Journal of Frontiers of Computer Science and Technology ›› 2014, Vol. 8 ›› Issue (6): 760-767.DOI: 10.3778/j.issn.1673-9418.1306024

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Research on Particle Trajectories of Discrete PSO Algorithm

TAO Qian1,2, HUANG Zhexue Joshua2, GU Chunqin3+, CHANG Huiyou4, REN Dan4   

  1. 1. Department of Computer Science, Guangdong University of Education, Guangzhou 510310, China
    2. Shenzhen Institute of Advanced Technology, Chinese Academy of Sciences, Shenzhen, Guangdong 518055, China
    3. Department of Network Engineering, Zhongkai University of Agriculture and Engineering, Guangzhou 510255, China
    4. School of Software, Sun Yat-sen University, Guangzhou 510006, China
  • Online:2014-06-01 Published:2014-05-30


陶  乾1,2,黄哲学2,顾春琴3+,常会友4,任  丹4   

  1. 1. 广东第二师范学院 计算机科学系,广州 510310
    2. 中国科学院 深圳先进技术研究院,广东 深圳 518055
    3. 仲恺农业工程学院 网络工程系,广州 510225
    4. 中山大学 软件学院,广州 510006

Abstract: Considering the insufficiency of the theoretical research on discrete particle swarm optimization (PSO) algorithms, this paper studies the basic theory for discrete PSO algorithms. Firstly, this paper uses order difference equations to model the generalization trajectory of particles and proposes a basic framework for the theoretical research on discrete PSO algorithms. Secondly, this paper uses the basic mathematical methods, including the limit, series convergence and Cauchy convergence theorem, to analyze the trajectory characteristics of random particle in a multi-dimension discrete space, and then provides a formal proof that each particle of a discrete PSO algorithm converges to a stable point. Finally, combined with a classical discrete optimization problem, this paper presents the empirical analysis of stochastic particles in a 15-dimensional discrete space, and the experimental results support the conclusions drawn from the theoretical findings.

Key words: particle swarm optimization (PSO), discrete space, particle trajectory, theoretical research, convergence

摘要: 当前离散粒子群优化(particle swarm optimization,PSO)算法缺乏系统性的理论支撑,因此对离散PSO算法基础理论问题进行了研究。采用一阶非齐次差分方程组对粒子群在多维离散空间的通用轨迹进行建模,为离散PSO算法的理论研究构建了基础框架;采用极限、级数收敛和柯西审敛定理等基本数学理论分析了多维离散空间随机粒子的轨迹行为特性,并证明了轨迹的收敛性;结合经典的离散优化问题,在15维离散空间中对随机粒子运动轨迹进行了实证分析,验证了理论证明的相关结果。

关键词: 粒子群优化(PSO), 离散空间, 粒子轨迹, 理论研究, 收敛