引入多级扰动的混合型粒子群优化算法

为解决粒子群优化算法易陷入局部最优值的问题,提出一种引入多级扰动的混合型粒子群优化算法.该算法结合两种经典改进粒子群优化算法的优点,即带惯性参数的标准粒子群优化算法和带收缩因子的粒子群优化算法,在此基础上,引入多级扰动机制：在更新粒子位置时,引入一级扰动,使粒子对解空间的遍历能力得到加强;若优化过程陷入“局部最优”的情况,则引入二级扰动,使得优化过程继续,从而摆脱局部最优值.使用了6个测试函数——Sphere函数、Ackley函数、Rastrigin函数、Styblinski-Tang函数、Duadric函数及Rosenbrock函数来对所提出的混合型粒子群优化算法进行仿真运算和对比验证.模拟运算的结果表明：所提出的混合型粒子群优化算法在对测试函数进行仿真时,其收敛精度和收敛速度都优于另外两种经典的改进粒子群优化算法;另外,在处理多峰函数时,本算法不易被局部最优值所限制.     

混合拓扑结构的粒子群算法及其在测试数据生成中的应用研究

粒子群算法(PSO)的拓扑结构是影响算法性能的关键因素,为了从根源上避免粒子群算法易陷入局部极值及早熟收敛等问题,提出一种混合拓扑结构的粒子群优化算法(MPSO)并将其应用于软件结构测试数据的自动生成中。通过不同邻域拓扑结构对算法性能影响的分析,采用一种全局寻优和局部寻优相结合的混合粒子群优化算法。通过观察粒子群的多样性反馈信息,对每一代种群粒子以进化时选择全局拓扑结构模型(GPSO)或局部拓扑结构模型(LPSO)的方法进行。实验结果表明,MPSO使得种群的多样性得到保证,避免了粒子群陷入局部极值,提高了算法的收敛速度。     

一种新形式的微粒群算法

标准微粒群算法在优化多峰、多维的复杂函数时,其效果并不理想,容易早熟收敛。为了改进微粒群算法处理此类问题的性能,提出了一种新的微粒群算法。该算法将标准微粒群算法迭代公式中的群体最优位置用个体最优位置的中心代替,有利于增强群体的多样性,避免早熟收敛,同时保持了迭代公式的简洁形式。3个常用测试函数的数值模拟表明,新的微粒群算法较标准微粒群算法在寻优能力上有明显的提高。     

A modified particle swarm optimization for aggregate production planning

Particle swarm optimization (PSO) originated from bird flocking models. It has become a popular research field with many successful applications. In this paper, we present a scheme of an aggregate production planning (APP) from a manufacturer of gardening equipment. It is formulated as an integer linear programming model and optimized by PSO. During the course of optimizing the problem, we discovered that PSO had limited ability and unsatisfactory performance, especially a large constrained integral APP problem with plenty of equality constraints. In order to enhance its performance and alleviate the deficiencies to the problem solving, a modified PSO (MPSO) is proposed, which introduces the idea of sub-particles, a particular coding principle, and a modified operation procedure of particles to the update rules to regulate the search processes for a particle swarm. In the computational study, some instances of the APP problems are experimented and analyzed to evaluate the performance of the MPSO with standard PSO (SPSO) and genetic algorithm (GA). The experimental results demonstrate that the MPSO variant provides particular qualities in the aspects of accuracy, reliability, and convergence speed than SPSO and GA.     

多策略粒子群优化算法

为了克服粒子群优化算法易早熟、局部搜索能力弱的问题,提出了一种改进的粒子群优化算法--多策略粒子群优化算法。在群体寻优过程中,各粒子根据搜索到的最优位置的变动情况,从几种备选的策略中抉择出当代的最优搜索策略。其中,最优粒子有最速下降策略、矫正下降策略和随机移动策略可以选择,非最优粒子有聚集策略和扩散策略可以选择。四个典型测试函数的数值实验结果表明,新提出的算法比标准粒子群优化算法具有更强和更稳定的全局搜索能力。     

Using augmented Lagrangian particle swarm optimization for constrained problems in engineering">Using augmented Lagrangian particle swarm optimization for constrained problems in engineering

