进化计算优化前向神经网络的学习方法研究
|
摘要
系统仿真领域的研究难点和研究热点之一是对复杂系统进行仿真及建模研究。人工神经网络通过大量互连神经元之间连接权值的分布存储来表示网络的解题知识,具有并行处理、自学习和能以任意精度逼近任意非线性函数等特性,神经网络具有的这些优点使其适宜于复杂系统建模中。但神经网络在应用中还存在一些问题,譬如网络学习局部极小,收敛速度缓慢,网络结构设计复杂及泛化性能弱等缺点,神经网络的这些缺陷阻碍了其应用。神经网络学习从本质上说是网络结构与权值的优化过程,神经网络这些局限性都不可避免的会牵扯到网络学习中的优化问题。进化计算是一类模拟生物进化过程与机制求解问题的人工智能技术,进化计算具有智能性和本质并行性两大特点,它不受对象目标函数连续可微条件约束,在一些离散、多态、含噪声的优化问题中更显示出该方法独特的优势,进化计算具有的这些优点为解决神经网络自身缺陷提供了一条全新可行途径。
本文利用群体智能中的进化计算来解决神经网络在复杂系统建模中存在的主要问题,并将其应用于木材表面缺陷识别。主要研究内容如下：
首先,针对网络结构固定情况下传统BP学习方法对网络学习易陷入局部极值、学习精度不高等缺陷,提出一种基于BP算子的粒子群(PSO)优化神经网络权值的学习方法。该方法有效结合粒子群算法和BP算法优点,在PSO全局勘探和BP局部开发之间能给出一个较好的折中；更重要的是该结合方式能给PSO进化和BP搜索之间提供一个相互充分作用的机会,即在PSO每代寻优解的基础上执行BP操作可以获得精度更高的优化解,同时该优化解又返回到粒子群优化过程并共享其位置信息引导群体的快速进化,两种算法之间相辅相成,相互促进来达到共同的寻优目的。实验结果表明该学习方法学习精度高,收敛速度快,在性能上优于常规神经网络的学习方法。
其次,针对单一进化算法对复杂优化问题存在早熟收敛、优化效率低的问题,提出一种实数编码遗传算法与粒子群优化方法相结合的改进混合遗传算法(IHGA),该方法引入生态学中生态位构建思想,使得个体具有一定程度上的学习能力。采用遗传算法和粒子群算法的不同搜索机制共同作用于父代个体生成子代个体,一方面可以保持种群个体的多样性,同时也在一定程度上避免了算法早熟收敛。理论证明IHGA具有概率为1的全局收敛性,实验结果也表明该方法显著提高了算法优化性能及其优化解的可靠性。在此基础上,引入带连接开关的神经网络,提出一种基于IHGA的网络结构与权值并行调整优选方法,仿真结果表明该方法设计的网络学习精度高,结构节俭。
然后,研究了径向基网络(RBF)的设计问题,提出了一种基于PSO的RBF网络新设计方法,该方法由正则化正交最小二乘法与D-最优试验设计结合算法自动构建结构节俭的RBF网络模型；通过改进粒子群优化算法优选结合算法中影响网络泛化性能的三个学习参数,即基宽度参数、正则化系数和D-最优代价系数的最佳参数组合。仿真实例表明了该方法是一种较好的RBF网络设计方法。
在木材缺陷检测问题的研究工作中,表面缺陷检测技术一直占有重要的地位。木材表面缺陷模式识别通常采用人工神经网络技术,与其它检测技术相比,神经网络能够提高缺陷检测的准确率和检测效果,但同时仍然不能摆脱神经网络自身缺陷限制,使得其识别率不高。最后,将本文所提出的学习方法应用于木材表面缺陷识别中,与其它常见的网络学习方法做比较,并分析本文方法优缺点。结果表明采用本文方法构建的网络模型具有较高识别精度,且结构节俭,表明了本文提出的神经网络学习方法适宜应用于复杂网络模型建模中。
The research of simulation and modeling for the Complex System is one of a difficulty and a hot point in the System simulation research. The Artificial neural network, represents the network problem-solving knowledge through a large number of neurons which are connected to each other of using weights,has the characteristics of self-learning, parallel processing and also it can approximate any nonlinear function with arbitrary precision. The neural network is suitable for modeling complex systems because of its these advantages.However,there are some problems in the application of the neural network, for example, the minimum of network learning, the slow convergence speed,the compelx of network structure design and the weak of the generalization performance, all of these limitations prevent the neural network from applying in application fields. Neural network learning is essentially the optimization of network structure and weights, these limitations of the neural network will involve the optimal problems of network learning inevitably. The evolutionary computation is one of the artificial intelligence technology to simulate the evolution process and mechanism. The evolutionary computation is intelligent and parallelism of these two characteristics, and it is not affected by the target function which is continuously differentiable constrains,and it will show the unique advantage of this method in the problems of discrete,polymorphism and noise.The advantages of the evolutionary computation provide a new feasible way of solving the defects of neural network.
In this paper, we use evolutionary computation of the swarm intelligence to solve the main problems of neural networks in the modeling of complex systems, and also applied to the wood surface defect recognition. Main contents are as follows:
First of all, aiming at the problem that back-propagation (BP) learning algorithm is trapped easily in local minima and the BP learning precision is not high, a method for optimizing weights of neural network based on BP and particle swarm optimization is proposed. This method combines particle swarm optimization with back-propagation, and gives a good tradeoff between PSO global exploration and BP local exploitation. More importantly, this hybrid provides an opportunity to interact fully between PSO and BP, that is, BP operation can obtain better solution based on the result of PSO in each generation, meanwhile this solution returns back the PSO swarm and guides the swarm evolution rapidly through sharing its position information for swarm. The two algorithms supplement and promote each other to achieve the optimization purposes. Some simulation experiments show that this method has merits of high precision and rapid convergence speed, and its learning performance outperforms some prevail algorithms as to the neural network with fixed structure.
Single evolutionary algorithm has premature convergence, the low optimization efficiency, in complex optimization problems, so a improved hybrid genetic algorithm (IHGA), which is a combination of real-coded genetic algorithm and particle swarm optimization method, has been put forward.IHGA Introduces the idea of ecology niche construction, and makes individuals have the ability to learn. Different search mechanisms of genetic algorithm and particle swarm optimization to generate offspring, can maintain the diversity of the individuals,and to some extent avoid the algorithm premature convergence. Theory proved IHGA to have a probability of a global convergence.Experimental results also show that this method significantly improves the reliability of the algorithm to optimize performance and its optimal solution. On this basis, the neural network with the connection switch has been introduced and a method that simultaneously tunes structure and parameters of the neural network based on IHGA is proposed. The simulation results show that the network learning designed by the method has high precision and structure thrift.
Study on the radial basis function network (RBF) design problems, a new design method of RBF network based on PSO has been put forward. The method,which consists of regularized orthogonal least squares method and D-optimal experimental design combined algorithm automatically build the structure frugal RBF network model. Simulation examples show that the method is a better RBF network design method. Improved three learning parameters, base width parameter,regularization parameter,and D-optimal cost of coefficients,which affect generalization performance.The particle swarm optimization is used to search the optimal combination of three important learning parameters, i.e., the RBF width, the regularized parameter and D-optimality weight parameter, which influence the network's generalization ability.Simulation examples show that the method is a better RBF network design method.
Research in the wood defect detection problem, surface defects detection technology has always played an important role. The pattern recognition of surface defection commonly used artificial neural network technology. Compared with other detection technologies, the neural network can improve the accuracy and efficiency of detection, But still can not get rid of the neural network defect limits, which let the recognition rate be low. Finally, the proposed learning method is applied to the wood surface defect recognition and compared with other common network learning methods and analyze the advantages and disadvantages of this method. The results show that the network models constructed using the proposed method has higher recognition accuracy and frugality structure,and in this paper the neural network learning is a suitable method applied to a complex network modeling.
