摘要
差分进化算法是一种基于种群差异的进化算法,通过种群内个体间的合作与竞争来实现对优化问题的求解。与遗传算法相比,差分进化算法实现简单,搜索能力强,适于求解高维非线性问题的优化,但与其他的进化算法一样,也存在着收敛速度慢、产生局部最优等问题。
本论文从进化搜索空间的改进、进化控制参数的设置以及差分进化混合算法几个方面进行了深入研究。主要研究工作包括:
(1)针对标准差分进化算法进化操作只在一个进化种群中进行,提出了一种辅助种群差分进化算法。在选择阶段主种群中未被选中的进化个体放入辅助种群,经过交叉、变异以后,选择操作在辅助种群中的个体、主种群中的个体和父代种群中的个体之间进行,以此提高差分进化算法的进化效率。标准测试函数实验表明辅助种群可以极大地提高差分进化算法的全局搜索能力和测试函数的运行精度,收敛速度比单种群差分进化算法更快。针对聚类分析问题,提出一种加权总和有效性校验函数SWVF以实现聚类分析过程中有效性函数的分析,把辅助种群差分进化算法用于聚类分析,提出一种基于差分进化的聚类分析算法CDESec,该算法利用辅助种群的良好的全局搜索能力,在全局范围内寻找最优解。实验中表明CDESec聚类分析算法表现出了良好的性能。
(2)针对于jDE差分进化算法参数自适应设置的随机性,提出了不同于jDE的参数自适应设置算法SelfDE-F。SelfDE-F算法中控制参数的调整根据进化过程中子代的适应度是否优于父代进行。测试函数实验结果表明,该算法总体性能优异,有效地提高了进化的性能。将SelfDE-F算法与BP神经网络相结合,给出了SelfDE-FBPNN算法。由SelfDE-F对BP神经网络的权值进行优化,并将优化后的BP神经网络权值用于PID控制参数的设定,实验表明使用该方法比使用BP神经网络、标准DE优化BP神经网络、jDE优化神经网络获得的PID控制参数效率更高。
(3)标准差分进化采用实数型编码方案,提出了基于0/1矩阵的二进制编码方案,并给出了进化操作采用逻辑运算“与”、“或”、“异或”运算的二进制参数自适应差分进化算法。提出了两种基于种群的贝叶斯网络学习算法:进化MCMC贝叶斯网络学习算法EMCMCBN和二进制差分进化贝叶斯网络学习算法BINDEBN,两者在学习过程中不同个体(染色体)中的贝叶斯网络进行信息交换。实验结果表明,BINDEBN对训练数据集的依赖性更小,学习效率更高。
(4)针对高斯混合模型的参数学习和推理问题,提出了基于种群的高斯混合模型的参数学习方法,每个个体内采用Gibbs取样方法进行学习,在学习过程中使用差分进化进行个体间的信息交换,并使用MCMC方法对交换后的结果进行选择。将该方法应用到Motifs的概率学习,实验结果表明学习结果的标准偏差随着种群数的提高逐渐降低。
Differential Evolution algorithm is a kind of evolutionary algorithm based on population difference, it finds the solution of optimization problem through the cooperation and competition between individuals. Compared to Genetic Algorithm, Differential Evolution algorithm is easy to implement and has powerful search ability, which make it suitable to find optimal solution in high dimensional non-linear problems. Similar to other evolutionary algorithms, Differential Evolution algorithm convergents slowly and be trapped in the local optimal.
In this dissertation, the research involves the improvement of evolutionary algorithm search space, configuration of evolution control parameters and hybrid Differential Evolution algorithms. Main focuses in this dissertation include:
(1)Evolution operation of standard Differential Evolution algorithm involves only one population, different from standard Differential Evolution, a Differential Evolution with Secondary population(DESec) is proposed. In selection section, unselected individuals are put into Secondary population, individuals in main population and Secondary population evolve simultaneously and selection happens among individuals from main population, Secondary population and parental individuals. Experimental results of benchmark functions show the Secondary population can improve Differential Evolution’s search ability and its precision, the convergence of DESec is faster than standard Differential Evolution. To solve the Clustering analysis problem, a Summary Weighted Validity Function(SWVF) is proposed to analyze middle results in Clustering. A Clustering algorithm based on DESec(CDESec) is presented, with the excellent global search ability of DESec, the CDESec search the global optimal solution. Experimental results show better performance of CDSec.
(2)To solve the randomicity of parameters self adaption in jDE algorithm, self parameters control method (SelfDE-F) is presented. Control parameters in SelfDE-F are adapted according to the comparison between fitness of children and its parents. Experimental results of benchmark functions show SelfDE-F’s superiority, this algorithm can improve performance of Differential Evolution efficiently. SelfDE-FBPNN algorithm that uses SelfDE-F in training weights of Back Propagation(BP) Neural Network is presented and the optimized weights of BP Neural Network is used in configuration of PID control parameters, experimental results show this method is more efficient than BP Neural Network, BP Neural Network optimized with standard DE and BP Neural Network optimized with jDE.
