微粒群算法的性能分析与优化
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摘要
微粒群算法是一种模拟鸟类觅食、鱼群游动等生物群体社会行为的群体随机优化算法。不同于其它进化类随机优化算法,它不仅利用位置信息,而且利用速度所含的信息来对微粒飞行轨迹进行控制。微粒群算法具有编程简单、运算速度快等特点,已经成功应用于许多领域。论文通过分析影响微粒群算法性能的因素,从结构优化、参数选择、混合策略及适应值预测等方面对算法进行理论与应用研究。
标准微粒群算法在微分模型向差分模型转化时采用固定步长,这一局限使得其差分模型与微分模型之间存在较大误差,从而影响了算法计算效率。有鉴于此,论文将步长作为一个独立参数引入微粒群算法,提出微分进化微粒群算法模型,并利用绝对稳定性建立了步长的随机选择策略。由于鸟群的捕食时间在整个觅食过程中仅占极小的比例,这种随机的步长选择策略有利于捕捉鸟的捕食过程,因而更加符合微粒群算法的生物学背景。论文给出Euler、改进Euler及Runge-Kutta法的具体实现形式。数值优化的仿真结果表明,这些算法非常有效,尤其是4阶Runge-Kutte法,在求解高维优化问题时其性能远优于其它典型的改进算法。
从微粒群算法的差分模型出发,论文利用控制理论的Z-变换分析了算法结构,结果发现标准微粒群算法可视为一双输入单输出的反馈系统。在此基础上,论文通过增加控制器构建了一类全新的算法模型—带控制器的微粒群算法模型,以积分控制器与PID控制器为例讨论了算法的具体实现形式,并利用支撑集与稳定性理论给出参数选择策略。仿真结果表明带控制器的微粒群算法能有效地避免过早收敛现象,提高全局搜索性能。
最大速度上限是微粒群算法的重要参数,论文从算法收敛性和计算效率的角度分析了该参数的作用,进而提出两种高效的最大速度上限策略:最大速度上限的随机策略与个性化的最大速度上限策略。第一种策略在算法运行过程中随机调整全局搜索与局部搜索的比例;第二种策略则从生物学背景出发,探讨具有个性化行为的最大速度上限调整策略。论文将这两种策略应用于混沌系统的控制问题,仿真结果证明了它们的确有效。
在微粒群算法与变异算子的混合策略设计方面,论文利用线性控制理论分析了标准微粒群算法中认知部分的随机性与局部搜索性能之间的关系,并通过剔除该随机性弱化微粒群算法全局搜索能力、强化其局部搜索能力以提高混合算法的计算效率。该算法在非稳定线性系统逼近问题的应用得到了较优的结果。
针对一类需要大量计算适应值函数的应用问题,论文提出了两种适应值的预测策略:第一种策略利用加权平均的思想进行适应值的随机预测,第二种策略则利用可信度的概念,有针对性地进行适应值的预测。这两种策略在不确定规划的成功应用,表明了该思想的可行性和有效性。
As a population-based stochastic optimization algorithm, particle swarm optimization (PSO) simulates the social behavior among animal society such as bird flocking and fish schooling. Different from other evolutionary stochastic optimization algorithm, it employs not only the position information, but also the velocity information to control the particles’trajectories. Due to the easy implementation and the fast convergent speed, it has been successfully applied into many areas. In this thesis, the reason affecting the performance are analyzed, and several improvements, such as structure optimization, parameter selection, hybrid algorithm and estimation of fitness, are designed to make PSO more effective.
In standard PSO, the step is a constant when the differential model is translated into difference model, this limitation affects the performance greatly due to a large error between these two models. Therefore, this thesis proposes the differential evolutionary PSO model with an additional parameter– step, and the stochastic selection strategy is established with absolute stability theory. Because the prey time is very short compared with the whole searching food procedure, this selection strategy provides a more chance to observe the prey procedure, and is more fit for the biological background. Based on different numerical method such as Euler method, modified Euler method and Runge-Kutta method, three differential evolutionary PSO algorithms are designed, simulation results show they are effective and efficiency especially for Runge-Kutta method.
With the difference model of PSO, this thesis analyzes the structure with Z-translation, and finds the standard PSO can be viewed as a feedback system with two inputs and one output. Then, the controller is incorporated into the standard PSO to construct a new PSO model with controller. Furthermore, with different controllers such as integral controller and PID controller, the corresponding variants are designed, and the parameters’selection principles are obtained through stability analysis and support set theory. Simulation results show this type of PSO can improve the global exploration capability significantly.
As an important parameter, the affection of velocity threshold is analyzed from the viewpoint of convergence and calculation efficiency. Then, two effective velocity threshold adjustment strategies are designed: the stochastic strategy and individual strategy. The first one adjusts the ratio between the global exploration capability and the local exploitation capability randomly, whereas the second one investigates the velocity threshold setting with individual-charactered behavior inspired from biological background. Simulation results show both of them are effective when solving the control problem of chaotic system.
To design an effective hybrid algorithm combined with PSO and mutation operator, the relationship between the randomness of cognitive component and the local exploitation capability is analyzed with linear control theory. In order to improve the calculation efficiency, the randomness is eliminated from the cognitive component to reduce the global search capability, as well as enhance the local search capability. The application result of non-stable linear system approximation is superior than other previous reports.
For applications those need a large number of fitness calculation, this thesis proposes two estimation strategies. The first one makes a random estimation with weighted mean of fitness, while the second one estimates the fitness based on the reliability value. Both of them are effective and have been successfully applied to uncertain programming.
标准微粒群算法在微分模型向差分模型转化时采用固定步长,这一局限使得其差分模型与微分模型之间存在较大误差,从而影响了算法计算效率。有鉴于此,论文将步长作为一个独立参数引入微粒群算法,提出微分进化微粒群算法模型,并利用绝对稳定性建立了步长的随机选择策略。由于鸟群的捕食时间在整个觅食过程中仅占极小的比例,这种随机的步长选择策略有利于捕捉鸟的捕食过程,因而更加符合微粒群算法的生物学背景。论文给出Euler、改进Euler及Runge-Kutta法的具体实现形式。数值优化的仿真结果表明,这些算法非常有效,尤其是4阶Runge-Kutte法,在求解高维优化问题时其性能远优于其它典型的改进算法。
从微粒群算法的差分模型出发,论文利用控制理论的Z-变换分析了算法结构,结果发现标准微粒群算法可视为一双输入单输出的反馈系统。在此基础上,论文通过增加控制器构建了一类全新的算法模型—带控制器的微粒群算法模型,以积分控制器与PID控制器为例讨论了算法的具体实现形式,并利用支撑集与稳定性理论给出参数选择策略。仿真结果表明带控制器的微粒群算法能有效地避免过早收敛现象,提高全局搜索性能。
最大速度上限是微粒群算法的重要参数,论文从算法收敛性和计算效率的角度分析了该参数的作用,进而提出两种高效的最大速度上限策略:最大速度上限的随机策略与个性化的最大速度上限策略。第一种策略在算法运行过程中随机调整全局搜索与局部搜索的比例;第二种策略则从生物学背景出发,探讨具有个性化行为的最大速度上限调整策略。论文将这两种策略应用于混沌系统的控制问题,仿真结果证明了它们的确有效。
在微粒群算法与变异算子的混合策略设计方面,论文利用线性控制理论分析了标准微粒群算法中认知部分的随机性与局部搜索性能之间的关系,并通过剔除该随机性弱化微粒群算法全局搜索能力、强化其局部搜索能力以提高混合算法的计算效率。该算法在非稳定线性系统逼近问题的应用得到了较优的结果。
针对一类需要大量计算适应值函数的应用问题,论文提出了两种适应值的预测策略:第一种策略利用加权平均的思想进行适应值的随机预测,第二种策略则利用可信度的概念,有针对性地进行适应值的预测。这两种策略在不确定规划的成功应用,表明了该思想的可行性和有效性。
As a population-based stochastic optimization algorithm, particle swarm optimization (PSO) simulates the social behavior among animal society such as bird flocking and fish schooling. Different from other evolutionary stochastic optimization algorithm, it employs not only the position information, but also the velocity information to control the particles’trajectories. Due to the easy implementation and the fast convergent speed, it has been successfully applied into many areas. In this thesis, the reason affecting the performance are analyzed, and several improvements, such as structure optimization, parameter selection, hybrid algorithm and estimation of fitness, are designed to make PSO more effective.
In standard PSO, the step is a constant when the differential model is translated into difference model, this limitation affects the performance greatly due to a large error between these two models. Therefore, this thesis proposes the differential evolutionary PSO model with an additional parameter– step, and the stochastic selection strategy is established with absolute stability theory. Because the prey time is very short compared with the whole searching food procedure, this selection strategy provides a more chance to observe the prey procedure, and is more fit for the biological background. Based on different numerical method such as Euler method, modified Euler method and Runge-Kutta method, three differential evolutionary PSO algorithms are designed, simulation results show they are effective and efficiency especially for Runge-Kutta method.
With the difference model of PSO, this thesis analyzes the structure with Z-translation, and finds the standard PSO can be viewed as a feedback system with two inputs and one output. Then, the controller is incorporated into the standard PSO to construct a new PSO model with controller. Furthermore, with different controllers such as integral controller and PID controller, the corresponding variants are designed, and the parameters’selection principles are obtained through stability analysis and support set theory. Simulation results show this type of PSO can improve the global exploration capability significantly.
As an important parameter, the affection of velocity threshold is analyzed from the viewpoint of convergence and calculation efficiency. Then, two effective velocity threshold adjustment strategies are designed: the stochastic strategy and individual strategy. The first one adjusts the ratio between the global exploration capability and the local exploitation capability randomly, whereas the second one investigates the velocity threshold setting with individual-charactered behavior inspired from biological background. Simulation results show both of them are effective when solving the control problem of chaotic system.
To design an effective hybrid algorithm combined with PSO and mutation operator, the relationship between the randomness of cognitive component and the local exploitation capability is analyzed with linear control theory. In order to improve the calculation efficiency, the randomness is eliminated from the cognitive component to reduce the global search capability, as well as enhance the local search capability. The application result of non-stable linear system approximation is superior than other previous reports.
For applications those need a large number of fitness calculation, this thesis proposes two estimation strategies. The first one makes a random estimation with weighted mean of fitness, while the second one estimates the fitness based on the reliability value. Both of them are effective and have been successfully applied to uncertain programming.
引文
[1]周登勇,戴汝为.人工生命[J].模式识别与人工智能, 1998, 4 (3): 412-418.
[2]史忠植,莫纯欢.人工生命[J].计算机研究与发展, 1995, 32 (12): 1-3.
[3] S.Levy. Artificial life: a report from the frontier where computers meet biology[M]: New York: Vintage Books, 1992.
[4]孟宪宇,涂序彦.广义人工生命概述[J].计算机应用研究, 2006, 23 (11): 4-6.
[5]李建会.走向计算主义[M]:北京:中国书籍出版社, 2004.
[6] Watts JM. Animats: Computer-simulated animals in behavioral research[J]. Journal of Animal Science, 1998, 76 (10): 2596-2604.
[7] Meyer JA. From natural to artificial life: Biomimetic mechanisms in animat designs[J]. Robotics and Autonomous Systems, 1997, 22 (1): 3-21.
[8] Franks NR, Deneubourg JL. Self-organizing nest construction in ants: individual worker behaviour and the nest's dynamics[J]. Animal Behaviour, 1997, 54: 779-796.
[9] Reynolds CW. Flocks, Herds, and Schools: A Distributed Behavioral Model[J]. Computer Graphics, 1987, 21 (4): 25-34.
[10]涂晓媛.人工鱼[M]:北京:清华大学出版社, 2001.
[11] Bonabeau E, Dorigo M, Theraulaz G. Swarm Intelligence: From Natural to Artificial Systems[M]: Santa Fe Institute Publications, 1999.
[12] Kennedy J, Eberhart RC, Shi Y. Swarm intelligence[M]: Morgan Kaufmann, 2001.
[13] Engelbrecht AP. Fundamentals of computational swarm intelligence[M]: John Wiley & Sons Inc, 2006.
[14]李夏,戴汝为.突现-系统研究的新观念[J].控制与决策, 1999, 14 (2): 97-102.
[15]钱学森,于景元,戴汝为.一个科学新领域—开放复杂巨系统及其方法论[J].自然杂志, 1990, 13 (1): 3-10.
[16] Cowan GA, Pines D, Meltzer D. Complexity: metaphors, models and reality[M]: Addison-Wesley, 1994.
[17] Holland J. Adaptation in natural and artificial systems: an introductory analysis with application to biology, control, and artificial intelligence, 2nd Edition[M]: Cambridge, MA: MIT Press, 1992.
[18] Dorigo M, Birattari M, Stutzle T. Ant colony optimization - Artificial ants as a computational intelligence technique[J]. IEEE Computational Intelligence Magazine, 2006, 1 (4): 28-39.
