基于近似动态规划的微粒群系统参数优化研究

从系统最优控制的角度对微粒群参数的动态优化问题进行探讨. 针对离散动态规划的``维数灾"问题, 将群体启发式随机搜索机制引入动态规划的最优策略求解, 提出了一种群体智能近似动态规划模式; 基于该模式给出简化的确定型微粒群反馈控制系统参数优化的近似计算方法, 并扩展应用于具有随机变量的微粒群系统; 仿真计算得到了微粒群加速因子的近似最优动态规律, 并将所得策略与一种时变加速因子(Time-varying acceleration coefficients, TVAC)策略进行了函数优化性能的比较与分析, 初步实验结果表明该近似动态规划模式可有效地用于微粒群系统参数的动态优化设置.     

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.     

基于拓扑结构与粒子变异改进的粒子群优化算法

为使粒子群优化算法(PSO)优化过程的多样性与收敛性得到合理解决,以提高算法优化性能,基于种群拓扑结构与粒子变异提出两种粒子群改进算法RSMPSO和RVMPSO.改进算法将具有信息定向流动的闭环拓扑结构与星型拓扑结构或四边形拓扑结构相结合,促使粒子在前期寻优过程中具有较高的多样性,保证搜索的广度,而在后期满足粒子群的整体收敛性,保证寻优的精度.同时,将布谷鸟搜索算法(CS)中的偏好随机游走变异策略引入改进算法中,增强粒子跳出局部最优的能力.对标准测试函数的仿真实验表明,所改进的PSO算法与其他6个对比算法相比不仅操作简单,优化精度高,而且在算法收敛性及稳健性方面都有着更出色的表现.     

采用种群平均信息和精英变异的改进粒子群算法

针对基本粒子群优化(PSO)算法早熟收敛和后期搜索效率低的问题,提出一种利用种群平均信息和精英变异的粒子群优化算法--MEPSO算法。该算法引入粒子个体与群体的平均信息,利用粒子平均信息来提高算法全局搜索能力,并采用时变加速系数(TVAC)以平衡算法的局部搜索和全局搜索能力;在算法后期,采用精英学习策略对精英粒子进行柯西变异操作,以进一步提高算法的全局搜索能力,减少算法陷入局部最优的危险。在6个典型的复杂函数上与基本PSO(BPSO)算法、时变加速因子PSO(PSO-TVAC)算法、时变惯性权重PSO(PSO-TVIW)算法和小波变异PSO(HPSOWM)算法进行对比,MEPSO的均值与标准方差均优于对比算法,且寻优时间最短,可靠性更好。结果表明, MEPSO能较好地兼顾局部搜索和全局搜索能力,收敛速度快,收敛精度和搜索效率高。     

带可变随机函数和变异算子的粒子群优化算法

标准粒子群优化算法的收敛分析表明,改变随机函数、个体历史最优,群体全局最优,有助于提高该算法的性能。为此,本文提出了一种带可变随机函数和变异算子的粒子群优化算法,即通过改变速度更新方程中的随机函数分布来调节粒子在迭代过程中飞向个体历史最优和群体全局最优的比重,通过对个体历史最优和群体全局最优进行变异来增强种群的搜索能力。实验结果证实了该算法的有效性。     

基于三次样条插值的自动入库泊车免疫粒子群改进算法

传统自动入库泊车轨迹优化算法不易寻到光滑、精确且优化的泊车轨迹。结合智能自动入库泊车原理,本文提出一种基于三次样条插值的自动入库泊车方法,从而获得理想优化的泊车参考轨迹。为了有效地提升自动入库泊车轨迹寻优算法的性能,以泊车轨迹最短作为优化目标来选定一组合适的泊车位置参考点,在三次样条插值的基础上,又提出一种免疫粒子群改进算法。首先,为提升算法全局搜索性能和收敛速度,引入自适应变异策略;然后,引入免疫机制来有效提升其全局优化能力。测试函数及自动入库泊车实际算例的仿真结果表明,所提出的自动入库泊车免疫粒子群改进算法具有更高的寻优精度和较快的收敛速度。     

