摘要
进化计算是一种人工智能技术，通过模拟自然界中生物的进化过程进行优化问题的求解，基本迭代过程如下：首先随机生成问题的解，然后通过迭代更新探索待优化问题的最优解，整个迭代过程中解的优劣程度由适应度值的高低进行评价。比较有代表性的进化算法有遗传算法、进化策略、进化规划、遗传规划以及近几年发展起来的粒子群优化算法（Particle Swarm Optimization， PSO）和量子行为粒子群优化算法（Quantum-behaved Particle Swarm Optimization，QPSO）。PSO算法的研究起源于鸟群的觅食行为，它认为鸟类寻找食物的过程与优化问题的求解过程非常类似，因此可以将待优化问题的每个解都看作是一只“鸟”在搜索空间中飞行。PSO算法参数设置简单、运算速度快，局部搜索能力强，但是一般的PSO算法不能保证以概率1搜索到全局最优解。将PSO算法扩展至量子空间，给出粒子具有量子行为的粒子群优化算法，即QPSO算法，相对于PSO算法来说，QPSO算法不需要粒子的速度信息，控制参数更少，全局搜索能力强。
本文从PSO算法和QPSO算法的基本原理和模型分析入手，提出几种改进算法，然后将算法应用于模糊神经网络、贝叶斯网络学习和蛋白质折叠。具体内容如下：
(1)简单介绍了进化算法中的常用算法、模糊神经网络、贝叶斯网络学习和蛋白质折叠的基本知识，对已经取得的成果和下一步的研究方向进行了简单总结，然后引出本文的研究重点和内容。详细描述了PSO算法和QPSO算法的基本原理和模型，并给出算法的行为分析及收敛性分析，最后简单介绍了几种改进算法。
(2)针对大部分现有QPSO及其改进算法迭代过程中解的维度是固定不变的现象，提出可变维度的QPSO算法，用于解决实际应用中的动态优化问题。在算法进化过程中，解的维度不是固定不变的，与粒子的位置一起作为优化目标迭代进化。种群中的粒子在寻优过程中既能够找到适合优化问题的最优维度，又能够找到该最优维度下的最优位置即全局最优解。将提出的可变维度QPSO算法用于模糊神经网络中模糊规则数的确定以测试算法性能，在模糊神经网络优化过程中，模糊规则数的确定也就是算法优化过程中最优维度的确定是一个NP难问题，现有很多算法基本上都采用专家经验值确定模糊规则数，本文提出的算法能够有效解决依赖专家个人经验导致主观性太强的问题。
(3)为解决QPSO算法在求解复杂的高维多峰优化问题时的早熟收敛问题，将综合学习策略与合作思想融合引入该算法。综合学习策略能够有效增加种群多样性，提升全局搜索能力，而合作思想使算法对每一次迭代粒子每一维的变化都得到反馈，避免进化过程中丢失粒子解的优势部分，并引导算法迅速进入局部搜索。在提出的算法中，首先使用综合学习策略更新局部吸引子的位置，然后使用合作思想对粒子的解向量进行分解，采用一种和遗传算法非常类似的交叉操作，对解向量每一维的更新都进行评价。标准测试函数和模糊神经网络应用实验结果验证了该算法能够有效提高QPSO算法性能。
(4)贝叶斯网是一种系统描述随机变量之间关系的语言，构造贝叶斯网络结构的方法有两种：第一种是通过咨询专家的经验知识进行手工构造，第二种方法是通过机器学习方法对数据集进行分析获得，前一种方法主观性比较强，因此本文重点研究后一种方法。将构造贝叶斯网络的过程也就是贝叶斯网络的结构学习归结成一个优化问题，采用离散的QPSO算法进行优化。为避免算法的早熟收敛，仍然将合作思想和综合学习策略引入离散QPSO算法，用于贝叶斯网络的结构学习，算法采用邻接矩阵或向量表示贝叶斯网络，进化过程中采用变量之间的互信息消除不合理的结构，并使用贝叶斯信息准则（Bayesian Information Criterion，BIC）评分对构造的网络结构进行打分，最终获得最优结构。最后，用两个经典测试网络结构对改进算法进行了测试，测试结果验证了算法的有效性。
(5)蛋白质折叠问题是由氨基酸序列预测蛋白质结构的问题，本文采用格点模型来表示蛋白质，选择自由能全局最小能量函数作为适应度函数，将基于统计学习和概率分布模型的分布估计算法与离散QPSO算法相结合用于蛋白质折叠研究。分布估计算法全局搜索能力强，而在算法迭代后期，离散QPSO算法的局部搜索能力优越，将两者结合，取各自优点，使算法的进化既能快速定位于最优解的大致范围，又能迅速收敛至最优位置。最后使用蛋白质序列对改进算法的性能进行了测试。
Evolutionary computation is a kind of artificial intelligence technology, which solves theoptimization problem through simulating the biological evolutionary process and mechanismsin nature. It starts from random solutions, obtaining the optimal solution by the iterativeprocess. In the iterative process, the fitness function is adopted to evaluate the solution. Somerepresenting evolutionary algorithms are listed as follows: Genetic Algorithm, EvolutionaryStrategies, Evolution Programming, Genetic Programming, Particle Swarm Optimization(PSO), which is inspired by bird flock looking for food, and Quantum-behaved ParticleSwarm Optimization (QPSO). PSO algorithm and QPSO algorithm are new evolutionarycomputation technique developed in recent years. In PSO algorithm, each potential solution ofoptimization algorithm, call a bird, flies in the search space. PSO algorithm is characterizedby simplicity in parameters setting, quickness in computing speed, and excellence in localsearch performance. However, the algorithm can not converge to the global minimum pointwith probability one under suitable condition. Base on the deep study of PSO algorithm andinspired by quantum physics, Quantum-behaved Particle Swarm Optimization (QPSO)algorithm is proposed. QPSO algorithm has much fewer parameters without the velocity ofparticles and much stronger global search ability than the PSO algorithm.
