粒子群优化算法模型分析

粒子群优化算法在优化问题中体现出良好的性能,但目前还没有对其运动特性,尤其是参数的选择与当粒子群体陷入局部极值点导致的早熟收敛情况的详细分析．分析了PSO算法中的三种粒子模型(Gbest,Pbest,Commom模型)的运动特性,给出了Gbest模型和Pbest 模型在没有新息获取时,单信息条件下的最大搜索空间．进一步证明了在减少了Lipschitz条件约束的条件下,Common模型渐进稳定的充分条件,将算法中惯量因子的取值范围扩大到 (-1,1),并从物理上进行了解释．     

A novel stability-based adaptive inertia weight for particle swarm optimization

Particle swarm optimization (PSO) is a stochastic population-based algorithm motivated by intelligent collective behavior of birds. The performance of the PSO algorithm highly depends on choosing appropriate parameters. Inertia weight is a parameter of this algorithm which was first proposed by Shi and Eberhart to bring about a balance between the exploration and exploitation characteristics of PSO. This paper presents an adaptive approach which determines the inertia weight in different dimensions for each particle, based on its performance and distance from its best position. Each particle will then have different roles in different dimensions of the search environment. By considering the stability condition and an adaptive inertia weight, the acceleration parameters of PSO are adaptively determined. The corresponding approach is called stability-based adaptive inertia weight (SAIW). The proposed method and some other models for adjusting the inertia weight are evaluated and compared. The efficiency of SAIW is validated on 22 static test problems, moving peaks benchmarks (MPB) and a real-world problem for a radar system design. Experimental results indicate that the proposed model greatly improves the PSO performance in terms of the solution quality as well as convergence speed in static and dynamic environments.     

Low-discrepancy sequence initialized particle swarm optimization algorithm with high-order nonlinear time-varying inertia weight

Particle swarm optimization (PSO) is a population-based stochastic optimization algorithm motivated by intelligent collective behavior of some animals such as flocks of birds or schools of fish. The most important features of the PSO are easy implementation and few adjustable parameters. A novel PSO method called LHNPSO, with low-discrepancy sequence initialized particles and high-order (1/π²) nonlinear time-varying inertia weight and constant acceleration coefficients, is proposed in this paper. The initial population particles are generated by using the Halton sequence to fill the search space efficiently. Nonlinear functions with orders varied within big ranges are employed to adjust the inertial weight, cognitive and social parameters. Based on the sensitivity analysis of PSO performance to the changes of the orders of these nonlinear functions, 1/π² order nonlinear function is selected to adjust the time-varying inertia weight and the two acceleration coefficients are set to be constants. A set of well-known benchmark optimization problems is then used to investigate the performance of the proposed LHNPSO algorithm and facilitate the comparison with other three types of PSO algorithms. The results show that the easily implemented LHNPSO can converge faster and give a much more accurate final solution for a variety of benchmark test functions.     

An improved particle swarm optimiser based on swarm success rate for global optimisation problems

Inertia weight is one of the control parameters that influences the performance of particle swarm optimisation (PSO) in the course of solving global optimisation problems, by striking a balance between exploration and exploitation. Among many inertia weight strategies that have been proposed in literature are chaotic descending inertia weight (CDIW) and chaotic random inertia weight (CRIW). These two strategies have been claimed to perform better than linear descending inertia weight (LDIW) and random inertia weight (RIW). Despite these successes, a closer look at their results reveals that the common problem of premature convergence associated with PSO algorithm still lingers. Motivated by the better performances of CDIW and CRIW, this paper proposed two new inertia weight strategies namely: swarm success rate descending inertia weight (SSRDIW) and swarm success rate random inertia weight (SSRRIW). These two strategies use swarm success rates as a feedback parameter. Efforts were made using the proposed inertia weight strategies with PSO to further improve the effectiveness of the algorithm in terms of convergence speed, global search ability and improved solution accuracy. The proposed PSO variants, SSRDIW_PSO and SSRRIW_PSO were validated using several benchmark unconstrained global optimisation test problems and their performances compared with LDIW-PSO, CDIW-PSO, RIW-PSO, CRIW-PSO and some other existing PSO variants. Empirical results showed that the proposed variants are more efficient.     

