惯性权重粒子群算法模型收敛性分析及参数选择

为提高粒子群算法的收敛性,基于动力系统的稳定性理论分析了带有惯性权重的粒子群算法模型的收敛性,提出了在算法模型收敛条件下惯性权重w和加速系数c的参数约束关系.使用4个测试函数对具有所提参数约束关系的惯性权重粒子群算法模型和典型参数取值惯性权重粒子群算法模型进行了对比仿真研究,实验结果表明,具有提出的参数约束关系的惯性权重粒子群算法模型在收敛性方面具有显著优越性.     

基于局部搜索惯性权重的粒子群优化算法*

粒子群优化算法的性能主要受其中参数的影响,尤其是惯性权重的影响,选择合理的ω能够平衡算法的全局和局部搜索能力.根据当前粒子的函数值调整学习因子,利用局部搜索的方法确定惯性权重,提高了算法的鲁棒性能.最后对一些标准测试函数进行验证,实验分析表明该算法具有优越性能.     

一种基于单纯形搜索的粒子群优化算法

为了改善粒子群优化算法的求解性能,提出了一种基于单纯形搜索和粒子群优化的混合算法。该算法一方面自适应地确定惯性权重、认知以及社会参数来达到免参数目的,另一方面利用单纯形搜索来引导部分粒子的搜索方向,从而加速算法收敛。数值实验结果表明,与传统的粒子群算法和其他基于单纯形的粒子群算法相比,提出算法在评估次数、求解精度方面表现良好。     

粒子群优化算法在函数优化中的应用及参数分析

为了更深入地分析探讨粒子群优化算法的性能,采用两种基本改进策略在MATLAB 7.0中对几个典型测试函数的优化问题进行了实验,即单独采用线性递减惯性权重策略以及在其基础上再加入收缩因子法,给出了这两种策略下函数的在线性能、离线性能变化图。为指导参数选取,用图示方式给出了不同参数组合对收敛性的影响。结论是：采用线性递减惯性权重策略加上收缩因子法比单独采用线性递减惯性权重策略的收敛性能好。若取固定惯性权重w,则w越小,收敛速度越快。     

基于自适应惯性权重的均值粒子群优化算法

针对粒子收敛速度慢、搜索精度不高和算法性能在很大程度上依赖参数选取等缺点,提出了一种基于自适应惯性权重的均值粒子群优化算法。对算法中的惯性权重参数采用动态自适应变化方式,在迭代过程中根据粒子适应度差值将种群划分为三个等级,对不同等级的粒子采用不同的惯性权重策略,使粒子能根据自己所处的位置选择合适的惯性权重值,更快地收敛到全局最优位置;同时分别用个体极值和全局极值的线性组合取代PSO算法中的全局最优位置与个体最优位置。通过实验仿真与对比,验证了新算法性能优于标准PSO及其它一些改进的PSO算法,能够用较少的迭代次数找到最优解,具有更快的收敛速度和更高的收敛精度。     

粒子群优化算法中加速系数的实验分析

基于粒子群优化的原理,利用标准测试函数对粒子群算法的参数设计进行实验分析,依据函数特性进行初步分类,揭示不同类型优化问题中加速系数与惯性权重的相互关系及其设计规律。该项研究成果为粒子群算法的理论研究提供了实验依据,并为算法的实际应用创造了有利条件。     

基于遗传交叉因子的改进粒子群优化算法

提出一种基于遗传交叉因子的改进粒子群优化算法,通过自适应变化惯性权重来改善算法的收敛性能,借鉴遗传算法中的选择交叉操作增加粒子多样性,通过引入交叉因子增强群体粒子的优良特性,减小了算法陷入局部极值的可能。对几个典型的测试函数进行仿真表明,该算法较标准粒子群优化算法(PSO)提高了全局搜索能力和收敛速度,改善了优化性能。     

