Dynamic Multiple Swarms in Multiobjective Particle Swarm Optimization

A multiple-swarm multiobjective particle swarm optimization (PSO) algorithm, named dynamic multiple swarms in multiobjective PSO, is proposed in which the number of swarms is adaptively adjusted throughout the search process via the proposed dynamic swarm strategy. The strategy allocates an appropriate number of swarms as required to support convergence and diversity criteria among the swarms. Additional novel designs include a PSO updating mechanism to better manage the communication within a swarm and among swarms and an objective space compression and expansion strategy to progressively exploit the objective space during the search process. Comparative study shows that the performance of the proposed algorithm is competitive in comparison to the selected algorithms on standard benchmark problems. In particular, when dealing with test problems with multiple local Pareto fronts, the proposed algorithm is much less computationally demanding. Sensitivity analysis indicates that the proposed algorithm is insensitive to most of the user-specified design parameters.     

基于微粒群与混合蛙跳融合的群体智能算法

针对微粒群算法和混合蛙跳算法存在的早熟收敛问题,提出一种基于微粒群与混合蛙跳算法融合的群体智能算法。新算法将整个群体分成数目相等的蛙群和微粒群群体。在两群体独立进化过程中,设计了一种两群之间的信息替换策略：比较蛙群与微粒群的最佳适应值,如果蛙群进化较好,利用蛙群各子群中最差个体替换微粒群一部分较好个体;否则,用微粒群中较好的一部分个体替换蛙群各子群的最好个体。同时,设计了一种两群之间的相互协作方式。为避免微粒群因早熟收敛而影响信息替换策略效果,适时对其所有个体最好位置进行随机扰动。仿真实验表明,新算法可以有效提高全局搜索能力及收敛速度,对于高维复杂函数问题,算法具有很好的稳定性。     

粒子带质量的粒子群算法

针对粒子群算法在陷入局部最优时难于跳出的缺陷提出了一种带有质量的粒子群算法。该算法受运动学原理启发,粒子位置的更新不仅受自身最优和种群最优的影响,还受到由粒子质量引起的梯度场的影响。当粒子群出现早熟现象时,用电磁学原理与动量守恒定理更新种群的最优位置,使群体能及时摆脱局部最优区域。仿真结果表明,该算法优化4种具有代表性的基准函数,无论是在优化精度方面还是在优化效率方面,均较以往提出的改进粒子群算法在性能上有所改进。     

多量子粒子群协同优化算法研究

针对标准粒子群优化（PSO）算法及其改进算法存在的局部收敛与收敛速度问题,提出了一种多量子粒子群协同优化（QPSCO）方法。该算法采用双层的多粒子群协同优化结构：用多个量子粒子群在底层独立地搜索解空间,同时引入参数变异策略,以扩大搜索范围;上层用1个量子粒子群追逐当前全局最优解,并对飞离搜索区域粒子的位置用新位置取代,以加快算法收敛。在此基础上,将该算法应用于实际控制系统低阶时滞对象的PID控制器设计中。仿真结果表明,QPSCO是一种有效的参数优化算法,与标准PSO、QPSO等算法相比具有更好的全局收敛性能。     

Annealing-based particle swarm optimization to solve the redundant reliability problem with multiple component choices

In this paper, the performance of a particle swarm optimization (PSO) algorithm named Annealing-based PSO (APSO) is investigated to solve the redundant reliability problem with multiple component choices (RRP-MCC). This problem aims to choose an optimal combination of components and redundancy levels for a system with a series–parallel configuration that maximizes the overall system reliability. PSO is a population-based meta-heuristic algorithm inspired by the social behavior of the biological swarms that is designed for continuous decision spaces. As a local search engine (LSE), the proposed APSO employs the Metropolis-Hastings strategy, the key idea behind the simulated annealing (SA) algorithm. In APSO, the best position among all particles in each iteration is dynamically improved using the inner loop of the SA (i.e., equilibrium loop) while the temperature is updated in the main loop of the PSO algorithm. The well-known benchmarks are used to verify the performance of the proposed APSO. Even though APSO fails to outperform the best solution obtained in the literature, the contribution of this paper is comprised of the implementation of APSO as a hybrid meta-heuristic as well as the effect of Metropolis-Hastings strategy on the performance of the classical PSO.     

A MULTISWARM COMPETITIVE PARTICLE SWARM ALGORITHM FOR OPTIMIZATION CONTROL OF AN ETHYLENE CRACKING FURNACE

A fuzzy C-means (FCM) multiswarm competitive particle swarm optimization (FCMCPSO) algorithm is proposed, in which FCM clustering is used to divide swarms adaptively into different clusters. The large-scale swarms are according to the standard particle swarm optimization (PSO) algorithm, whereas the small-scale swarms search randomly in the neighborhood of the optimal solution to increase the probability of jumping out of the local optimization point. Within every cluster, the adaptive value gained by competitive learning is respectively found and arranged in order. Swarms of small adaptive value were integrated with the neighboring swarms of large adaptive value to search the optimal solution competitively by the swarms. The algorithm's validity was tested by benchmark functions and compared with other PSO algorithms. Furthermore, an integrated FCMCPSO-radial basis function neural network was studied for nonlinear system modeling and intelligent optimization control of cracking depth of an ethylene cracking furnace application in a chemical process.     

