Self-organising swarm (SOSwarm)

This paper introduces a novel version of the particle swarm optimisation (PSO) algorithm which we call self-organising swarm SOSwarm. SOSwarm can be used for unsupervised learning. In the algorithm, input vectors are projected into a lower-dimensional map space producing a visual representation of the input data in a manner similar to a self-organising map (SOM). In SOSwarm, particles react to input data during the learning process by modifying their velocities using an adaptation of the PSO velocity update function. SOSwarm is successfully applied to ten benchmark problems drawn from the UCI Machine Learning repository. The paper also demonstrates how the canonical SOM can be explored within the PSO paradigm. Illustrating this linkage between the heretofore distinct literatures of SOM and PSO opens up several new avenues of research for the development of novel self-organising algorithms.     

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.     

基于改进PSO算法的机器人路径规划及实验

针对粒子群优化（PSO）算法存在的优化精度低以及早熟的缺点,提出一种改进的PSO算法用于机器人路径规划．根据梯度下降法中变量沿负梯度方向变化的原则,提出了改进的粒子速度更新模型．为了提高粒子的搜寻效率及精度,增加了自适应粒子位置更新系数．引入ε贪心策略设计了改进的粒子群优化算法．在部分优化测试函数上的多次试验结果表明,所提算法较其他算法模型搜索精度至少提高2倍,收敛速度也有大幅度的提升．将所提算法和改进的DC-HPSO（动态聚类混合粒子群优化）算法应用于静态障碍物下的路径规划仿真和实际试验,结果表明所提模型具有高精度、高效率、高成功率的优点．     

基于改进粒子群算法的无线传感器网络节点定位

针对传统距离矢量-跳数(DV-Hop)算法中最小二乘法的估计误差过大、粒子群(PSO)算法易陷入局部最优的问题,提出了一种改进粒子群算法与DV-Hop的融合算法。首先从粒子速度、惯性权重、学习策略、变异方面对粒子群算法进行改进,增强算法跳出局部最优的能力,提高迭代后期算法的搜索速度;然后在DV-Hop算法第三阶段采用改进粒子群算法优化节点的定位结果。仿真结果表明:相比传统DV-Hop算法、基于混沌粒子群算法的DV-Hop改进算法(MPSO1-DV-Hop)和基于改进型粒子群优化的DV-Hop算法(MPSO2-DV-Hop),该算法的定位精度高,稳定性好,适用于定位精度和稳定性要求较高的场景。     

A particle swarm optimizer with modified velocity update and adaptive diversity regulation

This study introduces reverse direction supported particle swarm optimization (RDS‐PSO) with an adaptive regulation procedure. It benefits from identifying the global worst and global best particles to increase the diversity of the PSO. The velocity update equation of the original PSO was changed according to this idea. To control the impacts of the global best and global worst particles on the velocity update equation, the alpha parameter was added to the velocity update equation. Moreover, a procedure for diversity regulation based on cosine amplitude or max–min methods was introduced. Alpha value was changed adaptively with respect to this diversity measure. Besides, RDS‐PSO was implemented with both linearly increasing and decreasing inertia weight (with 1,000 and 2,000 iterations) in order to survey the effects of these variations on RDS‐PSO performances. Six most commonly used benchmark functions and three medical classification problems were selected as experimental data sets. All experimental results showed that when the grain searching ability is not so small in the last generations, the algorithm performance continues to increase. Experimental proof of it was showed up especially in RDS‐PSO using the cosine amplitude approach. Because the best results among all the RDS‐PSO types for decreasing inertia weight modes were obtained with 2,000 maximal iterations rather than 1,000 ones.     