Common model analysis and improvement of particle swarm optimizer

Particle swarm optimizer （PSO）, a new evolutionary computation algorithm, exhibits good performance for optimization problems, although PSO can not guarantee convergence of a global minimum, even a local minimum. However, there are some adjustable parameters and restrictive conditions which can affect performance of the algorithm. In this paper, the algorithm are analyzed as a time-varying dynamic system, and the sufficient conditions for asymptotic stability of acceleration factors, increment of acceleration factors and inertia weight are deduced. The value of the inertia weight is enhanced to （-1, 1）. Based on the deduced principle of acceleration factors, a new adaptive PSO algorithm- harmonious PSO （HPSO） is proposed. Furthermore it is proved that HPSO is a global search algorithm. In the experiments, HPSO are used to the model identification of a linear motor driving servo system. An Akaike information criteria based fitness function is designed and the algorithms can not only estimate the parameters, but also determine the order of the model simultaneously. The results demonstrate the effectiveness of HPSO.     

Acceleration Factor Harmonious Particle Swarm Optimizer

A Particle Swarm Optimizer (PSO) exhibits good performance for optimization problems, although it cannot guarantee convergence to a global, or even local minimum. However, there are some adjustable parameters, and restrictive conditions, which can affect the performance of the algorithm. In this paper, the sufficient conditions for the asymptotic stability of an acceleration factor and inertia weight are deduced, the value of the inertia weight ω is enhanced to (-1,1). Furthermore a new adaptive PSO algorithm - Acceleration Factor Harmonious PSO (AFHPSO) is proposed, and is proved to be a global search algorithm. AFHPSO is used for the parameter design of a fuzzy controller for a linear motor driving servo system. The performance of the nonlinear model for the servo system demonstrates the effectiveness of the optimized fuzzy controller and AFHPSO.     

Common model analysis and improvement of particle swarm optimizer

Particle swarm optimizer (PSO), a new evolutionary computation algorithm, exhibits good performance for optimization problems, although PSO can not guarantee convergence of a global minimum, even a local minimum. However, there are some adjustable parameters and restrictive conditions which can affect performance of the algorithm. In this paper, the algorithm are analyzed as a time-varying dynamic system, and the sufficient conditions for asymptotic stability of acceleration factors, increment of acceleration factors and inertia weight are deduced. The value of the inertia weight is enhanced to (?1, 1). Based on the deduced principle of acceleration factors, a new adaptive PSO algorithmharmonious PSO (HPSO) is proposed. Furthermore it is proved that HPSO is a global search algorithm. In the experiments, HPSO are used to the model identification of a linear motor driving servo system. An Akaike information criteria based fitness function is designed and the algorithms can not only estimate the parameters, but also determine the order of the model simultaneously. The results demonstrate the effectiveness of HPSO.     

粒子群优化算法中惯性权值调整的一种新策略

惯性权值的设置对粒子群优化（PSO）算法的性能起着关键作用,现有的基于惯性权值的改进算法提高了算法的性能,但都把惯性权值作为全局参数,很难控制算法的搜索能力。本文在充分分析惯性权值的关键作用基础上给出一种新的惯性权值调整策略及其相应的粒子群优化算法,使用不同的惯性权值更新同一代种群。测试结果表明,新算法提高了算算法的性能,并具有更快的收敛速度和跳出局部最优的能力。     