[19]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[J].系统工程理论与实践, 2002, 22 (11): 32-38.
[20] Eberhart R, Kennedy J. New optimizer using particle swarm theory[C]. In: MHS'95 Proceedings of the Sixth International Symposium on Micro Machine and Human Science. IEEE, Piscataway, NJ, USA, 1995: 39-43.
[21] Kennedy J, Eberhart RC. Particle swarm optimization[C]. In: Proceedings of ICNN'95 - IEEE International Conference on Neural Networks. IEEE, Piscataway, NJ, USA, 1995: 1942-1948.
[22]王晓陵,陆军.最优化方法与最优控制[M]:哈尔滨:哈尔滨工程大学出版社, 2006.
[23] Zhang D, Zuo WM. Computational intelligence-based biometric technologies[J]. IEEE Computational Intelligence Magazine, 2007, 2 (2): 26-36.
[24] Fogel LJ, Owens AJ, Walsh MJ. Artificial Intelligence Through Simulated Evolution[M]: New York: Wiley Publishing, 1966.
[25] Beyer H-G, Schwefel H-P. Evolution strategies– A comprehensive introduction[J]. Natural Computing, 2002, 1 (1): 3-52.
[26] Suman B, Kumar P. A survey of simulated annealing as a tool for single and multiobjective optimization[J]. Journal of the Operational Research Society, 2006, 57 (10): 1143-1160.
[27] Maenhout B, Vanhoucke M. An electromagnetic meta-heuristic for the nurse scheduling problem[J]. Journal of Heuristics, 2007, 13 (4): 359-385.
[28] Irizarry R. Hybrid dynamic optimization using artificial chemical process: Extended LARES-PR[J]. Industrial & Engineering Chemistry Research, 2006, 45 (25): 8400-8412.
[29]曾建潮,介婧,崔志华.微粒群算法[M]:北京:科学出版社, 2004.
[30]吴启迪,汪镭.智能微粒群算法研究及应用[M]:江苏:江苏教育出版社, 2005.
[31] Karaboga D, Basturk B. On the performance of artificial bee colony (ABC) algorithm[J]. Applied Soft Computing, 2008, 8 (1): 687-697.
[32] Sahan S, Polat K, Kodaz H, et al. A new hybrid method based on fuzzy-artificial immune system and k-nn algorithm for breast cancer diagnosis[J]. Computers in Biology and Medicine, 2007, 37 (3): 415-423.
[33]刘宝,丁永生.一种基于睾丸素分泌调节原理的双层结构控制器[J].上海交通大学学报, 2006, 40 (5): 822-824.
[34] Liu J, Zhong WC, Hao LC. An organizational evolutionary algorithm for numerical optimization[J]. IEEE Transactions on Systems Man and Cybernetics Part B-Cybernetics, 2007, 37 (4): 1052-1064.
[35] Ho YC, Pepyne DL. Simple explanation of the no-free-lunch theorem and its implications[J]. Journal of Optimization Theory and Applications, 2002, 115 (3): 549-570.
[36] Koppen M, Wolpert DH, Macready WG. Remarks on a recent paper on the '' No free lunch '' theorems[J]. IEEE Transactions on Evolutionary Computation, 2001, 5 (3): 295-296.
[37] Kennedy J. The particle swarm: Social adaptation of knowledge[C]. In: Proceedings of 1997 IEEE International Conference on Evolutionary Computation. 1997: 303-308.
[38] Bergh FVd. An Analysis of Particle Swarm Optimizers[D]: South Africa: University of Pretoria, 2001.
[39] Shi Y, Eberhart R. A modified particle swarm optimizer[C]. In: Proceedings of 1998 IEEE International Conference on Evolutionary Computation IEEE, Piscataway, NJ, USA, 1998: 69-73.
[40] Shi Y, Eberhart RC. Parameter selection in particle swarm optimization[C]. In: Porto VW, Saravanan N, Waagen D, Eiben AE, Proceedings of 7th International Conference-Evolutionary Programming VII. Springer-Verlag, German, 1998: 591-600.
[41] Shi Y, Eberhart RC. Empirical study of particle swarm optimization[C]. In: Proceedings of the 1999 Congress on Evolutionary Computation. IEEE, Piscataway, NJ, USA, 1999: 1945-1950 Vol. 1943.
[42] Zheng YL, Ma LH, Zhang LY, et al. On the convergence analysis and parameter selection in particle swarm optimization[C]. In: Proceedings of 2003 International Conference on Machine Learning and Cybernetics. IEEE, Piscataway, NJ, USA, 2003: 1802-1807.
[43] Zheng YL, Ma LH, Zhang LY, et al. Empirical study of particle swarm optimizer with an increasing inertia weight[C]. In: Proceedings of 2003 Congress on Evolutionary Computation. IEEE, Piscataway, NJ, USA, 2003: 221-226.
[44] Jiang CW, Etorre B. A self-adaptive chaotic particle swarm algorithm for short term hydroelectric system scheduling in deregulated environment[J]. Energy Conversion and Management, 2005, 46 (17): 2689-2696.
[45] Lei KY, Qiu YH, Wang XF, et al. High dimension complex functions optimization using adaptive particle swarm optimizer[C]. In: Wang G, Peters JF, Skowron YY, Yao YY, Proceedings of Rough Sets and Knowledge Technology, Lecture Notes in Artificial Intelligence. Springer-Verlag Berlin, 2006: 321-326.
[46]陈贵敏,贾建援.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, 40 (1): 53-56.
[47] Chatterjee A, Siarry P. Nonlinear inertia weight variation for dynamic adaptation in particle swarm optimization[J]. Computers & Operations Research, 2006, 33 (3): 859-871.
[48] Huang CP, Zhang YL, Jiang DG, et al. On some non-linear decreasing inertia weight strategies in particle swarm optimization[C]. In: Cheng DZ, Wu M, Proceedings of the 26th Chinese Control Conference. Beijing: Beijing Univ Aeronautics & Astronautics Press, 2007: 750-753.
[49] Huang CP, Xiong WL, Xu BG. Study on strategies of non-linear decreasing inertia weight in particale swarm optimization algorithm[C]. In: Zhang SY, Wang F, Proceedings of the 2007 Chinese Control and Decision Conference. Boston: Northeastern University Press, 2007: 481-484.
[50] Arumugam MS, Rao MVC. On the improved performances of the particle swarm optimization algorithms with adaptive parameters, cross-over operators and root mean square (RMS) variants for computing optimal control of a class of hybrid systems[J]. Applied Soft Computing, 2008, 8 (1): 324-336.
[51] Arumugam MS, Rao MVC. On the optimal control of single-stage hybrid manufacturing systemsvia novel and different variants of particle swarm optimization algorithm[J]. Discrete Dynamics in Nature and Society, 2005, (3): 257-279.
[52] Qin Z, Yu F, Shi ZW, et al. Adaptive inertia weight particle swarm optimization[C]. In: Rutkowski L, Tadeusiewicz R, Zadeh LA, Zurada J, Proceedings of Artificial Intelligence and Soft Computing - Icaisc 2006, Lecture Notes in Computer Science. Springer-Verlag Berlin, 2006: 450-459.
[53]张选平,杜玉平,秦国强, et al.一种动态改变惯性权的自适应粒子群算法[J].西安交通大学学报, 2005, 39 (10): 1039-1042.
[54] Yang X, Yuan J, Yuan J, et al. A modified particle swarm optimizer with dynamic adaptation[J]. Applied Mathematics and Computation, 2007, 189 (2): 1205-1213.
[55] Jie J, Zeng JC, Han CZ. Adaptive particle swarm optimization with feedback control of diversity[C]. In: Li K, Irwin GW, Proceedings of Computational Intelligence and Bioinformatics, Lecture Notes in Computer Science. Springer-Verlag Berlin, 2006: 81-92.
[56] Gao LQ, Wang K, Li D, et al. Adaptive particle swarm optimization algorithm for reactive power optimization of power system[J]. Dynamics of Continuous Discrete and Impulsive Systems-Series B-Applications & Algorithms, 2006, 13E: 1312-1315.
[57] Iwasaki N, Yasuda K. Adaptive particle swarm optimization using velocity feedback[J]. International Journal of Innovative Computing Information and Control, 2005, 1 (3): 369-380.
[58] Ueno G, Yasuda K, Iwasaki N. Robust adaptive particle swarm optimization[C]. In: Proceedings of IInternational Conference on Systems, Man and Cybernetics. IEEE, Piscataway, NJ, USA, 2005: 3915-3920.
[59] Yasuda K, Iwasaki N. Adaptive particle swarm optimization via velocity feedback[C]. In: Abraham A, Dote Y, Furuhashi T, Koppen M, Ohuchi A, Ohsawa Y, Proceedings of Soft Computing as Transdisciplinary Science and Technology,Advances in Soft Computing. Springer-Verlag Berlin, 2005: 423-432.
[60] Shi YH, Eberhart RC. Fuzzy adaptive particle swarm optimization[C]. In: Proceedings of the 2001 Congress on Evolutionary Computation. IEEE, Piscataway, NJ, USA, 2001: 101-106.
[61] Bajpai P, Singh SN. Fuzzy adaptive particle swarm optimization for bidding strategy in uniform price spot market[J]. IEEE Transactions on Power Systems, 2007, 22 (4): 2152-2160.
[62] Saber AY, Senjyu T, Urasaki N, et al. Unit commitment computation - A novel fuzzy adaptive particle swarm optimization approach[C]. In: 2006 IEEE Power Systems Conference and Exposition. IEEE, Piscataway, NJ, USA, 2006: 1820-1828.
[63] Lei KY, Qiu YH, He Y. A new adaptive well-chosen inertia weight strategy to automatically harmonize global and local search ability in particle swarm optimization[C]. In: Proceedings of 1st International Symposium on Systems and Control in Aerospace and Astronautics. IEEE, Piscataway, NJ, USA, 2006: 977-980.
[64] Eberhart RC, Shi YH. Tracking and optimizing dynamic systems with particle swarms[C]. In: Proceedings of the 2001 Congress on Evolutionary Computation. IEEE, Piscataway, NJ, USA, 2001: 94-100.
[65] Shen XJ, Li YX, Wang WW, et al. A dynamic adaptive particle swarm optimization for knapsack problem[C]. In: Proceedings of Wcica 2006: Sixth World Congress on Intelligent Control and Automation. IEEE, 2006: 3183-3187.
[66]胡建秀,曾建潮.二阶微粒群算法[J].计算机研究与发展, 44 (11): 1825-1831.
[67] Jiang CW, Etorre B. A hybrid method of chaotic particle swarm optimization and linear interior for reactive power optimisation[J]. Mathematics and Computers in Simulation, 2005, 68 (1): 57-65.
[68] Ozcan E, Mohan CK. Particle swarm optimization: surfing the waves[C]. In: Proceedings of IEEE Congress on Evolutionary Computation. IEEE, Piscataway, NJ, USA, 1999: 1944-1949.
[69] Venter G, Sobieszczanski-Sobieski J. Particle swarm optimization[C]. In: Collection of Technical Papers - AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics and Materials Conference. American Inst. Aeronautics and Astronautics Inc., 2002: 282-290.
[70] Venter G, Sobieszczanski-Sobieski J. Particle swarm optimization[J]. Aiaa Journal, 2003, 41 (8): 1583-1589.
[71] Venter G, Sobieszczanski-Sobieski J. Multidisciplinary optimization of a transport aircraft wing using particle swarm optimization[J]. Structural and Multidisciplinary Optimization, 2004, 26 (1-2): 121-131.
[72] Ratnaweera A, Halgamuge SK, Watson HC. Self-organizing hierarchical particle swarm optimizerwith time-varying acceleration coefficients[J]. IEEE Transactions on Evolutionary Computation, 2004, 8 (3): 240-255.
[73] Yamaguchi T, Yasuda K. Adaptive particle swarm optimization - Self-coordinating mechanism with updating information[C]. In: Proceedings of 2006 IEEE International Conference on Systems, Man, and Cybernetics. IEEE, Piscataway, NJ, USA, 2006: 2303-2308.
[74] Ge Y, Rubo Z. An emotional particle swarm optimization algorithm[C]. In: Advances in Natural Computation, . Lecture Notes in Computer Science, Vol.3612, Springer-Verlag Berlin, German, 2005: 553-561.
[75] Yen GG, Lu HM. Dynamic population strategy assisted particle swarm optimization[C]. In: Proceedings of the 2003 IEEE International Symposium on Intelligent Control. IEEE, Piscataway, NJ, USA, 2003: 697-702.
[76] Shi Y, Eberhart RC. Parameter selection in particle swarm optimization[C]. In: Proceedings of 7th International Conference on Evolutionary Programming VII Lecture Notes in Computer Science, Vol.1447, Springer-Verlag Berlin, German, 1998: 591-600.