基于蚁群系统的参数自适应粒子群算法及其应用

为了解决粒子群算法惯性权重自适应问题,提出一种基于蚁群系统的惯性权重自适应粒子群算法(AS-PSO).AS-PSO首先将惯性权重取值区间离散化,各个惯性权重子区间在初期赋予相同的信息素;然后,粒子群算法中的各个粒子,根据各个惯性权重子区间中的信息素浓度和粒子在搜索空间中分布的先验知识,确定各个惯性权重子区间的选择概率,并进而实现粒子的空间搜索;最后,基于粒子的进化信息,实现惯性权重子区间信息素浓度的更新.仿真研究表明,AS-PSO算法在种群进化寻优的同时,能根据种群的进化信息,通过蚁群算法实现惯性权重参数的自适应调整和进化,且不增加测试函数的调用次数;算法寻优性能优于传统的自适应粒子群算法和根据速度信息自适应调整参数的粒子群算法.同时,算法实际应用于复杂系统模型参数的优化估计,获得满意结果.     

多策略融合粒子群算法及其收敛性分析

针对使用经典线性递减策略来确定惯性权重的粒子群优化算法在实际运算过程中与粒子寻优的非线性变化特点不匹配的问题,提出一种改进的粒子群算法。该算法采用多次随机初始化的策略初始种群位置,再对惯性权重引入随机因子,使其基于粒子适应度大小来动态调节惯性权重,更好地引导粒子进行搜索,提高算法的收敛精度,并证明其能以概率1全局收敛。为了验证该算法的寻优性能,通过8个经典测试函数将标准粒子群算法、惯性权重递减的粒子群算法及提出的改进算法在不同维度下进行测试比较。结果表明,该算法的寻优精度更高。     

带有权重函数学习因子的粒子群算法

粒子群算法(PSO)中惯性权重和学习因子的独自调整策略削弱了算法进化过程的统一性和粒子群的智能特性,很难适应复杂的非线性优化,为此提出一种利用惯性权重来控制学习因子的PSO算法。该算法将学习因子视作惯性权重的线性、非线性以及三角函数,在惯性权重随时间线性或非线性递减的过程中,学习因子发生相应的递减或递增变化,进而通过增强两者之间的相互作用来平衡算法的全局探索和局部开发能力,更好地引导粒子进行优化搜索。同时为了分析惯性权重和学习因子的融合性能,采用线性和非线性权重法进行比较,测试函数的优化结果表明了采用非线性递减权重的优越性。最后通过对多个基准测试函数的优化分析,并与带有异步线性变化和三角函数学习因子调整方法的PSO进行比较发现,该策略利用惯性权重调整学习因子,能达到平衡粒子个体学习能力和向群体学习能力的作用,提高了算法的优化精度。     

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.     

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.     

Non-parametric particle swarm optimization for global optimization

In recent years, particle swarm optimization (PSO) has extensively applied in various optimization problems because of its simple structure. Although the PSO may find local optima or exhibit slow convergence speed when solving complex multimodal problems. Also, the algorithm requires setting several parameters, and tuning the parameters is a challenging for some optimization problems. To address these issues, an improved PSO scheme is proposed in this study. The algorithm, called non-parametric particle swarm optimization (NP-PSO) enhances the global exploration and the local exploitation in PSO without tuning any algorithmic parameter. NP-PSO combines local and global topologies with two quadratic interpolation operations to increase the search ability. Nineteen (19) unimodal and multimodal nonlinear benchmark functions are selected to compare the performance of NP-PSO with several well-known PSO algorithms. The experimental results showed that the proposed method considerably enhances the efficiency of PSO algorithm in terms of solution accuracy, convergence speed, global optimality, and algorithm reliability.     

Particle swarm optimization with grey evolutionary analysis

Based on grey relational analysis, this study attempts to propose a grey evolutionary analysis (GEA) to analyze the population distribution of particle swarm optimization (PSO) during the evolutionary process. Then two GEA-based parameter automation approaches are developed. One is for the inertia weight and the other is for the acceleration coefficients. With the help of the GEA technique, the proposed parameter automation approaches would enable the inertia weight and acceleration coefficients to adapt to the evolutionary state. Such parameter automation behaviour also makes an attempt on the GEA-based PSO to perform a global search over the search space with faster convergence speed. In addition, the proposed PSO is applied to solve the optimization problems of twelve unimodal and multimodal benchmark functions for illustration. Simulation results show that the proposed GEA-based PSO could outperform the adaptive PSO, the grey PSO, and two well-known PSO variants on most of the test functions.     