本文利用群体智能中的进化计算来解决神经网络在复杂系统建模中存在的主要问题,并将其应用于木材表面缺陷识别。主要研究内容如下：
首先,针对网络结构固定情况下传统BP学习方法对网络学习易陷入局部极值、学习精度不高等缺陷,提出一种基于BP算子的粒子群(PSO)优化神经网络权值的学习方法。该方法有效结合粒子群算法和BP算法优点,在PSO全局勘探和BP局部开发之间能给出一个较好的折中；更重要的是该结合方式能给PSO进化和BP搜索之间提供一个相互充分作用的机会,即在PSO每代寻优解的基础上执行BP操作可以获得精度更高的优化解,同时该优化解又返回到粒子群优化过程并共享其位置信息引导群体的快速进化,两种算法之间相辅相成,相互促进来达到共同的寻优目的。实验结果表明该学习方法学习精度高,收敛速度快,在性能上优于常规神经网络的学习方法。
其次,针对单一进化算法对复杂优化问题存在早熟收敛、优化效率低的问题,提出一种实数编码遗传算法与粒子群优化方法相结合的改进混合遗传算法(IHGA),该方法引入生态学中生态位构建思想,使得个体具有一定程度上的学习能力。采用遗传算法和粒子群算法的不同搜索机制共同作用于父代个体生成子代个体,一方面可以保持种群个体的多样性,同时也在一定程度上避免了算法早熟收敛。理论证明IHGA具有概率为1的全局收敛性,实验结果也表明该方法显著提高了算法优化性能及其优化解的可靠性。在此基础上,引入带连接开关的神经网络,提出一种基于IHGA的网络结构与权值并行调整优选方法,仿真结果表明该方法设计的网络学习精度高,结构节俭。
然后,研究了径向基网络(RBF)的设计问题,提出了一种基于PSO的RBF网络新设计方法,该方法由正则化正交最小二乘法与D-最优试验设计结合算法自动构建结构节俭的RBF网络模型；通过改进粒子群优化算法优选结合算法中影响网络泛化性能的三个学习参数,即基宽度参数、正则化系数和D-最优代价系数的最佳参数组合。仿真实例表明了该方法是一种较好的RBF网络设计方法。
在木材缺陷检测问题的研究工作中,表面缺陷检测技术一直占有重要的地位。木材表面缺陷模式识别通常采用人工神经网络技术,与其它检测技术相比,神经网络能够提高缺陷检测的准确率和检测效果,但同时仍然不能摆脱神经网络自身缺陷限制,使得其识别率不高。最后,将本文所提出的学习方法应用于木材表面缺陷识别中,与其它常见的网络学习方法做比较,并分析本文方法优缺点。结果表明采用本文方法构建的网络模型具有较高识别精度,且结构节俭,表明了本文提出的神经网络学习方法适宜应用于复杂网络模型建模中。
The research of simulation and modeling for the Complex System is one of a difficulty and a hot point in the System simulation research. The Artificial neural network, represents the network problem-solving knowledge through a large number of neurons which are connected to each other of using weights,has the characteristics of self-learning, parallel processing and also it can approximate any nonlinear function with arbitrary precision. The neural network is suitable for modeling complex systems because of its these advantages.However,there are some problems in the application of the neural network, for example, the minimum of network learning, the slow convergence speed,the compelx of network structure design and the weak of the generalization performance, all of these limitations prevent the neural network from applying in application fields. Neural network learning is essentially the optimization of network structure and weights, these limitations of the neural network will involve the optimal problems of network learning inevitably. The evolutionary computation is one of the artificial intelligence technology to simulate the evolution process and mechanism. The evolutionary computation is intelligent and parallelism of these two characteristics, and it is not affected by the target function which is continuously differentiable constrains,and it will show the unique advantage of this method in the problems of discrete,polymorphism and noise.The advantages of the evolutionary computation provide a new feasible way of solving the defects of neural network.
In this paper, we use evolutionary computation of the swarm intelligence to solve the main problems of neural networks in the modeling of complex systems, and also applied to the wood surface defect recognition. Main contents are as follows:
First of all, aiming at the problem that back-propagation (BP) learning algorithm is trapped easily in local minima and the BP learning precision is not high, a method for optimizing weights of neural network based on BP and particle swarm optimization is proposed. This method combines particle swarm optimization with back-propagation, and gives a good tradeoff between PSO global exploration and BP local exploitation. More importantly, this hybrid provides an opportunity to interact fully between PSO and BP, that is, BP operation can obtain better solution based on the result of PSO in each generation, meanwhile this solution returns back the PSO swarm and guides the swarm evolution rapidly through sharing its position information for swarm. The two algorithms supplement and promote each other to achieve the optimization purposes. Some simulation experiments show that this method has merits of high precision and rapid convergence speed, and its learning performance outperforms some prevail algorithms as to the neural network with fixed structure.
Single evolutionary algorithm has premature convergence, the low optimization efficiency, in complex optimization problems, so a improved hybrid genetic algorithm (IHGA), which is a combination of real-coded genetic algorithm and particle swarm optimization method, has been put forward.IHGA Introduces the idea of ecology niche construction, and makes individuals have the ability to learn. Different search mechanisms of genetic algorithm and particle swarm optimization to generate offspring, can maintain the diversity of the individuals,and to some extent avoid the algorithm premature convergence. Theory proved IHGA to have a probability of a global convergence.Experimental results also show that this method significantly improves the reliability of the algorithm to optimize performance and its optimal solution. On this basis, the neural network with the connection switch has been introduced and a method that simultaneously tunes structure and parameters of the neural network based on IHGA is proposed. The simulation results show that the network learning designed by the method has high precision and structure thrift.
Study on the radial basis function network (RBF) design problems, a new design method of RBF network based on PSO has been put forward. The method,which consists of regularized orthogonal least squares method and D-optimal experimental design combined algorithm automatically build the structure frugal RBF network model. Simulation examples show that the method is a better RBF network design method. Improved three learning parameters, base width parameter,regularization parameter,and D-optimal cost of coefficients,which affect generalization performance.The particle swarm optimization is used to search the optimal combination of three important learning parameters, i.e., the RBF width, the regularized parameter and D-optimality weight parameter, which influence the network's generalization ability.Simulation examples show that the method is a better RBF network design method.
Research in the wood defect detection problem, surface defects detection technology has always played an important role. The pattern recognition of surface defection commonly used artificial neural network technology. Compared with other detection technologies, the neural network can improve the accuracy and efficiency of detection, But still can not get rid of the neural network defect limits, which let the recognition rate be low. Finally, the proposed learning method is applied to the wood surface defect recognition and compared with other common network learning methods and analyze the advantages and disadvantages of this method. The results show that the network models constructed using the proposed method has higher recognition accuracy and frugality structure,and in this paper the neural network learning is a suitable method applied to a complex network modeling.
引文
[1]李坚.中国木材研究.哈尔滨：东北林业大学出版社,1995：6-25
[2]Tatt Hee Oong, N.A.M. Isa.Adaptive Evolutionary Artificial Neural Networks for Pattern Classification. IEEE Transactions on Neural Networks.2011,22(11):1823-1836
[3]王克奇,白雪冰.木材表面缺陷的模式识别方法.北京：科学出版社,2011：1-3,49-52
[4]Kuan-Hao Su, Liang-Chih Wu, Jih-Shian Lee, et al. A Novel Method to Improve Image Quality for 2-D Small Animal PET Reconstruction by Correcting a Monte Carlo-Simulated System Matrix Using an Artificial Neural Network. IEEE Transactions on Nuclear Science. 2009,56(3):704-714