[77] Fourie PC, Groenwold AA. The particle swarm optimization algorithm in size and shape optimization[J]. Structural and Multidisciplinary Optimization, 2002, 23 (4): 259-267.
[78] Fan H. A modification to particle swarm optimization algorithm[J]. Engineering Computations (Swansea, Wales), 2002, 19 (7-8): 970-989.
[79] Schutte JF, Groenwold AA. Sizing design of truss structures using particle swarms[J]. Structural and Multidisciplinary Optimization, 2003, 25 (4): 261-269.
[80] Clerc M. The swarm and the queen: towards a deterministic and adaptive particle swarm optimization[C]. In: Proceedings of the 1999 IEEE Congress on Evolutionary Computation. 1999: 1951-1957.
[81] Riget J, Vesterstrom JS. A diversity-guided particle swarm optimizer- the ARPSO[R]. Department of Computer Science, University of Aarhus, Denmark, 2002.
[82] Mendes R, Kennedy J. The Fully Informed Particle Swarm: Simpler, Maybe Better[J]. IEEE Transactions of Evolutionary Computation, 2004, 8 (3): 204--210
[83] Liang JJ, Qin AK, Suganthan PN, et al. Comprehensive learning particle swarm optimizer for global optimization of multimodal functions[J]. IEEE Transactions on Evolutionary Computation, 2006, 10 (3): 281-295.
[84] Liang JJ, Suganthan PN. Adaptive comprehensive learning particle swarm optimizer with history learning[C]. In: Wang TD, Li X, Chen SH, Wang X, Abbass H, Iba H, Chen G, Yao X, Proceedings of 6th International Conference on Simulated Evolution and Learning. Lecture Notes in Computer Science, Vol.4247, Springer-Verlag Berlin, German, 2006: 213-220.
[85]赫然,王永吉,王青, et al.一种改进的自适应逃逸微粒群算法及实验分析[J].软件学报, 2005, 16 (12): 2036-2044.
[86] Cui ZH, Zeng JC. A guaranteed global convergence particle swarm optimizer[C]. In: Tsumoto S, Slowinski R, Komorowski J, GrzymalaBusse JW, Rough Sets and Current Trends in Computing. Lecture Notes in Artificial Intelligence, Vol.3066, Springer-Verlag Berlin, German, 2004: 762-767.
[87] Cui ZH, Zeng JC, Cai XJ. A new stochastic particle swarm optimizer[C]. In: Cec2004: Proceedings of the 2004 Congress on Evolutionary Computation. IEEE, Piscataway, NJ, USA, 2004: 316-319.
[88]曾建潮,崔志华.一种保证全局收敛的PSO算法[J].计算机研究与发展, 2004, 41 (8): 1333-1338.
[89] Kennedy J. Stereotyping: Improving particle swarm performance with cluster analysis[C]. In: Proceedings of the 2000 Congress on Evolutionary Computation. IEEE, Piscataway, NJ, USA, 2000: 1507-1512.
[90] Kennedy J, Mendes R. Population structure and particle swarm performance[C]. In: Cec'02: Proceedings of the 2002 Congress on Evolutionary Computation. IEEE, Piscataway, NJ, USA, 2002: 1671-1676.
[91]王芳.粒子群算法的研究[D]:西南大学博士论文, 2006.4.
[92]李宁,刘飞,孙德宝.基于带变异算子粒子群优化算法的约束布局优化研究[J].计算机学报, 2004, 27 (7): 891-897.
[93] Monson CK, Seppi KD. The Kalman swarm - A new approach to particle motion in swarm optimization. Genetic and Evolutionary Computation - Gecco 2004, Pt 1, Proceedings, 2004: 140-150.
[94] Monson CK, Seppi KD. The Kalman swarm - A new approach to particle motion in swarm optimization[C]. In: Deb K, Poli R, Banzhaf W, Beyer HG, Burke E, Darwen P, Dasgupta D, Floreano D, Foster O, Harman M, Holland O, Lanzi PL, Spector L, Tettamanzi A, Thierens D, Tyrrell A, Genetic and Evolutionary Computation - Gecco 2004, Pt 1, Proceedings. 2004: 140-150.
[95] Monson CK, Seppi KD. Bayesian optimization models for particle swarms[C]. In: Beyer HG, Gecco 2005: Genetic and Evolutionary Computation Conference. 2005: 193-200.
[96] Sun J, Feng B, Xu W. Particle swarm optimization with particles having quantum behavior[C]. In: Cec2004: Proceedings of the 2004 Congress on Evolutionary Computation. IEEE, Piscataway, NJ, USA, 2004: 325-331.
[97] Sun J, Xu WB, Feng B. A global search strategy of quantum-behaved particle swarm optimization[C]. In: 2004 IEEE Conference on Cybernetics and Intelligent Systems. IEEE, Piscataway, NJ, USA, 2004: 111-116.
[98] Sun J, Xu WB, Feng B. Adaptive parameter control for quantum-behaved particle swarm optimization on individual level[C]. In: Proceedings of International Conference on Systems, Man and Cybernetics. IEEE, Piscataway, NJ, USA, 2005: 3049-3054.
[99] Sun J, Xu WB, Liu J. Parameter selection of quantum-behaved Particle Swarm Optimization[C]. In: Advances in Natural Computation. Lecture Notes in Computer Science, Vol. 3612, Springer, German, 2005: 543-552.
[100]曾建潮,王丽芳.一种广义微粒群算法模型[J].模式识别与人工智能, 2005, 18 (6): 685-688.
[101] Wang F, Qiu YH. A modified Particle Swarm Optimizer with roulette selection operator[C]. In: Proceedings of the 2005 IEEE International Conference on Natural Language Processing and Knowledge Engineering. IEEE, Piscataway, NJ, USA, 2005: 765-768.
[102] Angeline PJ. Using selection to improve particle swarm optimization[C]. In: 1998 IEEE International Conference on Evolutionary Computation - Proceedings. IEEE, Piscataway, NJ, USA, 1998: 84-89.
[103] Yang DY, Chen FY, Naofumi M. Self-adaptive crossover particle swarm optimizer for multi-dimension functions optimization[C]. In: Icnc 2007: Proceedings of the Third International Conference on Natural Computation. IEEE, Piscataway, NJ, USA, 2007: 160-164.
[104] Krink T, Lovbjerg M. The LifeCycle model: combining particle swarm optimisation, genetic algorithms and HillClimbers[C]. In: Guervos JJM, Adamidis P, Beyer HG, Fernandez-Villacanas JL, Schwefel HP, Parallel Problem Solving from Nature - PPSN VII 7th International Conference Proceedings Lecture Notes in Computer Science Vol.2439, Springer, German, 2002: 621-630.
[105] Huang C-L, Tung C-H. Using mutation to improve discrete particle swarm optimization for single machine total weighted tardiness problem[C]. In: Proceedings of 2006 World Automation Congress, WAC'06. IEEE, Piscataway, NJ, USA, 2007: 4259934.
[106] Higashi N, Iba H. Particle swarm optimization with Gaussian mutation[C]. In: Proceedings of the 2003 IEEE Swarm Intelligence Symposium. IEEE, Piscataway, NJ, USA, 2003: 72-79.
[107] Stacey A, Jancic M, Grundy I. Particle Swarm Optimization with mutation[C]. In: Cec: 2003 Congress on Evolutionary Computation, Vols 1-4, Proceedings. IEEE, Piscataway, NJ, USA, 2003: 1425-1430.
[108] Li N, Qin YQ, Sun DB, et al. Particle swarm optimization with mutation operator[C]. In: Proceedings of the 2004 Internatinal Conference on Machine Learning and Cybernetics. IEEE, Piscataway, NJ, USA, 2004: 2251-2256.
[109] Qin YQ, Sun DA, Li N, et al. Path planning for mobile robot using the particle swarm optimization with mutation operator[C]. In: Proceedings of the 2004 Internatinal Conference on Machine Learning and Cybernetics. IEEE, Piscataway, NJ, USA, 2004: 2473-2478.
[110] Fu GJ, Wang SM, Chen MJ, et al. Particle swarm optimizer with C-Pg mutation[C]. In: Proceedings of International Conference on Computational Intelligence and Security. Lecture Notes in Artificial Intelligence, Vol.3801, , 2005: 638-644.
[111] Liu J, Xu WB, Sun J. Quantum-behaved Particle Swarm Optimization with mutation operator[C]. In: Lim A, Ictai 2005: 17th IEEE International Conference on Tools with Artificial Intelligence, Proceedings. IEEE, Piscataway, NJ, USA, 2005: 237-240.
[112] Zhao ZG, Gu XY, Su YD. A particle swarm optimizer with mutation operator[C]. In: Zhang S, 2005 International Symposium on Computer Science and Technology, Proceedings. IEEE, Piscataway, NJ, USA, 2005: 182-187.
[113] Andrews PS. An investigation into mutation operators for Particle Swarm Optimization[C]. In: Proceedings of 2006 IEEE Congress on Evolutionary Computation. IEEE, Piscataway, NJ, USA, 2006: 1029-1036.
[114] Chen JF, Ren ZW, Fan XN. Particle swarm optimization with adaptive mutation and its application research in tuning of PID parameters[C]. In: Isscaa 2006: 1st International Symposium on Systems and Control in Aerospace and Astronautics. 2006: 990-994.
[115] Jia DL, Li LH, Zhang YQ, et al. Particle swarm optimization combined with chaotic and Gaussian mutation[C]. In: Wcica 2006: Sixth World Congress on Intelligent Control and Automation, Conference Proceedings. IEEE, Piscataway, NJ, USA, 2006: 3281-3285.
[116] Liu J, Sun J, Xu WB. Quantum-behaved particle swarm optimization with adaptive mutation operator[C]. In: Advances in Natural Computation. Lecture Notes in Computer Science, Vol.4221, Springer-Verlag Berlin, German, 2006: 959-967.
[117] Zhao FQ, Zhu AH, Yu DM, et al. Integrated process planning and production scheduling in holonic manufacturing system-with a hybrid self-adaptive mutation particle swarm optimization(PSO) algorithm[C]. In: Proceedings of 2006 International Conference on Artificial Intelligence - 50 Years' Achievements, Future Directions and Social Impacts. 2006: 585-590.
[118] Gao XW, Mang DY. Algorithms and applications of particle swarm optimization with adaptive mutation based on entropy maximization[C]. In: Zhang SY, Wang F, Proceedings of the 2007 Chinese Control and Decision Conference. 2007: 371-374.
[119] Gao YL, Ren ZH. Adaptive particle swarm optimization algorithm with genetic mutation operation[C]. In: Icnc 2007: Third International Conference on Natural Computation, Proceedings. Lecture Notes in Computer Science, Springer-Verlag Berlin, German, 2007: 211-215.
[120] Higashitani M, Ishigame A, Yasuda K. Particle Swarm Optimization with Controlled Mutation[J]. IEEE Transactions on Electrical and Electronic Engineering, 2007, 2 (2): 192-194.
[121] Hou ZX, Zhou YC, Li HQ. Multimodal function optimization based on multigrouped mutation particle swarm optimization[C]. In: Icnc 2007: Third International Conference on Natural Computation, Proceedings. Lecture Notes in Computer Science, Springer-Verlag Berlin, German, 2007: 554-557.
[122] Lee S, Park H, Jeon M. Binary particle swarm optimization with bit change mutation[J]. Ieice Transactions on Fundamentals of Electronics Communications and Computer Sciences, 2007, E90A (10): 2253-2256.
[123] Li CH, Liu Y, Zhou AM, et al. A fast particle swarm optimization algorithm with cauchy mutation and natural selection strategy[C]. In: Kang L, Liu Y, Zeng S, Advances in Computation and Intelligence, Proceedings. Lecture Notes in Computer Science, Vol.4683, Springer-Verlag Berlin, German, 2007: 334-343.
[124] Liu JH, Fan XP, Qu ZH. An improved particle swarm optimization with mutation based on similarity[C]. In: Icnc 2007: Third International Conference on Natural Computation, Proceedings. Lecture Notes in Computer Science, Springer-Verlag Berlin, German, 2007: 824-828.
[125] Liu S, Wang X-Y, You X-M. Cultural based adaptive mutation Particle Swarm Optimization algorithm for numerical optimization problems[J]. Jilin Daxue Xuebao (Gongxueban)/Journal of Jilin University (Engineering and Technology Edition), 2007, 37 (SUPPL): 100-104.
[126] Sun G, Zhang Y, Xiong Z. Novel particle swarm optimization with mutation for intrusion detection[J]. Journal of Computational Information Systems, 2007, 3 (1): 233-241.
[127] Omran MGH, Engelbrecht AP, Salman A. Differential evolution based particle swarm optimization[C]. In: Proceedings of the 2007 IEEE Swarm Intelligence Symposium, SIS 2007. IEEE, Piscataway, NJ, USA, 2007: 112-119.
