Cellular particle swarm optimization

This paper proposes a cellular particle swarm optimization (CPSO), hybridizing cellular automata (CA) and particle swarm optimization (PSO) for function optimization. In the proposed CPSO, a mechanism of CA is integrated in the velocity update to modify the trajectories of particles to avoid being trapped in the local optimum. With two different ways of integration of CA and PSO, two versions of CPSO, i.e. CPSO-inner and CPSO-outer, have been discussed. For the former, we devised three typical lattice structures of CA used as neighborhood, enabling particles to interact inside the swarm; and for the latter, a novel CA strategy based on “smart-cell” is designed, and particles employ the information from outside the swarm. Theoretical studies are made to analyze the convergence of CPSO, and numerical experiments are conducted to compare the proposed algorithm with different variants of PSO. According to the experimental results, the proposed method performs better than other variants of PSO on benchmark test functions.     

A parameter selection strategy for particle swarm optimization based on particle positions

In this study, we found that engineering experience can be used to determine the parameters of an optimization algorithm. We came to this conclusion by analyzing the dynamic characteristics of PSO through a large number of experiments. We constructed a relationship between the dynamic process of particle swarm optimization and the transition process of a control system. A novel parameter strategy for PSO was proven in this paper using the overshoot and the peak time of a transition process. This strategy not only provides a series of flexible parameters for PSO but it also provides a new way to analyze particle trajectories that incorporates engineering practices. In order to validate the new strategy, we compared it with published results from three previous reports, which are consistent or approximately consistent with our new strategy, using a suite of well-known benchmark optimization functions. The experimental results show that the proposed strategy is effective and easy to implement. Moreover, the new strategy was applied to equally spaced linear array synthesis examples and compared with other optimization methods. Experimental results show that it performed well in pattern synthesis.     

一种基于栅格的动态粒子数微粒群算法

微粒群算法的全局搜索性能容易受到局部极值点的影响,对此,提出一种基于栅格的动态粒子数微粒群算法(GB-DPPPSO).通过设计栅格信息更新策略、粒子产生策略和粒子消灭策略,可以根据种群搜索情况动态控制粒子数变化,以保持种群多样性,提高全局搜索性能,通过对4个典型数学验证函数的仿真实验,表明了该算法相对于DPPPSO)在全局搜索成功率和搜索效率两方面均有明显改进.     

Stochastic convergence analysis and parameter selection of the standard particle swarm optimization algorithm

This letter presents a formal stochastic convergence analysis of the standard particle swarm optimization (PSO) algorithm, which involves with randomness. By regarding each particle's position on each evolutionary step as a stochastic vector, the standard PSO algorithm determined by non-negative real parameter tuple {ω,c₁,c₂} is analyzed using stochastic process theory. The stochastic convergent condition of the particle swarm system and corresponding parameter selection guidelines are derived.     

改进的粒子群算法

为改善基本粒子群算法的搜索性能,针对粒子群算法随机性较强、收敛较慢的问题,利用数学中的外推技巧给出了两个新的粒子位置更新公式,由此构造出一种新的算法--强引导型粒子群算法.新算法对粒子位置更新加以引导,试图减少算法的随机性以提高搜索效率.用4个基准函数对新算法进行试验,结果表明,新算法在稳定性和收敛性上优于基本粒子群算法.     

A study of particle swarm optimization particle trajectories

Particle swarm optimization (PSO) has shown to be an efficient, robust and simple optimization algorithm. Most of the PSO studies are empirical, with only a few theoretical analyses that concentrate on understanding particle trajectories. These theoretical studies concentrate mainly on simplified PSO systems. This paper overviews current theoretical studies, and extend these studies to investigate particle trajectories for general swarms to include the influence of the inertia term. The paper also provides a formal proof that each particle converges to a stable point. An empirical analysis of multi-dimensional stochastic particles is also presented. Experimental results are provided to support the conclusions drawn from the theoretical findings.     

粒子群算法的改进策略述评

首先介绍了基本粒子群算法。其次分析出四类粒子群算法改进策略即混沌优化策略、调整参数取值策略、混合启发式算法策略、保持种群多样性策略;同时,对算法各种改进策略实现原理及实现方法进行介绍。第三对粒子群算法四类改进策略性能进行分析。最后对粒子群算法改进策略进行展望。     

改进的粒子群优化算法

针对基本粒子群优化算法(PSO)易陷入局部极值点,进化后期收敛慢,精度较差等缺点,提出了一种改进的粒子群优化算法.该算法用一种无约束条件的随机变异操作代替速度公式中的惯性部分,并且使邻居最优粒子有条件地对粒子行为产生影响,提高了粒子间的多样性差异,从而改善了算法能力.通过与其它算法的对比实验表明,该算法能够有效地进行全局和局部搜索,在收敛速度和收敛精度上都有显著提高.     