[5]Boely N,Botez R M.New Approach for the identification and validation of a nonlinear F/A-18 model by use of neural networks. IEEE Transactions on Neural Networks,2010,21(11):1759-1765
[6]Nascimento C F,Oliveria A A,Goedtel A,Silva I N,Serni P J A. Neural network-based approach for identification of the harmonic content of a nonlinear load in a single-phase system.IEEE Latin America Transactions,2010,8(1):65-73
[7]Zhao H Q,Zeng X P,He Z Y.Low-complexity nonlinear adaptive filter based on a pipelined bilinear recurrent neural network.IEEE Transactions on Neural Networks,2011,22(9):1494-1507
[8]Barbounis T QTheocharis J B.A locally recurrent fuzzy neural network with application to the wind speed prediction using spatial correlation.Neurocomputing,2006,70(7-9):1525-1542
[9]F.N. Khan, T.S.R. Shen, Yudi Zhou, et al. Optical Performance Monitoring Using Artificial Neural Networks Trained With Empirical Moments of Asynchronously Sampled Signal Amplitudes. IEEE Photonics Technology Letters.2012,24(12):982-984
[10]E. Ostlin, H. Zepernick, H. Suzuki. Macrocell Path-Loss Prediction Using Artificial Neural Networks. IEEE Transactions on Vehicular Technology.2010,59(6):2735-2747
[11]Ferrari S.Multiobjective algebraic synthesis of neural control systems by implicit model following.IEEE Transactions on Neural Networks,2009,20(3):406-419
[12]Park J H,Kim S H,Moon C J.Adaptive neural control for strict-feedback nonlinear systems without backstepping. IEEE Transactions on Neural Networks,2009,20(7).1204-1209
[13]Hou Z G, Gupta M M,Nikiforuk P N,Tan M,Cheng L.A recurrent neural network for hierarchical control of interconnected dynamic systems.IEEE Transactions on Neural Networks,2007,18(2):466-481
[14]Talebi H A,Khorasani K,Tafazoli S.A recurrent neural-network-based sensor and actuator fault detection and isolation for nonlinear systems with application to the satellite, s attitude control subsystem.IEEE Transactions on Neural Networks,2009,20(1):45-60
[15]Cho H C,Knowles J,Fadali M S,Lee K S.Fault detection and isolation of induction motors using recurrent neural networks and dynamic Bayesian modeling.IEEE Transactions on Control Systems Technology,2010,18(2):430-437
[16]Mousapha A I,Selmic R R.Wireless sensor network modeling using modified recurrent neural networks:application to fault detection.IEEE Transactions on Instrumentation and Measurement,2008,57(5):981-988
[17]Siakavara, K., Goulemes, V. Artificial Neural Network and Analytical Method-Based Control of Higher Harmonic Radiation From Active Antenna Arrays. IEEE Antennas and Wireless Propagation Letters.2008,7:26-30
[18]Vapnik V, Levin E, LeCun Y. Measuring the VC-dimension of a learning machine.Neural Computation,1994,(6):851-876
[19]魏海坤,徐嗣鑫,宋文忠.神经网络的泛化理论和泛化方法.自动化学报,2001,27(6)：806-815
[20]Chi-Keong Goh, Eu-Jin Teoh, Kay Chen Tan. Hybrid Multiobjective Evolutionary Design for Artificial Neural Networks. IEEE Transactions on Neural Networks.2008,19(9):1531-1548
[21]Castro P.A.D., Von Zuben F.J. Learning Ensembles of Neural Networks by Means of a Bayesian Artificial Immune System. IEEE Transactions on Dielectrics and Electrical Insulation.2011,22(2):304-316
[22]Mkadem F., Boumaiza S. Extended Hammerstein Behavioral Model Using Artificial Neural Networks. IEEE Transactions on Microwave Theory and Techniques.2009, 57(4):745-751
[23]McFall K.S., Mahan J.R. Artificial Neural Network Method for Solution of Boundary Value Problems With Exact Satisfaction of Arbitrary Boundary Conditions. IEEE Transactions on Neural Networks.2009,20(8):1221-1233
[24]C.R.Darwin.On the Origin of Species by Means of Natural Selection or Preservation of Favoured Races in the Struggle for Life. Murray, London,1859
[25]Andries P. Engelbrecht.计算群体智能基础.谭营等译.北京：清华大学出版社,2009：47-54,39-40,47-48,61-66
[26]J.H.Holland.Adaptation in Natural and Artificial Systems.The University of Michigan Press,1975
[27]Xiangning Lin, Shuohao Ke, Zhengtian Li. A Fault Diagnosis Method of Power Systems Based on Improved Objective Function and Genetic Algorithm-Tabu Search. IEEE Transactions on Power Delivery,2010,25(3):1268-1274
[28]GuangJian Tian, Yong Xia, Yanning Zhang. Hybrid Genetic and Variational Expectation-Maximization Algorithm for Gaussian-Mixture-Model-Based Brain MR Image Segmentation. IEEE Transactions on Information Technology in Biomedicine.2011, 15(3):373-380
[29]Youngjun Ahn, Jiseong Park, Cheol-Gyun Lee et al. Novel Memetic Algorithm implemented With GA (Genetic Algorithm) and MADS (Mesh Adaptive Direct Search) for Optimal Design of Electromagnetic System. IEEE Transactions on Magnetics.2010, 46(6):1982-1985
[30]Aminifar F., Lucas C, Khodaei A. et al. Optimal Placement of Phasor Measurement Units Using Immunity GeneticAlgorithm. IEEE Transactions on IPower Delivery.2009, 24(3):1014-1020
[31]Wei Cheng, Haoshan Shi, Xipeng Yin et al. An Elitism Strategy Based Genetic Algorithm for Streaming Pattern Discovery in Wireless Sensor Networks. IEEE Communications Letters.2011,15(4):419-421
[32]Gonzalez-Longatt F.M., Wall, P., Regulski P.et al.Optimal Electric Network Design for a Large Offshore Wind Farm Based on a Modified Genetic Algorithm Approach. IEEE Systems Journal.2012,6(1):164-172
[33]J. A. Vasconcelos, J. A. Ramirez, R. H. C. Takahashi, et al. Improvements in Genetic Algorithms. IEEE Transactions on Magnetics.2001,37(5):3414-3417
[34]Y. W. Leung, Y. P. Wang. An Orthogonal Genetic Algorithm with Quantization for Global Numerical Optimization. IEEE Transactions on Evolutionary Computation.2001,5(1):41-53
[35]庄健,杨清宇,杜海峰,于德弘.一种高效的复杂系统遗传算法.软件学报,2010,21(11)：2790-2801
[36]F. H. F. Leung, H. K. Lam, S. H. Ling, et al. Tuning of the Structure and Parameters of a Neural Network Using an Improved Genetic Algorithm. IEEE Transactions on Neural Networks.2003,14(l):79-88
[37]彭晓波,桂卫华,黄志武,胡志坤,李勇刚.GAPSO：一种高效的遗传粒子混合算法及其应用.系统仿真学报,2008,20(18)：5025-5027
[38]Z. G.Tu, Y. Lu. A Robust Stochastic Genetic Algorithm (StGA) for Global Numerical Optimization. IEEE Transactions on Evolutionary Computation.2004,8(5):456-470
[39]D.W. Boeringer, D. H.Werner, D. Machuga. A Simultaneous Parameter Adaptation Scheme for Genetic Algorithms with Application to Phased Array Synthesis. IEEE Transactions on Antennas and Propagation.2005,53(1):356-371
[40]X. D. Chen, J. G. Qian, G. Z. Ni, et al. An Improved Genetic Algorithm for Global Optimization of Electromagnetic Problems. IEEE Transactions on Magnetics.2001, 37(5):3579-3583
[41]C. Y. Lee. Entropy-Boltzmann Selection in the Genetic Algorithms. IEEE Transactions on System, Man, and Cybernetics-Part B:Cybernetics.2003,33(1):138-142
[42]W. C. Zhong, J. Liu, M. Z. Xue, et al. A Multiagent Genetic Algorithm for Global Numerical Optimization. IEEE Transactions on System, Man, and Cybernetics-Part B: Cybernetics.2004,34(2):1128-1141
[43]J. Kennedy, R. C. Eberhart. Particle Swarm Optimization. Proceedings of IEEE International Conference on Neural Networks. Perth, WA, Australia,1995:1942-1948
[44]Das Sharma K.,Chatterjee A.,Rakshit A. A Random Spatial 1best PSO-Based Hybrid Strategy for Designing Adaptive Fuzzy Controllers for a Class of Nonlinear Systems.IEEE Transactions on Instrumentation and Measurement.2012,61(6):1605-1621