[128] Moore PW, Venayagamoorthy GK. Evolving digital circuits using hybrid particle swarm optimization and differential evolution[J]. International Journal of Neural Systems, 2006, 16 (3): 163-177.
[129] Paterlini S, Krink T. Differential evolution and particle swarm optimisation in partitional clustering[J]. Computational Statistics & Data Analysis, 2006, 50 (5): 1220-1247.
[130] Tasgetiren MF, Liang YC, Sevkli M, et al. Particle swarm optimization and differential evolution for the single machine total weighted tardiness problem[J]. International Journal of Production Research, 2006, 44 (22): 4737-4754.
[131] Chakraborti N, Das S, Jayakanth R, et al. Genetic algorithms applied to Li+ ions contained in carbon nanotubes: An investigation using particle swarm optimization and differential evolution along with molecular dynamics[J]. Materials and Manufacturing Processes, 2007, 22 (5-6): 562-569.
[132] Xu R, Venayagamoorthy GK, Wunsch DC. Modeling of gene regulatory networks with hybrid differential evolution and particle swarm optimization[J]. Neural Networks, 2007, 20 (8): 917-927.
[133] Wang F, Qiu YH, Feng NQ. Multi-model function optimization by a new hybrid nonlinear simplex search and Particle Swarm Algorithm[C]. In: Advances in Natural Computation, Proceedings. Lecture Notes in Computer Science, Vol.3612, Springer-Verlag Berlin, German, 2005: 562-565.
[134] Fan SKS, Liang YC, Zahara E. Hybrid simplex search and particle swarm optimization for the global optimization of multimodal functions[J]. Engineering Optimization, 2004, 36 (4): 401-418.
[135] Fan SKS, Liang YC, Zahara E. A genetic algorithm and a particle swarm optimizer hybridized with Nelder-Mead simplex search[J]. Computers & Industrial Engineering, 2006, 50 (4): 401-425.
[136]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, 32 (4): 630-635.
[137] Wang F, Qiu YH. Improving the particle swarm optimization algorithm using the simplex method at late stage[C]. In: Li DL, Wang B, Proceedings of 2nd International Conference on Artificial Intelligence Applications and Innovations. 2005: 355-361.
[138] Chuanwen J, Bompard E. A self-adaptive chaotic particle swarm algorithm for short term hydroelectric system scheduling in deregulated environment[J]. Energy Conversion and Management, 2005, 46 (17): 2689-2696.
[139] Chuanwen J, Bompard E. A hybrid method of chaotic particle swarm optimization and linear interior for reactive power optimisation[J]. Mathematics and Computers in Simulation, 2005, 68 (1): 57-65.
[140] Jiang CW, Bompard E. A hybrid method of chaotic particle swarm optimization and linear interior for reactive power optimisation[J]. Mathematics and Computers in Simulation, 2005, 68 (1): 57-65.
[141] Liu Z-F, Ge S-Y, Yu Y-X. Optimal reactive power dispatch using chaotic particle swarm optimization algorithm[J]. Dianli Xitong Zidonghua/Automation of Electric Power Systems, 2005, 29 (7): 53-57.
[142] Chandramouli K, Izquierdo E. Image classification using chaotic particle swarm optimization[C]. In: 2006 IEEE International Conference on Image Processing, Icip 2006, Proceedings. IEEE, Piscataway, NJ, USA, 2006: 3001-3004.
[143] Meng H-J, Zheng P, Mei G-H, et al. Particle swarm optimization algorithm based on chaotic series[J]. Kongzhi yu Juece/Control and Decision, 2006, 21 (3): 263-266.
[144] Tatsumi K, Sasaki S, Tanino T. Chaotic particle swarm optimization method exploiting sinusoidal perturbations[C]. In: Proceedings of 2006 Sice-Icase International Joint Conference. 2006: 3074-3077.
[145] Zhao Q, Yan SZ. Collision-free path planning for mobile robots using chaotic particle swarm optimization[C]. In: Advances in Natural Computation. Lecture Notes in Computer Science, Vol.3612, Springer-Verlag Berlin, German, 2005: 632-635.
[146] Meng Y, Kazeem O, Juan M. A hybrid ACO/PSO control algorithm for distributed swarm robots[C]. In: Proceedings of IEEE Swarm Intelligence Symposium. IEEE, Piscataway, NJ, USA, 2007: 273-280.
[147] Clerc M, Kennedy J. The particle swarm - Explosion, stability, and convergence in a multidimensional complex space[J]. IEEE Transactions on Evolutionary Computation, 2002, 6 (1): 58-73.
[148] van den Bergh F, Engelbrecht AP. A study of particle swarm optimization particle trajectories[J]. Information Sciences, 2006, 176 (8): 937-971.
[149] Yasuda K, Ide A, Iwasaki N. Adaptive particle swarm optimization[C]. In: 2003 IEEE International Conference on Systems, Man and Cybernetics, Proceedings. IEEE, Piscataway, NJ, USA, 2003: 1554-1559.
[150] Trelea IC. The particle swarm optimization algorithm: convergence analysis and parameter selection[J]. Information Processing Letters, 2003, 85 (6): 317-325.
[151]李宁,孙德宝,邹彤, et al.基于差分方程的PSO算法粒子运动轨迹分析[J].计算机学报, 2006, 29 (11): 2052-2061.
[152] Jiang M, Luo Y, Yang S. Stagnation analysis in particle swarm optimization[C]. In: Institute of Electrical and Electronics Engineers Computer Society, Piscataway, NJ 08855-1331, United States, 2007: 92-99.
[153] Jiang M, Luo YP, Yang SY. Stochastic convergence analysis and parameter selection of the standard particle swarm optimization algorithm[J]. Information Processing Letters, 2007, 102 (1): 8-16.
[154] :Jiang M, Luo YP, Yang SY. Stagnation analysis in particle swarm optimization. 2007 IEEE Swarm Intelligence Symposium, 2007: 92-99.
[155] Solis F, Wets R. Minimization by Random Search Techniques[J]. Mathematics of Operations Research, 1981, (6): 19-30.
[156] Parsopoulos KE, Vrahatis MN. Particle Swarm Optimization method for Constrained Optimization problems. In: Sincak P, Vascak J, Kvasnicka V, Pospichal J, editors. Intelligent Technologies - Theory and Applications - New Trends in Intelligent Technologies, 2002: 214-220.
[157] Hu XH, Eberhart R. Solving constrained nonlinear optimization problems with particle swarm optimization[C]. In: Callaos N, Leng T, Sanchez B, 6th World Multiconference on Systemics, Cybernetics and Informatics, Proceedings 2002: 203-206.
[158] Kennedy J, Eberhart RC. Discrete binary version of the particle swarm algorithm[C]. In: Proceedings of the IEEE International Conference on Systems, Man and Cybernetics. IEEE, Piscataway, NJ, USA, 1997: 4104-4108.
[159] Fukuyama Y, Yoshida H. A particle swarm optimization for reactive power and voltage control in electric power systems[C]. In: Proceedings of the 2001 Congress on Evolutionary Computation. IEEE, Piscataway, NJ, USA, 2001: 87-93.
[160] Fukuyama Y, Takayama S, Nakanishi Y, et al. A particle swarm optimization for reactive power and voltage control in electric power systems[C]. In: Banzhaf W, Daida J, Eiben AE, Garzon MH, Honavar V, Jakiela M, Smith RE, Gecco-99: Proceedings of the Genetic and Evolutionary Computation Conference. 1999: 1523-1528.
[161] Cui X, Hardin CT, Ragade RK, et al. Tracking non-stationary optimal solution by particle swarm optimizer[C]. In: Sixth International Conference on Software Engineerng, Artificial Intelligence, Networking and Parallel/Distributed Computing and First Aics International Workshop on Self-Assembling Wireless Networks, Proceedings. 2005: 133-138.
[162] van den Bergh F, Engelbrecht AP. Training product unit networks using Cooperative Particle Swarm Optimisers[C]. In: Ijcnn'01: International Joint Conference on Neural Networks, Proceedings. 2001: 126-131.
[163] Yin P-Y. A discrete particle swarm algorithm for optimal polygonal approximation of digital curves[J]. Journal of Visual Communication and Image Representation, 2004, 15 (2): 241-260.
[164] Liu B, Wang L, Jin YH. An effective hybrid particle swarm optimization for no-wait flow shop scheduling[J]. International Journal of Advanced Manufacturing Technology, 2007, 31 (9-10): 1001-1011.
[165] Liu B, Wang L, Jin YH. An effective PSO-based memetic algorithm for flow shop scheduling[J]. IEEE Transactions on Systems Man and Cybernetics Part B-Cybernetics, 2007, 37 (1): 18-27.
[166] Zhang B, Teng HF, Shi YJ. Layout optimization of satellite module using soft computing techniques[J]. Applied Soft Computing, 2008, 8 (1): 507-521.
[167] Jeon JY, Okuma M. Acoustic radiation optimization using the particle swarm optimization algorithm[J]. Jsme International Journal Series C-Mechanical Systems Machine Elements and Manufacturing, 2004, 47 (2): 560-567.
[168] Shawn Matott L, Rabideau AJ. Calibration of subsurface batch and reactive-transport models involving complex biogeochemical processes[J]. Advances in Water Resources, 2008, 31 (2): 269-286.
[169] :Shi Y, Eberhart R. A modified particle swarm optimizer. Proceedings of 1998 IEEE International Conference on Evolutionary Computation IEEE, Piscataway, NJ, USA: Anchorage, AK,, 1998: 69-73.
[170]王能超.计算方法:算法设计及其MATLAB实现[M]:北京:高等教育出版社, 2005.
[171]李庆扬,关治,白峰杉.数值计算原理[M]:北京:清华大学出版社, 2000.
[172]王高雄.常微分方程(第二版)[M]:高等教育出版社, 1987.
[173] Yao X, Liu Y, Lin GM. Evolutionary programming made faster[J]. IEEE Transactions on Evolutionary Computation, 1999, 3 (3): 82-102.
[174] Shang YW, Qiu YH. A note on the extended Rosenbrock function[J]. Evolutionary Computation, 2006, 14 (1): 119-126.
[175] Cui Z, Zeng J, Sun G. Adaptive velocity threshold particle swarm optimization[C]. In: Lecture Notes in Computer Science, Vol.4062, Springer Verlag, Heidelberg, D-69121, Germany, 2006: 327-332.
[176] Schutte JF, Groenwold AA. A study of global optimization using particle swarms[J]. Journal of Global Optimization, 2005, 31 (1): 93-108.
[177] Shi Y, Eberhart RC. Empirical study of particle swarm optimization[C]. In: Proceedings of the Congress on Evolutionary Computation. IEEE, Piscataway, NJ, USA, 1999: 1945-1950.
[178] Kennedy J. Bare bones particle swarms[C]. In: Proceedings of the 2003 IEEE Swarm Intelligence Symposium. IEEE, Piscataway, NJ, USA, 2003: 80-87.
[179] Poli R, Langdon WB. Markov chain models of bare-bones particle swarm optimizers[C]. In: Association for Computing Machinery, New York, NY 10036-5701, United States, 2007: 142-149.
[180] Lee CY, Yao X. Evolutionary programming using mutations based on the Levy probability distribution[J]. IEEE Transactions on Evolutionary Computation, 2004, 8 (1): 1-13.
[181] Richer TJ, Blackwell TM. The Levy particle swarm[C]. In: 2006 IEEE Congress on Evolutionary Computation. IEEE, Piscataway, NJ, USA, 2006: 808-815.
[182] Mantegna R. Fast, accurate algorithm for numerical simulation of Levy stable stochastic process[J]. Physics Review E, 1994: 4677-4683.
[183] Chen G, Dong X. From chaos to order: methodologies, perspectives, and applications[M]: Singapore: World Scientific, 1998.
[184]刘波.复杂系统基于微粒群的优化与调度理论与方法研究[D].北京:清华大学, 2007.
[185]夏德钤.自动控制理论[M]:机械工业出版社, 1990.
[186] Kennedy J, Eberhart R. Particle swarm optimization[C]. In: IEEE, Piscataway, NJ, USA, 1995: 1942-1948.
[187] Yao X, Liu Y, Lin GM. Evolutionary programming made faster[J]. IEEE Transactions on Evolutionary Computation, 1999, 3 (2): 82-102.
[188] Zheng YL, Ma LH, Zhang LY, et al. On the convergence analysis and parameter selection in particle swarm optimization[C]. In: 2003 International Conference on Machine Learning and Cybernetics, Proceedings. IEEE, Piscataway, NJ, USA, 2003: 1802-1807.
[189]公茂果,杜海峰,焦李成.基于人工免疫相应的线性系统逼近[J].中国科学(E辑), 2005, 35 (12): 12881303.
[190] Cheng SL, Huang CY. Optimal approximation of linear systems by a differential evolution algorithm[J]. IEEE Transactions on Systems, Man, and Cybernetics- Part A, 2001, 31 (6): 698-707.