(3)Different from the individual coding with real number of standard Differential Evolution, binary individual coding based on 0/1 matrix is presented and binary parameter self-adaptive Differential Evolution with logical operation AND, OR, XOR is proposed. In this section, two Bayesian Network learning algorithms is presented: Evolutionary MCMC Bayesian Network learning algorithm(EMCMCBN) and binary Differential Evolution Bayesian Network learning algorithm(BINDEBN), Bayesian Networks from different individuals exchange information in learning process. Experimental results show that BINDEBN has less dependency on original datasets and be more efficient.
(4) To solve parameter learning and inference problem of Gaussian Mixture model, an approach based on population is presented. Gibbs sampling is applied in every individual and information exchange happened between individuals with Differential Evolution, MCMC method is used to sample the exchanged results. This method is applied to probability learning of Motifs, experimental results show that standard deviation of learning results will decrease with population size increasing.
引文
[1]王凌.智能优化算法及其应用[M].北京:清华大学出版社,2001.
[2]Russell S J, Norvig P. Artificial Intelligence: A Modern Approach (2nd ed.)[M], Upper Saddle River, New Jersey: Prentice Hall, 2003.
[3]Ypma T J. Historical development of the Newton-Raphson method[J]. SIAM Review, 1995, 37 (4):531–551.
[4]Kiwiel K C. Convergence and efficiency of subgradient methods for quasiconvex minimization[J]. Mathematical Programming (Series A) ,2001, 90 (1): 1-25.
[5]Hestenes M R, Stiefel E. Methods of Conjugate Gradients for Solving Linear Systems[J]. Journal of Research of the National Bureau of Standards. 1952, 49 (6): 409-436.
[6]Davidon W C. New least-square algorithms[J]. Journal of Optimization Theory and Applications. 1976, 18(2): 187–197.
[7] Box M J, Davies D, Swann W H. Non-Linear optimisation Techniques[M]. Oliver & Boyd. 1969.
[8]Richard W, Cottle B. Curtis E等. Memorial Resolution: George Bernard Dantzig[R]. Stanford Report, June 7, 2006.
[9] Shor N Z, Zhurbenko N G. The minimization method using space dilatation in direction of difference of two sequential gradients[J]. Kibernetika. 1971(3): 51-59.
[10]Rastrigin L A. The convergence of the random search method in the extremal control of a many parameter system[J]. Automation and Remote Control. 1963, 24 (10): 1337–1342.
[11]Matyas J. Random optimization[J]. Automation and Remote Control. 1965, 26 (2): 246–253.
[12]Rechenberg I, Cybernetic solution path of an experimental problem. in Farborough Hants: Royal Aircraft Establishment, August 1965, Library Translation 1122, English Translation of lecture given at the Annual Conference of the WGLR at Berlin in September, 1964[C].
[13]Nelder, J.A.; Mead, R. A simplex method for function minimization[J]. Computer Journal. 1965(7): 308–313.
[14]Fogel L. Owens A J. Walsh M J. Artificial Intelligence through Simulated Evolution[M]. Wiley. 1966.
[15]Kirkpatrick S, Gelatt Jr, C D, Vecchi M P. Optimization by Simulated Annealing[J]. Science. 1983, 220 (4598): 671–680.
[16]Glover F. Future Paths for Integer Programming and Links to Artificial Intelligence. Computers and Operations Research[J]. 1986, 13(5): 533–549.
[17]Kennedy J, Eberhart R. Particle Swarm Optimization. Proceedings of IEEE International Conference on Neural Networks, 1995[C]. IEEE. 4:1942–1948.
[18]Wolpert D H, Macready W G. No free lunch theorems for optimization[J]. IEEE Transactions on Evolutionary Computation. 1997,1 (1): 67–82.
[19]Storn R, Price K. Differential Evolution– A Simple and Efficient Heuristic for Global Optimization over Continuous Spaces[J]. Journal of Global Optimization. 1997(11): 341–359.
[20]Nakrani S, Tovey S. On honey bees and dynamic server allocation in Internet hosting centers[J]. Adaptive Behaviour. 2004(12): 223-240.
[21]Krishnanand K, Ghose D. Detection of multiple source locations using a glowworm metaphor with applications to collective robotics. Proceedings of Swarm Intelligence Symposium, 2005. SIS 2005[C]. IEEE. 84–91.
[22] Kammerdiner A R, Mucherino A,Pardalos P M. Application of Monkey Search Meta-heuristic to Solving Instances of the Multidimensional Assignment Problem[J]. Optimization and Cooperative Control Strategies, Lecture Notes in Control and Information Sciences. 2009(381):385-397.