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.     

Monitoring of particle swarm optimization

In this paper, several diversity measurements will be discussed and defined. As in other evolutionary algorithms, first the population position diversity will be discussed followed by the discussion and definition of population velocity diversity which is different from that in other evolutionary algorithms since only PSO has the velocity parameter. Furthermore, a diversity measurement called cognitive diversity is discussed and defined, which can reveal clustering information about where the current population of particles intends to move towards. The diversity of the current population of particles and the cognitive diversity together tell what the convergence/divergence stage the current population of particles is at and which stage it moves towards.     

一种多样性控制的粒子群优化算法

针对粒子群优化(PSO)算法的早熟收敛问题,提出一种新的基于群体多样性控制的PSO算法(DCPSO).该方法使得粒子在收缩状态下充分搜索,在发散状态下能够飞离群体的聚集位置,不断的收缩-发散过程保证了群体能在较大的空间进行搜索,减少了粒子群算法的早熟收敛现象.通过对多个标准测试函数的实验结果表明,DCPSO算法在复杂优化问题中具有较强的全局搜索能力,而且比现有的多样性指导的PSO算法(ARPSO)具有更好的性能.     

基于混沌粒子群优化的SVM分类器研究

支持向量机(SVM)分类器能较好地解决小样本、非线性、高维等分类问题,具有很强的实用性。然而,支持向量机训练参数的选择对其分类精度有着很大的影响。常用的支持向量机优化方法有遗传算法、粒子群算法都存在易陷入局部极值,优化效果较差的不足。为解决上述问题在粒子群优化算法中引入混沌思想,提出了基于混沌粒子群优化算法(CPSO)的SVM分类器优化方法,CPSO算法能提高种群的多样性和粒子搜索的遍历性,从而有效地提高了PSO算法的收敛速度和精度,更好的优化SVM分类器。并以网络异常入侵检测为研究对象进行仿真,实验结果表明,根据混沌粒子群优化的SVM分类器比传统算法优化的SVM分类器的精度高,速度快。     

一种精英退火微粒群算法

提出一种针对部分较优微粒进行退火操作的精英退火微粒群算法.在退火操作中,结合Logistic方程的特点设计了一种新的错位调整方式,对当前已知最优区域重点搜索.该算法能增强算法的探索和开发能力,避免计算量过度增加.典型测试函数结果显示,该方法可同时提高算法的搜索速度和搜索精度.将基于该方法的PID控制器应用于发电机电压调节系统(AVR),计算结果表明,该PID控制器可以获得更为满意的控制性能指标.     

Co-evolutionary particle swarm optimization to solve constrained optimization problems

This paper presents a co-evolutionary particle swarm optimization (CPSO) algorithm to solve global nonlinear optimization problems. A new co-evolutionary PSO (CPSO) is constructed. In the algorithm, a deterministic selection strategy is proposed to ensure the diversity of population. Meanwhile, based on the theory of extrapolation, the induction of evolving direction is enhanced by adding a co-evolutionary strategy, in which the particles make full use of the information each other by using gene-adjusting and adaptive focus-varied tuning operator. Infeasible degree selection mechanism is used to handle the constraints. A new selection criterion is adopted as tournament rules to select individuals. Also, the infeasible solution is properly accepted as the feasible solution based on a defined threshold of the infeasible degree. This diversity mechanism is helpful to guide the search direction towards the feasible region. Our approach was tested on six problems commonly used in the literature. The results obtained are repeatedly closer to the true optimum solution than the other techniques.     

Gene selection using hybrid particle swarm optimization and genetic algorithm

Selecting high discriminative genes from gene expression data has become an important research. Not only can this improve the performance of cancer classification, but it can also cut down the cost of medical diagnoses when a large number of noisy, redundant genes are filtered. In this paper, a hybrid Particle Swarm Optimization (PSO) and Genetic Algorithm (GA) method is used for gene selection, and Support Vector Machine (SVM) is adopted as the classifier. The proposed approach is tested on three benchmark gene expression datasets: Leukemia, Colon and breast cancer data. Experimental results show that the proposed method can reduce the dimensionality of the dataset, and confirm the most informative gene subset and improve classification accuracy.     