一种基于差异演化的协同粒子群优化算法

提出一种协同进化PSO算法,用于保持粒子种群的多样性并避免发生“早熟”的问题．该方法采用两个不同的分群;其中分群一的粒子采用标准PSO算法进行搜索寻优,分群二的粒子采用差异演化算法进行搜索和寻找最优解．在搜索过程中,如果标准PSO算法的适应度变化率低于一个阈值,则按照黄金分割率用分群二中的若干优势粒子取代分群一中的劣势粒子．用所提出的PSO算法和标准PSO算法对4种常用函数进行优化．结果表明,该粒子群优化算法比标准粒子群优化算法更容易找到最优解,而且优化效率和优化性能明显提高．     

两群微粒群优化算法及其应用

针对微粒群优化算法容易陷入局部极值的缺陷,提出两群微粒群优化算法．通过对5种常用测试函数进行测试和比较,结果表明两群微粒群优化算法比基本微粒群优化算法更容易找到全局最优解,优化效率明显提高．然后将两群微粒群优化算法用于催化裂化装置主分馏塔轻柴油95%点软测量建模,通过与实际工业数据对比,表明该软测量模型具有高的精度、好的性能和广阔的应用前景．     

A multi-swarm optimizer based fuzzy modeling approach for dynamic systems processing

Inspired by the phenomenon of symbiosis in natural ecosystems a multi-swarm cooperative particle swarm optimizer (MCPSO) is proposed as a new fuzzy modeling strategy for identification and control of non-linear dynamical systems. In MCPSO, the population consists of one master swarm and several slave swarms. The slave swarms execute particle swarm optimization (PSO) or its variants independently to maintain the diversity of particles, while the particles in the master swarm enhance themselves based on their own knowledge and also the knowledge of the particles in the slave swarms. With four benchmark functions, MCPSO is proved to have better performance than PSO and its variants. MCPSO is then used to automatically design the fuzzy identifier and fuzzy controller for non-linear dynamical systems. The proposed algorithm (MCPSO) is shown to outperform PSO and some other methods in identifying and controlling dynamical systems.     

求解整数非线性规划结合正交杂交的离散PSO 算法

针对整数非线性规划问题,提出一种结合正交杂交的离散粒子群优化(PSO)算法.首先采用舍入取整方法,为了减少舍入误差,对PSO中的每个粒子到目前为止的最好位置进行随机修正,将基于正交实验设计的正交杂交算子引入离散PSO算法,以增强搜索性能;然后对PSO算法中的惯性权重和收缩因子采用动态调整策略,以提高算法的搜索效率;最后对一些不同维数的整数非线性规划问题进行数值仿真实验,实验结果表明了所提出算法的有效性.     

Cooperative Velocity Updating model based Particle Swarm Optimization

Particle swarm optimization (PSO) has shown its good performance in many optimization problems. This paper proposes a Cooperative Velocity Updating algorithm based Particle Swarm Optimization (CVUPSO), which is inspired by the competition and cooperation methods of different populations in natural swarm living, such as bees, ants, birds, fish, etc. In this algorithm, before an elite is introduced from other sub-swarms or a new particle is randomly born, the weak particle will be eliminated out of its sub-swarm. In each iteration process, every sub-swarm abandons a least potential particle. The CVUPSO recorded four special positions: pbest, lbest, gbest and lworst. The pbest represents the current particle’s best position while lbest represents the current sub swarm’s best position, and gbest is the best position among the whole swarm, lworst is the position of the particle with the worst performance. A new update method is adopted in CVUPSO, where the particles are more likely to follow lbest than follow gbest in the early stage of iteration, but opposite in the later stage. In this paper, two variants of CVUPSO are proposed, one variant is CVUPSO with Random inertia weight (for short CVUPSO-R), and another is CVUPSO with Exponential decline inertia weight (for short CVUPSO-E). By making comparative experiments on several widely used benchmark functions, analysis results show that the performance of these two improved variants are more promising than the recently developed PSO algorithms for searching multiple peak values of multiple objects optimization problem.     

基于种群多样性的自适应PSO算法求解VRPSPD问题

为有效求解逆向物流车辆路径(VRPSPD)模型,本文提出一种基于种群多样性的自适应PSO算法(SDAPSO)。在SDAPSO运行时,根据种群多样性,自适应地对种群中运行较差的粒子进行扰动操作,提升这些粒子向最优解收敛的能力;同时,对全局最优粒子进行概率扰动,以增加种群的多样性。标准检测函数的仿真结果表明SDAPSO算法是对基本PSO算法的有效改进。在对VRPSPD模型求解中,通过与其它粒子群算法相比,表明SDAPSO是求解该类问题的一种有效方法。     

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.     