Theoretical analyses and algorithm improving on PSO algorithm and QPSO algorithmare mainly discussed in the dissertation and the application of QPSO algorithm on fuzzyneural networks (FNN), Bayesian network and protein folding are also studied. The maincontents are as follows:
(1) Firstly, the background of the research work, including the basic concept of Bayesiannetwork learning, fuzzy neural networks, protein folding and the development of someevolutionary algorithms are introduced. Then the achieved results and future research isreviewed. On this basis, the research topic and significance of this subject are presented. Thebasic principles and models, the behavior analysis and convergence analysis of PSO algorithmand QPSO algorithm are described in detail. Finally some improved algorithms are proposed.
(2) The major drawback of QPSO algorithm and some improved QPSO algorithms isthat the dimension of search space is fixed. In many optimization problems, the optimumdimension is dynamic. In order to address this problem, the variable-dimensional QPSO(VDQPSO) algorithm, which negates the need of fixing the dimension of the solution space inadvance, is presented. In the proposed algorithm, the optimal dimension, which is regarded asan optimization objective, is updated together with the position of particles. At last, all theparticles can converge to the global solution on the optimum dimension in a simultaneous way.The structure learning of FNN, which is a NP-hard problem, is adopted to test theperformance of VDQPSO. It is difficult to determine the proper number of fuzzy rules inadvance. Most algorithms obtain the number of fuzzy rules by expert experiences. The noveltechnique can address the drawback. And the optimum dimension converged at the end of theoptimization process corresponds to a unique FNN structure where the optimum parameterscan be achieved.
(3) A novel QPSO algorithm with comprehensive learning and cooperative learningapproach (CCQPSO) is introduced to improve the premature convergence of QPSO forsolving multimodal problems. The comprehensive learning strategy of algorithm can makethe swarm diversity increase and improve the global convergence property of QPSO. Thecooperative learning approach can avoid loss some components that had moved closer to theglobal optimal solution in the vector by feeding back each dimension update of particle, andlead the algorithm to local search quickly. In the proposed algorithm, the position of localattractors is updated by comprehensive learning strategy firstly. Then splits the particlesolution with composite high-dimensional into several one-dimensional sub-parts andevaluates each updated dimension of particle solution through adopting a crossover operationthat similar to GA. The results of standard test functions experiment and learning of FNNhave showed that in contrast to other algorithm, the CCQPSO algorithm performs better onglobal convergence and has stronger ability to escape from the local optimal solution duringthe search process especially with high dimension multimodal functions.
(4) Bayesian network is a language to describe the relationship systematically betweenrandom variables. The conformation of Bayesian network includes two way: one is constructmanually by expert experiences, the other is obtain the network by analyzing data set withmachine learning. The former method is subjective. Hence the latter method is the ourresearch topic. The conformation process of Bayesian network is an optimization problem sothat it can be optimize by discrete QPSO algorithm. Comprehensive learning and cooperativelearning approach are introduced too to address the premature convergence appeared indiscrete QPSO algorithm. The proposed approach is used in structure learning of Bayesiannetwork, which is represented by adjacent matrix or vectors. Unreasonable structure iseliminated by mutual information between the variables in the process. After that the optimalnetwork can be obtained. For evaluating the best matching degree between Bayesian networkand sample data sets, Bayesian information criterion(BIC) score is proposed. Finally, twobenchmarks of Bayesian networks are used to test the new approach. The results ofexperiments show that the proposed technique converges more rapidly than other evolutionarycomputation methods.