[23]Yang X S, Deb S. Cuckoo search via Levy flights. World Congress on Nature & Biologically Inspired Computing. 2009[C]. IEEE. USA:210–214.
[24] KIM M. Convergence of the Nelder–Mead simplex method to a non-stationary point[J]. SIAM Journal on Optimization. 1999(9): 148–158.
[25]Holland J H. Adaptation in Natural and Artificial Systems[M]. University of Michigan Press. 1975
[26] Bruce L. The Harpy Speech Recognition System[D]. Carnegie Mellon University. 1976.
[27]Luger G, Stubblefield W. Artificial Intelligence: Structures and Strategies for Complex Problem Solving (5th ed.)[M]. The Benjamin/Cummings Publishing Company, Inc.2004.
[28]Koza J R. Genetic Programming[M]. MIT Press. 1992.
[29]Price K, Storn R, Lampinen J A. Differential Evolution: A Practical Approach to Global Optimization[M]. Springer. 2005.
[30]Liu J, Lampinen J. A fuzzy adaptive differential evolution algorithm[J]. Soft Computing.2005,9(6): 448–462.
[31]Brest J, Greiner S, Boskovic B等. Self-Adapting Control Parameters in Differential Evolution: A Comparative Study on Numerical Benchmark Problems[J]. IEEE Transactions on Evolutionary Computation. 2006, 10( 6): 646-657.
[32]陈荣元,林立宇,王四春等。数据同化框架下基于差分进化的遥感图像融合[J].自动化学报2010,36(3):392-398.
[33]Paterlini S, Krink T. High Performance Clustering with Differential Evolution. CEC2004[C]. IEEE, 2004(2): 2004-2011.
[34]O’Neill M, Brabazon A. Grammatical Differential Evolution. International Conference on Artificial Intelligence (ICAI’06)[C]. 2006:231-236
[35]Basturk A, Gunay E. Efficient edge detection in digital images using a cellular neural network optimized by differential evolution algorithm[J]. Expert Systems with Applications. 2009, (36): 2645–2650
[36]Rami N. Khushaba, Ahmed Al-Ani, Adel Al-Jumaily. Differential Evolution based Feature Subset Selection. 19th International Conference on Pattern Recognition, Tampa, FL. 2008. IEEE. ICPR 2008[C]: 1-4.
[37]Cheng S L, Hwang C. Optimal Approximation of Linear Systems by a Differential Evolution Algorithm[J]. IEEE Transactions on Systems, Man, and Cybernetics-Part A: System and Humans. 2001, 31(6): 598-707
[38]覃晖,周建中,王光谦等.基于多目标差分进化算法的水库多目标防洪调度研究[J].水利学报. 2009, 40(5): 513-519
[39]潘克家,陈华,谭永基.基于差分进化算法的核磁共振T2谱多指数反演[J].物理学报. 2008,(579):5856- 5861
[40]王凌,黄付卓,李灵坡.基于混合双种群差分进化的电力系统经济负荷分配[J].控制与决策. 2009, 24(8): 1156-1160,1166
[41]Wang Y, Li B, Weise T. Estimation of distribution and differential evolution cooperation for large scale economic load dispatch optimization of power systems[J]. Information Sciences. 2010, 180(12): 2405-2420
[42]Xue F, Sanderson A C, Graves R J. Multi-Objective Differential Evolution and Its Application to Enterprise Planning. Proceedings of the 2003 IEEE International Conference on Robotics & Automation[C]. IEEE, 2003(3): 3535-3541
[43]Angira R, Babu B V. Optimization of process synthesis and design problems: A modified differential evolution approach[J]. Chemical Engineering Science. 2006(61): 4707-4721
[44]范瑜,金荣洪,耿军平等.基于差分进化算法和遗传算法的混合优化算法及其在阵列天线方向图综合中的应用[J].电子学报. 2004. 32(12): 1997-2000
[45]Jiang Y M, Chapman N R, Gerstoft P. Estimation of Geoacoustic Properties of Marine Sediment Using a Hybrid Differential Evolution Inversion Method[J].Oceanic Engineering, 2010, 35(1):59– 69.
[46]Rogalsky T, Derksen R W, Kocabiyik S. Differential Evolution in Aerodynamic Optimization. In: Proc. of 46h Annual Conf of Canadian Aeronautics and Space Institute[C]. 1999: 29-36
[47]Feoktistov V. Differential evolution: in search of solutions[M]. In: Optimization and its applications, vol 5. Springer, New York, USA. 2006
[48]Zaharie D. Critical values for control parameters of differential evolution algorithm. In Proceedings of MENDEL 2002, Eighth International Conference on Soft Computing[C]. June 5-7, 2002, Brno, Czech Republic, Brno. 62-67.