基于高斯扰动的量子粒子群优化算法

针对量子粒子群优化（QPSO）算法在优化过程中面临早熟问题,提出了在粒子的平均位置或全局最优位置上加入高斯扰动的QPSO算法,可以有效地阻止粒子的停滞,因此较容易地使粒子避免陷入局部最优。为了评估算法的性能,利用标准测试函数对标准PSO算法、QPSO算法以及基于高斯扰动的QPSO算法进行了比较测试。其结果表明,该算法具有较强的全局搜索能力和较快的收敛速度。     

Novel algorithms of particle swarm optimisation with decision criteria

The particle swarm optimisation (PSO) is a stochastic, optimisation technique based on the movement and intelligence of swarms. In this paper, three new effective optimisation algorithms BPSO, HPSO and WPSO, by incorporating some decision criteria into PSO, have been proposed and analysed both in terms of their efficiency, resistance to the problem of premature convergence and the ability to avoid local optima. In the new algorithms, for each particle except position, two sets of velocities are generated and the profit matrix is constructed. Using the decision criteria the best strategy is selected. Simulations for benchmark test nonlinear function show that the algorithms in which the decision criteria have been applied, are beneficial over classical PSO in terms of their performance and efficiency.     

依概率收敛的改进粒子群优化算法

粒子群优化算法是一种随机优化算法,但它不依概率1收敛到全局最优解。因此提出一种新的依概率收敛的粒子群优化算法。在该算法中,首先引入了具有探索和开发能力的两个变异算子,并依一定概率对粒子当前最好位置应用这两个算子,然后证明了该算法是依概率1收敛到ε-最优解。最后,把该算法应用到13个典型的测试函数中,并与其他粒子群优化算法比较,数值结果表明所给出的算法能够提高求解精度和收敛速度。     

基于质心和自适应指数惯性权重改进的粒子群算法

针对粒子群优化(PSO)算法易出现早熟收敛及寻优精度低等问题,为提高粒子群优化算法寻优能力,提出了一种基于质心和自适应指数惯性权重改进的粒子群优化算法(CEPSO)。首先,使用各粒子的适应度计算权重系数;然后,分别使用各粒子当前位置和迄今为止最优位置构造了加权的种群质心和最优个体质心,使用平均粒距来度量群体状态,并依据群体状态设计了分段指数惯性权重;最后,结合使用分段指数惯性权重和双质心调整了粒子速度更新公式。仿真结果表明,CEPSO能增强寻优能力,并具有较强的稳定性。     

A meta optimisation analysis of particle swarm optimisation velocity update equations for watershed management learning

Particle swarm optimisation (PSO) is a general purpose optimisation algorithm used to address hard optimisation problems. The algorithm operates as a result of a number of particles converging on what is hoped to be the best solution. How the particles move through the problem space is therefore critical to the success of the algorithm. This study utilises meta optimisation to compare a number of velocity update equations to determine which features of each are of benefit to the algorithm. A number of hybrid velocity update equations are proposed based on other high performing velocity update equations. This research also presents a novel application of PSO to train a neural network function approximator to address the watershed management problem. It is found that the standard PSO with a linearly changing inertia, the proposed hybrid Attractive Repulsive PSO with avoidance of worst locations (AR PSOAWL) and Adaptive Velocity PSO (AV PSO) provide the best performance overall. The results presented in this paper also reveal that commonly used PSO parameters do not provide the best performance. Increasing and negative inertia values were found to perform better.     

基于动态多粒子群的多目标优化算法

为了让多目标粒子群优化算法在运行过程中保持粒子的多样性,提出了一种初始化方法和动态多粒子群协作的多目标优化算法。根据粒子群在决策空间中的分布情况动态增加或者减少粒子群数量;为避免粒子收敛速度过快,改进了决定粒子飞行速度的因素,速度值依赖于粒子当前速度惯性、粒子最优值,群最优值和所有群最优值。用五个测试函数对算法进行了测试并与多目标粒子群优化进行了比较,测试结果表明提出的算法优于多目标粒子群优化算法。     

基于粒子群算法的模糊控制在倒立摆中的应用

粒子群算法是一种仿生进化算法,源于对鸟群觅食行为的模拟,由于其计算简单、快速,被广泛应用。但是,基本粒子群算法在求解的过程中存在着全局搜索能力和局部求精能力两个性能指标之间的矛盾,算法容易陷入局部极值,进化后期的收敛速度慢。针对上述问题,提出了基于混沌变异算子的粒子群算法,可以使粒子摆脱局部极值,继续优化,加快收敛速度。将基于混沌变异的粒子群算法与模糊算法相结合,用于控制倒立摆系统的平衡。仿真实验表明,混沌变异粒子群算法优化了倒立摆系统模糊控制器的设计,改善了控制效果。