(5) Protein folding problem is to predict the dimensional folding configurations from itsamino acid sequence. The HP lattice model, which depicts the protein, and the globalminimum energy conformation, which is fitness function, are introduced in this paper. Theestimation of distribution algorithms based on statistical learning and probability distributionmodel are introduced to discrete QPSO algorithm for protein folding. The improved algorithmhas the advantage of estimation of distribution algorithms and discrete QPSO algorithm,which includes the global convergence property of the estimation of distribution algorithmsand the local convergence property in the latter iterative of the discrete QPSO algorithm. Thenovel algorithm can not only locate quickly the approximate range of the optimal solution, but also converge rapidly to the optimal solution. Nine amino acid sequences are suggested to testthe performance of improved algorithm.
引文
1.王宇平.进化计算的理论和方法[M].北京:科学出版社,2011.1-6
2.王正志,薄涛.进化计算[M].长沙:国防科技大学出版社,2000.252-300
3. Kennedy J, Eberhart R C. Particle Swarm Optimization[C]. In: Proc. of IEEE International Conferenceon Neural Networks. Piscataway, NJ: IEEE Conference Publications,1995.1942-1948
4. Sun J, Bin Feng, Wenbo Xu, Particle Swarm Optimization With Particles Having Quantumbehavior[C]. In: Proc. of IEEE Congress on Evolutionary Computation. Piscataway, NJ: IEEEConference Publications,2004.325-331
5. Sun J, Wenbo Xu, Bin Feng, A Global Search Strategy of Quantum-behaved Particle SwarmOptimization[C]. In: Proc. of IEEE Conference on Cybernetics and Intelligent Systems. Piscataway,NJ: IEEE Conference Publications,2004.111-116
6.张连文,郭海鹏.贝叶斯网引论[M].北京:科学出版社,2006.34-65,172-192
7.曾霞,基于贝叶斯网的Web服务信任模型研究[D]:[硕士学位论文].西安:西安工业大学,2010
8.孙啸,陆祖宏,谢建明.生物信息学基础[M].北京:清华大学出版社,2005.1-30
9. Kennedy J, The Particle Swarm: Social Adaptation of Knowledge[C]. In: Proc. of IEEE InternationalConference on Evolutionary Computation. Piscataway, NJ: IEEE Conference Publications,1997.303-308
10. Kennedy J, Eberhart R C. A New Optimizer Using Particle Swarm Theory[C]. In: Proc. of the6thInternational Symposium on Micro Machine and Human Science. Piscataway, NJ: IEEE ConferencePublications, l995.39-43
11. Kennedy J. The behavior of particle[C]. In: Proto V M, Saravanan N, Waagen D,eds. Proc. of the7thEvolutionary Programming. San Diego, California, USA: Springer Berlin Heidelberg,1998.579-589
12. Bergh F V d. An Analysis of Particle Swarm Optimizers [D]:[Ph.D. dissertation]. South Africa:University of Pretoria,2001
13. Bergh F V d. A New Locally Convergent Particle Swarm Optimizer [C]. In: Kamel A E, MellouliK,Borne P, eds. Proc. of IEEE International Conference on systems, Man and Cybernetics. Piscataway,NJ: IEEE Conference Publications,2002.3-6
14. Clerc M, Kennedy J. The Particle Swarm: Explosion, Stability and Convergence in a Multi-Dimensional Complex Space [J]. IEEE Transactions on Evolutionary Computation,2002,6(1):58-73
15. Trelea I C. The Particle Swarm Optimization Algorithm: Convergence Analysis and ParameterSelection [J]. Information Processing Letters,2003,85(6):317-325
16. Kennedy J. Why does it need velocity?[C]. In: Proc. of IEEE Swarm Intelligence Symposium.Pasadena, California: IEEE Conference Publications,2005.38-44.