[49]Lampinen J, Zelinka I. On stagnation of the differential evolution algorithm. In: Proceedings of the 6th international Mendel conference on soft computing[C]. 2000. 76–83
[50]Liu J, Lampinen J. On setting the control parameter of the differential evolution algorithm. In: Proceedings of the 8th international Mendel conference on soft computing[C]. 2002. 11–18
[51]Ronkkonen J, Kukkonen S, Price K V. Real-parameter optimization with differential evolution. The 2005 IEEE Congress on Evolutionary Computation[C]. IEEE, 2005(1): 506-513
[52]Zhang W J, Xie X F. DEPSO: Hybrid Particle Swarm with Differential Evolution Operator. ICSMC2003[C]. IEEE, 2003(14): 3816 - 3821
[53]Chen J, Xin B, Peng Z H等. Statistical learning makes the hybridization of particle swarm and differential evolution more efficient—a novel hybrid optimizer[J]. Sci China Ser F-Inf Sci, 2009, 52(7): 1278–1282
[54]Caponio A, Neri F, Tirronen V. Super-fit control adaptation in memetic differential evolution frameworks[J]. Soft Comput. 2009(13):811–831
[55]胡中波,熊盛武.基于模拟退火的混合差分进化算法研究[J].计算机工程与设计. 2007,28(9): 1989-1991,2102
[56]卢有麟,周建中,覃晖等.基于自适应混合差分进化算法的水火电力系统短期发电计划优化[J].电网技术. 2009, 33(13): 32-36
[57]Das S, Dasgupta S, Biswas A等. Automatic Circle Detection on Images with Annealed Differential Evolution. IEEE Congress on Evolutionary Computation, 2007. CEC 2007[C]. IEEE, 2007: 1926– 1933
[58]Yan J Y, Ling Q, Sun D M, A Differential Evolution with Simulated Annealing Updating Method. International Conference on Machine Learning and Cybernetics, Dalian, China.2006[C]. IEEE,2006:2103-2106.
[59]Thangaraj R, Pant M, Abraham A等. Hybrid Evolutionary Algorithm for Solving Global Optimization Problems[J]. Hybrid Artificial Intelligence Systems,Lecture Notes in Computer Science, 2009(5572): 310-318
[60]Pant M, Ali M, Abraham A. Mixed Mutation Strategy Embedded Differential Evolution. CEC 2009[C]. IEEE, 2009: 1240– 1246
[61]Gong W Y, Cai Z H, Ling C X. DE/BBO: A hybrid differential evolution with biogeography-based optimization for global numerical optimization[J]. Soft Computing. 2010,15(4): 645-665
[62]Becerra R L, Coello Coello C A. Optimization with Constraints using a Cultured Differential Evolution Approach. GECCO’05. June 25–29, 2005, Washington, DC, USA[C].ACM, 2005: 27-35
[63]王钧炎,黄德先.基于混合差分进化算法的混沌系统参数估计[J].物理学报. 2008, 57(5): 2755-2760
[64]Draa A, Meshoul S, Talbi H等. A Quantum-Inspired Differential Evolution Algorithm for Solving the N-Queens Problem[J]. The International Arab Journal of Information Technology. 2010, 7(1): 21-27
[65]贾东立,郑国莘.基于混沌和高斯局部优化的混合差分进化算法[J].控制与决策. 2010, 25(6): 899-902
[66]Coelho L S, Mariani V C. Combining of Chaotic Differential Evolution and Quadratic Programming for Economic Dispatch Optimization With Valve-Point Effect[J]. IEEE Transactions on Power Systems. 2006. 21(2):989-996
[67]Gong W Y, Cai Z H, Jiang L X. Enhancing the performance of differential evolution using orthogonal design method[J]. Applied Mathematics and Computation 2008. 206(1): 56-69
[68]Kaelo P, Ali M M. Differential evolution algorithms using hybrid mutation[J]. Comput Optim Appl (2007) 37: 231–246
[69]Zhang X, Duan H, Jin J.DEACO: Hybrid ant colony optimization with differential evolution. In: Proceedings of the IEEE congress on evolutionary computation, 2008[C]. IEEE, 2008: 921–927
[70]吴亮红,王耀南,周少武等.双种群伪并行差分进化算法研究及应用[J].控制理论与应用. 2007, 24(3): 453-458