The comparatively new stochastic method of particle swarm optimization (PSO) has been applied to engineering problems especially of nonlinear, non-differentiable, or non-convex type. Its robustness and its simple applicability without the need for cumbersome derivative calculations make PSO an attractive optimization method. However, engineering optimization tasks often consist of problem immanent equality and inequality constraints which are usually included by inadequate penalty functions when using stochastic algorithms. The simple structure of basic particle swarm optimization characterized by only a few lines of computer code allows an efficient implementation of a more sophisticated treatment of such constraints. In this paper, we present an approach which utilizes the simple structure of the basic PSO technique and combines it with an extended non-stationary penalty function approach, called augmented Lagrange multiplier method, for constraint handling where ill conditioning is a far less harmful problem and the correct solution can be obtained even for finite penalty factors. We describe the basic PSO algorithm and the resulting method for constrained problems as well as the results from benchmark tests. An example of a stiffness optimization of an industrial hexapod robot with parallel kinematics concludes this paper and shows the applicability of the proposed augmented Lagrange particle swarm optimization to engineering problems.     

A perturbed particle swarm algorithm for numerical optimization

The canonical particle swarm optimization (PSO) has its own disadvantages, such as the high speed of convergence which often implies a rapid loss of diversity during the optimization process, which inevitably leads to undesirable premature convergence. In order to overcome the disadvantage of PSO, a perturbed particle swarm algorithm (pPSA) is presented based on the new particle updating strategy which is based upon the concept of perturbed global best to deal with the problem of premature convergence and diversity maintenance within the swarm. A linear model and a random model together with the initial max–min model are provided to understand and analyze the uncertainty of perturbed particle updating strategy. pPSA is validated using 12 standard test functions. The preliminary results indicate that pPSO performs much better than PSO both in quality of solutions and robustness and comparable with GCPSO. The experiments confirm us that the perturbed particle updating strategy is an encouraging strategy for stochastic heuristic algorithms and the max–min model is a promising model on the concept of possibility measure.     

A modified particle swarm optimization for production planningproblems in the TFT Array process

In this study, a practical production planning problem in the TFT (thin film transistor) Array process is introduced. Several researchers have referred to the capacitated production lot-sizing allocation problems as NP-Hard. Naturally, it is harder to solve the capacitated production allocation problem considering its practical characteristics and constraints, such as allocation problems among bottleneck machines, photo masks, and products with different re-entrant layers. In response to this, we proposed a novel variation of the particle swarm optimization (PSO) model called the modified PSO (MPSO), which is a binary PSO model with dynamic inertia weight and mutation mechanism. It improves some weaknesses as opposed to the original version of the PSO, including a propensity for obstruction near the optimal solution regions that hardly improve solution quality by fine tuning. In addition, it is converted to be able to solve the model of binary decision variables. In order to illustrate effectiveness, the traditional PSO (TPSO), genetic algorithm (GA), and the proposed MPSO are compared by application of the literature’s well-known test problems as well as the practical production planning problem in the TFT Array process. Based on the results of the investigation, it can be concluded that the proposed MPSO is more effective than the other approaches in terms of superiority of solution and required CPU time.     

Adaptive PSODV algorithm for OPF with non-smooth cost functions and statistical analysis

This paper presents a particle swarm optimization with differentially perturbed velocity hybrid algorithm with adaptive acceleration coefficient (APSO-DV) for solving the optimal power flow problem with non-smooth and non-convex generator fuel cost characteristics. The APSO-DV employs differentially perturbed velocity with adaptive acceleration coefficient for updating the positions of particles for the particle swarm optimization. The feasibility of the proposed approach was tested on IEEE 30-bus and IEEE 118-bus systems with three different objective functions. Several cases were investigated to test and validate the robustness of the proposed method in finding the optimal solution. The effectiveness of the proposed approach was tested including contingency also. Simulation results demonstrate that the APSO-DV provides superior results compared to classical DE, PSO, PSO-DV and other methods recently reported in the literature. An innovative statistical analysis based on central tendency measures and dispersion measures was carried out on the bus voltage profiles and voltage stability indices.     

BP-MPSO混合算法在机器人空间路径中的应用

在对PUMA机器人空间路径进行BP算法环境建模与目标建模的基础上,针对传统粒子群优化（PSO）算法搜索空间有限、容易陷入局部最优点的缺陷,提出了一种改进的粒子群优化（MPSO）算法。该算法引入了基于全局信息反馈的重新初始化过程机制,并对PUMA机器人空间路径进行了优化。仿真实验表明,该算法的应用不仅降低了求解逆运动方程的难度,还能得到全局最优解。显著地提高了PUMA机器人空间路径优化的效率。     

