proc. 4th Asia-Pacific Conf. Simulated Evol.Learning, 2002, pp. 692-696.
[105] D. Beasley, D. R. Bull, and R. R. Martin, A sequential niche technique for multimodal functionoptimization, Evol. Comput, vol. 1, no. 2, 1993, pp101-125.
[106] R. Thomsen, Multimodal optimization using crowding-based differential evolution, in Proc. 2004 Congr. Evol. Comput, vol. 2, 2004, pp1382-1389.
[107] A. Petrowski, A clearing procedure as a niching method for genetic algorithms, in Proc. 1996 IEEE Int. Conf. Evol. Comput, 1996, pp.798–803.
[108] J. P. Li, M. E. Balazs, G. Parks, and P. J. Clarkson,“A species conserving genetic algorithm for multimodal function optimization,”Evol. Comput, vol. 10, no. 3, 2002, pp. 207-234.
[109] X. Li, Adaptively choosing neighborhood bests using species in a particle swarm optimizer for multimodal function optimization, in Proc. Genetic Evol. Comput. Conf., K. Deb et al., Eds., 2004, pp. 105-116. Lecture Notes in Computer Science (LNCS 3102).
[110] D. Parrott and X. Li, A particle swarm model for tacking multiple peaks in a dynamic environment using speciation, in Proc. Genetic Evol. Comput. Conf., 2004, pp. 98–103.
[111] R Brits, A.P. Engelbrect, F. Van Den Bergh: Scalability of niche PSO, in Proc. IEEE Swarm Intell. Symp. Indianapolis, IN, 2003, pp. 228–234.
[112] R. C. Eberhart and Y. Shi, Tracking and optimizing dynamic systems with particle swarms, in Proc. Congr. Evol. Comput, 2001, pp. 94–100.
[113] A. Carlisle and G. Dozier, Adapting particle swarm optimization to dynamic environments, in Proc. Int. Conf. Artif. Intell, Las Vegas, NV, 2000, pp. 429–434.
[114] X. Hu and R. C. Eberhart, Adaptive particle swarm optimization: Detection and response to dynamic systems, in Proc. IEEE Congr. Evol. Comput, 2002, pp. 1666–1670.
[115] T. M. Blackwell and P. J. Bentley, Dynamic search with charged swarms, in Proc. Genetic Evol. Comput. Conf., New York, 2002, pp.19–26.Authorized licensed
[116] Carlisle A, Dozier G. Adapting Particle Swarm Optimization to Dynamic Environments [A]. Proceedings of International Conference
[117] Carlisle A, Dozier G. Tracking Changing Extrema with Adaptive Particle Swarm Optimizer [A]. ISSCI, 2002 World Automation Congress, Orlando FL USA, June, 2002: 265-270.
[118] Angeline, J.P.: Tracking Extrema in Dynamic Environments. Proceeding of the Evolutionary Programming VI, 1997, Indianapolis, IN, Berlin: Springer-Verlag, p.335-345
[119] Li Xiaodong , Khanh Hoa Dam. Comparing Particle Swarms for Tracking Extrema in Dynamic Environments [A]. In Congress on Evolutionary Computation[C], 2003 ,3:1772–1779
[120] Morrison R W, De Jong K A. A test problem generator for non-stationary environments [A]. In Congress on Evolutionary Computation[C] , 1999 ,3 : 2047– 2053
[121] Shan S M, Deng G S. Improved adaptive particle swarm optimizer in dynamic environment [J]. Systems Engineering - Theory & Practice, 2006, 26(3):39 - 44.
[122] J. Branke, Evolutionary Optimization in Dynamic Environments. Norwell, MA: Kluwer , 2002.
[123]李言俊.系统辨识理论及应用[M] .北京:国防工业出版社,2003.
[124]王琳,马平.系统辨识方法综述[J] .电力情报,2001 , 4 : 63 - 66.
[125] Kristinn K. System identifacation and control using gas [J]. IEEE Trans on SMC, 1992, 22(5): 1033 - 1046.
[126]方崇智,萧德云.过程辨识[M] .北京:清华大学出版社,1988.
[127]韩爱国,周云飞,戴怡,陈学东,一种系统在线辨识算法的改进研究[J]华中科技大学学报(自然科学版)2005,33(10)
[128]徐小平,钱富才,刘丁,王峰.基于PSO算法的系统辨识方法[J].系统仿真学报, 2008,(13) .
[129]王峰,邢科义,徐小平.系统辨识的粒子群优化方法[J].西安交通大学学报, 2009,(02)
[130]黄炯,邬永革,李军等.基于遗传算法的系统在线辨识[J].信息与控制, 1996,25(3):171-176
[131]杨旭东,张彤,张家余,遗传算法应用于系统在线辨识研究哈尔滨工业大学学报2000,32(1)
[132]李孝安,张小缋,戴冠中.一种基于遗传算法与进化编程的系统辨识方法[J].控制与决策.1996 ,11(3):404-407.