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。     

求解独立任务调度的离散粒子群优化算法

针对独立任务调度问题,提出一种改进的离散粒子群算法,采用基于任务的编码方式,对粒子的位置和速度更新方法进行重新定义。为防止粒子群算法的早熟收敛,给出利用模拟退火算法的局部搜索能力在最优解附近进行精细搜索,以改善解的质量。仿真结果表明,与遗传算法和基本粒子群算法相比,该混合算法具有较好的优化性能。     

Identification using ANFIS with intelligent hybrid stable learning algorithm approaches and stability analysis of training methods

This paper proposes a novel hybrid learning algorithm with stable learning laws for Adaptive Network based Fuzzy Inference System (ANFIS) as a system identifier and studies the stability of this algorithm. The new hybrid learning algorithm is based on particle swarm optimization (PSO) for training the antecedent part and forgetting factor recursive least square (FFRLS) for training the conclusion part. Two famous training algorithms for ANFIS are the gradient descent (GD) to update antecedent part parameters and using GD or recursive least square (RLS) to update conclusion part parameters. Lyapunov stability theory is used to study the stability of the proposed algorithms. This paper, also studies the stability of PSO as an optimizer in training the identifier. Stable learning algorithms for the antecedent and consequent parts of fuzzy rules are proposed. Some constraints are obtained and simulation results are given to validate the results. It is shown that instability will not occur for the leaning rate and PSO factors in the presence of constraints. The learning rate can be calculated on-line and will provide an adaptive learning rate for the ANFIS structure. This new learning scheme employs adaptive learning rate that is determined by input–output data. Also, stable learning algorithms for two common methods are proposed based on Lyapunov stability theory and some constraints are obtained.     

基于非对称学习因子调节的粒子群优化算法

分析粒子群优化算法中2个学习因子对粒子收敛性的影响,通过Benchmark标准测试函数对不同取值的学习因子进行测试,提出一种基于非对称学习因子调节策略的改进粒子群算法。在搜索初期使粒子获得更好的多样性及较强的摆脱局部极值的能力,在搜索后期加快粒子的收敛速度,提高全局寻优能力。该算法已在复合齿轮传动系统的传动比优化设计中得到了成功应用。     

A particle swarm optimization based simultaneous learning framework for clustering and classification

A particle swarm optimization based simultaneous learning framework for clustering and classification (PSOSLCC) is proposed in this paper. Firstly, an improved particle swarm optimization (PSO) is used to partition the training samples, the number of clusters must be given in advance, an automatic clustering algorithm rather than the trial and error is adopted to find the proper number of clusters, and a set of clustering centers is obtained to form classification mechanism. Secondly, in order to exploit more useful local information and get a better optimizing result, a global factor is introduced to the update strategy update strategy of particle in PSO. PSOSLCC has been extensively compared with fuzzy relational classifier (FRC), vector quantization and learning vector quantization (VQ+LVQ3), and radial basis function neural network (RBFNN), a simultaneous learning framework for clustering and classification (SCC) over several real-life datasets, the experimental results indicate that the proposed algorithm not only greatly reduces the time complexity, but also obtains better classification accuracy for most datasets used in this paper. Moreover, PSOSLCC is applied to a real world application, namely texture image segmentation with a good performance obtained, which shows that the proposed algorithm has a potential of classifying the problems with large scale.     

Comprehensive learning particle swarm optimizer for global optimization of multimodal functions

This paper presents a variant of particle swarm optimizers (PSOs) that we call the comprehensive learning particle swarm optimizer (CLPSO), which uses a novel learning strategy whereby all other particles' historical best information is used to update a particle's velocity. This strategy enables the diversity of the swarm to be preserved to discourage premature convergence. Experiments were conducted (using codes available from http://www.ntu.edu.sg/home/epnsugan) on multimodal test functions such as Rosenbrock, Griewank, Rastrigin, Ackley, and Schwefel and composition functions both with and without coordinate rotation. The results demonstrate good performance of the CLPSO in solving multimodal problems when compared with eight other recent variants of the PSO.     