AN EFFICIENT EVOLUTIONARY NEURAL FUZZY CONTROLLER FOR THE INVERTED PENDULUM SYSTEM

In this article we propose an evolutionary neural fuzzy controller for the planetary train–type inverted pendulum system (IPS) and verify its effectiveness. The novel hybrid particle swarm optimization (HPSO) learning algorithm of the proposed controller is based on approaches of the fuzzy entropy clustering (FEC), the modified PSO (MPSO), and recursive singular value decomposition (RSVD). The FEC is applied to generate base particles and the MPSO is proposed to effectively improve the performance of the traditional PSO. There are mainly two different characteristics between the MPSO and its original version; that is, the initial parameters of the MPSO are calculated by an effective local approximation method (ELAM), and the global optimum is chosen by the multi-elites strategy (MES). In addition, we use the RSVD to determine the optimal consequent parameters of fuzzy rules, in order to reduce requirements of the computational time and space. Experimental results show that the proposed approach outperforms the proportional–integral–derivative (PID), PSO, and MPSO in terms of better abilities of tracking and noise rejection for planetary train–type IPS.     

哈夫曼编码的协同粒子群优化算法

针对粒子群优化（PSO）算法在优化问题过程中易陷入局部最优的问题,提出一种基于哈夫曼编码的协同粒子群优化（HC PSO）算法。采用哈夫曼编码将种群划分成2个子种群并对2个子种群进行独立优化,同时,2子种群之间协同完成搜索种群的全局最优解。采用6个标准测试函数来测试算法性能。实验结果表明,该算法可以有效地避免种群陷入局部最优,具有较好的优化性能和稳定性,收敛精度得到了显著的提高。     

Optimal design of fractional-order PID controller for five bar linkage robot using a new particle swarm optimization algorithm

This paper introduces a new version of the particle swarm optimization (PSO) method. Two basic modifications for the conventional PSO algorithm are proposed to improve the performance of the algorithm. The first modification inserts adaptive accelerator parameters into the original velocity update formula of the PSO which speeds up the convergence rate of the algorithm. The ability of the algorithm in escaping from local optima is improved using the second modification. In this case, some particles of the swarm, which are named the superseding particles, are selected to be mutated with some probability. The proposed modified PSO (MPSO) is simple to be implemented, fast and reliable. To validate the efficiency and applicability of the MPSO, it is applied for designing optimal fractional-order PID (FOPID) controllers for some benchmark transfer functions. Then, the introduced MPSO is applied for tuning the parameters of FOPID controllers for a five bar linkage robot. Sensitivity analysis over the fractional order of the PID controller is also provided. Numerical simulations reveal that the MPSO can optimally tune the parameters of FOPID controllers.     

PSO算法原理及应用

粒子群优化（Particle swarm optimization,PSO）算法在众多的优化问题上都表现出有益的性能,已经开始广泛应用于实际工程项目中。回顾了PSO算法的发展过程,介绍了PSO算法的基本原理,在标准PSO算法的基础上,介绍了tsP—SO、EOPSO和MPSO等扩展算法,对几种改进算法的性能和改进效果进行了总结。并对PSO算法在电网规划和建筑结构损伤中的应用进行了仿真实验。实验结果表明,改进的PSO算法能够在一定时间内给出令人满意的优化方案,符合工程应用的实际要求,具有推广意义。     

Dynamic particle swarm optimizer with escaping prey for solving constrained non-convex and piecewise optimization problems

This paper presents a novel meta-heuristic algorithm, dynamic particle swarm optimizer with escaping prey (DPSOEP), for solving constrained non-convex and piecewise optimization problems. In DPSOEP, the particles developed from two different species are classified into three different types, consisting of preys, strong particles and weak particles, to simulate the behavior of hunting and escaping characteristics observed in nature. Compared to other variants of particle swarm optimizer (PSO), the proposed algorithm takes account of an escaping mechanism for the preys to circumvent the problem of local optimum and also develops a classification mechanism to cope with different situations in the search space so as to achieve a good balance between its global exploration and local exploitation abilities. Simulation results obtained based on thirteen benchmark functions and two practical economic dispatch problems prove the effectiveness and applicability of the DPSOEP to deal with non-convex and piecewise optimization problem, considering the integration of linear equality and inequality constraints.     