[45]Chia-Nan Ko, Ying-Pin Chang, Chia-Ju Wu. A PSO Method With Nonlinear Time-Varying Evolution for Optimal Design of Harmonic Filters. IEEE Transactions on Power Systems. 2009,24(1):437-444
[46]Vlachogiannis J.G, Lee K.Y. Economic Load Dispatch—A Comparative Study on Heuristic Optimization Techniques With an Improved Coordinated Aggregation-Based PSO. IEEE Transactions on Power Systems.2009,24(2):991-1001
[47]Y. Shi, R. C. Eberhart. Parameter Selection in Particle Swarm Optimization. Proceedings ofEvolutinary Programming VII:EP98. New York,1998:591-600
[48]R. C. Eberhart, Y. Shi. Evolving Artificial Neural Network. Proceedings of Int'1 Conference on Neural Networks and Brain. Beijing, P.R.C.,1998
[49]Y. Shi, R. C. Eberhart. Fuzzy Adaptive Particle Swarm Optimization. Proceedings of the 2001 Congress on Evolutionary Computation. Seoul, South Korea,2001:101-106
[50]J. Riget, J. S. Vesterstroem. A Diversity-Guided Particle Swarm Optimizer-The ARPSO. Technical Report No.2002-02. Department of Computer Science, University of Aarhus, 2002
[51]M. Clerc, J. Kennedy. The Particle Swarm-Explosion, Stability, and Convergence in a Multidimensional Complex Space. IEEE Transactions on Evolutionary Computation.2002, 6(1):58-73
[52]J. Robinson, Y. Rahmat-Samii. Particle Swarm Optimization in Electronmagnetics. IEEE Transactions on Antennas and Propagation.2004,52(2):397-407
[53]G.Ciuprina, D. loan, I. Munteanu. Use of Intelligent-Particle Swarm Optimization in Electromagnetics. IEEE Transactions on Magnetics.2002,38(2):1037-1040
[54]慕彩红,焦李成,刘逸。M-精英协同进化数值优化算法.软件学报,2009,20(11)：2925-2938
[55]倪庆剑,张志政,王幕蔡,邢汉承。一种基于可变多簇结构的动态概率粒子群优化 算法.软件学报,2009,20(2)：339-349
[56]S. Naka, T. Genji, T. Yura, et al. A Hybrid Particle Swarm Optimization for Distribution State Estimation. IEEE Transactions on Power System.2003,18(1):60-68
[57]迟玉红,孙富春等.基于空间缩放和吸引子的粒子群优化算法.计算机学报,2011,34(1)：115-130
[58]A. A. A. Esmin, G.Lambert-Torres, A. C. Z. de Souza. A Hybrid Particle Swarm Optimization Applied to Loss Power Minimization. IEEE Transactions on Power System. 2005,20(2):859-866
[59]许相莉,利彪,向东,等.基于粒子群的图像检索相关反馈算法[J].电子学报,2010,38(8)：1935-1940
[60]吴扬,姜守达.基于嵌套粒子群算法的多涡环微下击暴流模型参数选择方法.电子学报,2012,40(1)：204-208
[61]Y. Liu, Z. Qin, Z. W. Shi, et al. Center Particle Swarm Optimization. Neurocomputing. 2007,70(4-6):672-679
[62]F. van den Bergh, A. P. Engelbrecht. A Cooperative Approach to Particle Swarm Optimization. IEEE Transactions on Evolutionary Computation.2004,8(3):225-239
[63]S.Das ectal.Particle Swarm Optimization and Differential Evolution Algorithms:Technical Analysis,Applications and Hybridization Prespectives.Studies in Computional Intelligence.2008,116:1-38
[64]B. Zhao, C. X. Guo, Y. J. Cao. A Multiagent-Based Particle Swarm Optimization Approach for Optimal Reactive Power Dispatch. IEEE Transactions on Power System.2005, 20(2):1070-1078
[65]Yi-Tung Kao. Erwie Zahara. A hybrid genetic algorithm and particle swarm optimization for multimodal functions. Applied Soft Computing.2008,8:849-857
[66]Zhang Feizhou, Cao Xuejun, Yang Dongkai. Intelligent scheduling of public traffic vehicles based on a hybrid genetic algorithm. Tsinghua Science and Technology.2008, 13(5):625-631
[67]Taejin Park, Kwang Ryel Ryu. A Dual-Population Genetic Algorithm for Adaptive Diversity Control. IEEE Transactions on Evolutionary Computation.2010,14(6):865-884
[68]Xiao Min Hu, Jun Zhang, Yan Yu et al. Hybrid Genetic Algorithm Using a Forward Encoding Scheme for Lifetime Maximization of Wireless Sensor Networks. IEEE Transactions on Evolutionary Computation.2010,15(4):766-781
[69]Shutao Li Mingkui Tan, Tsang I.W. et al. A Hybrid PSO-BFGS Strategy for Global Optimization of Multimodal Functions. IEEE Transactions on Systems, Man, and Cybernetics, Part B:Cybernetics,2011,41(4):1003-1014
[70]X. Yao. A Review of Evolutionary Artificial Neural Networks. International Journal of Intelligent Systems.1993,8(4):539-567
[71]D. E. Rumelhart, G E. Hinton, R. J. Williams. Learning Representation by Back-Propagation Errors. Nature.1986,7:149-154
[72]S. E. Fahlman. Faster Learning Variations on Backpropagation:An Empirical Study. Proceedings of the Connectionist Models Summer School. San Mateo:Morgan Kauffmann, 1988:38-51
[73]R. Battiti. First and Second Order Methods for Learning:Between Steepest Descent and Newton's Method. Neural Computation.1992,4(2):141-166
[74]孙健,柴毅,李华锋,朱智勤.一种基于极点配置稳定的新型局部递归神经网络.自动化学报,2012,38(2)：183-196
[75]韩冰,韩敏.基于动态BP算法的非线性滞后系统辨识.大连理工大学学报,2010,50(5)：777-781
[76]S. Shah, F. Palmieri, M. Datum. Optimal Filtering Algorithms for Learning in Feedforward Neural Network. Neural Networks.1992,5(5):779-787
[77]杨国为,王守觉,闫庆旭.分式线性神经网络及其非线性逼近能力研究.计算机学报,2007,30(2)：189-199
[78]陈果.神经网络模型的预测精度影响因素分析及其优化.模式识别与人工智能,2005,18(5)：528-534
[79]李祚泳,易勇鸷.BP网络学习能力与泛化能力之间的定量关系式.电子学报,2003,31(9)：1341-1344
[80]杨甲沛,李锵,刘郑,袁晓琳.基于自适应学习速率的改进型BP算法研究.计算机工程与应用,2009,45(11)：56-58
[81]S. Acikbas, M.T. Soylemez. Coasting point optimisation for mass rail transit lines using artificial neural networks and genetic algorithms. IET Electric Power Applications.2008, 2(3):172-182
[82]C. S. Koh, O. A. Mohammed, S. Y. Hahn. Detection of Magnetic Body Using Artificial Neural Network with Modified Simulated Annealing. IEEE Transactions on Magnetics. 1994,30(5):3644-3647
[83]李祚泳,汪嘉杨,郭淳.PSO算法优化BP网络的新方法及仿真实验.电子学报,2008,36(11)：2224-2228
[84]郝红卫,蒋蓉蓉.基于最近邻规则的神经网络训练样本选择方法.自动化学报,2007,33(12)：1247-1251
[85]潘昊,王晓勇,陈琼,等.基于遗传算法的BP神经网络技术的应用.计算机应用,2005,25(12)：2777-2779
[86]潘昊,侯清兰.基于粒子群优化算法的BP网络学习研究.计算机工程与应用,2006,16：41-43
[87]X.Yao.Evolving Artificial Neural Networks. Proceedings of the IEEE.1999,87:1423-1447
[88]D.Yi,X.R.Ge. An Improved PSO-Based Ann with Simulated Annealing Technique. Neurocomputing.2005,63:527-533
[89]杨博,苏小红,王亚东.基于注意力模型的混合学习算法.软件学报,2005,16(6)：1073-1080
[90]X. D. Cai, N. Zhang, G. K. Venayagamoorthy, et al. Time Series Prediction with Recurrent Neural Networks Trained by a Hybrid PSO-EA Algorithm. Neurocomputing.2007,70(13-15):2342-2353
[91]Y.Song, Z.Q.Chen,Z.Z.Yuan. New Chaotic PSO-Based Neural Network Predictive Control for Nonlinear Process. IEEE Transactions on Neural Networks.2007,18(2):595-600
[92]Y. Shi, R. C. Eberhart. A Modified Particle Swarm Optimizer. Proceedings of IEEE International Conference on Evolutionary Computation. Anchorage, AK, USA,1998:69-73
[93]J. Kennedy. The Particle Swarm:Social Adaptation of Knowledge. Proceedings of IEEE International Conference on Evolutionary Computation. Indianapolis, IN, USA,1997:303-308
[94]P.N.Suganthan.Particle Swarm Optimiser with Neighborhood Operator. In Proceedings of the IEEE Congress on Evolutionary Computation,1999:1958-1962
[95]J. Kennedy and R. Mendes. Population structure and particle swarm performance. In Proceedings of the IEEE Congress on Evolutionary Computation,2002,2:1671-1676
[96]Jung-Hsien Chiang, Shing-Hua Ho. A Combination of Rough-Based Feature Selection and RBF Neural Network for Classification Using Gene Expression Data.IEEE Transactions on NanoBioscience.2008,7(1):91-99
[97]Ahn CW, Ramakrishna RS. Elitism-Based compact genetic algorithms. IEEE Trans, on Evolutionary Computation,2003,7(4):367-385
[98]Huang T, Mohan A S, A hybrid boundary condition for robust particle swarm optimization. IEEE Antennas and Wireless Propagation Letters,2005,4(1):112-117
[99]Eduardo D.SONTAG.VC dimension of neural network. Neural Networks and Machine Learning,1998,168:69-95.