基于粒子群优化算法的学习资源推荐方法

针对学习者的能力、学习目标、学习时间的个别差异,提出以粒子群优化（PSO）算法为基础的学习资源推荐方法,提供每位学习者个性化的数字课程。综合概念图和知识结构相关理论构建知识点网络结构图,运用项目反应理论（IRT）分析不同学习者的学习目标和能力程度,再应用PSO算法从多样性的学习资源中挑选学习内容,形成个性化的课程推荐给学生。初始化粒子时考虑学习者的学习时间上下限,过滤掉一些不必要的粒子来提高算法效率,在确定最优解位置时,使用Sigmoid函数修正粒子更新速度,保证其在有效范围内。实验结果表明,随着迭代次数增加,所推荐的内容与学习者预定目标差异为0,挑选出的课程与学习者能力差异为0.6,整体差异为0.25,说明所使用的方法具有较好的收敛性,推荐的学习资源能够满足学习者要求。     

基于群能量恒定的粒子群优化算法

针对标准粒子群优化(PSO)算法在寻优过程中容易出现早熟的情况,提出一种群能量恒定的粒子群优化(SEC-PSO)算法.算法根据粒子内能进行动态分群,对较优群体采取引入最差粒子的速度更新策略,对较差群体采取带有惩罚机制的速度更新策略,由其分担由于较优群体速度降低而产生的整群能量损失,从而有效地避免了PSO算法的早熟.典型优化问题的仿真结果表明,该算法具有较强的全局搜索能力和较快的收敛速度,优化性能得到显著的提高.     

A new ARIMA-based neuro-fuzzy approach and swarm intelligence for time series forecasting

Time series forecasting is an important and widely interesting topic in the research of system modeling. We propose a new computational intelligence approach to the problem of time series forecasting, using a neuro-fuzzy system (NFS) with auto-regressive integrated moving average (ARIMA) models and a novel hybrid learning method. The proposed intelligent system is denoted as the NFS–ARIMA model, which is used as an adaptive nonlinear predictor to the forecasting problem. For the NFS–ARIMA, the focus is on the design of fuzzy If-Then rules, where ARIMA models are embedded in the consequent parts of If-Then rules. For the hybrid learning method, the well-known particle swarm optimization (PSO) algorithm and the recursive least-squares estimator (RLSE) are combined together in a hybrid way so that they can update the free parameters of NFS–ARIMA efficiently. The PSO is used to update the If-part parameters of the proposed predictor, and the RLSE is used to adapt the Then-part parameters. With the hybrid PSO–RLSE learning method, the NFS–ARIMA predictor may converge in fast learning pace with admirable performance. Three examples are used to test the proposed approach for forecasting ability. The results by the proposed approach are compared to other approaches. The performance comparison shows that the proposed approach performs appreciably better than the compared approaches. Through the experimental results, the proposed approach has shown excellent prediction performance.     

Particle swarm optimization with adaptive time-varying topology connectivity

Particle swarm optimization (PSO) has shown its competitive performance for solving benchmark and real-world optimization problems. Nevertheless, it requires better control of exploration/exploitation searches to prevent the premature convergence of swarms. Thus, this paper proposes a new PSO variant called PSO with adaptive time-varying topology connectivity (PSO-ATVTC) that employs an ATVTC module and a new learning framework. The proposed ATVTC module specifically aims to balance the algorithm's exploration/exploitation searches by varying the particle's topology connectivity with time according to its searching performance. The proposed learning framework consists of a new velocity update mechanism and a new neighborhood search operator to improve the algorithm's performance. A comprehensive study was conducted on 24 benchmark functions and one real-world problem. Compared with nine well-established PSO variants and six other cutting-edge metaheuristic search algorithms, the searching performance of PSO-ATVTC was proven to be more prominent in majority of the tested problems.     