17.潘峰,陈杰,甘明刚,等.粒子群优化算法模型分析[J].自动化学报,2006,32(3):368-377
18.李宁,孙德宝,邹彤.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
19. Jiang M, Luo Y P, Yang S Y. Stochastic Convergence Analysis and Parameter Selection of theStandard Particle Swarm Optimization Algorithm[J]. Information Processing Letters.2007,102(1):8-16
20. Kennedy J, Eberhart R C. A Discrete Version of the Particle Swarm Algorithm[C]. In: Proc. of theIEEE Conference on System, Man and Cybernetics. Piscataway, NJ: IEEE Conference Publications,1997.4104-4109
21. Angeline P J. Using Selection to Improve Particle Swarm Optimization[C]. In: Proc. of IEEEInternational Conference on Evolutionary Computation. Piscataway, NJ: IEEE ConferencePublications,1998.84-89
22. Angeline P J. Evolutionary Optimization Versus Particle Swarm Optimization: Philosophy andperformance Differences[C]. In: Proto V M, Saravanan N, Waagen D,eds. Proc. of the7thEvolutionaryProgramming. San Diego, California, USA: Springer Berlin Heidelberg,1998.601-610
23. Suganthan P N. Particle Swarm Optimiser with Neighbourhood Operator[C]. In: Proc. of the1999Congress on Evolutionary Computation. Piscataway, NJ: IEEE Conference Publications,1999.1958-1962
24. Kennedy J. Small Worlds and Mega-minds: Effects of Neighborhood Topology on Particle Swarmperformance[C]. In: Proc. of the1999Congress on Evolutionary Computation. Piscataway, NJ: IEEEConference Publications,1999.1931-1938
25.柯晶,钱积新,乔谊正.一种改进粒子群优化算法[J].电路与系统学报,2003,8(5):87-91
26. Kennedy J. Probability and Dynamics in the Particle Swarm[C]. In: Proc. of IEEE Congress onEvolutionary Computation. Piscataway, NJ: IEEE Conference Publications,2004.340-347
27. Mendes R, Kennedy J, Neves J. The Fully Informed Particle Swarm: Simpler, Maybe Better[J]. IEEETransactions on Evolutionary Computation,2004,8(3):204-210
28. Bergh F V D, Engelbrecht A P. A Cooperative Approach to Particle Swarm Optimization[J]. IEEETransactions on Evolutionary Computation,2004,8(3):225-239
29. Liang J J, Qin A K, Suganthan P N. Comprehensive Learning Particle Swarm Optimizer for GlobalOptimization of Multimodal Functions[J]. IEEE Transactions on Evolutionary Computation,2006,10(3):281-295
30.高海兵,周驰,高亮.广义粒子群优化模型[J].计算机学报,2005,28(12):1980-1987
31.窦全胜,周春光,马铭.粒子群优化的两种改进策略[J].计算机研究与发展,2005,42(5):897-904
32.俞欢军,张丽平,陈德钊,等.基于反馈策略的自适应粒子群优化算法[J].浙江大学学报（工学版）,2005,39(9):12-17
33.崔志华,曾建潮.基于控制理论的微粒群算法分析与改进[J].小型微型计算机系统,2006,27(5):849-853
34.崔志华,曾建潮.基于微分模型的改进微粒群算法[J].计算机研究与发展,2006,43(4):646-653
35.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
36.刘宇,覃征,史哲文.简约粒子群优化算法[J].西安交通大学学报,2006,40(8):883-887
37.刘洪波,王秀坤,谭国真.粒子群优化算法的收敛性分析及其混沌改进算法[J].控制与决策,2006,21(6):636-640,645
38. Kirabyaz S, Pulkkinen J, Gabbouj M. Multi-Dimensional Particle Swarm Optimization in DynamicEnvironments[J]. Expert Systems with Applications,2011,38(3):2112-2223
39. Shi Y, Eberhart R C. A Modified Particle Swarm Optimizer[C]. In: Proc. of the IEEE InternationalConference on Evolutionary Computation. Piscataway, NJ: IEEE Conference Publications,1998.69-73
40. Shi Y, Eberhart R C. Fuzzy Adaptive Particle Swarm Optimization[C]. Proceedings of the2001Congress on Evolutionary Computation,2001,1:101-106
41. Clerc M. The Swarm and the Queen: Towards a Deterministic and Adaptive Particle SwarmOptimization[C]. In: Proc. of the IEEE Congress on Evolutionary Computation. Piscataway, NJ: IEEEConference Publications,1999.1951-1957
42.王俊伟,汪定伟.粒子群算法中惯性权重的实验与分析[J].系统工程学报,2005,20(2):194-198
43. Jiang C W, Bompard E. A Hybrid Method of Chaotic Particle Swarm Optimization and Linear Interiorfor Reactive Power Optimization[J]. Mathematics and Computers in Simulation,2005,68(1):57-65
44. Eberhart R C, Shi Y H. Particle Swarm Optimization: Developments, Applications and Resources. In:Proc. of the IEEE Congress on Evolutionary Computation. Piscataway, NJ: IEEE ConferencePublications,2001.81-86
45. Chen J, Pan F, Cai T. Acceleration Factor Harmonious Particle Swarm Optimizer[J]. InternationalJournal of Automation and Computing,2006,3(1):41-46
46.高鹰.一种自适应扩展粒子群优化算法[J].计算机工程与应用,2006,42(15):12-15
47.曾建潮,介婧,崔志华.微粒群算法[M].北京:科学出版社,2004.