[100]Mass W. Neural nets with superlinear VC-dimension. Neural Computation,1994, (6):877-884
[101]Y. Q. Chen, D. W. Thomas, M. S. Nixon. Generating-Shrinking Algorithm for Learning Arbitrary Classification. Neural Networks.1994,7(9):1477-1489
[102]C. C. Teng, B.W.Wah. Automated Learning for Reducing the Configuration of a Feedforward Neural Network. IEEE Transactions on Neural Networks.1996,7(5):1072-1085
[103]高海兵,高亮,周驰,等.基于粒子群优化的神经网络训练算法研究.电子学报,2004,32(9)：1572-1574
[104]J. B. Yu, L. F. Xi, S. J. Wang. An Improved Particle Swarm Optimization for Evolving Feedforward Artificial Neural Networks. Neural Processing Letters.2007,26(3):217-231
[105]X. Yao, Y. Liu. A New Evolutionary System for Evolving Artificial Neural Networks. IEEE Transactions on Neural Networks.1997,8(3):694-713
[106]A. Blum, R. L. Rivest. Training a 3-node Neural Network Is NP-Complete. Neural Networks.1992,5(1):117-127
[107]T. Back. Selective Pressure in Evolutionary Algorithms:A Characterization of Selection Mechanisms. In Proceedings of the First IEEE Conference on Evolutionary Computation, 1994,1:57-62
[108]韩晓卓,李自珍,惠苍,岳东霞.物种生态位构建理论与双点位基因模型应用.西北植物学报,2004,24(3)：558—562
[109]S.C. Esquivel and C. A. Coello. On the Use of Particle Swarm Optimization with Multimodal Functions. In Proceedings of the IEEE Transactions on Evotutionary Computation,2003,2(12):1130-1136
[110]焦李成,刘静,钟伟才.协同进化计算与多智能体系统.北京：科学出版社,2006：84-87
[111]江瑞,罗予频,胡东成,等.一种协调勘探和开采的遗传算法：收敛性及性能分析.计算机学报.2001,24(12)：1233-1241
[112]G.Rudolph. Convergence Analysis of Canonical Genetic Algorithms. IEEE Transactions on Neural Networks.1994,5(1):96-101
[113]M. Iosifescu. Finite Markov Processes and Their Applications. Willey,1980
[114]刘波.粒子群优化算法及其在机电设备中的应用研究.中北大学博士学位论文,2011：39-45
[115]X. Yao, Y. Liu, G. M. Lin. Evolutionary Programming Made Faster. IEEE Transactions on Evolutionary Computation.1999,3(2):82-102
[116]J. T. Tsai, J. H. Chou, T. K. Liu. Tuning the Structure and Parameters of a Neural Network by Using Hybrid Taguchi-Genetic Algorithm. IEEE Transactions on Neural Networks.2006,17(1):69-80
[117]H. K. Lam, S. H. Ling, F. H. F. Leung, et al. Tuning of the Structure and Parameters of Neural Network Using an Improved Genetic Algorithm. The 27th Annual Conference of the IEEE Industrial Electronics Society. Denver, CO, USA,2001:25-30
[118]Mingli Song, Dacheng Tao, Xiaoqin Huang et al. Three-Dimensional Face Reconstruction From a Single Image by a Coupled RBF Network. IEEE Transactions on Image Processing.2012,21(5):2887-2897
[119]Ke Meng, Zhao Yang Dong, Dian Hui Wang et al. A Self-Adaptive RBF Neural Network Classifier for Transformer Fault Analysis.IEEE Transactions on Power Systems.2010, 25(3):1350-1360
[120]Muzhou Hou, Xuli Han. Constructive Approximation to Multivariate Function by Decay RBF Neural Network.IEEE Transactions on Neural Networks.2010,21(9):1517-1523
[121]X. Hong, C. J. Harris. Nonlinear Model Structure Design and Construction Using Orthogonal Least Squares and D-Optimality Design. IEEE Transactions on Neural Networks.2002,13(5):1245-1250
[122]Platt J.A resource-allocating network for function interpolation. Neural Computation, 1991,3(2):213-225
[123]Lu Y W,Sundararajan N,Saratchandran P.A sequential learning scheme for function approximation using minimal radial basis function neural networks.Neural Computation, 1997,9(2):461-478
[124]Esposito A,Marinaro M,Oricchio D,Scarpetta S.Approximation of continuous and discontinuous mappings by a growing neural RBF-based algorithm.Neural Networks, 2000,13(6):651-665
[125]Gonzalez J,Rojas I,Ortega J,Pomares H.Multiobjective evolutionary optimization of the size,shape,and position parameters of radial basis function networks for function approximation.IEEE Transactions on Neural Networks,2003,14(6):1478-1495
[126]L. Guo, D. S. Huang,W. B. Zhao. Combining Genetic Optimisation with Hybrid Learning Algorithm for Radial Basis Function Neural Networks. Electronics Letters, 2003,39(22):1600-1601
[127]Fu X J,Wang L P.Data dimensionality reduction with application to simplifying RBF network structure and improving classification performance.IEEE Transactions on Systems,Man,and Cybernetics,Part B:Cybernetics,2003,33(3):399-409
[128]Huang G B,Saratchandran P,Sundararajan N.A generalized growing and pruning RBF(GGAP-RBF)neural network for function approximation.IEEE Transactions on Neural Networks,2005,16(1):57-57
[129]Feng H M.Self-generation RBFNs using evolutional PSO learning.Neurocomputing, 2006,70(1-3):241-251
[130]F. A. Guerra, L. dos S. Coelho. Multi-step Ahead Nonlinear Identification of Lorenz's Chaotic System Using Radial Basis Neural Network with Learning by Clustering and Particle Swarm Optimization. Chaos, Solitons & Fractals.2008,35(5):967-979
[131]Lian J M,Lee Y G,Scott D S,Stanislaw H Z.Self-organizing radial basis function network for real-time approximation of continuous-time dynamical systems.IEEE Transactions on Neural Networks,2008,19(3):460-474
[132]Huang D S,Du J X.A constructive hybrid structure optimization methodology for radial basis probabilistic neural networks.IEEE Transactions on Neural Networks,2008, 19(12):2099-2115
[133]Chen S,Hong X,Luk B L,Harris C J.Construction of tunable radial basis function networks using orthogonal forward selection.IEEE Transactions on Systems,Man,and Cybernetics,Part B:Cybernetics,2009,39(2):457-466
[134]乔俊飞,韩红桂.RBF神经网络的结构动态优化设计.自动化学报,2010,36(6)：865-872
[135]韩红桂,乔俊飞,薄迎春.基于信息强度的RBF神经网络结构设计研究.自动化学报,2012,38(7)：1083-1090
[136]S. Chen, C. F. N. Cowan, P. M. Grant. Orthogonal Least Squares Learning Algorithm for Radial Basis Function Neural Networks. IEEE Transactions on Neural Networks.1991, 2(2):302-309
[137]S. Chen, E. S. Chng, K. Alkadhimi. Regularized Orthogonal Least Squares Algorithm for Constructing Radial Basis Function Networks. International Journal of Control.1996, 64(5):829-837
[138]X. Hong, C. J. Harris. Nonlinear Model Structure Detection Using Optimum Experimental Design and Orthogonal Least Squares. IEEE Transactions on Neural Networks,2001,12(2):435-439
[139]S. Chen, X. Hong, C. J. Harris. Sparse Kernel Regression Modeling Using Combined Locally Regularized Orthogonal Least Squares and D-Optimality Experimental Design. IEEE Transactions on Automatic Control.2003,48(6):1029-1036
[140]X. Hong, P. M. Sharkey, K. Warwick. A Robust Nonlinear Identification Algorithm Using PRESS Statistic and Forward Regression. IEEE Transactions on Neural Networks. 2003,14(2):454-458
[141]X. Hong, C. J. Harris, S. Chen, et al. Robust Nonlinear Model Identification Methods Using Forward Regression. IEEE Transactions on System, Man, and Cybernetics-Part A: Systems and Humans.2003,33(4):514-523
[142]S. Chen, Y. Wu, B. L. Luk. Combined Genetic Algorithm Optimization and Regularized Orthogonal Least Squares Learning for Radial Basis Function Networks. IEEE Transactions on Neural Networks.1999,10(5):1239-1243
[143]赵温波,杨鹭怡,王立明.径向基概率神经网络的混合结构优化算法.系统仿真学报,2004,16(10)：2175-2180
[144]白雪冰,王克奇,王辉.基于灰度共生矩阵的木材纹理分类方法的研究.哈尔滨工业大学学报,2005,37(12)：1667-1670
[145]马明宇,王桂芸,黄安民,张卓勇,相玉红,顾轩.人工神经网络结合近红外光谱用于木 材树种识别.光谱学与光谱分析,2012,32(9)：2377-2381
[146]孙建平,王逢瑚,胡英成.基于声发射和神经网络的木材受力损伤过程检测.仪器仪表学报,2011,32(2)：342-347
[2]Tatt Hee Oong, N.A.M. Isa.Adaptive Evolutionary Artificial Neural Networks for Pattern Classification. IEEE Transactions on Neural Networks.2011,22(11):1823-1836
[3]王克奇,白雪冰.木材表面缺陷的模式识别方法.北京：科学出版社,2011：1-3,49-52