[191] Zhong WC, Liu J, Xue MZ, et al. A multiagent genetic algorithm for global numerical optimization[J]. IEEE Transactions on Systems, Man, and Cybernetics- Part B, 2004, 34 (2): 1128-1141.
[192]刘宝碇,赵瑞清,王纲.不确定规划及应用[M]:清华大学出版社, 2003.
[193] Takagi H. Interactive evolutionary computation as humanized computational intelligence technology. In: Reusch B, editor. Computational Intelligence: Theory and Applications, Proceedings, 2001: 1-1.
[194] Takagi H. Design and measurement with interactive evolutionary computation. In: Abraham A, Dote Y, Furuhashi T, Koppen M, Ohuchi A, Ohsawa Y, editors. Soft Computing as Transdisciplinary Science and Technology, 2005: 6-7.
[195] Henmi S, Iwashita S, Takagi H. Interactive evolutionary computation with evaluation characteristics of Multi-IEC users[C]. In: 2006 IEEE International Conference on Systems, Man, and Cybernetics, Proceedings. IEEE, Piscataway, NJ, USA, 2006: 3475-3480.
[196] Raich A, Liszkai T. Benefits of implicit redundant genetic algorithms for structural damage detection in noisy environments[C]. In: Genetic and Evolutionary Computation - Gecco 2003,Proceedings. Lecture Notes in Computer Science, Vol.2724, Springer-Verlag Berlin, German, 2003: 2418-2419.
[197] Jin Y, Branke H. Evolutionary optimization in uncertain environments - A survey[J]. IEEE Transactions on Evolutionary Computation, 2005, 9 (3): 303-317.
[198] Grierson DE, Pak WH. Optimal sizing, geometrical and topological design using a geneticalgorithm[J]. Structural Optimization, 1993, 6 (3): 151-159.
[199] Jourdan L, Dhaenens C, Talbi EG. Using datamining techniques to help metaheuristics: A short survey. Hybrid Metaheuristics, Proceedings, 2006: 57-69.
[200] Jin Y. A comprehensive survey of fitness approximation in evolutionary computation[J]. Soft Computing, 2005, 9 (1): 3-12.
[201] Eby D, Averill R, Punch W, et al. Evaluation of injection island model GA performance on flywheel design optimization[C]. In: Proceedings of the 3rd Conference on Adaptive Computing in Design and Manufacturing. 1998: 121-136.
[202] Sefrioui M, Periaux J. A hierarchical genetic algorithm using multiple models for optimization. Parallel Problem Solving from Nature. Springer, 2000: 879-888.
[203] Rasheed K. An incremental-approximate-clustering approach for developing dynamic reduced models for design optimization[C]. In: Proceedings of the 2000 Congress on Evolutionary Computation. IEEE, Piscataway, NJ, USA, 2000: 986-993.
[204] Abboud K, Schoenauer M. Surrogate deterministic mutation: Preliminary results[C]. In: Collet P, Fonlupt C, Hao JK, Lutton E, Schoenauer M, Proceedings of 5th International Conference on Artficial Evolution. Lecture Notes in Computer Science, Vol.2310, Springer-Verlag Berlin, German, 2002: 104-116.
[205] Rasheed K, Xiao N, Vattam S. Comparison of methods for developing dynamic reduced models for design optimization[C]. In: Cec'02: Proceedings of the 2002 Congress on Evolutionary Computation. IEEE, Piscataway, NJ, USA, 2002: 390-395.
[206] Lee J, Hajela P. Parallel genetic algorithms implementation for multidisciplineary rotor blade design[J]. Journal of Aircraft, 1996, 33 (5): 962-969.
[207] Jin YC, Sendhoff B. Reducing fitness evaluations using clustering techniques and neural network ensembles[C]. In: Genetic and Evolutionary Computation - Gecco 2004, Proceedings. Lecture Notes in Computer Science, Vol.3102, Springer-Verlag Berlin, German, 2004: 688-699.
[208] Zhou ZZ, Ong YS, Lim MH, et al. Memetic algorithm using multi-surrogates for computationally expensive optimization problems[J]. Soft Computing, 2007, 11 (10): 957-971.
[209] Xie HY, Zhang MJ, Andreae P. Population clustering in genetic programming[C]. In: Genetic Programming, Proceedings. Lecture Notes in Computer Science, Vol.3905, Springer-Verlag Berlin, German, 2006: 190-201.
[210] Liu B. Theory and Practice of Uncertain Programming[M]: Physica-Verlag, Heidelberg, 2002.
[211] Ravi V, Murty BS, Reddy PJ. Nonequilibrium simulated annealing algorithm applied to reliability optimization of complex systems[J]. IEEE Transactions on Reliability, 1997, 46: 233-239.
[212] Zhou J, Liu B. New stochastic models for capacitated location-allocation problem[J]. Computers & Industrial Engineering, 2003, 45 (1): 111-125.
[213] Peng J, Liu B. Parallel machine scheduling models with fuzzy processing times[J]. Information Sciences, 2004, 166 (1): 49-66.
[214] Salami M, Hendtlass T. A fast evaluation strategy for evolutionary algorithms[J]. Applied Soft Computing, 2003, 2 (3): 156-173.
[215] Liu B. Uncertain Programming[M]: New York: Wiley, 1999.
[2]史忠植,莫纯欢.人工生命[J].计算机研究与发展, 1995, 32 (12): 1-3.
[3] S.Levy. Artificial life: a report from the frontier where computers meet biology[M]: New York: Vintage Books, 1992.
[4]孟宪宇,涂序彦.广义人工生命概述[J].计算机应用研究, 2006, 23 (11): 4-6.
[5]李建会.走向计算主义[M]:北京:中国书籍出版社, 2004.
[6] Watts JM. Animats: Computer-simulated animals in behavioral research[J]. Journal of Animal Science, 1998, 76 (10): 2596-2604.
[7] Meyer JA. From natural to artificial life: Biomimetic mechanisms in animat designs[J]. Robotics and Autonomous Systems, 1997, 22 (1): 3-21.
[8] Franks NR, Deneubourg JL. Self-organizing nest construction in ants: individual worker behaviour and the nest's dynamics[J]. Animal Behaviour, 1997, 54: 779-796.
[9] Reynolds CW. Flocks, Herds, and Schools: A Distributed Behavioral Model[J]. Computer Graphics, 1987, 21 (4): 25-34.
[10]涂晓媛.人工鱼[M]:北京:清华大学出版社, 2001.
[11] Bonabeau E, Dorigo M, Theraulaz G. Swarm Intelligence: From Natural to Artificial Systems[M]: Santa Fe Institute Publications, 1999.
[12] Kennedy J, Eberhart RC, Shi Y. Swarm intelligence[M]: Morgan Kaufmann, 2001.
[13] Engelbrecht AP. Fundamentals of computational swarm intelligence[M]: John Wiley & Sons Inc, 2006.
[14]李夏,戴汝为.突现-系统研究的新观念[J].控制与决策, 1999, 14 (2): 97-102.
[15]钱学森,于景元,戴汝为.一个科学新领域—开放复杂巨系统及其方法论[J].自然杂志, 1990, 13 (1): 3-10.
[16] Cowan GA, Pines D, Meltzer D. Complexity: metaphors, models and reality[M]: Addison-Wesley, 1994.
[17] Holland J. Adaptation in natural and artificial systems: an introductory analysis with application to biology, control, and artificial intelligence, 2nd Edition[M]: Cambridge, MA: MIT Press, 1992.
[18] Dorigo M, Birattari M, Stutzle T. Ant colony optimization - Artificial ants as a computational intelligence technique[J]. IEEE Computational Intelligence Magazine, 2006, 1 (4): 28-39.
[19]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[J].系统工程理论与实践, 2002, 22 (11): 32-38.
[20] Eberhart R, Kennedy J. New optimizer using particle swarm theory[C]. In: MHS'95 Proceedings of the Sixth International Symposium on Micro Machine and Human Science. IEEE, Piscataway, NJ, USA, 1995: 39-43.
[21] Kennedy J, Eberhart RC. Particle swarm optimization[C]. In: Proceedings of ICNN'95 - IEEE International Conference on Neural Networks. IEEE, Piscataway, NJ, USA, 1995: 1942-1948.
[22]王晓陵,陆军.最优化方法与最优控制[M]:哈尔滨:哈尔滨工程大学出版社, 2006.
[23] Zhang D, Zuo WM. Computational intelligence-based biometric technologies[J]. IEEE Computational Intelligence Magazine, 2007, 2 (2): 26-36.
[24] Fogel LJ, Owens AJ, Walsh MJ. Artificial Intelligence Through Simulated Evolution[M]: New York: Wiley Publishing, 1966.
[25] Beyer H-G, Schwefel H-P. Evolution strategies– A comprehensive introduction[J]. Natural Computing, 2002, 1 (1): 3-52.
[26] Suman B, Kumar P. A survey of simulated annealing as a tool for single and multiobjective optimization[J]. Journal of the Operational Research Society, 2006, 57 (10): 1143-1160.
[27] Maenhout B, Vanhoucke M. An electromagnetic meta-heuristic for the nurse scheduling problem[J]. Journal of Heuristics, 2007, 13 (4): 359-385.
[28] Irizarry R. Hybrid dynamic optimization using artificial chemical process: Extended LARES-PR[J]. Industrial & Engineering Chemistry Research, 2006, 45 (25): 8400-8412.
[29]曾建潮,介婧,崔志华.微粒群算法[M]:北京:科学出版社, 2004.
[30]吴启迪,汪镭.智能微粒群算法研究及应用[M]:江苏:江苏教育出版社, 2005.
[31] Karaboga D, Basturk B. On the performance of artificial bee colony (ABC) algorithm[J]. Applied Soft Computing, 2008, 8 (1): 687-697.
[32] Sahan S, Polat K, Kodaz H, et al. A new hybrid method based on fuzzy-artificial immune system and k-nn algorithm for breast cancer diagnosis[J]. Computers in Biology and Medicine, 2007, 37 (3): 415-423.
[33]刘宝,丁永生.一种基于睾丸素分泌调节原理的双层结构控制器[J].上海交通大学学报, 2006, 40 (5): 822-824.
[34] Liu J, Zhong WC, Hao LC. An organizational evolutionary algorithm for numerical optimization[J]. IEEE Transactions on Systems Man and Cybernetics Part B-Cybernetics, 2007, 37 (4): 1052-1064.
[35] Ho YC, Pepyne DL. Simple explanation of the no-free-lunch theorem and its implications[J]. Journal of Optimization Theory and Applications, 2002, 115 (3): 549-570.
[36] Koppen M, Wolpert DH, Macready WG. Remarks on a recent paper on the '' No free lunch '' theorems[J]. IEEE Transactions on Evolutionary Computation, 2001, 5 (3): 295-296.
[37] Kennedy J. The particle swarm: Social adaptation of knowledge[C]. In: Proceedings of 1997 IEEE International Conference on Evolutionary Computation. 1997: 303-308.
[38] Bergh FVd. An Analysis of Particle Swarm Optimizers[D]: South Africa: University of Pretoria, 2001.
[39] Shi Y, Eberhart R. A modified particle swarm optimizer[C]. In: Proceedings of 1998 IEEE International Conference on Evolutionary Computation IEEE, Piscataway, NJ, USA, 1998: 69-73.
[40] Shi Y, Eberhart RC. Parameter selection in particle swarm optimization[C]. In: Porto VW, Saravanan N, Waagen D, Eiben AE, Proceedings of 7th International Conference-Evolutionary Programming VII. Springer-Verlag, German, 1998: 591-600.
[41] Shi Y, Eberhart RC. Empirical study of particle swarm optimization[C]. In: Proceedings of the 1999 Congress on Evolutionary Computation. IEEE, Piscataway, NJ, USA, 1999: 1945-1950 Vol. 1943.
[42] Zheng YL, Ma LH, Zhang LY, et al. On the convergence analysis and parameter selection in particle swarm optimization[C]. In: Proceedings of 2003 International Conference on Machine Learning and Cybernetics. IEEE, Piscataway, NJ, USA, 2003: 1802-1807.
[43] Zheng YL, Ma LH, Zhang LY, et al. Empirical study of particle swarm optimizer with an increasing inertia weight[C]. In: Proceedings of 2003 Congress on Evolutionary Computation. IEEE, Piscataway, NJ, USA, 2003: 221-226.
[44] Jiang CW, Etorre B. A self-adaptive chaotic particle swarm algorithm for short term hydroelectric system scheduling in deregulated environment[J]. Energy Conversion and Management, 2005, 46 (17): 2689-2696.
[45] Lei KY, Qiu YH, Wang XF, et al. High dimension complex functions optimization using adaptive particle swarm optimizer[C]. In: Wang G, Peters JF, Skowron YY, Yao YY, Proceedings of Rough Sets and Knowledge Technology, Lecture Notes in Artificial Intelligence. Springer-Verlag Berlin, 2006: 321-326.
