[1]胡成玉,吴湘宁,颜雪松.微粒群算法中粒子运动稳定性分析[J].智能系统学报,2011,6(5):445-449.
HU Chengyu,WU Xiangning,YAN Xuesong.Stability analysis of the particle dynamics in a particle swarm optimization[J].CAAI Transactions on Intelligent Systems,2011,6(5):445-449.
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HU Chengyu,WU Xiangning,YAN Xuesong.Stability analysis of the particle dynamics in a particle swarm optimization[J].CAAI Transactions on Intelligent Systems,2011,6(5):445-449.
微粒群算法中粒子运动稳定性分析
《智能系统学报》[ISSN 1673-4785/CN 23-1538/TP] 卷:
6
期数:
2011年第5期
页码:
445-449
栏目:
学术论文—人工智能基础
出版日期:
2011-10-30
- Title:
- Stability analysis of the particle dynamics in a particle swarm optimization
- 文章编号:
- 1673-4785(2011)05-0445-05
- Keywords:
- particle swarm optimization; particle dynamics; stability analysis; evaluation function; stochastic process; timevarying differential system
- 分类号:
- TP301.6
- 文献标志码:
- A
- 摘要:
- 在研究微粒群算法是否收敛时，粒子运动稳定是微粒群算法收敛的前提条件，在分析粒子运动稳定性时，大多数文献假定微粒群只有单个粒子，最优粒子位置和局部最优粒子位置固定不动，并且忽略粒子运动的随机性，这些假定忽视了粒子算法中粒子运动的本质.首先从评估函数出发，考虑到粒子间的交换性，给出了吸引位置存在的证明，然后利用随机过程理论对粒子的运动进行分析，证明了最优粒子的位置序列是不断靠近吸引位置，最后考虑粒子运动的随机性，利用时变差分系统理论，构造李亚普诺夫能量函数，得到了微粒群中任意粒子运动稳定的条件.
- Abstract:
- When investigating the convergence of a particle swarm optimization, the stability of the particle dynamics must be guaranteed first. When analyzing stability of particle dynamics, most studies assume that the particle swarm has only one particle and that the positions of the optimum particle and the locally optimum particle are fixed and invariable. Furthermore, the randomicity of particle movement is omitted. These assumptions ignore the essence of particle movement in a particle swarm optimization. Starting from the evaluation function, this paper proved the existence of the attraction position, taking into consideration the exchangeability among multiple particles. It also analyzed the movement of particles using the stochastic process theory, proving that the position sequence of the optimum particle is continuously approaching the attraction position. Finally, considering the randomicity of particle movement and using the timevarying model, the Lyapunov energy function was constructed and the condition for stability of any particle’s movement in the particle swarm was given.
- 参考文献/References:
-
［1］KENNEDY J. The behavior of particles［C］//Proceedings of 7th International Conference on Evolutionary Programming VII. San Diego, USA, 1998: 581589.
［2］OZCAN E, MOHAN C K. Analysis of a simple particle swarm optimization system［M］//DAGLI C H, AKAY M, BUCZAK A L. Intelligent Engineering Systems Through Artificial Neural Networks: Volume 8. ［S.l.］: ASME, 1998: 253258.
［3］OZCAN E, MOHAN C K. Particle swarm optimization: surfing the waves［C］//Proceedings of the IEEE Congress on Evolutionary Computation. Piscataway, USA: IEEE, 1999: 19391944.
［4］CLERC M, KENNEDY J. The particle swarm： explosion, stability, and convergence in a multidimensional complex space［J］. IEEE Transactions on Evolutionary Computation, 2002, 6(1): 5873.
［5］TRELEA I C. The particle swarm optimization algorithm: convergence analysis and parameter selection［J］. Information Processing Letters, 2003, 85(6): 317325.
［6］CAMPANA E F, FASANO G, PINTO A. Dynamic system analysis and initial particles position in particle swarm optimization［C］//IEEE Swarm Intelligence Symposium. Indianapolis, USA, 2006: 202209.
［7］KADIRKAMANATHAN V, SELVARAJAH K, FLEMING P J. Stability analysis of the particle dynamics in particle swarm optimizer［J］. IEEE Transactions on Evolutionary Computation, 2006, 10(3): 245255.
［8］BLACKWELL T M. Particle swarms and population diversity［J］. Soft Computing, 2005, 9(11): 793802.
［9］Van Den BERGH F. An analysis of particle swarm optimizers［D］. Pretoria, South Africa: Department of Computer Science, University of Pretoria, 2002.
［10］CUI Zhihua, ZENG Jianchao. A guaranteed global convergence particle swarm optimizer［J］. Lecture Notes on Computer Science, 2004, 3066: 762767.
- 相似文献/References:
-
[1]吴晓威,张井岗.基于微粒群算法的灰色预测PID控制器[J].智能系统学报,2007,2(5):63.
WU Xiao-wei,ZHANG Jing-gang.Grey prediction PID controller based on particle swarm optimization approach[J].CAAI Transactions on Intelligent Systems,2007,2():63.
备注/Memo
收稿日期：2011-06-14.
基金项目：国家自然科学基金资助项目(60873107)；中央高校基本科研业务费专项资金资助项目（CUGL090236）.
通信作者：胡成玉.E-mail: huchengyu@cug.edu.cn.
作者简介：
胡成玉，男，1978年生，讲师，博士，CCF会员.主要研究方向为群集智能算法、动态优化，发表学术论文10余篇.
吴湘宁，男，1972年生，副教授，主要研究方向为计算机体系结构、蚁群优化算法，主持湖北省自然科学基金项目.
颜雪松，1977年生，副教授，博士，主要研究方向为演化计算与演化硬件.主持国家“863”计划项目、地质过程与矿产资源国家重点实验室开放课题基金和“十一五”民用航天预先研究项目各1项，作为主要骨干参加过多项国家自然科学基金项目、国家“863”计划项目以及航天技术创新基金项目.发表学术论文10余篇.
更新日期/Last Update:
2011-11-16