[4]Kuan-Hao Su, Liang-Chih Wu, Jih-Shian Lee, et al. A Novel Method to Improve Image Quality for 2-D Small Animal PET Reconstruction by Correcting a Monte Carlo-Simulated System Matrix Using an Artificial Neural Network. IEEE Transactions on Nuclear Science. 2009,56(3):704-714
[5]Boely N,Botez R M.New Approach for the identification and validation of a nonlinear F/A-18 model by use of neural networks. IEEE Transactions on Neural Networks,2010,21(11):1759-1765
[6]Nascimento C F,Oliveria A A,Goedtel A,Silva I N,Serni P J A. Neural network-based approach for identification of the harmonic content of a nonlinear load in a single-phase system.IEEE Latin America Transactions,2010,8(1):65-73
[7]Zhao H Q,Zeng X P,He Z Y.Low-complexity nonlinear adaptive filter based on a pipelined bilinear recurrent neural network.IEEE Transactions on Neural Networks,2011,22(9):1494-1507
[8]Barbounis T QTheocharis J B.A locally recurrent fuzzy neural network with application to the wind speed prediction using spatial correlation.Neurocomputing,2006,70(7-9):1525-1542
[9]F.N. Khan, T.S.R. Shen, Yudi Zhou, et al. Optical Performance Monitoring Using Artificial Neural Networks Trained With Empirical Moments of Asynchronously Sampled Signal Amplitudes. IEEE Photonics Technology Letters.2012,24(12):982-984
[10]E. Ostlin, H. Zepernick, H. Suzuki. Macrocell Path-Loss Prediction Using Artificial Neural Networks. IEEE Transactions on Vehicular Technology.2010,59(6):2735-2747
[11]Ferrari S.Multiobjective algebraic synthesis of neural control systems by implicit model following.IEEE Transactions on Neural Networks,2009,20(3):406-419
[12]Park J H,Kim S H,Moon C J.Adaptive neural control for strict-feedback nonlinear systems without backstepping. IEEE Transactions on Neural Networks,2009,20(7).1204-1209
[13]Hou Z G, Gupta M M,Nikiforuk P N,Tan M,Cheng L.A recurrent neural network for hierarchical control of interconnected dynamic systems.IEEE Transactions on Neural Networks,2007,18(2):466-481
[14]Talebi H A,Khorasani K,Tafazoli S.A recurrent neural-network-based sensor and actuator fault detection and isolation for nonlinear systems with application to the satellite, s attitude control subsystem.IEEE Transactions on Neural Networks,2009,20(1):45-60
[15]Cho H C,Knowles J,Fadali M S,Lee K S.Fault detection and isolation of induction motors using recurrent neural networks and dynamic Bayesian modeling.IEEE Transactions on Control Systems Technology,2010,18(2):430-437
[16]Mousapha A I,Selmic R R.Wireless sensor network modeling using modified recurrent neural networks:application to fault detection.IEEE Transactions on Instrumentation and Measurement,2008,57(5):981-988
[17]Siakavara, K., Goulemes, V. Artificial Neural Network and Analytical Method-Based Control of Higher Harmonic Radiation From Active Antenna Arrays. IEEE Antennas and Wireless Propagation Letters.2008,7:26-30
[18]Vapnik V, Levin E, LeCun Y. Measuring the VC-dimension of a learning machine.Neural Computation,1994,(6):851-876
[19]魏海坤,徐嗣鑫,宋文忠.神经网络的泛化理论和泛化方法.自动化学报,2001,27(6)：806-815
[20]Chi-Keong Goh, Eu-Jin Teoh, Kay Chen Tan. Hybrid Multiobjective Evolutionary Design for Artificial Neural Networks. IEEE Transactions on Neural Networks.2008,19(9):1531-1548
[21]Castro P.A.D., Von Zuben F.J. Learning Ensembles of Neural Networks by Means of a Bayesian Artificial Immune System. IEEE Transactions on Dielectrics and Electrical Insulation.2011,22(2):304-316
[22]Mkadem F., Boumaiza S. Extended Hammerstein Behavioral Model Using Artificial Neural Networks. IEEE Transactions on Microwave Theory and Techniques.2009, 57(4):745-751
[23]McFall K.S., Mahan J.R. Artificial Neural Network Method for Solution of Boundary Value Problems With Exact Satisfaction of Arbitrary Boundary Conditions. IEEE Transactions on Neural Networks.2009,20(8):1221-1233
[24]C.R.Darwin.On the Origin of Species by Means of Natural Selection or Preservation of Favoured Races in the Struggle for Life. Murray, London,1859
[25]Andries P. Engelbrecht.计算群体智能基础.谭营等译.北京：清华大学出版社,2009：47-54,39-40,47-48,61-66
[26]J.H.Holland.Adaptation in Natural and Artificial Systems.The University of Michigan Press,1975
[27]Xiangning Lin, Shuohao Ke, Zhengtian Li. A Fault Diagnosis Method of Power Systems Based on Improved Objective Function and Genetic Algorithm-Tabu Search. IEEE Transactions on Power Delivery,2010,25(3):1268-1274
[28]GuangJian Tian, Yong Xia, Yanning Zhang. Hybrid Genetic and Variational Expectation-Maximization Algorithm for Gaussian-Mixture-Model-Based Brain MR Image Segmentation. IEEE Transactions on Information Technology in Biomedicine.2011, 15(3):373-380
[29]Youngjun Ahn, Jiseong Park, Cheol-Gyun Lee et al. Novel Memetic Algorithm implemented With GA (Genetic Algorithm) and MADS (Mesh Adaptive Direct Search) for Optimal Design of Electromagnetic System. IEEE Transactions on Magnetics.2010, 46(6):1982-1985
[30]Aminifar F., Lucas C, Khodaei A. et al. Optimal Placement of Phasor Measurement Units Using Immunity GeneticAlgorithm. IEEE Transactions on IPower Delivery.2009, 24(3):1014-1020
[31]Wei Cheng, Haoshan Shi, Xipeng Yin et al. An Elitism Strategy Based Genetic Algorithm for Streaming Pattern Discovery in Wireless Sensor Networks. IEEE Communications Letters.2011,15(4):419-421
[32]Gonzalez-Longatt F.M., Wall, P., Regulski P.et al.Optimal Electric Network Design for a Large Offshore Wind Farm Based on a Modified Genetic Algorithm Approach. IEEE Systems Journal.2012,6(1):164-172
[33]J. A. Vasconcelos, J. A. Ramirez, R. H. C. Takahashi, et al. Improvements in Genetic Algorithms. IEEE Transactions on Magnetics.2001,37(5):3414-3417
[34]Y. W. Leung, Y. P. Wang. An Orthogonal Genetic Algorithm with Quantization for Global Numerical Optimization. IEEE Transactions on Evolutionary Computation.2001,5(1):41-53
[35]庄健,杨清宇,杜海峰,于德弘.一种高效的复杂系统遗传算法.软件学报,2010,21(11)：2790-2801
[36]F. H. F. Leung, H. K. Lam, S. H. Ling, et al. Tuning of the Structure and Parameters of a Neural Network Using an Improved Genetic Algorithm. IEEE Transactions on Neural Networks.2003,14(l):79-88
[37]彭晓波,桂卫华,黄志武,胡志坤,李勇刚.GAPSO：一种高效的遗传粒子混合算法及其应用.系统仿真学报,2008,20(18)：5025-5027
[38]Z. G.Tu, Y. Lu. A Robust Stochastic Genetic Algorithm (StGA) for Global Numerical Optimization. IEEE Transactions on Evolutionary Computation.2004,8(5):456-470
[39]D.W. Boeringer, D. H.Werner, D. Machuga. A Simultaneous Parameter Adaptation Scheme for Genetic Algorithms with Application to Phased Array Synthesis. IEEE Transactions on Antennas and Propagation.2005,53(1):356-371
[40]X. D. Chen, J. G. Qian, G. Z. Ni, et al. An Improved Genetic Algorithm for Global Optimization of Electromagnetic Problems. IEEE Transactions on Magnetics.2001, 37(5):3579-3583
[41]C. Y. Lee. Entropy-Boltzmann Selection in the Genetic Algorithms. IEEE Transactions on System, Man, and Cybernetics-Part B:Cybernetics.2003,33(1):138-142
[42]W. C. Zhong, J. Liu, M. Z. Xue, et al. A Multiagent Genetic Algorithm for Global Numerical Optimization. IEEE Transactions on System, Man, and Cybernetics-Part B: Cybernetics.2004,34(2):1128-1141
[43]J. Kennedy, R. C. Eberhart. Particle Swarm Optimization. Proceedings of IEEE International Conference on Neural Networks. Perth, WA, Australia,1995:1942-1948
[44]Das Sharma K.,Chatterjee A.,Rakshit A. A Random Spatial 1best PSO-Based Hybrid Strategy for Designing Adaptive Fuzzy Controllers for a Class of Nonlinear Systems.IEEE Transactions on Instrumentation and Measurement.2012,61(6):1605-1621