[71]Rahnamayan S, Tizhoosh H R, Salama M A. Opposition-Based Differential Evolution[J]. IEEE Transactions on Evolutionary Computation. 2008.12(1): 84-79
[72]Bergey P K, Ragsdale C. Modified differential evolution: a greedy random strategy for genetic recombination[J]. Omega. 2005, (33): 255-265
[73]Konstantinos E. Parsopoulos. Cooperative Micro–Differential Evolution for High-Dimensional Problems. GECCO’09[C]. ACM, 2009: 531-538
[74]Teo J. Exploring dynamic self-adaptive populations in differential evolution[J]. Soft Comput. 2006. 10: 673–686
[75]Qing A Y. Dynamic differential evolution strategy and applications in electromagnetic inverse scattering problems[J]. IEEE Transactions on Geoscience and Remote Sensing. 2006. 44(1): 116-125
[76]姚峰,杨卫东,张明等.改进自适应变空间差分进化算法[J].控制理论与应用. 2010, 27(1): 32-38
[77]常彦鑫,高正红.自适应差分进化算法在气动优化设计中的应用[J].航空学报2009,30(9):1590-1596
[78]Mallipeddi R, Suganthan P N. Differential Evolution Algorithm with Ensemble of Parameters and Mutation and Crossover Strategies[EB/OL]. http://web.mysites.ntu. edu.sg/epnsugan/PublicSite/Shared/Documents /LNCS-EPSDE-Fin.pdf
[79]姜立强,刘光斌,郭铮.分工差分进化算法[J].小型微型计算机系统. 2009(7): 1302-1304
[80]高岳林,刘俊梅.一种带有随机变异的动态差分进化算法[J].计算机应用. 2009. 29(10): 2719-1922
[81]池元成,方杰,蔡国飙.中心变异差分进化算法[J].系统工程与电子技术. 2010. 32(5):1105-1108
[82]Mezura-Montes E, Velazquez-Reyes J. Coello Coello C A. Modified Differential Evolution for Constrained Optimization[A]. IEEE Congress on Evolutionary Computation, 2006. CEC 2006[C]. IEEE, 2006: 25 - 32
[83]Ali M, Pant M, Singh V P. Two modified differential evolution algorithms and their applications to engineering design problems[J]. World Journal of Modelling and Simulation. 2010. 6 (1): 72-80
[84]Das S, Abraham A, Chakraborty U K等. Differential Evolution Using a Neighborhood-Based Mutation Operator[J]. IEEE Transaction on Evolutionary Computation. 2009. 13(3): 526-553
[85]Zhang J Q, Sanderson A C. JADE: Adaptive Differential Evolution with Optional External Archive[J]. IEEE Transactions on Evolutionary Computation. 2009. 13(5): 945-958
[86]Liu B, Fernández F V, Gielen G. Fuzzy Selection Based Differential Evolution Algorithm for Analog Cell Sizing Capturing Imprecise Human Intentions. CEC 2009[C]. IEEE, 2009: 622 - 629
[87]Lin C, Qing A Y, Feng Q Y. A new differential mutation base generator for differential evolution[J]. Journal of Global Optimization. 2011,49(1):69-90.
[88]Fan H Y, Lampinen J. A Trigonometric Mutation Operation to Differential Evolution[J]. Journal of Global Optimization. 2003. 27(1): 105–129
[89]Ali M, Pant M. Improving the performance of differential evolution algorithm using Cauchy mutation[J]. Soft Computing. 2010,15(5):991-1007
[90]Zamuda A, Boskovi B. Large Scale Global Optimization Using Differential Evolution With Self-adaptation and Cooperative Co-evolution.2008 IEEE Congress on Evolutionary Computation (CEC2008)[C]. IEEE, 2008: 3178-3125
[91]Mendes R, Mohais A S. DynDE: a Differential Evolution for Dynamic Optimization Problems. CEC2005[C].IEEE, 2005(3): 2808-2815
[92]Qin A K, Huang V L, Suganthan P N. Differential evolution algorithm with strategy adaptation for global numerical optimization[J], IEEE Transactions on Evolutionary Computation. 2009, 13(2): 398-417.
[93]Noman N,Iba H. Enhancing Differential Evolution Performance with Local Search for High Dimensional Function Optimization. GECCO2005[C]. ACM, 2005: 967-974
[94]Lin C, Qing A Y, Feng Q Y. A comparative study of crossover in differential evolution[J]. Journal of Heuristics. 2010. In press.