[46]陈贵敏,贾建援.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, 40 (1): 53-56.
[47] Chatterjee A, Siarry P. Nonlinear inertia weight variation for dynamic adaptation in particle swarm optimization[J]. Computers & Operations Research, 2006, 33 (3): 859-871.
[48] Huang CP, Zhang YL, Jiang DG, et al. On some non-linear decreasing inertia weight strategies in particle swarm optimization[C]. In: Cheng DZ, Wu M, Proceedings of the 26th Chinese Control Conference. Beijing: Beijing Univ Aeronautics & Astronautics Press, 2007: 750-753.
[49] Huang CP, Xiong WL, Xu BG. Study on strategies of non-linear decreasing inertia weight in particale swarm optimization algorithm[C]. In: Zhang SY, Wang F, Proceedings of the 2007 Chinese Control and Decision Conference. Boston: Northeastern University Press, 2007: 481-484.
[50] Arumugam MS, Rao MVC. On the improved performances of the particle swarm optimization algorithms with adaptive parameters, cross-over operators and root mean square (RMS) variants for computing optimal control of a class of hybrid systems[J]. Applied Soft Computing, 2008, 8 (1): 324-336.
[51] Arumugam MS, Rao MVC. On the optimal control of single-stage hybrid manufacturing systemsvia novel and different variants of particle swarm optimization algorithm[J]. Discrete Dynamics in Nature and Society, 2005, (3): 257-279.
[52] Qin Z, Yu F, Shi ZW, et al. Adaptive inertia weight particle swarm optimization[C]. In: Rutkowski L, Tadeusiewicz R, Zadeh LA, Zurada J, Proceedings of Artificial Intelligence and Soft Computing - Icaisc 2006, Lecture Notes in Computer Science. Springer-Verlag Berlin, 2006: 450-459.
[53]张选平,杜玉平,秦国强, et al.一种动态改变惯性权的自适应粒子群算法[J].西安交通大学学报, 2005, 39 (10): 1039-1042.
[54] Yang X, Yuan J, Yuan J, et al. A modified particle swarm optimizer with dynamic adaptation[J]. Applied Mathematics and Computation, 2007, 189 (2): 1205-1213.
[55] Jie J, Zeng JC, Han CZ. Adaptive particle swarm optimization with feedback control of diversity[C]. In: Li K, Irwin GW, Proceedings of Computational Intelligence and Bioinformatics, Lecture Notes in Computer Science. Springer-Verlag Berlin, 2006: 81-92.
[56] Gao LQ, Wang K, Li D, et al. Adaptive particle swarm optimization algorithm for reactive power optimization of power system[J]. Dynamics of Continuous Discrete and Impulsive Systems-Series B-Applications & Algorithms, 2006, 13E: 1312-1315.
[57] Iwasaki N, Yasuda K. Adaptive particle swarm optimization using velocity feedback[J]. International Journal of Innovative Computing Information and Control, 2005, 1 (3): 369-380.
[58] Ueno G, Yasuda K, Iwasaki N. Robust adaptive particle swarm optimization[C]. In: Proceedings of IInternational Conference on Systems, Man and Cybernetics. IEEE, Piscataway, NJ, USA, 2005: 3915-3920.
[59] Yasuda K, Iwasaki N. Adaptive particle swarm optimization via velocity feedback[C]. In: Abraham A, Dote Y, Furuhashi T, Koppen M, Ohuchi A, Ohsawa Y, Proceedings of Soft Computing as Transdisciplinary Science and Technology,Advances in Soft Computing. Springer-Verlag Berlin, 2005: 423-432.
[60] Shi YH, Eberhart RC. Fuzzy adaptive particle swarm optimization[C]. In: Proceedings of the 2001 Congress on Evolutionary Computation. IEEE, Piscataway, NJ, USA, 2001: 101-106.
[61] Bajpai P, Singh SN. Fuzzy adaptive particle swarm optimization for bidding strategy in uniform price spot market[J]. IEEE Transactions on Power Systems, 2007, 22 (4): 2152-2160.
[62] Saber AY, Senjyu T, Urasaki N, et al. Unit commitment computation - A novel fuzzy adaptive particle swarm optimization approach[C]. In: 2006 IEEE Power Systems Conference and Exposition. IEEE, Piscataway, NJ, USA, 2006: 1820-1828.
[63] Lei KY, Qiu YH, He Y. A new adaptive well-chosen inertia weight strategy to automatically harmonize global and local search ability in particle swarm optimization[C]. In: Proceedings of 1st International Symposium on Systems and Control in Aerospace and Astronautics. IEEE, Piscataway, NJ, USA, 2006: 977-980.
[64] Eberhart RC, Shi YH. Tracking and optimizing dynamic systems with particle swarms[C]. In: Proceedings of the 2001 Congress on Evolutionary Computation. IEEE, Piscataway, NJ, USA, 2001: 94-100.
[65] Shen XJ, Li YX, Wang WW, et al. A dynamic adaptive particle swarm optimization for knapsack problem[C]. In: Proceedings of Wcica 2006: Sixth World Congress on Intelligent Control and Automation. IEEE, 2006: 3183-3187.
[66]胡建秀,曾建潮.二阶微粒群算法[J].计算机研究与发展, 44 (11): 1825-1831.
[67] Jiang CW, Etorre B. A hybrid method of chaotic particle swarm optimization and linear interior for reactive power optimisation[J]. Mathematics and Computers in Simulation, 2005, 68 (1): 57-65.
[68] Ozcan E, Mohan CK. Particle swarm optimization: surfing the waves[C]. In: Proceedings of IEEE Congress on Evolutionary Computation. IEEE, Piscataway, NJ, USA, 1999: 1944-1949.
[69] Venter G, Sobieszczanski-Sobieski J. Particle swarm optimization[C]. In: Collection of Technical Papers - AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics and Materials Conference. American Inst. Aeronautics and Astronautics Inc., 2002: 282-290.
[70] Venter G, Sobieszczanski-Sobieski J. Particle swarm optimization[J]. Aiaa Journal, 2003, 41 (8): 1583-1589.
[71] Venter G, Sobieszczanski-Sobieski J. Multidisciplinary optimization of a transport aircraft wing using particle swarm optimization[J]. Structural and Multidisciplinary Optimization, 2004, 26 (1-2): 121-131.
[72] Ratnaweera A, Halgamuge SK, Watson HC. Self-organizing hierarchical particle swarm optimizerwith time-varying acceleration coefficients[J]. IEEE Transactions on Evolutionary Computation, 2004, 8 (3): 240-255.
[73] Yamaguchi T, Yasuda K. Adaptive particle swarm optimization - Self-coordinating mechanism with updating information[C]. In: Proceedings of 2006 IEEE International Conference on Systems, Man, and Cybernetics. IEEE, Piscataway, NJ, USA, 2006: 2303-2308.
[74] Ge Y, Rubo Z. An emotional particle swarm optimization algorithm[C]. In: Advances in Natural Computation, . Lecture Notes in Computer Science, Vol.3612, Springer-Verlag Berlin, German, 2005: 553-561.
[75] Yen GG, Lu HM. Dynamic population strategy assisted particle swarm optimization[C]. In: Proceedings of the 2003 IEEE International Symposium on Intelligent Control. IEEE, Piscataway, NJ, USA, 2003: 697-702.
[76] Shi Y, Eberhart RC. Parameter selection in particle swarm optimization[C]. In: Proceedings of 7th International Conference on Evolutionary Programming VII Lecture Notes in Computer Science, Vol.1447, Springer-Verlag Berlin, German, 1998: 591-600.
[77] Fourie PC, Groenwold AA. The particle swarm optimization algorithm in size and shape optimization[J]. Structural and Multidisciplinary Optimization, 2002, 23 (4): 259-267.
[78] Fan H. A modification to particle swarm optimization algorithm[J]. Engineering Computations (Swansea, Wales), 2002, 19 (7-8): 970-989.
[79] Schutte JF, Groenwold AA. Sizing design of truss structures using particle swarms[J]. Structural and Multidisciplinary Optimization, 2003, 25 (4): 261-269.
[80] Clerc M. The swarm and the queen: towards a deterministic and adaptive particle swarm optimization[C]. In: Proceedings of the 1999 IEEE Congress on Evolutionary Computation. 1999: 1951-1957.
[81] Riget J, Vesterstrom JS. A diversity-guided particle swarm optimizer- the ARPSO[R]. Department of Computer Science, University of Aarhus, Denmark, 2002.
[82] Mendes R, Kennedy J. The Fully Informed Particle Swarm: Simpler, Maybe Better[J]. IEEE Transactions of Evolutionary Computation, 2004, 8 (3): 204--210
[83] Liang JJ, Qin AK, Suganthan PN, et al. Comprehensive learning particle swarm optimizer for global optimization of multimodal functions[J]. IEEE Transactions on Evolutionary Computation, 2006, 10 (3): 281-295.
[84] Liang JJ, Suganthan PN. Adaptive comprehensive learning particle swarm optimizer with history learning[C]. In: Wang TD, Li X, Chen SH, Wang X, Abbass H, Iba H, Chen G, Yao X, Proceedings of 6th International Conference on Simulated Evolution and Learning. Lecture Notes in Computer Science, Vol.4247, Springer-Verlag Berlin, German, 2006: 213-220.
[85]赫然,王永吉,王青, et al.一种改进的自适应逃逸微粒群算法及实验分析[J].软件学报, 2005, 16 (12): 2036-2044.
[86] Cui ZH, Zeng JC. A guaranteed global convergence particle swarm optimizer[C]. In: Tsumoto S, Slowinski R, Komorowski J, GrzymalaBusse JW, Rough Sets and Current Trends in Computing. Lecture Notes in Artificial Intelligence, Vol.3066, Springer-Verlag Berlin, German, 2004: 762-767.
[87] Cui ZH, Zeng JC, Cai XJ. A new stochastic particle swarm optimizer[C]. In: Cec2004: Proceedings of the 2004 Congress on Evolutionary Computation. IEEE, Piscataway, NJ, USA, 2004: 316-319.
[88]曾建潮,崔志华.一种保证全局收敛的PSO算法[J].计算机研究与发展, 2004, 41 (8): 1333-1338.
[89] Kennedy J. Stereotyping: Improving particle swarm performance with cluster analysis[C]. In: Proceedings of the 2000 Congress on Evolutionary Computation. IEEE, Piscataway, NJ, USA, 2000: 1507-1512.
[90] Kennedy J, Mendes R. Population structure and particle swarm performance[C]. In: Cec'02: Proceedings of the 2002 Congress on Evolutionary Computation. IEEE, Piscataway, NJ, USA, 2002: 1671-1676.
[91]王芳.粒子群算法的研究[D]:西南大学博士论文, 2006.4.
[92]李宁,刘飞,孙德宝.基于带变异算子粒子群优化算法的约束布局优化研究[J].计算机学报, 2004, 27 (7): 891-897.
[93] Monson CK, Seppi KD. The Kalman swarm - A new approach to particle motion in swarm optimization. Genetic and Evolutionary Computation - Gecco 2004, Pt 1, Proceedings, 2004: 140-150.
[94] Monson CK, Seppi KD. The Kalman swarm - A new approach to particle motion in swarm optimization[C]. In: Deb K, Poli R, Banzhaf W, Beyer HG, Burke E, Darwen P, Dasgupta D, Floreano D, Foster O, Harman M, Holland O, Lanzi PL, Spector L, Tettamanzi A, Thierens D, Tyrrell A, Genetic and Evolutionary Computation - Gecco 2004, Pt 1, Proceedings. 2004: 140-150.
[95] Monson CK, Seppi KD. Bayesian optimization models for particle swarms[C]. In: Beyer HG, Gecco 2005: Genetic and Evolutionary Computation Conference. 2005: 193-200.
[96] Sun J, Feng B, Xu W. Particle swarm optimization with particles having quantum behavior[C]. In: Cec2004: Proceedings of the 2004 Congress on Evolutionary Computation. IEEE, Piscataway, NJ, USA, 2004: 325-331.
[97] Sun J, Xu WB, Feng B. A global search strategy of quantum-behaved particle swarm optimization[C]. In: 2004 IEEE Conference on Cybernetics and Intelligent Systems. IEEE, Piscataway, NJ, USA, 2004: 111-116.
[98] Sun J, Xu WB, Feng B. Adaptive parameter control for quantum-behaved particle swarm optimization on individual level[C]. In: Proceedings of International Conference on Systems, Man and Cybernetics. IEEE, Piscataway, NJ, USA, 2005: 3049-3054.
[99] Sun J, Xu WB, Liu J. Parameter selection of quantum-behaved Particle Swarm Optimization[C]. In: Advances in Natural Computation. Lecture Notes in Computer Science, Vol. 3612, Springer, German, 2005: 543-552.