[45]Chia-Nan Ko, Ying-Pin Chang, Chia-Ju Wu. A PSO Method With Nonlinear Time-Varying Evolution for Optimal Design of Harmonic Filters. IEEE Transactions on Power Systems. 2009,24(1):437-444
[46]Vlachogiannis J.G, Lee K.Y. Economic Load Dispatch—A Comparative Study on Heuristic Optimization Techniques With an Improved Coordinated Aggregation-Based PSO. IEEE Transactions on Power Systems.2009,24(2):991-1001
[47]Y. Shi, R. C. Eberhart. Parameter Selection in Particle Swarm Optimization. Proceedings ofEvolutinary Programming VII:EP98. New York,1998:591-600
[48]R. C. Eberhart, Y. Shi. Evolving Artificial Neural Network. Proceedings of Int'1 Conference on Neural Networks and Brain. Beijing, P.R.C.,1998
[49]Y. Shi, R. C. Eberhart. Fuzzy Adaptive Particle Swarm Optimization. Proceedings of the 2001 Congress on Evolutionary Computation. Seoul, South Korea,2001:101-106
[50]J. Riget, J. S. Vesterstroem. A Diversity-Guided Particle Swarm Optimizer-The ARPSO. Technical Report No.2002-02. Department of Computer Science, University of Aarhus, 2002
[51]M. Clerc, J. Kennedy. The Particle Swarm-Explosion, Stability, and Convergence in a Multidimensional Complex Space. IEEE Transactions on Evolutionary Computation.2002, 6(1):58-73
[52]J. Robinson, Y. Rahmat-Samii. Particle Swarm Optimization in Electronmagnetics. IEEE Transactions on Antennas and Propagation.2004,52(2):397-407
[53]G.Ciuprina, D. loan, I. Munteanu. Use of Intelligent-Particle Swarm Optimization in Electromagnetics. IEEE Transactions on Magnetics.2002,38(2):1037-1040
[54]慕彩红,焦李成,刘逸。M-精英协同进化数值优化算法.软件学报,2009,20(11)：2925-2938
[55]倪庆剑,张志政,王幕蔡,邢汉承。一种基于可变多簇结构的动态概率粒子群优化 算法.软件学报,2009,20(2)：339-349
[56]S. Naka, T. Genji, T. Yura, et al. A Hybrid Particle Swarm Optimization for Distribution State Estimation. IEEE Transactions on Power System.2003,18(1):60-68
[57]迟玉红,孙富春等.基于空间缩放和吸引子的粒子群优化算法.计算机学报,2011,34(1)：115-130
[58]A. A. A. Esmin, G.Lambert-Torres, A. C. Z. de Souza. A Hybrid Particle Swarm Optimization Applied to Loss Power Minimization. IEEE Transactions on Power System. 2005,20(2):859-866
[59]许相莉,利彪,向东,等.基于粒子群的图像检索相关反馈算法[J].电子学报,2010,38(8)：1935-1940
[60]吴扬,姜守达.基于嵌套粒子群算法的多涡环微下击暴流模型参数选择方法.电子学报,2012,40(1)：204-208
[61]Y. Liu, Z. Qin, Z. W. Shi, et al. Center Particle Swarm Optimization. Neurocomputing. 2007,70(4-6):672-679
[62]F. van den Bergh, A. P. Engelbrecht. A Cooperative Approach to Particle Swarm Optimization. IEEE Transactions on Evolutionary Computation.2004,8(3):225-239
[63]S.Das ectal.Particle Swarm Optimization and Differential Evolution Algorithms:Technical Analysis,Applications and Hybridization Prespectives.Studies in Computional Intelligence.2008,116:1-38
[64]B. Zhao, C. X. Guo, Y. J. Cao. A Multiagent-Based Particle Swarm Optimization Approach for Optimal Reactive Power Dispatch. IEEE Transactions on Power System.2005, 20(2):1070-1078
[65]Yi-Tung Kao. Erwie Zahara. A hybrid genetic algorithm and particle swarm optimization for multimodal functions. Applied Soft Computing.2008,8:849-857
[66]Zhang Feizhou, Cao Xuejun, Yang Dongkai. Intelligent scheduling of public traffic vehicles based on a hybrid genetic algorithm. Tsinghua Science and Technology.2008, 13(5):625-631
[67]Taejin Park, Kwang Ryel Ryu. A Dual-Population Genetic Algorithm for Adaptive Diversity Control. IEEE Transactions on Evolutionary Computation.2010,14(6):865-884
[68]Xiao Min Hu, Jun Zhang, Yan Yu et al. Hybrid Genetic Algorithm Using a Forward Encoding Scheme for Lifetime Maximization of Wireless Sensor Networks. IEEE Transactions on Evolutionary Computation.2010,15(4):766-781
[69]Shutao Li Mingkui Tan, Tsang I.W. et al. A Hybrid PSO-BFGS Strategy for Global Optimization of Multimodal Functions. IEEE Transactions on Systems, Man, and Cybernetics, Part B:Cybernetics,2011,41(4):1003-1014
[70]X. Yao. A Review of Evolutionary Artificial Neural Networks. International Journal of Intelligent Systems.1993,8(4):539-567
[71]D. E. Rumelhart, G E. Hinton, R. J. Williams. Learning Representation by Back-Propagation Errors. Nature.1986,7:149-154
[72]S. E. Fahlman. Faster Learning Variations on Backpropagation:An Empirical Study. Proceedings of the Connectionist Models Summer School. San Mateo:Morgan Kauffmann, 1988:38-51
[73]R. Battiti. First and Second Order Methods for Learning:Between Steepest Descent and Newton's Method. Neural Computation.1992,4(2):141-166
[74]孙健,柴毅,李华锋,朱智勤.一种基于极点配置稳定的新型局部递归神经网络.自动化学报,2012,38(2)：183-196
[75]韩冰,韩敏.基于动态BP算法的非线性滞后系统辨识.大连理工大学学报,2010,50(5)：777-781
[76]S. Shah, F. Palmieri, M. Datum. Optimal Filtering Algorithms for Learning in Feedforward Neural Network. Neural Networks.1992,5(5):779-787
[77]杨国为,王守觉,闫庆旭.分式线性神经网络及其非线性逼近能力研究.计算机学报,2007,30(2)：189-199
[78]陈果.神经网络模型的预测精度影响因素分析及其优化.模式识别与人工智能,2005,18(5)：528-534
[79]李祚泳,易勇鸷.BP网络学习能力与泛化能力之间的定量关系式.电子学报,2003,31(9)：1341-1344
[80]杨甲沛,李锵,刘郑,袁晓琳.基于自适应学习速率的改进型BP算法研究.计算机工程与应用,2009,45(11)：56-58
[81]S. Acikbas, M.T. Soylemez. Coasting point optimisation for mass rail transit lines using artificial neural networks and genetic algorithms. IET Electric Power Applications.2008, 2(3):172-182
[82]C. S. Koh, O. A. Mohammed, S. Y. Hahn. Detection of Magnetic Body Using Artificial Neural Network with Modified Simulated Annealing. IEEE Transactions on Magnetics. 1994,30(5):3644-3647
[83]李祚泳,汪嘉杨,郭淳.PSO算法优化BP网络的新方法及仿真实验.电子学报,2008,36(11)：2224-2228
[84]郝红卫,蒋蓉蓉.基于最近邻规则的神经网络训练样本选择方法.自动化学报,2007,33(12)：1247-1251
[85]潘昊,王晓勇,陈琼,等.基于遗传算法的BP神经网络技术的应用.计算机应用,2005,25(12)：2777-2779
[86]潘昊,侯清兰.基于粒子群优化算法的BP网络学习研究.计算机工程与应用,2006,16：41-43
[87]X.Yao.Evolving Artificial Neural Networks. Proceedings of the IEEE.1999,87:1423-1447
[88]D.Yi,X.R.Ge. An Improved PSO-Based Ann with Simulated Annealing Technique. Neurocomputing.2005,63:527-533
[89]杨博,苏小红,王亚东.基于注意力模型的混合学习算法.软件学报,2005,16(6)：1073-1080
[90]X. D. Cai, N. Zhang, G. K. Venayagamoorthy, et al. Time Series Prediction with Recurrent Neural Networks Trained by a Hybrid PSO-EA Algorithm. Neurocomputing.2007,70(13-15):2342-2353
[91]Y.Song, Z.Q.Chen,Z.Z.Yuan. New Chaotic PSO-Based Neural Network Predictive Control for Nonlinear Process. IEEE Transactions on Neural Networks.2007,18(2):595-600
[92]Y. Shi, R. C. Eberhart. A Modified Particle Swarm Optimizer. Proceedings of IEEE International Conference on Evolutionary Computation. Anchorage, AK, USA,1998:69-73
[93]J. Kennedy. The Particle Swarm:Social Adaptation of Knowledge. Proceedings of IEEE International Conference on Evolutionary Computation. Indianapolis, IN, USA,1997:303-308
[94]P.N.Suganthan.Particle Swarm Optimiser with Neighborhood Operator. In Proceedings of the IEEE Congress on Evolutionary Computation,1999:1958-1962
[95]J. Kennedy and R. Mendes. Population structure and particle swarm performance. In Proceedings of the IEEE Congress on Evolutionary Computation,2002,2:1671-1676
[96]Jung-Hsien Chiang, Shing-Hua Ho. A Combination of Rough-Based Feature Selection and RBF Neural Network for Classification Using Gene Expression Data.IEEE Transactions on NanoBioscience.2008,7(1):91-99
[97]Ahn CW, Ramakrishna RS. Elitism-Based compact genetic algorithms. IEEE Trans, on Evolutionary Computation,2003,7(4):367-385
[98]Huang T, Mohan A S, A hybrid boundary condition for robust particle swarm optimization. IEEE Antennas and Wireless Propagation Letters,2005,4(1):112-117
[99]Eduardo D.SONTAG.VC dimension of neural network. Neural Networks and Machine Learning,1998,168:69-95.