融合隶属度函数的自适应惯性权重模式的粒子群优化算法

粒子群算法(Particle Swarm Optimization,PSO)的性能极大地依赖于其惯性权重参数的选择策略。当在一次迭代中更新粒子速度时,PSO忽略了粒子间的差异,在所有粒子上应用了相同的惯性权重。针对这一问题,提出一种自适应惯性权重的粒子群算法PSO-AIWA,有效合理地均衡PSO的全局搜索和局部搜索能力。根据当前粒子与全局最优粒子间的差异,算法可以通过基于粒子间距的隶属度函数动态调整粒子的惯性权重,使得每次迭代中,粒子可以根据当前状态在每个维度上的搜索空间内选择合适的惯性权重进行状态更新。在6种基准函数下进行了算法的性能测试,结果表明,与随机式惯性权重PSO算法与线性递减惯性权重PSO-LDIW算法相比,该算法可以获得更好的粒子分布和收敛性。     

求解TSP问题的模糊自适应粒子群算法

由于惯性权值的设置对粒子群优化（PSO）算法性能起着关键的作用,本文通过引入模糊技术,给出了一种惯性权值的模糊自适应调整模型及其相应的粒子群优化算法,并用于求解旅行商（TSP）问题。实验结果表明了改进算法在求解组合优化问题中的有效性,同时提高了算法的性能,并具有更快的收敛速度。     

基于强化学习的适应性微粒群算法

惯性权重足微粒群算法(PSO)的重要参数,它可以甲衡算法的全局和局部搜索能力的关系,改善算法的性能.对此,提出一种基于强化学习的适应性微粒群算法(RPSO).首先将不同惯性权重调整策略视为粒子的行动集合;然后通过计算Q函数值.考察粒子多步进化的效果;进而选择粒_了最优进化策略,动态调整惯性权重,以增强算法寻找全局最优的...     

Grey particle swarm optimization

With the help of grey relational analysis, this study attempts to propose two grey-based parameter automation strategies for particle swarm optimization (PSO). One is for the inertia weight and the other is for the acceleration coefficients. By the proposed approaches, each particle has its own inertia weight and acceleration coefficients whose values are dependent upon the corresponding grey relational grade. Since the relational grade of a particle is varying over the iterations, those parameters are also time-varying. Even if in the same iteration, those parameters may differ for different particles. In addition, owing to grey relational analysis involving the information of population distribution, such parameter automation strategies make an attempt on the grey PSO to perform a global search over the search space with faster convergence speed. The proposed grey PSO is applied to solve the optimization problems of 12 unimodal and multimodal benchmark functions for illustration. Simulation results are compared with the adaptive PSO (APSO) and two well-known PSO variants, PSO with linearly varying inertia weight (PSO-LVIW) and PSO with time-varying acceleration coefficients (HPSO-TVAC), to demonstrate the search performance of the grey PSO.     

一类新颖的粒子群优化算法

粒子群优化(PSO)是一类有效的随机全局优化技术。它利用一个粒子群搜索解空间,每个粒子表示一个被优化问题的解,通过粒子间的相互作用发现复杂搜索空间中的最优区域。提出一类新颖的PSO算法,该算法在基本PSO算法的粒子位置更新公式中增加了一个积分控制项。积分控制项根据每个粒子的适应值决定粒子位置的变化,改善了PSO算法摆脱局部极小点的能力。另外,该算法增加了限制搜索空间范围的机制,这对某些函数优化问题是必需的。用5个基准函数做的对比实验结果显示,该算法优于基本PSO算法以及自适应修改惯性因子的PSO算法。     

一种改进的微粒群优化算法

基于惯性权重对微粒群优化算法（Particle Swarm Optimization,PSO）优化性能的显著影响,提出了一种改变惯性权重的方法以改进PSO算法的优化性能。算法中惯性权重的动态改变是通过对其进行PSO寻优来控制的。经过对标准函数的测试计算,无论是二维还是多维的问题,这种改变惯性权重的PSO算法的寻优结果的准确度和精度均得以提高,收到了良好的效果,尤其在高维情况下,显示出算法性能得到了明显改善。     

