多阶段多模型的改进微粒群优化算法

针对微粒群优化算法在解决复杂优化问题时易于出现早熟收敛现象,提出了一种多阶段多模型的改进微粒群优化算法。考虑寻优不同阶段的开发与探测能力需求的差异,算法将寻优过程分成3个阶段,各阶段采用不同的模型进行进化。第一阶段利用标准微粒群优化算法发现局部极值的邻域;第二阶段利用Cognition Only模型快速找到局部极值点,提高寻优效率;第三阶段,提出了一种改进的进化模型,利于粒子快速跳出局部极值点,寻找到全局最优点。4种复杂测试函数的实验结果表明：该算法比标准微粒群优化算法（PSO）和基于不同进化模型的两群优化算法（TSE-PSO）更容易找到全局最优解,相比两群微粒群优化算法,还能在一定程度上提高优化效率。     

多子群协同进化的多目标微粒群优化算法

微粒群优化(PSO)算法是一种非常有竞争力的求解多目标优化问题的群智能算法,因其容易陷入局部极值,导致非劣解集的收敛性和正确性不理想。为此提出一种基于多目标分解进化策略的多子群协同进化的多目标微粒群优化算法(MOPSO_MC),算法中每个子群对应于一个多目标分解之后的子问题,并构造了一种新的速率更新策略,每个粒子跟踪自身历史最优值、子群最优值和子群邻域最优值,从而在增强算法的局部寻优能力的同时,也能从邻域子群获得进化信息,实现协同进化。最后通过仿真实验,与现在主流的多目标微粒群算法在ZDT基准测试函数上比较,验证了算法的收敛性,解分布的均匀性和正确性。     

基于混沌序列的多峰函数微粒群寻优算法

基于混沌序列的多峰函数微粒群寻优算法的目标就是找到多峰函数的所有局部优化峰值。在分析微粒群优化算法中各个参数对微粒运动影响的基础上,对微粒群算法进行改造,让微粒运动从初始位置沿优化函数曲线向优化峰值方向爬行,直至找到所在区域的局部优化峰值;要想求得尽可能多的局部优化峰值,就要求微粒群中微粒的初始位置分布具有随机性和遍历性,为此采用混沌序列设置微粒初始位置;为使每一个局部最优值点都可能有微粒群中的微粒经过,采用变步长的迭代计算;为防止优化函数曲线的某些局部峰附近没有微粒分布,从而漏掉该局部峰值,对计算进行重复,直至两轮求得的优化函数的局部峰值之差小于给定阈值。仿真结果表明,该算法具有很好的局部寻优特性,计算过程简捷,寻优效果良好,可有效地应用于多峰函数的局部寻优并求取全局最优值。     

差分进化粒子群混合优化算法的研究与应用

对基本粒子群算法（PSO）和差分进化算法（DE）进行了分析,有机结合两种进化算法提出了一种新型差分进化粒子群混合优化算法,该算法将优化过程分成两阶段,两分群分别采用PSO算法和DE算法同时进行。迭代过程中引入进化速度因子并通过群体间的信息交流阻止算法陷入局部最优。对4个高维复杂函数寻优测试表明算法的鲁棒性、收敛速度和精度,全局搜索能力均优于常规PSO和DE。将提出的改进算法用于乙烯收率软测量建模,应用结果表明模型精度较高、泛化性能较好。     

多峰函数优化的改进群居蜘蛛优化算法

针对群居蜘蛛优化（SSO）算法求解复杂多峰函数成功率不高和收敛精度低的问题,提出了一种自适应多种群回溯群居蜘蛛优化（AMBSSO）算法。引入自适应决策半径概念,动态地将蜘蛛种群分成多个种群,种群内适应度不同的个体采取不同的更新方式,提高了种群样本多样性;提出回溯迭代进化策略,在筛选全局极值的基础上,根据进化程度执行回溯迭代更新,保证了算法全局寻优能力。高维多峰函数仿真结果表明,同SSO算法、PSO算法等优化算法相比,AMBSSO算法具有较快的收敛速度和较高的收敛精度,尤其适用复杂高维多峰函数优化问题。     