[100]Mass W. Neural nets with superlinear VC-dimension. Neural Computation,1994, (6):877-884
[101]Y. Q. Chen, D. W. Thomas, M. S. Nixon. Generating-Shrinking Algorithm for Learning Arbitrary Classification. Neural Networks.1994,7(9):1477-1489
[102]C. C. Teng, B.W.Wah. Automated Learning for Reducing the Configuration of a Feedforward Neural Network. IEEE Transactions on Neural Networks.1996,7(5):1072-1085
[103]高海兵,高亮,周驰,等.基于粒子群优化的神经网络训练算法研究.电子学报,2004,32(9)：1572-1574
[104]J. B. Yu, L. F. Xi, S. J. Wang. An Improved Particle Swarm Optimization for Evolving Feedforward Artificial Neural Networks. Neural Processing Letters.2007,26(3):217-231
[105]X. Yao, Y. Liu. A New Evolutionary System for Evolving Artificial Neural Networks. IEEE Transactions on Neural Networks.1997,8(3):694-713
[106]A. Blum, R. L. Rivest. Training a 3-node Neural Network Is NP-Complete. Neural Networks.1992,5(1):117-127
[107]T. Back. Selective Pressure in Evolutionary Algorithms:A Characterization of Selection Mechanisms. In Proceedings of the First IEEE Conference on Evolutionary Computation, 1994,1:57-62
[108]韩晓卓,李自珍,惠苍,岳东霞.物种生态位构建理论与双点位基因模型应用.西北植物学报,2004,24(3)：558—562
[109]S.C. Esquivel and C. A. Coello. On the Use of Particle Swarm Optimization with Multimodal Functions. In Proceedings of the IEEE Transactions on Evotutionary Computation,2003,2(12):1130-1136
[110]焦李成,刘静,钟伟才.协同进化计算与多智能体系统.北京：科学出版社,2006：84-87
[111]江瑞,罗予频,胡东成,等.一种协调勘探和开采的遗传算法：收敛性及性能分析.计算机学报.2001,24(12)：1233-1241
[112]G.Rudolph. Convergence Analysis of Canonical Genetic Algorithms. IEEE Transactions on Neural Networks.1994,5(1):96-101
[113]M. Iosifescu. Finite Markov Processes and Their Applications. Willey,1980
[114]刘波.粒子群优化算法及其在机电设备中的应用研究.中北大学博士学位论文,2011：39-45
[115]X. Yao, Y. Liu, G. M. Lin. Evolutionary Programming Made Faster. IEEE Transactions on Evolutionary Computation.1999,3(2):82-102
[116]J. T. Tsai, J. H. Chou, T. K. Liu. Tuning the Structure and Parameters of a Neural Network by Using Hybrid Taguchi-Genetic Algorithm. IEEE Transactions on Neural Networks.2006,17(1):69-80
[117]H. K. Lam, S. H. Ling, F. H. F. Leung, et al. Tuning of the Structure and Parameters of Neural Network Using an Improved Genetic Algorithm. The 27th Annual Conference of the IEEE Industrial Electronics Society. Denver, CO, USA,2001:25-30
[118]Mingli Song, Dacheng Tao, Xiaoqin Huang et al. Three-Dimensional Face Reconstruction From a Single Image by a Coupled RBF Network. IEEE Transactions on Image Processing.2012,21(5):2887-2897
[119]Ke Meng, Zhao Yang Dong, Dian Hui Wang et al. A Self-Adaptive RBF Neural Network Classifier for Transformer Fault Analysis.IEEE Transactions on Power Systems.2010, 25(3):1350-1360
[120]Muzhou Hou, Xuli Han. Constructive Approximation to Multivariate Function by Decay RBF Neural Network.IEEE Transactions on Neural Networks.2010,21(9):1517-1523
[121]X. Hong, C. J. Harris. Nonlinear Model Structure Design and Construction Using Orthogonal Least Squares and D-Optimality Design. IEEE Transactions on Neural Networks.2002,13(5):1245-1250
[122]Platt J.A resource-allocating network for function interpolation. Neural Computation, 1991,3(2):213-225
[123]Lu Y W,Sundararajan N,Saratchandran P.A sequential learning scheme for function approximation using minimal radial basis function neural networks.Neural Computation, 1997,9(2):461-478
[124]Esposito A,Marinaro M,Oricchio D,Scarpetta S.Approximation of continuous and discontinuous mappings by a growing neural RBF-based algorithm.Neural Networks, 2000,13(6):651-665
[125]Gonzalez J,Rojas I,Ortega J,Pomares H.Multiobjective evolutionary optimization of the size,shape,and position parameters of radial basis function networks for function approximation.IEEE Transactions on Neural Networks,2003,14(6):1478-1495
[126]L. Guo, D. S. Huang,W. B. Zhao. Combining Genetic Optimisation with Hybrid Learning Algorithm for Radial Basis Function Neural Networks. Electronics Letters, 2003,39(22):1600-1601
[127]Fu X J,Wang L P.Data dimensionality reduction with application to simplifying RBF network structure and improving classification performance.IEEE Transactions on Systems,Man,and Cybernetics,Part B:Cybernetics,2003,33(3):399-409
[128]Huang G B,Saratchandran P,Sundararajan N.A generalized growing and pruning RBF(GGAP-RBF)neural network for function approximation.IEEE Transactions on Neural Networks,2005,16(1):57-57
[129]Feng H M.Self-generation RBFNs using evolutional PSO learning.Neurocomputing, 2006,70(1-3):241-251
[130]F. A. Guerra, L. dos S. Coelho. Multi-step Ahead Nonlinear Identification of Lorenz's Chaotic System Using Radial Basis Neural Network with Learning by Clustering and Particle Swarm Optimization. Chaos, Solitons & Fractals.2008,35(5):967-979
[131]Lian J M,Lee Y G,Scott D S,Stanislaw H Z.Self-organizing radial basis function network for real-time approximation of continuous-time dynamical systems.IEEE Transactions on Neural Networks,2008,19(3):460-474
[132]Huang D S,Du J X.A constructive hybrid structure optimization methodology for radial basis probabilistic neural networks.IEEE Transactions on Neural Networks,2008, 19(12):2099-2115
[133]Chen S,Hong X,Luk B L,Harris C J.Construction of tunable radial basis function networks using orthogonal forward selection.IEEE Transactions on Systems,Man,and Cybernetics,Part B:Cybernetics,2009,39(2):457-466
[134]乔俊飞,韩红桂.RBF神经网络的结构动态优化设计.自动化学报,2010,36(6)：865-872
[135]韩红桂,乔俊飞,薄迎春.基于信息强度的RBF神经网络结构设计研究.自动化学报,2012,38(7)：1083-1090
[136]S. Chen, C. F. N. Cowan, P. M. Grant. Orthogonal Least Squares Learning Algorithm for Radial Basis Function Neural Networks. IEEE Transactions on Neural Networks.1991, 2(2):302-309
[137]S. Chen, E. S. Chng, K. Alkadhimi. Regularized Orthogonal Least Squares Algorithm for Constructing Radial Basis Function Networks. International Journal of Control.1996, 64(5):829-837
[138]X. Hong, C. J. Harris. Nonlinear Model Structure Detection Using Optimum Experimental Design and Orthogonal Least Squares. IEEE Transactions on Neural Networks,2001,12(2):435-439
[139]S. Chen, X. Hong, C. J. Harris. Sparse Kernel Regression Modeling Using Combined Locally Regularized Orthogonal Least Squares and D-Optimality Experimental Design. IEEE Transactions on Automatic Control.2003,48(6):1029-1036
[140]X. Hong, P. M. Sharkey, K. Warwick. A Robust Nonlinear Identification Algorithm Using PRESS Statistic and Forward Regression. IEEE Transactions on Neural Networks. 2003,14(2):454-458
[141]X. Hong, C. J. Harris, S. Chen, et al. Robust Nonlinear Model Identification Methods Using Forward Regression. IEEE Transactions on System, Man, and Cybernetics-Part A: Systems and Humans.2003,33(4):514-523
[142]S. Chen, Y. Wu, B. L. Luk. Combined Genetic Algorithm Optimization and Regularized Orthogonal Least Squares Learning for Radial Basis Function Networks. IEEE Transactions on Neural Networks.1999,10(5):1239-1243
[143]赵温波,杨鹭怡,王立明.径向基概率神经网络的混合结构优化算法.系统仿真学报,2004,16(10)：2175-2180
[144]白雪冰,王克奇,王辉.基于灰度共生矩阵的木材纹理分类方法的研究.哈尔滨工业大学学报,2005,37(12)：1667-1670
[145]马明宇,王桂芸,黄安民,张卓勇,相玉红,顾轩.人工神经网络结合近红外光谱用于木 材树种识别.光谱学与光谱分析,2012,32(9)：2377-2381
[146]孙建平,王逢瑚,胡英成.基于声发射和神经网络的木材受力损伤过程检测.仪器仪表学报,2011,32(2)：342-347