Kennedy J, Eberhart R C. Particle swarm optimization. In: Proceedings of IEEE International Conference on Neural Networks. Perth, WA: IEEE, 1995. 1942-1948
[2]
Zeng Zhi-Hua, Cui Jian-Chao. Analysis and improvement about particle swarm optimization based on linear control theory. Journal of Chinese Computer Systems, 2006, 27(5): 849-853(崔志华, 曾建潮. 基于控制理论的微粒群算法的分析与改进. 小型微型计算机系统, 2006, 27(5): 849-853)
[3]
Kadirkamanathan V, Selvarajah K, Fleming P J. Stability analysis of the particle dynamics in particle swarm optimizer. IEEE Transactions on Evolutionary Computation, 2006, 10(3): 245-255
[4]
Fern？ndez-Martínez J L, García-Gonzalo E, Saraswathi S, Jernigan R, Kloczkowski A. Particle swarm optimization: a powerful family of stochastic optimizers: analysis, design and application to inverse modelling. In: Proceedings of the 2nd International Conference on Advances in Swarm Intelligence. Berlin, Heidelberg: Springer-Verlag, 2011. 1-8
[5]
Clere M. Stagnation analysis in particle swarm optimization or what happens when nothing happens [Online], available: http://clerc.maurice.free.fr/pso/stagnation, May 1, 2006
[6]
Jiang M, Luo Y P, Yang S Y. Stagnation analysis in particle swarm optimization. In: Proceedings of Swarm Intelligence Symposium. Honolulu, HI: IEEE, 2007. 92-99
[7]
Pan F, Chen J, Cai T, Gan M G, Wang G H. Stability, convergence of harmonious particle swarm optimizer and its application. Journal of Beijing Institute of Technology, 2009, 17(1): 35-40
[8]
Zhang H B, Wang H B, Hu Z J. Analysis of particle swarm optimization algorithm global convergence method. Computer Engineering and Applications, 2011, 47(34): 61-63
[9]
Sahin C S, Gundry S, Uyar M ü. Markov chain analysis of self-organizing mobile nodes self-organizing mobile nodes. Journal of Intelligent and Robotic Systems, 2012, 67(12): 133-153
[10]
Yuan Dai-Lin, Chen Qiu. Particle swarm optimization algorithm based on Markov model and its stochastic process analysis. Computer Engineering and Applications, 2009, 45(31): 49-52(袁代林, 陈虬. 马氏模型PSO及其随机过程分析. 计算机工程与应用, 2009, 45(31): 49-52)
[11]
Li Ning. Analysis and Application of Particle Swarm Optimization [Ph.D. dissertation], Huazhong University of Science and Technology, China, 2006(李宁. 粒子群优化算法的理论分析与应用研究 [博士学位论文], 华中科技大学, 中国, 2006)
[12]
Cai Zhao-Quan, Huang Han, Zheng Zong-Hui, Luo Wei. Convergence improvement of particle swarm optimization based on the expanding attaining-state set. Journal of Huazhong University of Science and Technology (Nature Science Edition), 2009, 37(6): 44-47(蔡昭权, 黄翰, 郑宗晖, 罗伟. 基于可达状态集扩张的粒子群算法收敛性改进. 华中科技大学学报(自然科学版), 2009, 37(6): 44-47)
[13]
Shi Y H, Eberhart R C. Parameter selection in particle swarm optimization. In: Proceedings of the 7th International Conference on Evolutionary Programming. New York, USA, 1998. 591-600
[14]
Trelea I C. The particle swarm optimization algorithm: convergence analysis and parameter selection. Information Processing Letters, 2003, 85(6): 317-325
[15]
Clerc M, Kennedy J. The particle swarm: explosion, stability, and convergence in a multidimensional complex space. IEEE Transactions on Evolutionary Computation, 2002, 6(1): 58-73
[16]
Zeng Jian-Chao, Cui Zhi-Hua. A new unified model of particle swarm optimization and its theoretical analysis. Journal of Computer Research and Development, 2006, 43(1): 96-100(曾建潮, 崔志华. 微粒群算法的统一模型及分析. 计算机研究与发展, 2006, 43(1): 96-100)
[17]
Pan Feng, Chen Jie, Gan Ming-Gang, Cai Tao, Tu Xu-Yan. Model analysis of particle swarm optimizer. Acta Automatica Sinica, 2006, 32(3): 368-377(潘峰, 陈杰, 甘明刚, 蔡涛, 涂序彦. 粒子群优化算法模型分析. 自动化学报, 2006, 32(3): 368-377)
[18]
Poli R, Broomhead D. Exact analysis of the sampling distribution for the canonical particle swarm optimiser and its convergence during stagnation. In: Proceedings of the 9th Annual Conference on Genetic and Evolutionary Computation. London, England: ACM, 2007. 134-141
[19]
Pan Feng, Chen Jie, Xin Bin, Zhang Juan. Several characteristics analysis of particle swarm optimizer. Acta Automatica Sinica, 2009, 35(7): 1010-1016(潘峰, 陈杰, 辛斌, 张娟. 粒子群优化方法若干特性分析. 自动化学报, 2009, 35(7): 1010-1016)
[20]
van den Bergh F. An Analysis of Particle Swarm Optimizers [Ph.D. dissertation], University of Pretoria, South Africa, 2001
[21]
van den Bergh F, Engelbrecht A P. A study of particle swarm optimization particle trajectories. Information Sciences, 2006, 176(8): 937-971
[22]
Jiang M, Luo Y P, Yang S Y. Stochastic convergence analysis and parameter selection of the standard particle swarm optimization algorithm. Information Processing Letters, 2007, 102(1): 8-16
[23]
Nakama T. Markov chain analysis of genetic algorithms applied to fitness functions perturbed concurrently by additive and multiplicative noise. Computational Optimization and Applications, 2012, 51(2): 601-622
[24]
Zhang Y A, Ma Q L, Sakamoto M, Furutani H. Effect of mutation to distribution of optimum solution in genetic algorithm. Natural Computing, 2010, 2(3): 380-387
[25]
Jin Xin-Lei, Ma Long-Hua, Wu Tie-Jun, Qian Ji-Xin. Convergence analysis of the particle swarm optimization based on stochastic processes. Acta Automatica Sinica, 2007, 33(12): 1263-1268(金欣磊, 马龙华, 吴铁军, 钱积新. 基于随机过程的 PSO 收敛性分析. 自动化学报, 2007, 33(12): 1263-1268)
[26]
Ren Zi-Hui, Wang Jian, Gao Yue-Lin. The global convergence analysis of particle swarm optimization algorithm based on Markov chain. Control Theory and Applications, 2011, 28(4): 462-466(任子晖, 王坚, 高岳林. 马尔科夫链的粒子群优化算法全局收敛性分析. 控制理论与应用, 2011, 28(4): 462-466)
[27]
Poli R, Langdon W B. Markov chain models of bare-bones particle swarm optimizers. In: Proceedings of the 9th Annual Conference on Genetic and Evolutionary Computation. London, England: ACM, 2007. 142-149