[133] Edward W. Knightly , Ness B. Shroff, Admission control for statistical QoS :Theory and practicel, IEEE Network , 1999 , 13 (2) : 20-29
[134] Lu CY, Abdelzaher TF, Stankovic JA, Son SH. A feedback control approach for guaranteeing relative delays in Web servers. In: Proc. of the IEEE Real-Time Technology and Applications Symp. Taipei: IEEE, 2001. 51?62.
[135] Diao Y, Gandhi N, Hellerstein J, Parekh S, Tilbury D. Using MIMO feedback control to enforce policies for interrelated metrics with application to the apache Web server. In: Network Operations and Management. 2002. 219?234.
[136] Lu Y, Abdelzaher TF, Saxena A. Design, implementation, and evaluation of differentiated caching services. IEEE Trans. on Parallel and Distributed Systems, 2004,15(5):440?452.
[137] Lu CY, Lu Y, Abdelzaher TF, Stankovic JA, Son SH. Feedback control architecture and design methodology for service delay guarantees in Web servers. IEEE Trans. on Parallel and Distributed Systems, 2006, 17(9):1014?1027.
[138]江滢,孟丹;基于接纳时间比控制和比例积分调节器的接纳控制机制[J],计算机研究与发展, 2007, 44(1):65-70
[139] Franklin GF, Powell JD, Workman M. Digital Control of Dynamic Systems. 3rd ed., New York: Addison-Wesley, 1998.
[140]谢新民,丁锋.自适应控制系统[M]北京:清华大学出版社2002.9
[141] K. J. Astrom and B. Wittenmark , Adaptive Control, Prentice Hall 1994
[142] Apache Web server,http://www.apache.org/
[143] D. Mosberger, T. Jin. Httperf: A tool for measuring Web server performance[C]. SIGMENTRICS Workshop on Internet Server Performance, Madison,1998
[144] Carroll T L, Pecora L M. Synchronization in chaotic systems [J]. Physics Review Let ters, 1990, 64 (8):821 - 824.
[145] Fang J Q 2002 Control Chaos and Develop High Technique (Beijing :Atom Energy Press)
[146] Chen G R, Lv J H. 2003 Dynamics of the Lorenz System Family :Analysis , Control and Synchronization (Beijing : Science Press)
[147] Duchateau A, Bradshaw N P, Bersini H, A multi-model solution for the control of chaos ,Int. J. Control 1999(72).
[148]王东风.基于遗传算法的统一混沌系统比例-积分-微分控制[J].物理学报,2005,54(4):1495-1550
[149]关新平,彭海朋,李丽香,王益群;Lorenz混沌系统的参数辨识与控制[J];物理学报;2001,50(1):6,
[150]戴栋,马西奎,李富才等.一种基于遗传算法的混沌系统参数估计方法[J],物理学报2002 51(11): 2459-2462
[151]李丽香,彭海朋,杨义先等.基于混沌蚂蚁群算法的Lorenz混沌系统的参数估计[J].物理学报, 2007 , 56 (1) :51-55
[152] Chen, G., T. Ueta, Yet another chaotic attractor, Int. J. of Bifur. Chaos, 9 (1999), 1465-1466.
[153] Ueta, T., G. Chen, Bifurcation analysis of Chen's equation, Int. J. of Bifur. Chaos, 10(2000), 1917-1931
[154]谢宝义.工程机械状态检测与故障诊断技术[J].计量与测试技术,2002.4:40-43.
[155]张桂材,石铁林,轩建平等.高阶统计量与RBF网络结合用于齿轮故障分类[J].中国机械工程,1999,10(11):1250-1252.
[156] Shaohua T A N, Jianbin H A O, Joos V. Efficient identification of RBF neural net models for nonlinear discrete-time multivariab dynamical systems[J]. Neurocomputing, 1995, 9(1):11-26.
[157]戴赟,郁飞.进化神经网络在柴油机故障诊断中的应用[J] .华东船舶工业学院学报:自然科学版,2004 ,18 (5) :71274.
[158]吝伶艳,田慕琴,吕永卫.基于遗传算法和神经网络相融合的异步电动机故障建模[J] .煤矿机械,2008 ,28 (8) :2112213.
[159] Yang J M, Kao C Y. A robust evolutionary algorithm fort raining neural networks [J]. Neural Computing and Application, 2001, 10 (3):214-230.
[160]思科技新产品研发中心,神经网络理论与MATLAB7实现[M],北京:电子工业出版社, 2005:234-235.
[161] Lorenz, E. N., Deterministic nonperiodic flow, J. Atmos. Sci., 20, 130-141, 1963.
[162] V. Gafiychuk, B. Datsko, V. Meleshko, D. Blackmore, Chaos Solitons Fractals, doi:10.1016/j.chaos.2008.04.039.
[163] Y. Wang, C. Li, Phys. Lett. A 363 (2007) 414.
[164]王洪斌,杨香兰,王洪瑞等.一种改进的RBF神经网络学习算法[J].系统工程与电子技术, 2002; 24(6) : 103-105
[165] J. Kennedy, Small Worlds and Mega-Minds: Effects of Neighborhood Topology on Particle Swarm Performance, in Proceedings of the Congres on Evolutionary Computation,pp 1931-1938,July 1999.