Attributed multi-objective comprehensive learning particle swarm optimization for optimal security of networks

In particle swarm optimization (PSO) each particle uses its personal and global or local best positions by linear summation. However, it is very time consuming to find the global or local best positions in case of complex problems. To overcome this problem, we propose a new multi-objective variant of PSO called attributed multi-objective comprehensive learning particle swarm optimizer (A-MOCLPSO). In this technique, we do not use global or local best positions to modify the velocity of a particle; instead, we use the best position of a randomly selected particle from the whole population to update the velocity of each dimension. This method not only increases the speed of the algorithm but also searches in more promising areas of the search space. We perform an extensive experimentation on well-known benchmark problems such as Schaffer (SCH), Kursawa (KUR), and Zitzler–Deb–Thiele (ZDT) functions. The experiments show very convincing results when the proposed technique is compared with existing versions of PSO known as multi-objective comprehensive learning particle swarm optimizer (MOCLPSO) and multi-objective particle swarm optimization (MOPSO), as well as non-dominated sorting genetic algorithm II (NSGA-II). As a case study, we apply our proposed A-MOCLPSO algorithm on an attack tree model for the security hardening problem of a networked system in order to optimize the total security cost and the residual damage, and provide diverse solutions for the problem. The results of our experiments show that the proposed algorithm outperforms the previous solutions obtained for the security hardening problem using NSGA-II, as well as MOCLPSO for the same problem. Hence, the proposed algorithm can be considered as a strong alternative to solve multi-objective optimization problems.     

基于改进微粒群优化的学习路径优化控制方法

对学生学习的路径控制在智能化教学系统中是一个重要的问题。该文以知识空间理论为基础建立了学习状态空间,通过改进的微粒群算法对该学习状态空间的学习路径进行最优化控制,并利用死亡惩罚函数法把约束最优化学习路径问题转化成了无约束的最优化学习路径控制问题,引入交换子和交换序的概念对微粒群算法进行改进。在结果分析中,通过动态参数法,即动态变化交换子保留概率的方法提高微粒群的收敛效果,达到了最优化学习路径控制的目的。     

Multi swarm bare bones particle swarm optimization with distribution adaption

Bare bones PSO is a simple swarm optimization approach that uses a probability distribution like Gaussian distribution in the position update rules. However, due to its nature, Bare bones PSO is highly prone to premature convergence and stagnation. The characteristics of the probability distribution functions used in the update rule have a tense impact on the performance of the bare bones PSO. As a result, this paper investigates the use of different methods for estimating the probability distributions used in the update rule. Four methods or strategies are developed that are using Gaussian or multivariate Gaussian distributions. The choice of an appropriate updating strategy for each particle greatly depends on the characteristics of the fitness landscape that surrounds the swarm. To deal with issue, the cellular learning automata model is incorporated with the proposed bare bones PSO, which is able to adaptively learn suitable updating strategies for the particles. Through the interactions among its elements and the learning capabilities of its learning automata, cellular learning automata gradually learns to select the best updating rules for the particles based on their surrounding fitness landscape. This paper also, investigates a new and simple method for adaptively refining the covariance matrices of multivariate Gaussian distributions used in the proposed updating strategies. The proposed method is compared with some other well-known particle swarm approaches. The results indicate the superiority of the proposed approach in terms of the accuracy of the achieved results and the speed in finding appropriate solutions.     

An Improved Particle Swarm Optimization for Evolving Feedforward Artificial Neural Networks

This paper presents a new evolutionary artificial neural network (ANN) algorithm named IPSONet that is based on an improved particle swarm optimization (PSO). The improved PSO employs parameter automation strategy, velocity resetting, and crossover and mutations to significantly improve the performance of the original PSO algorithm in global search and fine-tuning of the solutions. IPSONet uses the improved PSO to address the design problem of feedforward ANN. Unlike most previous studies on only using PSO to evolve weights of ANNs, this study puts its emphasis on using the improved PSO to evolve simultaneously structure and weights of ANNs by a specific individual representation and evolutionary scheme. The performance of IPSONet has been evaluated on several benchmarks. The results demonstrate that IPSONet can produce compact ANNs with good generalization ability.