PSO算法扰动优化策略及其收敛性研究

为进一步提升求解精度、有效抑制早熟收敛，各类扰动（变异或跳转）优化策略常用来对粒子群优化（Particle Swarm Optimization，PSO）算法的pBest、gBest进行极值扰动，由此增强粒子在多维空间的搜索能力、提升算法性能．为分析扰动优化策略下粒子（PSO算法的搜索引擎）在多维空间的轨迹行为特性，采用级数对多维空间中粒子进行了理论分析并证明了扰动后粒子轨迹的收敛性；最后，结合项目调度问题在多维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．

Research on perturbation optimization approach of PSO algorithm and convergence

In order to improve the precision of solution, to avoid the premature convergence, various perturbation (mutation or jump) optimization approaches have been developed to realize the perturbation of the pBest or gBest, so as to enhance the search capability of the high-dimensional space and improve the performance of the PSO algorithm. To analyze the trajectory behavior of particles (search engine of PSO algorithm) under perturbation optimization approaches in a multi-dimensional space, a theoretic analysis of particles is presented by series and the convergence of particle trajectory under perturbation optimization approaches is proved. Lastly, an empirical analysis of stochastic particles is also presented based on the project scheduling problem in a multi-dimensional space, and the experimental results are provided to support the conclusions drawn from the theoretical ?ndings.