A novel bankruptcy prediction model based on an adaptive fuzzy k-nearest neighbor method

Bankruptcy prediction is one of the most important issues in financial decision-making. Constructing effective corporate bankruptcy prediction models in time is essential to make companies or banks prevent bankruptcy. This study proposes a novel bankruptcy prediction model based on an adaptive fuzzy k-nearest neighbor (FKNN) method, where the neighborhood size k and the fuzzy strength parameter m are adaptively specified by the continuous particle swarm optimization (PSO) approach. In addition to performing the parameter optimization for FKNN, PSO is also utilized to choose the most discriminative subset of features for prediction. Adaptive control parameters including time-varying acceleration coefficients (TVAC) and time-varying inertia weight (TVIW) are employed to efficiently control the local and global search ability of PSO algorithm. Moreover, both the continuous and binary PSO are implemented in parallel on a multi-core platform. The proposed bankruptcy prediction model, named PTVPSO-FKNN, is compared with five other state-of-the-art classifiers on two real-life cases. The obtained results clearly confirm the superiority of the proposed model in terms of classification accuracy, Type I error, Type II error and area under the receiver operating characteristic curve (AUC) criterion. The proposed model also demonstrates its ability to identify the most discriminative financial ratios. Additionally, the proposed model has reduced a large amount of computational time owing to its parallel implementation. Promisingly, PTVPSO-FKNN might serve as a new candidate of powerful early warning systems for bankruptcy prediction with excellent performance.     

求解TSP的改进自组织PSO算法

针对粒子群算法（PSO）的早熟收敛现象,从种群多样性出发,基于自组织临界性特点改进PSO 算法的参数设置,采用自组织的惯性权重和加速系数,并增加了变异算子。借鉴交换子和交换序概念,设计出了能直接在离散域进行搜索的改进的自组织PSO算法。用于旅行商问题（TSP）的求解,并与基本及其他典型改进PSO算法进行性能比较。实验结果证实改进的自组织PSO算法是有效的。     

基于邻域混沌PSO算法的目标分配优化方法

针对基本粒子群算法在求解火力打击体系目标分配问题时易陷入局部极值、计算精度差的局限性,提出了一种基于混沌粒子群算法（ChaosParticleSwarmOptimization,CPSO）的目标分配优化方法。在综合考虑整体毁伤效能、打击匹配度和风险概率的基础上,分析了目标分配问题的数学模型,设计了相应的粒子编码方法、更新策略和有效性修订方法,提出一种在种群最优粒子邻域内进行混沌搜索的改进策略。仿真结果表明,所提CPSO算法的性能明显优于基本粒子群算法和变异粒子群算法。     

A novel and effective particle swarm optimization like algorithm with extrapolation technique

A novel competitive approach to particle swarm optimization (PSO) algorithms is proposed in this paper. The proposed method uses extrapolation technique with PSO (ePSO) for solving optimization problems. By considering the basics of the PSO algorithm, the current particle position is updated by extrapolating the global best particle position and the current particle positions in the search space. The position equation is formulated with the global best (gbest) position, local best position (pbest) and the current position of the particle. The proposed method is tested with a set of 13 standard optimization benchmark problems and the results are compared with those obtained through two existing PSO algorithms, the canonical PSO (cPSO), the Global-Local best PSO (GLBest PSO). The cPSO includes a time-varying inertia weight (TVIW) and time-varying acceleration co-efficients (TVAC) while the GLBest PSO consists of Global-Local best inertia weight (GLBest IW) with Global-Local best acceleration co-efficient (GLBestAC). The simulation results clearly elucidate that the proposed method produces the near global optimal solution. It is also observed from the comparison of the proposed method with cPSO and GLBest PSO, the ePSO is capable of producing a quality of optimal solution with faster convergence rate. To strengthen the comparison and prove the efficacy of the proposed method a real time application of steel annealing processing (SAP) is also considered. The optimal control objectives of SAP are computed through the above said three PSO algorithms and also through two versions of genetic algorithms (GA), namely, real coded genetic algorithm (RCGA) and hybrid real coded genetic algorithm (HRCGA) and the results are analyzed with the proposed method. From the results obtained through benchmark problems and the real time application of SAP, it is clearly seen that the proposed ePSO method is competitive to the existing PSO algorithms and also to GAs.     