48. Juang C F. A Hybrid of Genetic Algorithm and Particle Swarm Optimization for Recurrent NetworkDesign[J]. IEEE Transactions Systems, Man and Cybernetics, Part B,2004,34(2):997-1006
49. Cohen S C M, de Castro L N. Data Clustering with Particle Swarms[C]. In: Proc. of the IEEECongress on Evolutionary Computation. Piscataway, NJ: IEEE Conference Publications,2006.1792-1798
50. Rui X, Wunsch D C, Frank R L. Inference of Genetic Regulatory Networks with Recurrent NeuralNetwork Models Using Particle Swarm Optimization [J]. IEEE/ACM Transactions on ComputationalBiology and Bioinformatics,2007,4(4):286-291
51. Poli R, Kennedy J, Blackwell T, Particle Swarm Optimization: An Overview[J]. Swarm Intelligence,2007,(1):33-57,2007.
52. Banks A, Vincent J, Anyakoha C, A Review of Particle Swarm Optimization. Part II: Hybridisation,Combinatorial, Multicriteria and Constrained Optimization, and Indicative Applications[J]. NaturalComputing,2008,7(1):109-124
53.高尚,韩斌,吴小俊,等.求解旅行商问题的混合粒子群优化算法[J].控制与决策,2004,19(11):1286-1289
54. Fang W, Sun J, Ding Y R, etc. A Review of Quantum-behaved Particle Swarm Optimization[J]. IETETechnical Review,2010,27(7):336-348
55. Kennedy J. Some Issues and Practices for Particle Swarms[C]. In: Proc. of the IEEE SwarmIntelligence Symposium. Piscataway, NJ: IEEE Conference Publications,2007.162-169
56. Sun J, Xu W B, Liu J. Parameter Selection o Quantum-behaved Particle Swarm Optimization[C].In:wang L, Chen K, Ong Y S,eds. Proc. of the1stInternational Conference on Natural Computation,San Diego, California, USA: Springer Berlin Heidelberg,2005.543-552
57. Sun J, Xu W B, Feng B. Adaptive Parameter Control for Quantum-behaved Particle SwarmOptimization on Individual Level[C]. In: Proc. of the IEEE International Conference on Systems, Manand Cybernetics. Piscataway, NJ: IEEE Conference Publications,2005.3049-3054
58. Coelho L S. Novel Gaussian Quantum-behaved Particle Swarm Optimizer Applied to ElectromagneticDesign [J]. Science Measurement&Technology,2007,11(5):290-294
59. Coelho L S, Nedjah N, Mourelle L M. Gaussian Quantum-behaved Particle Swarm OptimizationApplied to Fuzzy PID Controller Design[J]. Quantum Inspired Intelligent Systems Studies inComputational Intelligence,2008(121):1-15
60. Coelho L S.Gaussian Quantum-behaved Particle Swarm Optimization Approaches For ConstrainedEngineering Design Problems[J]. Expert Systems with Applications,2010,37(2):1676-1683
61.方伟,孙俊,谢振平,等.量子粒子群优化算法的收敛性分析及控制参数研究[J].物理学报,2010,59(6):3686-3694
62. Gao H, Xu W B, Yu Y S. Quantum-behaved Particle Swarm Optimization with Learning Approach [J].Journal of Computational Information Systems,2008,4(4):1379-1384
63. Gao H, Xu W B, Gao T. A Cooperative Method Quantum-behaved Particle Swarm Optimization [C].In: Proc. of the IEEE International Symposium on Intelligent Signal Processing. Piscataway, NJ: IEEEConference Publications,2007.205-210
64.高浩.粒子群算法及其在图像分割中的应用与研究[D]:[博士学位论文],无锡:江南大学,2010
65.屈百达,焦竹青,徐保国.多量子粒子群协同优化算法研究[J].计算机工程与应用,2008,44(7):72-74
66. Lu S F, Sun C F. Coevolutionay Quantum-behaved Particle Swarm Optimization with HybridCooperative Search[C]. In: Zhang Y D, Tan H H, Luo Q,eds. Proc. of the Pacific-Asia Workshop onComputational Intelligence and Industrial Application. Los ALamitos, California: IEEE ComputerSociety,2008.109-113
67. Sun J, Xu W B, Fang W. Enhancing Global Search Ability of Quantum-behaved Particle SwarmOptimization by Maintaining Diversity of the Swarm [C]. In: Greco S,Hata Y,Hirano S,eds. Proc. ofthe5thInternational Conference on Rough Sets and Current Trends in Computing. San Diego,California, USA: Springer Berlin Heidelberg,2006.736-745