[95]Engelbrecht A P, Pampara G. Binary differential evolution strategies. IEEE Congress on Evolutionary Computation, 2007. CEC 2007[C]. Singapore IEEE, 2007: 1942 -1947
[96] He X S, Han L. A Novel Binary Differential Evolution Algorithm Based on Artificial Immune System. IEEE Congress on Evolutionary Computation, 2007. CEC 2007[C]. Singapore. IEEE, 2007: 2267-2272
[97]Pedersen M E H, Chipperfield A J. Tuning Differential Evolution For Artificial Neural Networks[R]. Hvass Laboratories Technical Report no. HL0803, 2008
[98]Brest J, Bo?kovic B, Greiner S等. Performance comparison of self-adaptive and adaptive differential evolution algorithms[J]. Soft Comput. 2007(11):617-629
[99]Brest J, Maucec M S. Population size reduction for the differential evolution algorithm[J]. Appl Intell. 2008(29): 228-247
[100] Brest J, Zamuda A, Boskovic B等. High-Dimensional Real-Parameter Optimization using Self-Adaptive Differential Evolution Algorithm with Population Size Reduction. CEC 2008[C]. IEEE,2008: 2032-2039
[101]Brest J, Zamuda A, Fister I. Large Scale Global Optimization using Self- adaptive Differential Evolution Algorithm.WCCI 2010[C]. IEEE, 2010:3097-3104
[102]Neri F, Tirronen V. Scale factor local search in differential evolution[J]. Memetic Comp. 2009(1):153–171
[103]Das S, Konar A, Chakraborty U K. Two Improved Differential Evolution Schemes for Faster Global Search. GECCO’05[C], ACM, 2005: 991-998
[104]Yang Z, He J, Yao X. Making a Difference to Differential Evolution. in Advances in Metaheuristics for Hard Optimization Advances in Metaheuristics for Hard Optimization. Natural Computing Series[M], 2008. Springer.
[105]Yang Z Y, Tang K, Yao X. Self-adaptive Differential Evolution with Neighborhood Search. CEC 2008[C]. IEEE, 2008: 1110-1116
[106]Pant M, Thangaraj R, Abraham A等. Differential Evolution with Laplace Mutation Operator. CEC 2009[C]. IEEE, 2009: 2841-2849
[107]刘俊梅,高岳林.带有自适应变异和指数递增交叉算子的差分进化算法[J].河南师范大学学报(自然科学版). 2009. 37(6): 18-21
[108]吴亮红,王耀南,袁小芳等.自适应二次变异差分进化算法[J].控制与决策.2006,21(8): 898-902
[109]杨小芹,黎明,周琳霞.基于熵的双群体遗传算法研究[J].模式识别与人工智能. 2005,18(3): 286-290
[110]王向军,向东,蒋涛等.一种双种群进化规划算法[J].计算机学报. 2006,29(5): 835-840
[111]孟红云,张小华,刘三阳.用于约束多目标优化问题的双群体差分进化算法[J].计算机学报. 2008, 31(2): 228-235
[112]武志峰,黄厚宽,张莹.基于Boltzmann机制的双子代竞争差异演化算法[J].南京大学学报(自然科学). 2008, 44(2): 195-203
[113]Yao X, Liu Y, Lin G M. Evolutionary Programming Made Faster[J]. IEEE Transactions on Evolutionary Computation. 1999, 3(2):82-102.
[114]Liang J J, Runarsson T P, Mezura-Montes, E等.Problem Definitions and Evaluation Criteria for the CEC 2006 Special Session on Constrained Real-Parameter Optimization[EB/OL], Nanyang Technological University, http://www.ntu.edu.sg /home/epnsugan/, Singapore 2006.
[115]Mallipeddi R, Suganthan P N. Problem Definitions and Evaluation Criteria for the CEC 2010 Competition on Constrained Real-Parameter Optimization[EB/OL], Nanyang Technological University,http://www3.ntu.edu.sg/home/epnsugan/ index_files/CEC10-Const/TR-April-2010.pdf, Singapore 2010
[116]JAIN A K, MURTY M N, FLYNN PJ. Data Clustering: A Review[J].ACM Computing Surveys. 1999, 31(3):264-323.
[117]Hastie T, Tibshirani R, Friedman J. The Elements of Statistical Learning (2nd ed.)[M]. New York: Springer. 2009.
[118] Agrawal R, Gehrke J, Gunopulos D等. Automatic Subspace Clustering of High Dimensional Data[J]. Data Mining and Knowledge Discovery. 2005,11(1):5-33.
[119]Mcqueen, J. Some methods for classification and analysis of multivariate observations. In Proceedings of the Fifth Berkeley Symposium on Mathematical Statistics and Probability[C]. University of California Press, 1967. 281-297.
[120]Raghavan V V, Birchand K. A clustering strategy based on a formalism of the reproductive process in a natural system.In Proceedings of the Second International Conference on Information Storage and Retrieval[C]. 1979. 10-22.
[121]Das S, Abraham A, Konar A. Automatic clustering using an improved differential evolution algorithm[J]. IEEE Transactions on Systems, Man and Cybernetics, Part A: Systems and Humans. 2008, 38: 218-237.
[122]Deza E, Deza M M. Encyclopedia of Distances[M]. Springer.2009.
[123]Krause E F. Taxicab Geometry[M]. Dover. 1987.