[100]曾建潮,王丽芳.一种广义微粒群算法模型[J].模式识别与人工智能, 2005, 18 (6): 685-688.
[101] Wang F, Qiu YH. A modified Particle Swarm Optimizer with roulette selection operator[C]. In: Proceedings of the 2005 IEEE International Conference on Natural Language Processing and Knowledge Engineering. IEEE, Piscataway, NJ, USA, 2005: 765-768.
[102] Angeline PJ. Using selection to improve particle swarm optimization[C]. In: 1998 IEEE International Conference on Evolutionary Computation - Proceedings. IEEE, Piscataway, NJ, USA, 1998: 84-89.
[103] Yang DY, Chen FY, Naofumi M. Self-adaptive crossover particle swarm optimizer for multi-dimension functions optimization[C]. In: Icnc 2007: Proceedings of the Third International Conference on Natural Computation. IEEE, Piscataway, NJ, USA, 2007: 160-164.
[104] Krink T, Lovbjerg M. The LifeCycle model: combining particle swarm optimisation, genetic algorithms and HillClimbers[C]. In: Guervos JJM, Adamidis P, Beyer HG, Fernandez-Villacanas JL, Schwefel HP, Parallel Problem Solving from Nature - PPSN VII 7th International Conference Proceedings Lecture Notes in Computer Science Vol.2439, Springer, German, 2002: 621-630.
[105] Huang C-L, Tung C-H. Using mutation to improve discrete particle swarm optimization for single machine total weighted tardiness problem[C]. In: Proceedings of 2006 World Automation Congress, WAC'06. IEEE, Piscataway, NJ, USA, 2007: 4259934.
[106] Higashi N, Iba H. Particle swarm optimization with Gaussian mutation[C]. In: Proceedings of the 2003 IEEE Swarm Intelligence Symposium. IEEE, Piscataway, NJ, USA, 2003: 72-79.
[107] Stacey A, Jancic M, Grundy I. Particle Swarm Optimization with mutation[C]. In: Cec: 2003 Congress on Evolutionary Computation, Vols 1-4, Proceedings. IEEE, Piscataway, NJ, USA, 2003: 1425-1430.
[108] Li N, Qin YQ, Sun DB, et al. Particle swarm optimization with mutation operator[C]. In: Proceedings of the 2004 Internatinal Conference on Machine Learning and Cybernetics. IEEE, Piscataway, NJ, USA, 2004: 2251-2256.
[109] Qin YQ, Sun DA, Li N, et al. Path planning for mobile robot using the particle swarm optimization with mutation operator[C]. In: Proceedings of the 2004 Internatinal Conference on Machine Learning and Cybernetics. IEEE, Piscataway, NJ, USA, 2004: 2473-2478.
[110] Fu GJ, Wang SM, Chen MJ, et al. Particle swarm optimizer with C-Pg mutation[C]. In: Proceedings of International Conference on Computational Intelligence and Security. Lecture Notes in Artificial Intelligence, Vol.3801, , 2005: 638-644.
[111] Liu J, Xu WB, Sun J. Quantum-behaved Particle Swarm Optimization with mutation operator[C]. In: Lim A, Ictai 2005: 17th IEEE International Conference on Tools with Artificial Intelligence, Proceedings. IEEE, Piscataway, NJ, USA, 2005: 237-240.
[112] Zhao ZG, Gu XY, Su YD. A particle swarm optimizer with mutation operator[C]. In: Zhang S, 2005 International Symposium on Computer Science and Technology, Proceedings. IEEE, Piscataway, NJ, USA, 2005: 182-187.
[113] Andrews PS. An investigation into mutation operators for Particle Swarm Optimization[C]. In: Proceedings of 2006 IEEE Congress on Evolutionary Computation. IEEE, Piscataway, NJ, USA, 2006: 1029-1036.
[114] Chen JF, Ren ZW, Fan XN. Particle swarm optimization with adaptive mutation and its application research in tuning of PID parameters[C]. In: Isscaa 2006: 1st International Symposium on Systems and Control in Aerospace and Astronautics. 2006: 990-994.
[115] Jia DL, Li LH, Zhang YQ, et al. Particle swarm optimization combined with chaotic and Gaussian mutation[C]. In: Wcica 2006: Sixth World Congress on Intelligent Control and Automation, Conference Proceedings. IEEE, Piscataway, NJ, USA, 2006: 3281-3285.
[116] Liu J, Sun J, Xu WB. Quantum-behaved particle swarm optimization with adaptive mutation operator[C]. In: Advances in Natural Computation. Lecture Notes in Computer Science, Vol.4221, Springer-Verlag Berlin, German, 2006: 959-967.
[117] Zhao FQ, Zhu AH, Yu DM, et al. Integrated process planning and production scheduling in holonic manufacturing system-with a hybrid self-adaptive mutation particle swarm optimization(PSO) algorithm[C]. In: Proceedings of 2006 International Conference on Artificial Intelligence - 50 Years' Achievements, Future Directions and Social Impacts. 2006: 585-590.
[118] Gao XW, Mang DY. Algorithms and applications of particle swarm optimization with adaptive mutation based on entropy maximization[C]. In: Zhang SY, Wang F, Proceedings of the 2007 Chinese Control and Decision Conference. 2007: 371-374.
[119] Gao YL, Ren ZH. Adaptive particle swarm optimization algorithm with genetic mutation operation[C]. In: Icnc 2007: Third International Conference on Natural Computation, Proceedings. Lecture Notes in Computer Science, Springer-Verlag Berlin, German, 2007: 211-215.
[120] Higashitani M, Ishigame A, Yasuda K. Particle Swarm Optimization with Controlled Mutation[J]. IEEE Transactions on Electrical and Electronic Engineering, 2007, 2 (2): 192-194.
[121] Hou ZX, Zhou YC, Li HQ. Multimodal function optimization based on multigrouped mutation particle swarm optimization[C]. In: Icnc 2007: Third International Conference on Natural Computation, Proceedings. Lecture Notes in Computer Science, Springer-Verlag Berlin, German, 2007: 554-557.
[122] Lee S, Park H, Jeon M. Binary particle swarm optimization with bit change mutation[J]. Ieice Transactions on Fundamentals of Electronics Communications and Computer Sciences, 2007, E90A (10): 2253-2256.
[123] Li CH, Liu Y, Zhou AM, et al. A fast particle swarm optimization algorithm with cauchy mutation and natural selection strategy[C]. In: Kang L, Liu Y, Zeng S, Advances in Computation and Intelligence, Proceedings. Lecture Notes in Computer Science, Vol.4683, Springer-Verlag Berlin, German, 2007: 334-343.
[124] Liu JH, Fan XP, Qu ZH. An improved particle swarm optimization with mutation based on similarity[C]. In: Icnc 2007: Third International Conference on Natural Computation, Proceedings. Lecture Notes in Computer Science, Springer-Verlag Berlin, German, 2007: 824-828.
[125] Liu S, Wang X-Y, You X-M. Cultural based adaptive mutation Particle Swarm Optimization algorithm for numerical optimization problems[J]. Jilin Daxue Xuebao (Gongxueban)/Journal of Jilin University (Engineering and Technology Edition), 2007, 37 (SUPPL): 100-104.
[126] Sun G, Zhang Y, Xiong Z. Novel particle swarm optimization with mutation for intrusion detection[J]. Journal of Computational Information Systems, 2007, 3 (1): 233-241.
[127] Omran MGH, Engelbrecht AP, Salman A. Differential evolution based particle swarm optimization[C]. In: Proceedings of the 2007 IEEE Swarm Intelligence Symposium, SIS 2007. IEEE, Piscataway, NJ, USA, 2007: 112-119.
[128] Moore PW, Venayagamoorthy GK. Evolving digital circuits using hybrid particle swarm optimization and differential evolution[J]. International Journal of Neural Systems, 2006, 16 (3): 163-177.
[129] Paterlini S, Krink T. Differential evolution and particle swarm optimisation in partitional clustering[J]. Computational Statistics & Data Analysis, 2006, 50 (5): 1220-1247.
[130] Tasgetiren MF, Liang YC, Sevkli M, et al. Particle swarm optimization and differential evolution for the single machine total weighted tardiness problem[J]. International Journal of Production Research, 2006, 44 (22): 4737-4754.
[131] Chakraborti N, Das S, Jayakanth R, et al. Genetic algorithms applied to Li+ ions contained in carbon nanotubes: An investigation using particle swarm optimization and differential evolution along with molecular dynamics[J]. Materials and Manufacturing Processes, 2007, 22 (5-6): 562-569.
[132] Xu R, Venayagamoorthy GK, Wunsch DC. Modeling of gene regulatory networks with hybrid differential evolution and particle swarm optimization[J]. Neural Networks, 2007, 20 (8): 917-927.
[133] Wang F, Qiu YH, Feng NQ. Multi-model function optimization by a new hybrid nonlinear simplex search and Particle Swarm Algorithm[C]. In: Advances in Natural Computation, Proceedings. Lecture Notes in Computer Science, Vol.3612, Springer-Verlag Berlin, German, 2005: 562-565.
[134] Fan SKS, Liang YC, Zahara E. Hybrid simplex search and particle swarm optimization for the global optimization of multimodal functions[J]. Engineering Optimization, 2004, 36 (4): 401-418.
[135] Fan SKS, Liang YC, Zahara E. A genetic algorithm and a particle swarm optimizer hybridized with Nelder-Mead simplex search[J]. Computers & Industrial Engineering, 2006, 50 (4): 401-425.
[136]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, 32 (4): 630-635.
[137] Wang F, Qiu YH. Improving the particle swarm optimization algorithm using the simplex method at late stage[C]. In: Li DL, Wang B, Proceedings of 2nd International Conference on Artificial Intelligence Applications and Innovations. 2005: 355-361.
[138] Chuanwen J, Bompard E. A self-adaptive chaotic particle swarm algorithm for short term hydroelectric system scheduling in deregulated environment[J]. Energy Conversion and Management, 2005, 46 (17): 2689-2696.
[139] Chuanwen J, Bompard E. A hybrid method of chaotic particle swarm optimization and linear interior for reactive power optimisation[J]. Mathematics and Computers in Simulation, 2005, 68 (1): 57-65.
[140] Jiang CW, Bompard E. A hybrid method of chaotic particle swarm optimization and linear interior for reactive power optimisation[J]. Mathematics and Computers in Simulation, 2005, 68 (1): 57-65.
[141] Liu Z-F, Ge S-Y, Yu Y-X. Optimal reactive power dispatch using chaotic particle swarm optimization algorithm[J]. Dianli Xitong Zidonghua/Automation of Electric Power Systems, 2005, 29 (7): 53-57.
[142] Chandramouli K, Izquierdo E. Image classification using chaotic particle swarm optimization[C]. In: 2006 IEEE International Conference on Image Processing, Icip 2006, Proceedings. IEEE, Piscataway, NJ, USA, 2006: 3001-3004.
[143] Meng H-J, Zheng P, Mei G-H, et al. Particle swarm optimization algorithm based on chaotic series[J]. Kongzhi yu Juece/Control and Decision, 2006, 21 (3): 263-266.
[144] Tatsumi K, Sasaki S, Tanino T. Chaotic particle swarm optimization method exploiting sinusoidal perturbations[C]. In: Proceedings of 2006 Sice-Icase International Joint Conference. 2006: 3074-3077.
[145] Zhao Q, Yan SZ. Collision-free path planning for mobile robots using chaotic particle swarm optimization[C]. In: Advances in Natural Computation. Lecture Notes in Computer Science, Vol.3612, Springer-Verlag Berlin, German, 2005: 632-635.
[146] Meng Y, Kazeem O, Juan M. A hybrid ACO/PSO control algorithm for distributed swarm robots[C]. In: Proceedings of IEEE Swarm Intelligence Symposium. IEEE, Piscataway, NJ, USA, 2007: 273-280.
[147] Clerc M, Kennedy J. The particle swarm - Explosion, stability, and convergence in a multidimensional complex space[J]. IEEE Transactions on Evolutionary Computation, 2002, 6 (1): 58-73.
[148] van den Bergh F, Engelbrecht AP. A study of particle swarm optimization particle trajectories[J]. Information Sciences, 2006, 176 (8): 937-971.
[149] Yasuda K, Ide A, Iwasaki N. Adaptive particle swarm optimization[C]. In: 2003 IEEE International Conference on Systems, Man and Cybernetics, Proceedings. IEEE, Piscataway, NJ, USA, 2003: 1554-1559.
[150] Trelea IC. The particle swarm optimization algorithm: convergence analysis and parameter selection[J]. Information Processing Letters, 2003, 85 (6): 317-325.
[151]李宁,孙德宝,邹彤, et al.基于差分方程的PSO算法粒子运动轨迹分析[J].计算机学报, 2006, 29 (11): 2052-2061.