粒子群优化算法的分析与改进

分析了惯性权值对粒子群优化(PSO)算法优化性能的影响，进而提出选择惯性权值的新策略．在随机选取惯性权值的同时，自适应地调整随机惯性权值的数学期望，有效地调整算法的全局与局部搜索能力．测试表明基于随机惯性权(RIW)策略的PSO算法，其全局搜优的速率与精度有明显提高．     

基于粒子熵的参数自适应变异PSO算法研究

为了避免普通粒子群算法（PSO）可能出现的局部收敛及精度不高现象,围绕影响PSO算法性能的两个重要参数[w]和[pgd],提出了一种面向全局优化的参数自适应变异PSO改进算法。算法定义了粒子熵集概念,可以精确反映粒子群数据的全局聚集特性,由粒子群各维数据的熵值大小决定是否对各维数据的惯性权重[w]进行回归变异,对全局变量[pgd]进行随机变异,并采取引入变异次数因子等方法来避免寻优发散。仿真研究表明该算法比常用算法在寻优精度、摆脱局部陷阱、稳定性等方面均有明显提高,在求解复杂多峰问题上有着良好的表现。     

微粒群算法中惯性权重的调整策略

惯性权重是微粒群算法中的关键参数,可以平衡算法全局搜索能力和局部搜索能力的关系,提高算法的收敛性能。该文分析了惯性权重对微粒群算法收敛性能的影响,为了进一步提高算法的全局最优性,提出了几种对惯性权重的调整策略。通过对4个测试函数的仿真实验,验证了这些策略的可行性,表明这些策略能够简便高效地提高算法的全局收敛性和收敛速度。     

一种单个粒子自适应修正的粒子群算法

在各类优化问题的解决过程中,群智能优化算法的局部搜索与全局搜索性能都起着重要的作用。在粒子群优化算法中,惯性权值的引入对粒子群算法的收敛性与稳定性都具有一定的影响。因此,在分析现有权值递减策略的基础上,提出一种基于单个粒子适应值的权值修正策略,区别对待同次迭代中适应值好与差的粒子,通过不同的权值赋值策略,以充分发挥各粒子的优势,以增强全局搜索和跳出局部最优的能力。通过对标准测试函数所做的对比实验,该策略可以使粒子在搜索初期获得更好的多样性,使粒子具有更强的摆脱陷入局部极值点的能力;在搜索末期可以加快粒子收敛速度以提高粒子群优化算法的快速性能。改进算法有效减少了早熟的发生,提高了粒子的收敛性能,取得了比较满意的仿真结果。     

基于惯性权重对数递减的粒子群优化算法

针对粒子群算法收敛速度慢和易陷入局部最优的问题,提出了基于惯性权重对数递减的粒子群算法,并引入对数调整因子,对数调整因子的不同取值保证了算法搜索成功率。选取八种典型函数分别进行给定迭代次数和给定精度的仿真实验,并与标准PSO算法、惯性权重线性递减PSO算法、惯性权重高斯函数递减PSO算法进行比较。测试结果表明,该策略可以简便高效地提高算法的全局收敛性和收敛速度,并且具有较好的稳定性。求解大多数优化问题时,即使不引入对数调整因子新算法就可以获得较好的效果。     

一类加权有理插值样条曲面及局部约束控制

目的 构造一类新的基于函数值与偏导数值的加权有理插值样条曲面,讨论该样条曲面的相关性质并分析曲面的局部约束控制。方法 一方面,先从x方向构造有理三次插值样条,再从y方向构造二元有理插值样条曲面;另一方面,按相反次序构造另一个二元有理插值样条曲面;最后将两种插值曲面加权得到一类新的有理插值样条曲面。结果 讨论插值曲面的性质,包括基函数、边界性质、积分加权系数的性质以及误差估计。通过选择合适的参数和加权系数,在不改变插值数据的前提下实现对插值区域内的局部约束控制。结论 实验结果表明,新的加权有理插值样条曲面具有良好的约束控制性质。