|关键词||粒子群优化算法 收敛性分析 轨迹 动态系统 惯性权重 学习因子 种群中心位置信息 种群多样性 位置变异概率 随机位置变异算子|
Recent years, with the high speed development of computer science technique, Particle Swarm Optimization (PSO), as a new class of Swarm Intelligence (SI) technique, has received much attention. PSO is an efficient heuristic for global optimization. Because PSO is simple, high speed, and easy to be implemented by programs, it has been successfully applied for solving many engineering area problems, such as function optimization, parameter tuning, artificial neural network training, fuzzy control, pattern recognition, and signal processing, etc. This thesis introduces the PSO algorithm at first. Then the convergence behavior, the parameter selection, and the modification of PSO are deeply studied. The main contents can be summarized as follows: Firstly, the convergence behavior of the PSO algorithm is discussed. PSO can be treated as a dynamic system. By using the standard results from the discrete dynamic system theory, the convergence of the trajectory of a simple PSO system is analyzed and the convergence conditions are derived. The convergence of basic PSO is also analyzed by adopting above conditions. The particle trajectories are investigated under the specific initial conditions. Furthermore, the parameter selection of the PSO algorithm is studied in this thesis. Parameter selection is important for PSO, and proper parameters will largely improve the optimization performance. Based on the theoretical analysis, two strategies of better choosing inertia weight and learning rates which called Improved Random Inertia Weight (IRIW) strategy and Dynamic Learning Rate (DLR) strategy are given. The results of the numerical simulations indicate the proposed strategies are effective. Moreover, an improved PSO algorithm called CPSO (Particle Swarm Optimization with Swarm Center Position Information) is proposed. The swarm center position information can provide useful information for particles finding the optimum, so we combine the standard PSO algorithm with the swarm center position information in this thesis. Experimental results and comparisons with Standard PSO (SPSO) show that CPSO can effectively enhance the searching ability and greatly improve the convergence speed. Finally, particle swarm optimization typically converges relatively rapidly at the beginning of the search and then slow down or stop. This behaviour has been attributed to the loss of diversity in the population. To deal with the problem mentioned above, this paper presents a novel Particle Swarm Optimization with Random Position Mutation (RPM-PSO), which combines SPSO with Genetic Algorithm (GA) mutation method. At each iteration, the particle’s position is mutated with a slight probability, which provides a good way to effectively maintain population diversity. Experimental results show that RPM-PSO owns high efficiency and strong stability. The methods in this thesis have been realized in MATLAB and many examples have been tested in computer.
|郭大庆. 粒子群优化算法的研究及改进[D]. 北京. 中国科学院研究生院,2007.|
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