一种基于单纯形法的改进微粒群优化算法及其收敛性分析

A Simplex Method Based Improved Particle Swarm Optimization and Analysis on Its Global Convergence

针对现有微粒群优化算法难以兼顾进化速度和求解质量这一难题,提出一种基于单纯形法的改进微粒群优化算法(Simplex method based improved particle swarm optimization,SM-IPSO).该算法采用多个优化种群,分别在奇数种群和偶数种群上并行运行微粒群算法和单纯形法,并通过周期性迁移相邻种群间的最优信息,达到微粒群算法和单纯形法的协同搜索:单纯形借助微粒群算法跳出局部收敛点,微粒群依靠单纯形提高局部开发能力.为强化两种算法所起作用,一种改进的微粒速度逃逸策略和Nelder-Mead单纯形法也被提出.最后,在Linux集群系统上运行所提算法,通过优化五个典型测试函数验证了算法的有效性.

Considering that the existing particle swarm optimizations （PSO） do not give simultaneously attention to evolution speed and solution＇s quality, a simplex method based improved particle swarm optimization （SM-IPSO） is proposed in this paper. In SM-IPSO, the conception of multipopulations is adopted, where PSO and SM run on odd populations and even populations, respectively. And a periodical migrating operation between adjacent populations is also introduced in SM-IPSO in order to achieve cooperative search of both PSO and SM for solution space： SM can get away from local converged points by virtue of PSO, and PSO can improve its local exploiting capability under the help of SM. Furthermore, an improved escape method of particle velocities and improved Nelder-Mead SM are proposed in order to enhance the functions of PSO and SM in this paper. Finally, the proposed algorithm is implemented on a Linux cluster system, and experimental results on optimizing five benchmark functions demonstrate its usefulness.