[124]Cantrell C D. Modern Mathematical Methods for Physicists and Engineers[M]. Cambridge University Press. 2000.
[125]Mahalanobis P C. On the generalised distance in statistics. Proceedings of the National Institute of Sciences of India[C]. 1936. 2 (1): 49–55.
[126]Sheng W G, Swift S, Zhang L S等. A weighted sum validity function for clustering with a hybrid niching genetic algorithm[J]. IEEE Transactions on System, Man, and Cybernetics- Part B: Cybernetics. 2005, 35(6): 1156-1167.
[127]Dunn J C. Well Separated Clusters and Optimal Fuzzy Partitions[J]. Journal of Cybernetica.1974, 4(1): 95-104.
[128]Marriott F H C. Optimization methods of cluster analysis[J]. Biometrika. 1982, 69(2): 417-422.
[129]Davies D L, Bouldin D W, Cluster Separation Measure[J]. IEEE Transactions on Pattern Analysis and Machine Intelligence. 1979,1(2):95-104.
[130]He J, Tan A, Tan C等. Clustering and Information Retrieval, chapter On Quantitative Evaluation of Clustering Systems[C]. Kluwer, 2003: 105-134.
[131]B?ck T. Adaptive business intelligence based on evolution strategies: some application examples of self-adaptive software[J]. Information Sciences. 2002, 148(1): 113–121.
[132]Wu Z F, Huang H K, Yang B等. A modified differential evolution algorithm with self-adaptive control parameters. 3rd International Conference on Intelligent System and Knowledge Engineering, 2008. ISKE 2008[C]. IEEE,2008: 524 - 527
[133]Warren M C, Pitts W. A Logical Calculus of Ideas Immanent in Nervous Activity[J]. Bulletin of Mathematical Biophysics. 1943, 5(4): 115–133.
[134]Rumelhart D E, Hinton G E, Williams R J, Learning internal representations by error propagation, Parallel Distributed Processing[M]. Cambridge, MA:MIT Press 1986.
[135]Jones A J, Genetic algorithms and their applications to the design of neural networks[J]. Neural Computing & Applications. 1993, 1(1): 32–45.
[136]Zhang J R, Zhang J, Lok T等. A hybrid particle swarm optimization–back -propagation algorithm for feedforward neural network training[J]. Applied Mathematics and Computation. 2007, 185(2): 1026-1037.
[137]Shaw D, Kinsner W. Chaotic simulated annealing in multilayer feedforward networks. Canadian Conference on Electrical and Computer Engineering, Calgary, Alta, Canada[C]. IEEE, 1996(1): 265-269.
[138]Karaboga D, Akay B, Ozturk C. Artificial Bee Colony (ABC) optimization algorithm for training Feed-Forward Neural Networks[J]. modeling decisions for Artificial Intelligence. Lecture Notes in Computer Science, 2007, 4617: 318-329.
[139]Masters T, Land W. A new training algorithm for the general regression neural network. IEEE International Conference on Systems, Man, and Cybernetics[C] IEEE, 1997(3): 1990-1994.
[140]Abbass H A. A Memetic Pareto Evolutionary Approach to Artificial Neural Networks[J]. AI 2001: Advances in Artificial Intelligence, Lecture Notes in Computer Science. 2001, 2256/2001: 113-152.
[141]Slowik A, Bialko M. Training of Artificial Neural Networks using Differential Evolution algorithm. Conference on Human System Interactions 2008[C], IEEE, 2008: 60-65.
[142]Zhu Q Y, Qin A K, Suganthan P N等. Evolutionary extreme learning machin. Pattern Recognition[J]. 2005, 38(10):1759-1763.
[143]Bryson A E, Ho Y C. Applied optimal control: optimization, estimation, and control[M]. Blaisdell Publishing Company or Xerox College Publishing. 1969.
[144]Werbos P J. Beyond Regression: New Tools for Prediction and Analysis in the Behavioral Sciences[D]. Cambridge: Harvard University, 1974
[145]Rumelhart D E, Hinton G E, Williams R J. Learning representations by back- propagating errors[J]. Nature. 1986, 323(6088): 533–536.
[146]Werbos P J. The Roots of Backpropagation From Ordered Derivatives to Neural Networks and Political Forecasting[M]. New York, NY: John Wiley & Sons, Inc. 1994.
[147] Funahashi K I. On the approximate realization of continuous mappings by neural networks[J].Neural Networks.1989,2(3):183-192
[148]刘金琨.先进PID控制及其MATLAB仿真[M].北京:电子工业出版社.2003.
[149]Lipták B G. Instrument Engineers' Handbook: Process control and optimization (4th ed.)[M]. CRC Press. 2003.
[150]Ogata K. Discrete-time control systems[M]. Prentice-Hall. 1987.
[151]Tay T T, Iven M J, Moore J B. High performance control[M]. Birkh?user. 1997.