68. Sun J, Xu W B, Fang W. Quantum-behaved Particle Swarm Optimization Algorithm with ControlledDiversity[C]. In: Alexandrov V N, Albada G D, Sloot P M, eds. Proc. of the6thInternationalConference on Computational Science. San Diego, California, USA: Springer Berlin Heidelberg,2006.847-854
69. Sun J, Xu W B, Fang W. A Diversity-guided Quantum-behaved Particle Swarm OptimizationAlgorithm[C]. In: Wang T D,Li X D,Chen S H, eds. Proc. of the6thInternational Conference onSimulated Evolution and Learning. San Diego, California, USA: Springer Berlin Heidelberg,2006.497-504
70. Sun J, Xu W B, Fang W. Quantum-behaved Particle Swarm Optimization with a Hybrid ProbabilityDistribution[C]. In: Yang Q, Webb G, eds. Proc. of the9thPacific Rim International Conference onArtificial Intelligence. San Diego, California, USA: Springer Berlin Heidelberg,2006.737-746
71. Wang J, Zhou Y. Quantum-behaved Particle Swarm Optimization with Generalized Local SearchOperator for Global Optimization[C]. In: Huang D S, Heutte L, Loog M, eds. Proc. of the3rdInternational Conference on Intelligent Computing. San Diego, California, USA: Springer BerlinHeidelberg,2007.851-860
72. Huang Z, Wang Y J, Yang C J, etc. A New Improved Quantum-behaved Particle Swarm OptimizationModel[C]. In: Proc. of the4thIEEE Conference on Industrial Electronics and Applications. Piscataway,NJ: IEEE Conference Publications,2009.1560-1564
73. Yang K, Nomura H. Quantum-behaved Particle Swarm Optimization with Chaotic Search[J]. IEICETransactions on Information and Systems,2008, E91-D(7):1963-1970
74. Xi M L, Sun J, Xu W B. An Improved Quantum-behaved Particle Swarm Optimization Algorithmwith Weighted Mean Best Position[J]. Applied Mathematics and Computation,2008,205(2):751-759
75. Liu J, Sun J, Xu W B. Improving Quantum-behaved Particle Swarm Optimization by SimulatedAnnealing[C]. In: Huang D S, Heutte L, Loog M, eds. Proc. of the International Conference onIntelligent Computing. San Diego, California, USA: Springer Berlin Heidelberg,2006.130-136
76. Liu J, Sun J, Xu W B, Kong X H. Quantum-behaved Particle Swarm Optimization Based on ImmuneMemory and Vaccination[C]. In: Proc. of the IEEE International Conference on Granular Computing.Piscataway, NJ: IEEE Conference Publications,2006.453-456
77. Liu J, Sun J, Xu W B. Quantum-behaved Particle Swarm Optimization with Immune Operator[C]. In:Ra Z W, Malerba D, Semeraro G, eds. Proc. of the International Symposium on Foundations ofIntelligent Systems. San Diego, California, USA: Springer Berlin Heidelberg,2006.77-83
78. Fang W, Sun J, Xu W B. Improved Quantum-behaved Particle Swarm Optimization Algorithm Basedon Differential Evolution Operator and Its Application[J]. Journal of System Simulation,2008,20(24):6740-6744
79. Liu J, Sun J, Xu W B. Quantum-behaved Particle Swarm Optimization with Mutation Operator[C]. In:Proc. of the17thIEEE International Conference on Tools with Artificial Intelligence. Piscataway, NJ:IEEE Conference Publications,2005.237-240
80. Sun J, Lai C,Xu W B, A Novel and More Efficient Search Strategy of Quantum-behaved ParticleSwarm Optimization[C]. In: Beliczynski B, Dzielinski A, Iwanowski M, eds. Proc. of the8thInternational Conference on Adaptive and Natural Computing Algorithms. San Diego, California,USA: Springer Berlin Heidelberg,2007.394-403
81. Long H X, Xu W B, Sun J. Binary Particle Swarm Optimization Algorithm with Mutation for MultipleSequence Alignment[J]. Rivista di Biologia/Biology Forum,2009,102(1):75-94
82.周頔.医学图像处理中的若干问题研究[D]:[博士学位论文].无锡:江南大学,2011
83.陈伟.群体智能算法及其在基因表达数据聚类中的应用[D]:[博士学位论文].无锡:江南大学,2011
84.孙俊.量子行为粒子群优化算法研究[D]:[博士学位论文].无锡:江南大学,2009
85.奚茂龙.群体智能算法及其在移动机器人路径规划与跟踪控制中的研究[D]:[博士学位论文].无锡:江南大学,2008
86.龙海侠.进化算法及其在生物信息中的应用[D]:[博士学位论文].无锡:江南大学,2010
87.赵吉.群体智能算法研究及其应用[D]:[博士学位论文].无锡:江南大学,2010
88.周迪,孙俊,须文波.基于二进制具有量子行为的粒子群算法的多边形近似[J].计算机应用,2007,27(8):2030-2032
89.孙俊,方伟,吴小俊,等.量子行为粒子群优化:原理及其应用[M].北京:清华大学出版社,2011.1-51
