离散PSO算法粒子轨迹研究  

Research on Particle Trajectories of Discrete PSO Algorithm

作　　者：陶乾[1,2] 黄哲学[2] 顾春琴[3] 常会友[4] 任丹[4] 

机构地区：[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

出　　处：《计算机科学与探索》2014年第6期760-767,共8页Journal of Frontiers of Computer Science and Technology

基　　金：中国博士后科学基金No.2013M542219;广东省重大科技攻关项目No.2012A080104022;高等学校博士学科点专项科研基金No.20120171110034;广东第二师范学院博士基金项目No.2012ARF05~~

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。Considering the insufficiency of the theoretical research on discrete particle swarm optimization （PSO） algo-rithms, this paper studies the basic theory for discrete PSO algorithms. Firstly, this paper uses order difference equa-tions 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 con-verges 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.

关 键 词：粒子群优化(PSO) 离散空间 粒子轨迹 理论研究 收敛 PARTICLE SWARM OPTIMIZATION (PSO) 

分 类 号：TP301[自动化与计算机技术—计算机系统结构]