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题名: 粒子群优化算法的研究及改进
作者: 郭大庆
答辩日期: 2007-06
导师: 李英凡
专业: 计算机应用技术
授予单位: 中国科学院研究生院
授予地点: 北京
学位: 硕士
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
摘要: 近年来,随着计算机技术的飞速发展,粒子群优化算法作为一种新型的演化计算技术,得到了广泛的关注。粒子群优化算法是一类有效的启发式全局优化技术,由于具有简单、高速和易于程序实现等特点,在工程实践中表现出巨大的潜力,现已经成功地应用于函数优化、参数整定、人工神经网络、模糊控制、模式识别以及信号处理等多个领域。本文首先介绍了粒子群优化算法,进而对算法的收敛性、参数的选择和算法的改进进行了深入的研究。本文的主要内容可以归纳如下:
1、讨论了粒子群优化算法的收敛行为。将粒子群优化算法看作一个动态系统,采用线性离散时间系统的研究方法,对简化粒子群系统中粒子轨迹的收敛性进行了相应的分析,导出了简化算法的收敛条件。根据上述理论,对基本粒子群优化算法进行定性分析。在特定初始条件下,对粒子群优化算法中粒子的轨迹进行了观测。
2、研究了粒子群优化算法的参数选择问题。粒子群优化算法中参数的选择是个极为重要的课题,适当的选择可极大地改善优化效果。从原理上对粒子群优化算法的参数选取进行了细致的分析,总结出了一些指导性的规律,提出了惯性权重和学习因子的选取策略,分别为“改进的随机惯性权重取值策略”和“动态学习因子取值策略”,并通过数值仿真实验验证了上述两种方法的有效性。
3、种群的中心位置为粒子群“捕获”问题最优解提供了有用的信息,为此本文将粒子群的中心位置信息引入到标准粒子群优化算法中,构造出一种带有种群中心位置信息的粒子群优化算法,分析了种群中心位置信息对算法优化过程所作的贡献。采用基准测试函数对算法测试表明,新算法的搜索能力和收敛速度均优于标准粒子群优化算法。
4、粒子群优化算法通常在搜索的初期具有较快的收敛速度,然后收敛速度逐渐变慢或停止,这种行为是因为算法在后期缺乏种群的多样性所导致的。结合遗传算法中的“变异”思想,提出一种带有随机位置变异的粒子群优化算法。在每一次迭代中,通过使粒子群优化算法中的位置信息以一个小概率发生变异,有效地保持了算法的种群多样性。实验结果表明,新算法优化效率较高,稳健型强。这些方法都在MATLAB上编程实现,并且在许多实例上得到了应用。
英文摘要: 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.
内容类型: 学位论文
URI标识: http://ir.xjipc.cas.cn/handle/365002/3511
Appears in Collections:多语种信息技术研究室_学位论文

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作者单位: 中国科学院新疆理化技术研究所

Recommended Citation:
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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