90. Zhao J, Chen W, Xu W B. Nonlinear System Identification Based on Radial Basis Function NeuralNetwork Using Improved Particle Swarm Optimization[C]. In: Wang H Y, Low K S, Wei K, eds. Proc.of the5thInternational Conference on Natural Computation. Los ALamitos, California: IEEEComputer Society,2009.409-413
91.方伟.群体智能算法及其在数字滤波器优化设计中的研究[D]:[博士学位论文].无锡:江南大学,2007
92.张智星,孙春在,水谷英二.神经-模糊和软计算[M].西安:西安交通大学出版社,2000.238-256
93. Mizumoto M, Fuzzy Controls under Various Approximate Reasoning Methods[J]. InformationSciences,1998,45(2):129-151
94.王雪苗.模糊神经网络优化及应用研究[D]:[硕士学位论文].大连:大连理工大学,2007
95.艾芳菊.模糊神经网络的结构优化研究[D]:[博士学位论文].成都:中国科学院成都计算机应用研究所,2006
96. Tang A M, Quek C, Ng G S, GA-TSKfnn, Parameters Tuning of Fuzzy Neural Network Using GeneticAlgorithms[J]. Expert Systems with Applications,2005,29(4):769-781
97. Lin C J, Lee C Y, Non-linear System Control Using A Recurrent Fuzzy Neural Network Based onImproved Particle Swarm Optimisation[J]. International Journal of Systems Science,2010,41(4):381-395
98. Jiao S H, Jiang Z Y, Bu J L, Application of Artificial Neural Network Based on GA-BP Algorithm toPredicting Mechanical Properties of TC4[J]. Advanced Materials Research,2011,146-147:1698-1701.
99. Juang C F, Wang C Y. A Self-generating Fuzzy System with Ant and Particle Swarm CooperativeOptimization[J]. Expert Systems with Applications,2009,36(3):5362–5370
100. Spirtes C, P Glymour, Seheines R. Causality from Probability. Evolving Knowledge in NaturalScience and Artificial Intelligence, London, Pitman,1990:181-199
101. Spirtes P, Glymour C, Scheines R. An Algorithm for Fast Recovery of Sparse Causal Grpahs[J]. SocialScience Computer Review,1991,9(l):62-72
102. Cheng J, Greiner R, Learning Bayesian Networks from Data: an Information Theory BasedApproach[J]. Artificial Intelligence,2002,137(l-2):43-90
103. Cooper G F, Herskovits E. A Bayesian Method for the Induction of Probabilistic Networks fromData[J]. Machine Learning,1992,9(4):309-347
104. Singh M, Valtorta M.Construction of Bayesian Network Structures from Data: a Brief Survey and anEfficient Algorithm[J]. International Journal of Approximate Reasoning,1995,12(2):111-131
105. Bouekaert R R. A Stratified Simulation Scheme for Inference in Bayesian Belief Networks[C]. In:Proc. of the10thConference on Uncertainty in AI. Seattle,WA,USA,1994:110-117
106. Lam W, Bacehus F. Learning Bayesian Belief Netwokrs: An Approach Based on The MDLPrinciple[J]. Computational Intelligence,1994,10(4):269-293
107. Chiekering D M, Geiger D. Learning Bayesian Networks: Search Methods And ExperimentalResults[C]. In: Proc. of5thConference on Artificial Intelligence and Statistics. Ft. Lauderdale, FL1995:112-128
108. Larrnaaga P. Structure Learning of Bayesian Networks by Genetic Algorithms: A PerformanceAnalysis of Control Parmaeters[J]. IEEE Transactions on Pattern Analysis and Machine Intelligence,1996,18b (9):912-926
109. Larrnaaga P. Searching for the Best Ordering in the Structure Learning of Bayesian Networks[J]. IEEETransactions on System, Man and Cybernetics,1996,26c(4):487-493
110. Suzuki J. A Construction of Bayesian Networks from Databases Based on an MDL Principle[C]. In:Proc. of the9th Conference on Uncertainty in Artificial Intelligence, Washington D.C.1996:266-273
111. Wong M L, Leung K S. An Efficient Data Mining Method for Learning Bayesian Networks Using anEvolutionary Algorithm-based Hybrid Approach[J]. IEEE Transactions on Evolutionary Computation,2004,8:378-404
112.刘大有,王飞等.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
113. Crescenzi P, Goldman D, Papadimitriou C, etc. On the Complexity of Protein Folding [J]. Journal ofComputational Biology,1998,5(3):423-465
114.解伟,王翼飞.蛋白质折叠的计算机模拟[J].上海大学学报(自然科学版),2006(2):189-193