具有随机惯性权重的PSO算法

微粒群算法（PSO算法）是模拟鸟类、鱼群等的群体智能行为的一种优化算法,当前,在相关领域内,倍受国内外学者关注。该文在分析基本PSO算法的速度进化方程的基础上,提出一种能更好描述微粒进化过程的速度方程,由其引出一种具有随机惯性权重的PSO算法;通过五个典型测试函数的仿真实验,验证了其可行性,同时也表明具有随机惯性权重的PSO算法较具有线性递减惯性权重的PSO算法在收敛速度和全局收敛性方面有明显提高。     

A new hybrid particle swarm and simulated annealing stochastic optimization method

A novel hybrid particle swarm and simulated annealing stochastic optimization method is proposed. The proposed hybrid method uses both PSO and SA in sequence and integrates the merits of good exploration capability of PSO and good local search properties of SA. Numerical simulation has been performed for selection of near optimum parameters of the method. The performance of this hybrid optimization technique was evaluated by comparing optimization results of thirty benchmark functions of different dimensions with those obtained by other numerical methods considering three criteria. These criteria were stability, average trial function evaluations for successful runs and the total average trial function evaluations considering both successful and failed runs. Design of laminated composite materials with required effective stiffness properties and minimum weight design of a three-bar truss are addressed as typical applications of the proposed algorithm in various types of optimization problems. In general, the proposed hybrid PSO-SA algorithm demonstrates improved performance in solution of these problems compared to other evolutionary methods The results of this research show that the proposed algorithm can reliably and effectively be used for various optimization problems.     

Adaptive fuzzy particle swarm optimization for global optimization of multimodal functions

This paper proposes an adaptive fuzzy PSO (AFPSO) algorithm, based on the standard particle swarm optimization (SPSO) algorithm. The proposed AFPSO utilizes fuzzy set theory to adjust PSO acceleration coefficients adaptively, and is thereby able to improve the accuracy and efficiency of searches. Incorporating this algorithm with quadratic interpolation and crossover operator further enhances the global searching capability to form a new variant, called AFPSO-QI. We compared the proposed AFPSO and its variant AFPSO-QI with SPSO, quadratic interpolation PSO (QIPSO), unified PSO (UPSO), fully informed particle swarm (FIPS), dynamic multi-swarm PSO (DMSPSO), and comprehensive learning PSO (CLPSO) across sixteen benchmark functions. The proposed algorithms performed well when applied to minimization problems for most of the multimodal functions considered.     

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。     

A hybrid multi-swarm particle swarm optimization to solve constrained optimization problems

In the real-world applications, most optimization problems are subject to different types of constraints. These problems are known as constrained optimization problems (COPs). Solving COPs is a very important area in the optimization field. In this paper, a hybrid multi-swarm particle swarm optimization (HMPSO) is proposed to deal with COPs. This method adopts a parallel search operator in which the current swarm is partitioned into several subswarms and particle swarm optimization (PSO) is severed as the search engine for each sub-swarm. Moreover, in order to explore more promising regions of the search space, differential evolution (DE) is incorporated to improve the personal best of each particle. First, the method is tested on 13 benchmark test functions and compared with three stateof-the-art approaches. The simulation results indicate that the proposed HMPSO is highly competitive in solving the 13 benchmark test functions. Afterward, the effectiveness of some mechanisms proposed in this paper and the effect of the parameter setting were validated by various experiments. Finally, HMPSO is further applied to solve 24 benchmark test functions collected in the 2006 IEEE Congress on Evolutionary Computation (CEC2006) and the experimental results indicate that HMPSO is able to deal with 22 test functions.     

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。