[152]Ogata K. Modern Control Engineering[M]. Prentice-Hall. 1997.
[153] Pearl J F. Propagation and structuring in belief networks[J].Artificial Intelligence. 1986, 29(3): 241-288.
[154]张连文,郭海鹏.贝叶斯网引论[M].北京:科学出版社.2006.
[155]Madigan, D., York, J. Bayesian graphical models for discrete data[J]. International Statistical Review, 1995, 63(2): 215-232.
[156] Cooper G F, Herskovits E. A Bayesian method for the induction of probabilistic networks from data[J]. Machine Learning. 1992,9(4):309-347
[157]Heckerman D. A Tutorial on Learning with Bayesian Networks[J]. Innovations in Bayesian Networks, Studies in Computational Intelligence. 2008,156/2008: 33-82.
[158]Rissanen J.Modeling by shortest data description[J]. Automatica. 1978, 14(5): 465-471.
[159] Akaike H. Information theory and an extension of the maximum likelihood principle. 2nd International Symposium and information Theory[C]. Akademiai Kiado, Budapes.1973. 267-281.
[160]Chickering D M, Heckerman D, Meek C. Large-Sample Learning of Bayesian Networks is NP-Hard[J]. Journal of Machine Learning Research. 2004(5): 1287- 1330.
[161]Lam W, Bacchus F. Using causal information and local measures to learn Bayesian networks. in: Proceeding Ninth Conference on Uncertainty in Artificial Intelligence[C]. Washington, DC, 1993: 243-250.
[162] Riggelsen C. Learning parameters of Bayesian networks from incomplete data via importance sampling[J]. International Journal of Approximate Reasoning. 2006, 42(1): 69-83
[163]Friedman, N. The Bayesian Structural EM Algorithm, Proceedings of the fourteenth international conference on uncertainty in artificial intelligence[C], 1998.
[164]Madigan D, York J. Bayesian graphical models for discrete data[J]. International Statistical Review. 1995, 63(2): 215-232.
[165]Liang F. and Wong W. H. Evolutionary Monte Carlo: Applications to Cp model sampling and change point problem[J]. Statistica Sinica 10, 2000:317–342.
[166]单冬冬,吕强,李亚飞等.贝叶斯网学习中一种有效的爬山算法[J].小型微型计算机系统. 2009, 12(30): 2457-2460.
[167] Gelman A D, Rubin B. Inference from iternative simulation using multiple sequences[J]. Statistical Science. 1992, 7(4): 457-511.
[168] Friedman N. Learning belief networks in the presence of missing values and hidden variables. In: The Fourteenth International Conference on Machine Learning, ICML1997(C): 125–133. San Francisco, 1997.
[169]Guo P, Li N X. An EM-MCMC algorithm for Bayesian structure learning. iccsit, pp.158-162, 2009 2nd IEEE International Conference on Computer Science and Information Technology, IEEE, 2009[C].
[170]刘大有,王飞,卢奕南等.基于遗传算法的Bayesian网结构学习研究[J].计算机研究与发展. 2001, 38(8): 916-922.
[171]Andrieu C, Freitas N D, Doucet A等. An Introduction to MCMC for Machine Learning[J]. Machine Learning. 2003, 50: 5–43.
[172]McGrory C A, Titterington D M. Variational approximations in Bayesian model selection for finite mixture distributions[J]. Computational Statistics & Data Analysis. 2007, 51: 5352– 5367.
[173]Mackay D . Choice of Basis for Laplace Approximation[J]. Machine Learning. 1998, 33: 77-86.
[174]Celeux G, Hurn M, Robert C P. Computational and inferential difficulties with mixture posterior distributions[J]. Journal of the American Statistical Association. 2000, 95: 957–970.
[175]Strens M, Bernhardt M, Everett N. Markov chain Monte Carlo sampling using direct search optimization. ICML2002[C]. Sydney: 602–609.
[176]ter Braak C J. A Markov Chain Monte Carlo version of the genetic algorithm Differential Evolution: easy Bayesian computing for real parameter spaces[J]. Stat Comput. 2006, 16: 239–249.
[177] Vrugt J A, ter Braak C J F, Diks C G H.等. Accelerating Markov chain Monte Carlo simulation by differential evolution with self-adaptive randomized subspace sampling[J]. International Journal of Nonlinear Sciences and Numerical Simulation 2009, 10 (3): 273–290.
[178]Kuncheva L I. Fitness functions in editing k-NN reference set by genetic algorithms[J]. Pattern Recognition. 1997, 30: 1041-1049.
[179]Blekas K, Fotiadis D I, Likas A. Greedy mixture learning for multiple motif discovery in biological sequences[J]. Bioinformatics. 2003, 19(5): 607-617.