Dispersed particle swarm optimization

In particle swarm optimization (PSO) literatures, the published social coefficient settings are all centralized control manner aiming to increase the search density around the swarm memory. However, few concerns the useful information inside the particles' memories. Thus, to improve the convergence speed, we propose a new setting about social coefficient by introducing an explicit selection pressure, in which each particle decides its search direction toward the personal memory or swarm memory. Due to different adaptation, this setting adopts a dispersed manner associated with its adaptive ability. Furthermore, a mutation strategy is designed to avoid premature convergence. Simulation results show the proposed strategy is effective and efficient.     

自适应小世界粒子群优化算法

提出一种基于小世界网络的自适应拓扑结构。每个粒子都与它的近邻粒子进行交互,其有一定概率通过小世界重置与远方的粒子进行沟通;为粒子群体的每个维度分配一个特定的小世界网络,不同维能够学习不同邻居的历史信息;粒子的邻域大小与小世界重置的概率将在种群收敛状态的基础上进行自适应调整。利用标准函数集对该算法进行测试,测试结果表明,通过该机制,粒子群体具有更好的搜索多样性,能够平衡全局探索与局部开发。     

An improved vector particle swarm optimization for constrained optimization problems

Increasing attention is being paid to solve constrained optimization problems (COP) frequently encountered in real-world applications. In this paper, an improved vector particle swarm optimization (IVPSO) algorithm is proposed to solve COPs. The constraint-handling technique is based on the simple constraint-preserving method. Velocity and position of each particle, as well as the corresponding changes, are all expressed as vectors in order to present the optimization procedure in a more intuitively comprehensible manner. The NVPSO algorithm [30], which uses one-dimensional search approaches to find a new feasible position on the flying trajectory of the particle when it escapes from the feasible region, has been proposed to solve COP. Experimental results showed that searching only on the flying trajectory for a feasible position influenced the diversity of the swarm and thus reduced the global search capability of the NVPSO algorithm. In order to avoid neglecting any worthy position in the feasible region and improve the optimization efficiency, a multi-dimensional search algorithm is proposed to search within a local region for a new feasible position. The local region is composed of all dimensions of the escaped particle’s parent and the current positions. Obviously, the flying trajectory of the particle is also included in this local region. The new position is not only present in the feasible region but also has a better fitness value in this local region. The performance of IVPSO is tested on 13 well-known benchmark functions. Experimental results prove that the proposed IVPSO algorithm is simple, competitive and stable.     

自适应粒子群优化算法研究及其化工报警阈值优化应用

生产装置能否安全有效地运行,已经成为衡量工业生产发展水平的主要标志之一。面临日益复杂的化工过程生产装置,提高化工过程报警系统的性能有着重要的指导意义。传统的报警阈值参数设置方法局限性大,为了提升化工过程报警系统性能,需要对某些过程参数的报警阈值进行优化设置。本文针对传统粒子群算法的不足,采用了参数自适应的粒子群算法,该自适应粒子群算法通过实时调节自身的参数,使得能够较快地寻找到最优个体,且不容易陷入局部最优解。通过对一标准函数的研究,结果表明该自适应粒子群算法比传统的粒子群算法能够较快的达到最优解。随后,用该算法优化TE过程某一参数的报警阈值,降低了报警过程中误报和漏报的总次数,提高了报警系统的性能。本文所提方法为指导生产装置的安全运行提供了有效策略。     

The particle swarm optimization algorithm in size and shape optimization

Shape and size optimization problems instructural design are addressed using the particle swarm optimization algorithm (PSOA). In our implementation of the PSOA, the social behaviour of birds is mimicked. Individual birds exchange information about their position, velocity and fitness, and the behaviour of the flock is then influenced to increase the probability of migration to regions of high fitness. New operators in the PSOA, namely the elite velocity and the elite particle, are introduced. Standard size and shape design problems selected from literature are used to evaluate the performance of the PSOA. The performance of the PSOA is compared with that of three gradient based methods, as well as the genetic algorithm (GA). In attaining the approximate region of the optimum, our implementation suggests that the PSOA is superior to the GA, and comparable to gradient based algorithms. Received December 18, 2000