非线性动态加速系数对粒子群算法的影响

粒子群算法(PSO)中的加速系数影响着粒子的个体认知和群体认知,而传统算法中的加速系数一般取常量.据研究发现,粒子的个体认识和群体认识分别主导着粒子的全局搜索能力和局部搜索能力,提高粒子个体认识可以有效增强算法的全局搜索能力,而提高粒子的群体认识可以有效增强算法的局部搜索能力.为进一步研究加速系数对粒子群算法的影响,本...     

A new and improved version of particle swarm optimization algorithm with global–local best parameters

This paper presents a new and improved version of particle swarm optimization algorithm (PSO) combining the global best and local best model, termed GLBest-PSO. The GLBest-PSO incorporates global–local best inertia weight (GLBest IW) with global–local best acceleration coefficient (GLBest Ac). The velocity equation of the GLBest-PSO is also simplified. The ability of the GLBest-PSO is tested with a set of bench mark problems and the results are compared with those obtained through conventional PSO (cPSO), which uses time varying inertia weight (TVIW) and acceleration coefficient (TVAC). Fine tuning variants such as mutation, cross-over and RMS variants are also included with both cPSO and GLBest-PSO to improve the performance. The simulation results clearly elucidate the advantage of the fine tuning variants, which sharpen the convergence and tune to the best solution for both cPSO and GLBest-PSO. To compare and verify the validity and effectiveness of the GLBest-PSO, a number of statistical analyses are carried out. It is also observed that the convergence speed of GLBest-PSO is considerably higher than cPSO. All the results clearly demonstrate the superiority of the GLBest-PSO.

差分和扰动混合的多策略粒子群优化算法

通常的粒子群优化算法采取单一的学习策略,不利于搜索信息的有效保留,因此将改进的差分变异策略引入到粒子的速度更新中以增强算法的群体多样性;综合利用差分变异与扰动策略两种不同的产生新解的方式,提出了一种多策略交叉学习机制算法DPPSO（hybrid particle swarm optimization with differential and per-turbation）。每一个粒子通过引进的差分变异操作和扰动操作分别产生一个中间粒子,再选择较好的粒子作为当前粒子的新位置,从而实现所有粒子动态地选择更好的生成策略来更新自己的位置和速度,因此该交叉策略能够有效提高PSO算法的群体多样性和搜索路径的多样性,粒子可以获取更好的启发式信息,沿着不同的路径被引向更有潜力的搜索区域。实验结果表明了两种策略的有效性和互补性,DPPSO算法比其他三种算法有更好的综合表现,具有有效的全局收敛能力和准确定位能力。     

Simultaneous optimization of parts and operations sequences in SSMS: a chaos embedded Taguchi particle swarm optimization approach

Simultaneous optimization of interrelated manufacturing processes viz. part sequencing and operation sequencing is required for the efficient allocation of production resources. Present paper addresses this problem with an integrated approach for Single Stage Multifunctional Machining System (SSMS), and identifies the best part sequence available in the part-mix. A mathematical model has been formulated to minimize the broad objectives of set-up cost and time simultaneously. The proposed approach has more realistic attributes as fixture related intricacies are also taken into account for model formulation. It has been solved by a new variant of particle swarm optimization (PSO) algorithm and named as Chaos embedded Taguchi particle swarm optimization (CE-TPSO) that draws its traits from chaotic systems, statistical design of experiments and time varying acceleration coefficients (TVAC). A simulated case study has been adopted from the literature and effectiveness of the proposed algorithm is proved. The results obtained with different variants of its own are compared along with the basic PSO and Genetic Algorithm (GA) to reveal the superiority of the proposed algorithm.     

