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1、太原理工大学 博士学位论文 粒子群优化算法研究及在阵列天线中的应用 姓名：张玮 申请学位级别：博士 专业： 指导教师：王华奎 20100301 太原理工大学博士研究生学位论文 I 粒子群优化算法研究及在阵列天线中的应用 摘 要 粒子群优化算法是近十几年新出现的一种基于群迭代的模拟群体生 物相互协同寻优的启发式优化算法， 因其收敛速度快和易于实现等特点， 已经成为计算智能领域新的研究热点。由于粒子群算法理论基础还不完 备，并存在早熟收敛的问题，因此，对算法进行深入的理论分析及改进 是研究者们的工作重点之一。基于这种情况，本文对标准粒子群算法的 收敛性及稳定性进行了分析，从提高系统动态特性的角度提
2、出了参数选 择策略，为了提高算法的全局搜索能力及收敛速度提出了鲶鱼粒子群算 法。本文主要研究内容如下： 从描述粒子轨迹的算式出发，通过劳斯稳定判据及终值定理，推出 粒子轨迹稳定收敛的条件及稳态值。通过对粒子迭代过程的分析，发现 当加速因子为 2 时， 粒子位置期望始终保持最优状态， 当加速因子取 1.85 时，粒子的寻优过程最稳定。从提高系统稳定性的角度出发，提出了一 个具有普遍意义的参数选择策略；同时，通过调整递减指数提高算法的 收敛效率，提出了一种高效的非线性递减惯性权重法。 采用线性离散系统的分析方法，研究了粒子收敛轨迹受系统特征根 分布区域的影响。发现当特征根为复数时，系统输出为利于寻
3、优的衰减 脉冲振荡序列。应用离散系统动态特性分析理论对收敛域内粒子轨迹的 动态行为首次进行了理论解释，指出决定复特征根模值和相角的量是最 大超调量和阻尼振荡角频率，从提高系统动态特性的角度出发，提出了 新的 PSO 参数选择原则。理论分析表明此原则满足 M. Jiang 所提出的 PSO 均方收敛条件与选优方案， 以及 Fernandez Martnez 提出的最佳取 值方案。 为提高算法的全局搜索能力、加快收敛速度和避免出现早熟收敛， 太原理工大学博士研究生学位论文 II 提出了鲶鱼粒子群优化算法。 算法中引入偏差阈值和冲撞力度两个概念， 来调整种群的探测和开发能力，达到优化算法性能的目的。
4、通过不同的 测试函数研究了偏差阈值和冲撞力度对算法的影响，鲶鱼粒子群优化算 法的提出为 PSO 算法的改进及性能的提高提供了新的思路。 智能天线可以提高频谱的利用效率，在移动通信等现代通信系统中 发挥着重要的作用，而方向图的综合正是智能天线的核心技术。采用本 文提出的 PSO 参数选择原则， 进行低副瓣的方向图综合取得了较好的优 化效果。 关键词：粒子群优化算法，特征根，鲶鱼粒子群算法，阵列天线 太原理工大学博士研究生学位论文 III RESEARCH ON PARTICLE SWARM OPTIMIZATION ALGORITHM AND ITS APPLICATION IN ARRAY A
5、NTENNA ABSTRACT Particle swarm optimization (PSO) algorithm is a kind of heuristic optimization algorithm based on swarm iteration. It has become a new hotspot in the area of computation intelligence for the rapid convergence and simple implementation. Recent research has drawn attention to in-depth
6、 theoretical study and improvement due to its incomplete theoretical basis and premature convergence. We has made a deep study on convergence and stability of PSO, and then proposed a parameter choice strategy to enhance its dynamic characteristic in this thesis. Catfish-PSO algorithm is proposed to
7、 enhance the overall search ability and the convergence rate. The major research work can be summarized as follows: The convergence conditions and the state values are derived from Routh stability criterion and final value theorem. Based on the analysis of iterative process， we find that the particl
8、e positions are expected to converge to the optimal positions all the time when the accelerating factor is 2, and keep high concentration all through the whole optimization process when the acceleration factor is 1.85. To enhance the system stability, a universal strategy of parameter selection is p
9、roposed and its effectiveness is showed through functions tests. At the same time, a nonlinear function of decreasing inertia weight is presented to enhance the convergence efficiency by adjusting descending index. 太原理工大学博士研究生学位论文 IV The effect of characteristic roots distribution on convergence tra
10、jectory of paticles is studied using linear discrete-time system analysis method in control theory. We find that the system output is the attenuation oscillation pulse sequence which will benefit to optimization when characteristic roots are complex. The dynamic behavior of the particle in convergen
11、ce domain is theoretically explained applying theory of dynamic analysis in discrete-time systems. And we point out for the first time that the critical factors affecting the modulus value and the phase angle of the complex characteristic roots are the maximum overshoot and angular frequency of damp
12、ed oscillation. Then the principle of parameters selection about PSO is proposed in order to improve the system dynamic characteristics. The principle is not only match the conditions of mean square convergence proposed by M. Jiang, but also match the best value program proposed by Fernandez Martnez
13、, and it is proved to be effective by simulation tests. A new algorithm of Catfish-PSO is proposed to enhance the global search ability and the convergence ability, and also to avoid premature convergence. The two concepts of deviation threshold and collision strength are used to adjust the explorat
14、ion and exploitation ability of Catfish-PSO algorithm in order to optimize its performance. The effect of deviation threshold and collision strength on Catfish-PSO is studied using different trial functions. The new algorithm provides a new way of thinking to improve the performance of PSO algorithm
15、. Smart antenna can improve the spectrum utilization efficiency and play an important role in mobile communications and other modern communications; moreover, the antenna synthesis becomes the core technology of smart antenna. The application of the new algorithm to the low-sidelobe pattern synthesi
16、s is presented. 太原理工大学博士研究生学位论文 V KEY WORDS: particle swarm optimization algorithm, characteristic roots, catfish-PSO, antenna arrary 太原理工大学博士研究生学位论文 a 符 号 说 明 ( )f x 目标函数 n R n维欧氏空间 S 解空间 D 搜索空间 N 总粒子数 i X 第 i 个粒子的位置 i V 第 i 个粒子的速度 t id v 粒子i 在第t 次迭代中第d 维的速度 i pbest 第i个粒子搜索到的最优位置 i gbest 整个粒子群搜索到的最优位置 12 ,c c 加速因子 r1,r2 均匀分布于0 ,1之间的随机数 max V 速度上限 惯性权重 t 当前迭代次数 tmax 最大迭代次数 ini 初始惯性权重 fin 终了惯性权重 收缩因子 ptid 粒子i 在第t次迭代中第d 维的个体最优位置 ptgd 粒子i 在第t次迭代中第d维的全局最优位置