115.王敞,陈增强,袁著祉.基于并行遗传算法的蛋白质空间结构预测[J].计算机科学,2003,30(7):147-149
116. Liu J F, Zhou Z L, Gao Z X, etc. Protein Folding Simulation Based on Improved Simulated AnnealingAlgorithm [J]. Advanced Materials Research.2012,424-425:246-249
117. Unger R, Moult J. Genetic Algorithms for Protein Folding Simulations[J].. Journal of MolecularBiology,1992,231:75–81
118. Liang F, Wong W H. Evolutionary Monte Carlo for Protein Folding Simulations. Journal of ChemicalPhysics,2001,115(7):3374-3380
119. Zhang X L, Li T T. Improved Particle Swarm Optimization Algorithm for2D Protein FoldingPrediction[C]. In: Proc. of the1st International Conference on Bioinformatics and BiomedicalEngineering Granular Computing. Piscataway, NJ: IEEE Conference Publications,2007.53-56
120. Alena S, Holger H H. An Improved Ant Colony Optimization Algorithm for the2D HP ProteinFolding Problem[C]. In: Yang Xiang Y, Chaib-Draa B, eds. Proc. of6th Conference on the CanadianSociety for Computational Studies of Intelligence. San Diego, California, USA: Springer BerlinHeidelberg,2003.400-417
121. Jiang T, Cui Q, Shi G, etc. Protein Folding Simulations of the Hydrophobic-hydrophilic Model byCombining Tabu Search with Genetic Algorithms[J]. Journal of Chemical Physics,2003,119(8):4592–4596
122. H. P. Hsu, V. Mehra, W. Nadler, P. Grassberger. Growth Algorithms for Lattice Heteropolymers at LowTemperatures[J]. Journal of Chemical Physics,2003,118(1):444-451
123. L. Z. Junni, S. L. Jun. A New Sequential Importance Sampling Method and its Application to theTwo-Dimensional Hydrophobic-Hydrophilic Model[J]. Journal of Chemical Physics,2002,117(7):3492-3498
124. G. Chikenji, M.Kikuchi, Y. Iba. Multi-Self-Overlap Ensemble for Protein Folding: Ground StateSearch and Thermodynami[J]. Physical Review Letters,1999,83(9):1886-1889
125.施彦.群体智能预测与优化[M].北京:国防工业出版社,2012.1-10
126. Cai Y, Sun J, Wang J,etc. Optimizing the Codon Usage of Synthetic Gene with QPSO Algorithm[J].Journal of Theoretical Biology,2008,254(1):123-127
127. Sun J, Wu X J, Palade V, etc. Convergence Analysis and Improvements of Quantum-behaved ParticleSwarm Optimization[J]. Journal of Information Science,2012,193:81-103
128.陈伟,周頔,孙俊,等.一种采用完全学习策略的量子行为粒子群优化算法[J].控制与决策,2012,27(5):719-723,730
129. Wolpert D H, Macready W G. No Free Lunch Theorems for Optimization[J]. IEEE Transactions onEvolutionary Computation,1997,1(1):67-82
130. Salomon R. Reevaluating Genetic Algorithm Performance under Coordinate Rotation of BenchmarkFunctions[J]. BioSystems,1996,39:263-278
131. Chiekering D M, Heekerman D, Meek C. Large-sample Learning of Bayesian Networks is NP-hard[J].Journal of Machine Learning Research,2004,9(5):1287-1330
132.周树德,孙增圻.分布估计算法综述[J].自动化学报,2007,33(2):113-124
133. Mühlenbein H, Paa G. From Recombination of Genes to The Estimation of Distributions I. BinaryParameters[C]. In: Hans-Michael Voigt H M, Ebeling W, Rechenberg I, eds. Proc. of4thInternationalConference on Parallel Problem Solving from Nature. San Diego, California, USA: Springer BerlinHeidelberg,1996.178-187
134. Ghebreab S, Jaffe C C, Smeulders A W M, Population-Based Incremental Interactive ConceptLearning for Image Retrieval by Stochastic String Segmentations[J]. IEEE Transactions on MedicalImaging,2004,23(6):676-689
135. Gallagher M, Frean M. Population-Based Continuous Optimization Probabilistic Modeling and MeanShift[J]. Evolutionary Computation,2005,13(1):29-42
136. Yang S Y, Ho S L, Ni G Z, eta. A New Implementation of Population Based Incremental LearningMethod for Optimizations in Electromagnetic[J]. IEEE Transactions on Magnetics,2007,43(4):1601-1604
137.王翼飞,史定华.生物信息学-智能化算法及其应用[M].北京:化学工业出版社,2006.141-143
138. Chan H S, Dill K A. Energy Landscapes and the Collapse Dynamics of Homopolymers[J]. Journal ofChemical Physics,1993,99(3):2116-2117