全变异粒子群优化算法

针对粒子群优化算法容易早熟、收敛精度低等缺点,通过采用全变异策略、最大搜索速度自适应调整等策略得到了一种全变异粒子群优化算法,其中的全变异策略是在陷入早熟的条件下全体粒子参加变异,并且当把粒子看成染色体时,每一个基因等概率地参加变异,可以克服算法的早熟而继续优化,提高了算法的收敛精度。对Shubert函数进行实验的结果表明了算法的有效性。     

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.     

二阶微粒群算法

为了提高标准微粒群算法的全局收敛性,提出了一种新的微粒群算法——二阶微粒群算法.首先,介绍了二阶微粒群算法的引入,分析了其收敛性,并且研究了其参数的选择范围.其次,在分析二阶微粒群算法的进化方程的基础上,引出了具有随机惯性权重的标准微粒群算法.再次,在二阶微粒群算法中加入振荡因子来调整微粒的速度变化率,更好地使二阶微粒群算法收敛于全局最优.最后,利用这几种改进方法对典型测试函数进行仿真,实验结果表明,这些方法能够有效克服早熟问题,在全局收敛性和收敛速度方面均优于标准微粒群算法.     

融合多策略的鸟群算法及油层识别ELM模型优化

为了改进鸟群算法易陷入局部最优、收敛速度慢以及种群多样性不足的缺点,提出融合多策略的鸟群算法。引入混沌权重和对称切线混沌加速系数以及高斯扰动策略,增强算法跳出局部最优的能力;引入混合多步选择和自适应步长因子策略,加快算法的收敛速度;引入小波变异策略,丰富算法的种群多样性。实验采用10个基准测试函数,将改进的算法与另外5种智能算法进行仿真对比,验证了改进的算法性能优于其他算法。另外,为了提高极限学习机（ELM）在油层识别中的精度,将改进的鸟群算法用于ELM模型的参数优化。实际测井应用表明基于改进鸟群算法优化的ELM模型在油层识别中效果显著,优于基于遗传算法、粒子群算法、蚁群算法优化的ELM模型。     

On the improved performances of the particle swarm optimization algorithms with adaptive parameters,cross-over operators and root mean square (RMS) variants for computing optimal control of a class of hybrid systems

This paper deals with the concept of including the popular genetic algorithm operator, cross-over and root mean square (RMS) variants into particle swarm optimization (PSO) algorithm to make the convergence faster. Two different PSO algorithms are considered in this paper: the first one is the conventional PSO (cPSO) and the second is the global-local best values based PSO (GLbest-PSO). The GLbest-PSO includes global-local best inertia weight (GLbestIW) with global-local best acceleration coefficient (GLbestAC), whereas the cPSO has a time varying inertia weight (TVIW) and either time varying acceleration coefficient (TVAC) or fixed AC (FAC). The effectiveness of the cross-over operator with both PSO algorithms is tested through a constrained optimal control problem of a class of hybrid systems. The experimental results illustrate the advantage of PSO with cross-over operator, which sharpens the convergence and tunes to the best solution. In order to compare and verify the validity and effectiveness of the new approaches for PSO, several statistical analyses are carried out. The results clearly demonstrate that the GLbest-PSO with the cross-over operator is a very promising optimization technique. Similar conclusions can be made for the GLbest-PSO with RMS variants also.     

A novel abstraction for swarm intelligence: particle field optimization

Particle swarm optimization (PSO) is a popular meta-heuristic for black-box optimization. In essence, within this paradigm, the system is fully defined by a swarm of “particles” each characterized by a set of features such as its position, velocity and acceleration. The consequent optimized global best solution is obtained by comparing the personal best solutions of the entire swarm. Many variations and extensions of PSO have been developed since its creation in 1995, and the algorithm remains a popular topic of research. In this work we submit a new, abstracted perspective of the PSO system, where we attempt to move away from the swarm of individual particles, but rather characterize each particle by a field or distribution. The strategy that updates the various fields is akin to Thompson’s sampling. By invoking such an abstraction, we present the novel particle field optimization algorithm which harnesses this new perspective to achieve a model and behavior which is completely distinct from the family of traditional PSO systems.