[152] Jiang M, Luo Y, Yang S. Stagnation analysis in particle swarm optimization[C]. In: Institute of Electrical and Electronics Engineers Computer Society, Piscataway, NJ 08855-1331, United States, 2007: 92-99.
[153] Jiang M, Luo YP, Yang SY. Stochastic convergence analysis and parameter selection of the standard particle swarm optimization algorithm[J]. Information Processing Letters, 2007, 102 (1): 8-16.
[154] :Jiang M, Luo YP, Yang SY. Stagnation analysis in particle swarm optimization. 2007 IEEE Swarm Intelligence Symposium, 2007: 92-99.
[155] Solis F, Wets R. Minimization by Random Search Techniques[J]. Mathematics of Operations Research, 1981, (6): 19-30.
[156] Parsopoulos KE, Vrahatis MN. Particle Swarm Optimization method for Constrained Optimization problems. In: Sincak P, Vascak J, Kvasnicka V, Pospichal J, editors. Intelligent Technologies - Theory and Applications - New Trends in Intelligent Technologies, 2002: 214-220.
[157] Hu XH, Eberhart R. Solving constrained nonlinear optimization problems with particle swarm optimization[C]. In: Callaos N, Leng T, Sanchez B, 6th World Multiconference on Systemics, Cybernetics and Informatics, Proceedings 2002: 203-206.
[158] Kennedy J, Eberhart RC. Discrete binary version of the particle swarm algorithm[C]. In: Proceedings of the IEEE International Conference on Systems, Man and Cybernetics. IEEE, Piscataway, NJ, USA, 1997: 4104-4108.
[159] Fukuyama Y, Yoshida H. A particle swarm optimization for reactive power and voltage control in electric power systems[C]. In: Proceedings of the 2001 Congress on Evolutionary Computation. IEEE, Piscataway, NJ, USA, 2001: 87-93.
[160] Fukuyama Y, Takayama S, Nakanishi Y, et al. A particle swarm optimization for reactive power and voltage control in electric power systems[C]. In: Banzhaf W, Daida J, Eiben AE, Garzon MH, Honavar V, Jakiela M, Smith RE, Gecco-99: Proceedings of the Genetic and Evolutionary Computation Conference. 1999: 1523-1528.
[161] Cui X, Hardin CT, Ragade RK, et al. Tracking non-stationary optimal solution by particle swarm optimizer[C]. In: Sixth International Conference on Software Engineerng, Artificial Intelligence, Networking and Parallel/Distributed Computing and First Aics International Workshop on Self-Assembling Wireless Networks, Proceedings. 2005: 133-138.
[162] van den Bergh F, Engelbrecht AP. Training product unit networks using Cooperative Particle Swarm Optimisers[C]. In: Ijcnn'01: International Joint Conference on Neural Networks, Proceedings. 2001: 126-131.
[163] Yin P-Y. A discrete particle swarm algorithm for optimal polygonal approximation of digital curves[J]. Journal of Visual Communication and Image Representation, 2004, 15 (2): 241-260.
[164] Liu B, Wang L, Jin YH. An effective hybrid particle swarm optimization for no-wait flow shop scheduling[J]. International Journal of Advanced Manufacturing Technology, 2007, 31 (9-10): 1001-1011.
[165] Liu B, Wang L, Jin YH. An effective PSO-based memetic algorithm for flow shop scheduling[J]. IEEE Transactions on Systems Man and Cybernetics Part B-Cybernetics, 2007, 37 (1): 18-27.
[166] Zhang B, Teng HF, Shi YJ. Layout optimization of satellite module using soft computing techniques[J]. Applied Soft Computing, 2008, 8 (1): 507-521.
[167] Jeon JY, Okuma M. Acoustic radiation optimization using the particle swarm optimization algorithm[J]. Jsme International Journal Series C-Mechanical Systems Machine Elements and Manufacturing, 2004, 47 (2): 560-567.
[168] Shawn Matott L, Rabideau AJ. Calibration of subsurface batch and reactive-transport models involving complex biogeochemical processes[J]. Advances in Water Resources, 2008, 31 (2): 269-286.
[169] :Shi Y, Eberhart R. A modified particle swarm optimizer. Proceedings of 1998 IEEE International Conference on Evolutionary Computation IEEE, Piscataway, NJ, USA: Anchorage, AK,, 1998: 69-73.
[170]王能超.计算方法:算法设计及其MATLAB实现[M]:北京:高等教育出版社, 2005.
[171]李庆扬,关治,白峰杉.数值计算原理[M]:北京:清华大学出版社, 2000.
[172]王高雄.常微分方程(第二版)[M]:高等教育出版社, 1987.
[173] Yao X, Liu Y, Lin GM. Evolutionary programming made faster[J]. IEEE Transactions on Evolutionary Computation, 1999, 3 (3): 82-102.
[174] Shang YW, Qiu YH. A note on the extended Rosenbrock function[J]. Evolutionary Computation, 2006, 14 (1): 119-126.
[175] Cui Z, Zeng J, Sun G. Adaptive velocity threshold particle swarm optimization[C]. In: Lecture Notes in Computer Science, Vol.4062, Springer Verlag, Heidelberg, D-69121, Germany, 2006: 327-332.
[176] Schutte JF, Groenwold AA. A study of global optimization using particle swarms[J]. Journal of Global Optimization, 2005, 31 (1): 93-108.
[177] Shi Y, Eberhart RC. Empirical study of particle swarm optimization[C]. In: Proceedings of the Congress on Evolutionary Computation. IEEE, Piscataway, NJ, USA, 1999: 1945-1950.
[178] Kennedy J. Bare bones particle swarms[C]. In: Proceedings of the 2003 IEEE Swarm Intelligence Symposium. IEEE, Piscataway, NJ, USA, 2003: 80-87.
[179] Poli R, Langdon WB. Markov chain models of bare-bones particle swarm optimizers[C]. In: Association for Computing Machinery, New York, NY 10036-5701, United States, 2007: 142-149.
[180] Lee CY, Yao X. Evolutionary programming using mutations based on the Levy probability distribution[J]. IEEE Transactions on Evolutionary Computation, 2004, 8 (1): 1-13.
[181] Richer TJ, Blackwell TM. The Levy particle swarm[C]. In: 2006 IEEE Congress on Evolutionary Computation. IEEE, Piscataway, NJ, USA, 2006: 808-815.
[182] Mantegna R. Fast, accurate algorithm for numerical simulation of Levy stable stochastic process[J]. Physics Review E, 1994: 4677-4683.
[183] Chen G, Dong X. From chaos to order: methodologies, perspectives, and applications[M]: Singapore: World Scientific, 1998.
[184]刘波.复杂系统基于微粒群的优化与调度理论与方法研究[D].北京:清华大学, 2007.
[185]夏德钤.自动控制理论[M]:机械工业出版社, 1990.
[186] Kennedy J, Eberhart R. Particle swarm optimization[C]. In: IEEE, Piscataway, NJ, USA, 1995: 1942-1948.
[187] Yao X, Liu Y, Lin GM. Evolutionary programming made faster[J]. IEEE Transactions on Evolutionary Computation, 1999, 3 (2): 82-102.
[188] Zheng YL, Ma LH, Zhang LY, et al. On the convergence analysis and parameter selection in particle swarm optimization[C]. In: 2003 International Conference on Machine Learning and Cybernetics, Proceedings. IEEE, Piscataway, NJ, USA, 2003: 1802-1807.
[189]公茂果,杜海峰,焦李成.基于人工免疫相应的线性系统逼近[J].中国科学(E辑), 2005, 35 (12): 12881303.
[190] Cheng SL, Huang CY. Optimal approximation of linear systems by a differential evolution algorithm[J]. IEEE Transactions on Systems, Man, and Cybernetics- Part A, 2001, 31 (6): 698-707.
[191] Zhong WC, Liu J, Xue MZ, et al. A multiagent genetic algorithm for global numerical optimization[J]. IEEE Transactions on Systems, Man, and Cybernetics- Part B, 2004, 34 (2): 1128-1141.
[192]刘宝碇,赵瑞清,王纲.不确定规划及应用[M]:清华大学出版社, 2003.
[193] Takagi H. Interactive evolutionary computation as humanized computational intelligence technology. In: Reusch B, editor. Computational Intelligence: Theory and Applications, Proceedings, 2001: 1-1.
[194] Takagi H. Design and measurement with interactive evolutionary computation. In: Abraham A, Dote Y, Furuhashi T, Koppen M, Ohuchi A, Ohsawa Y, editors. Soft Computing as Transdisciplinary Science and Technology, 2005: 6-7.
[195] Henmi S, Iwashita S, Takagi H. Interactive evolutionary computation with evaluation characteristics of Multi-IEC users[C]. In: 2006 IEEE International Conference on Systems, Man, and Cybernetics, Proceedings. IEEE, Piscataway, NJ, USA, 2006: 3475-3480.
[196] Raich A, Liszkai T. Benefits of implicit redundant genetic algorithms for structural damage detection in noisy environments[C]. In: Genetic and Evolutionary Computation - Gecco 2003,Proceedings. Lecture Notes in Computer Science, Vol.2724, Springer-Verlag Berlin, German, 2003: 2418-2419.
[197] Jin Y, Branke H. Evolutionary optimization in uncertain environments - A survey[J]. IEEE Transactions on Evolutionary Computation, 2005, 9 (3): 303-317.
[198] Grierson DE, Pak WH. Optimal sizing, geometrical and topological design using a geneticalgorithm[J]. Structural Optimization, 1993, 6 (3): 151-159.
[199] Jourdan L, Dhaenens C, Talbi EG. Using datamining techniques to help metaheuristics: A short survey. Hybrid Metaheuristics, Proceedings, 2006: 57-69.
[200] Jin Y. A comprehensive survey of fitness approximation in evolutionary computation[J]. Soft Computing, 2005, 9 (1): 3-12.
[201] Eby D, Averill R, Punch W, et al. Evaluation of injection island model GA performance on flywheel design optimization[C]. In: Proceedings of the 3rd Conference on Adaptive Computing in Design and Manufacturing. 1998: 121-136.
[202] Sefrioui M, Periaux J. A hierarchical genetic algorithm using multiple models for optimization. Parallel Problem Solving from Nature. Springer, 2000: 879-888.
[203] Rasheed K. An incremental-approximate-clustering approach for developing dynamic reduced models for design optimization[C]. In: Proceedings of the 2000 Congress on Evolutionary Computation. IEEE, Piscataway, NJ, USA, 2000: 986-993.
[204] Abboud K, Schoenauer M. Surrogate deterministic mutation: Preliminary results[C]. In: Collet P, Fonlupt C, Hao JK, Lutton E, Schoenauer M, Proceedings of 5th International Conference on Artficial Evolution. Lecture Notes in Computer Science, Vol.2310, Springer-Verlag Berlin, German, 2002: 104-116.
[205] Rasheed K, Xiao N, Vattam S. Comparison of methods for developing dynamic reduced models for design optimization[C]. In: Cec'02: Proceedings of the 2002 Congress on Evolutionary Computation. IEEE, Piscataway, NJ, USA, 2002: 390-395.
[206] Lee J, Hajela P. Parallel genetic algorithms implementation for multidisciplineary rotor blade design[J]. Journal of Aircraft, 1996, 33 (5): 962-969.
[207] Jin YC, Sendhoff B. Reducing fitness evaluations using clustering techniques and neural network ensembles[C]. In: Genetic and Evolutionary Computation - Gecco 2004, Proceedings. Lecture Notes in Computer Science, Vol.3102, Springer-Verlag Berlin, German, 2004: 688-699.
[208] Zhou ZZ, Ong YS, Lim MH, et al. Memetic algorithm using multi-surrogates for computationally expensive optimization problems[J]. Soft Computing, 2007, 11 (10): 957-971.
[209] Xie HY, Zhang MJ, Andreae P. Population clustering in genetic programming[C]. In: Genetic Programming, Proceedings. Lecture Notes in Computer Science, Vol.3905, Springer-Verlag Berlin, German, 2006: 190-201.
[210] Liu B. Theory and Practice of Uncertain Programming[M]: Physica-Verlag, Heidelberg, 2002.
[211] Ravi V, Murty BS, Reddy PJ. Nonequilibrium simulated annealing algorithm applied to reliability optimization of complex systems[J]. IEEE Transactions on Reliability, 1997, 46: 233-239.
[212] Zhou J, Liu B. New stochastic models for capacitated location-allocation problem[J]. Computers & Industrial Engineering, 2003, 45 (1): 111-125.
[213] Peng J, Liu B. Parallel machine scheduling models with fuzzy processing times[J]. Information Sciences, 2004, 166 (1): 49-66.
[214] Salami M, Hendtlass T. A fast evaluation strategy for evolutionary algorithms[J]. Applied Soft Computing, 2003, 2 (3): 156-173.
[215] Liu B. Uncertain Programming[M]: New York: Wiley, 1999.
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