Automatically extracting T–S fuzzy models using cooperative random learning particle swarm optimization

This paper proposes a methodology for automatically extracting T–S fuzzy models from data using particle swarm optimization (PSO). In the proposed method, the structures and parameters of the fuzzy models are encoded into a particle and evolve together so that the optimal structure and parameters can be achieved simultaneously. An improved version of the original PSO algorithm, the cooperative random learning particle swarm optimization (CRPSO), is put forward to enhance the performance of PSO. CRPSO employs several sub-swarms to search the space and the useful information is exchanged among them during the iteration process. Simulation results indicate that CRPSO outperforms the standard PSO algorithm, genetic algorithm (GA) and differential evolution (DE) on the functions optimization and benchmark modeling problems. Moreover, the proposed CRPSO-based method can extract accurate T–S fuzzy model with appropriate number of rules.     

Comparative performance analysis of various binary coded PSO algorithms in multivariable PID controller design

In this paper, comparative performance analysis of various binary coded PSO algorithms on optimal PI and PID controller design for multiple inputs multiple outputs (MIMO) process is stated. Four algorithms such as modified particle swarm optimization (MPSO), discrete binary PSO (DBPSO), modified discrete binary PSO (MBPSO) and probability based binary PSO (PBPSO) are independently realized using MATLAB. The MIMO process of binary distillation column plant, described by Wood and Berry, with and without a decoupler having two inputs and two outputs is considered. Simulations are carried out to minimize two objective functions, that is, time integral of absolute error (ITAE) and integral of absolute error (IAE) with single stopping criterion for each algorithm called maximum number of fitness evaluations. The simulation experiments are repeated 20 times with each algorithm in each case. The performance measures for comparison of various algorithms such as mean fitness, variance of fitness, and best fitness are computed. The transient performance indicators and computation time are also recorded. The inferences are made based on analysis of statistical data obtained from 20 trials of each algorithm and after having comparison with some recently reported results about same MIMO controller design employing real coded genetic algorithm (RGA) with SBX and multi-crossover approaches, covariance matrix adaptation evolution strategy (CMAES), differential evolution (DE), modified continuous PSO (MPSO) and biggest log modulus tuning (BLT). On the basis of simulation results PBPSO is identified as a comparatively better method in terms of its simplicity, consistency, search and computational efficiency.     

基于多粒子群算法的WSNs覆盖优化策略研究*

为了改善无线传感网络的性能,提高网络的覆盖率,在粒子进化的多粒子群算法的基础上,提出了一种无线传感网络覆盖的优化策略。该策略通过多个粒子群彼此独立地搜索解空间, 提高了算法的寻优能力,有效地避免了基本粒子群算法容易出现的“早熟”问题,提高了算法的稳定性。仿真实验表明,与基本粒子群算法、传统遗传算法和新量子遗传算法的优化效果相比较,其覆盖率分别提高了8.39％、3.07％和0.75％;收敛速度提高了25.3％、23.8％和23.8％。因此粒子进化的多粒子群优化策略具有比这三种算法更好的覆盖优化效果。     

基于粒子群优化的Wiener模型辨识与实例研究

针对一类工业过程中可描述成Wiener模型的非线性系统,其辨识问题可等价成以估计参数为优化变量的非线性极小值优化问题．利用粒子群优化(PSO)算法在整个参数空间内并行搜索获得极小值优化问题的最优解(Wiener模型的最优估计),通过对粒子的迭代轨迹进行分析,改进了PSO算法中惯性权重和学习因子的选择．通过一个Wiener模型的数值仿真验证了本文提出的辨识方法的有效性和实用性,并将该方法应用在连续退火机组加热炉产品质量模型的辨识研究,取得了满意的辨识效果．     

Modified particle swarm optimization structure approach to direction of arrival estimation

This study considers the problem of estimating the direction-of-arrival (DOA) for code-division multiple access (CDMA) signals. In this type of problem, the associated cost function of the DOA estimation is generally a computationally-expensive and highly-nonlinear optimization problem. A fast convergence of the global optimization algorithm is therefore required to attain results within a short amount of time. In this paper, we propose a new application of the modify particle swarm optimization (MPSO) structure to achieve a global optimal solution with a fast convergence rate for this type of DOA estimation problem.The MPSO uses a first-order Taylor series expansion of the objective function to address the issue of enhanced PSO search capacity for finding the global optimum leads to increased performance. The first-order Taylor series approximates the spatial scanning vector in terms of estimating deviation results in and reducing to a simple one-dimensional optimization problem and the estimating deviation has the tendency to fly toward a better search area. Thus, the estimating deviation can be used to update the velocity of the PSO. Finally, several numerical examples are presented to illustrate the design procedure and to confirm the performance of the proposed method.