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。     

基于多种群协同进化微粒群算法的径向基神经网络设计

神经网络结构和权值的联合设计一直是神经网络进化设计的一个研究方向.本文根据基本微粒群算法的特点,借鉴递阶编码的思想,构造出一种多种群协同进化微粒群算法.该算法具有种群内个体微粒自由运动特征分量与种群运动特征分量分层递阶进化的特征,克服了标准微粒群算法在多峰函数寻优时出现的微粒“早熟”现象.应用该算法进行径向基神经网络隐层结构和径向基函数参数联合自适应设计,在非线性系统辨识中显示了比较好的收敛性和训练精度,同时也使网络的泛化能力和逼近精度这一对矛盾得到了比较好的协调统一.     

基于排列的微粒群优化算法

针对基本微粒群优化算法(PSO)存在陷入局部最优的问题,提出一种基于排列的改进微粒群算法(RPSO).该算法对每次迭代过程中的个体历史最优解按照适应值的优劣顺序排列,然后选择若干个较优的个体历史最优解作为候选解,再以概率方式在候选解中确定群体历史最优解的位置.RPSO算法使基本PSO算法易于陷入局部最优的问题,得到有效的缓解.为了分析算法的性能,对几种典型的非线性函数进行了测试.实验结果表明,RPSO算法比基本PSO算法具有更好的寻优能力.     

一种混合的IWOPSO改进入侵性杂草优化算法

为了提高入侵性杂草优化算法(IWO)在搜索深度上的不足,使算法在处理连续性问题时具有更好的全局收敛性,根据杂草算法在搜索上的广度和粒子群算法(PSO)在搜索上的深度,提出了一种改进的IWOPSO混合算法。该算法在子代扩散中以PSO算法中的位置、速度公式代替了杂草算法中的正态分布方式,引入一个随机数对新的子代个体进一步正态分布,提高了算法后期的局部搜索能力,使算法收敛到更好的全局最优解。利用5个benchmark函数测试算法的寻优能力,仿真结果表明,无论对于多峰还是单峰函数,低维还是高维函数,IWOPSO算法的收敛速度和最优解都要优于标准IWO和PSO算法。     

基于综合改进型PSO算法的电网无功优化研究

为改善基本粒子群优化(PSO)算法的电网无功优化性能,提出了一种新的综合改进型PSO算法,该算法将蜜蜂进化机制、遗传选择机制与PSO算法相结合.在寻优前期,为提高粒子的全局寻优能力,采用蜜蜂进化机制与粒子群相结合的蜜蜂进化PSO算法,可有效地增加粒子的多样性;在寻优后期,为增加粒子的收敛速度,采用遗传选择机制与PSO算法相结合的选择PSO算法.利用综合改进型PSO算法和其他典型优化算法,分别对IEEE 14标准电网以及某地实际运行电网进行对比分析,结果显示,综合改进后的PSO算法进行无功优化时,其收敛速度明显加快,收敛能力显著提高,电网无功优化性能有了很大改善,验证了该算法的正确性和有效性.     

A new gradient based particle swarm optimization algorithm for accurate computation of global minimum

Stochastic optimization algorithms like genetic algorithms (GAs) and particle swarm optimization (PSO) algorithms perform global optimization but waste computational effort by doing a random search. On the other hand deterministic algorithms like gradient descent converge rapidly but may get stuck in local minima of multimodal functions. Thus, an approach that combines the strengths of stochastic and deterministic optimization schemes but avoids their weaknesses is of interest. This paper presents a new hybrid optimization algorithm that combines the PSO algorithm and gradient-based local search algorithms to achieve faster convergence and better accuracy of final solution without getting trapped in local minima. In the new gradient-based PSO algorithm, referred to as the GPSO algorithm, the PSO algorithm is used for global exploration and a gradient based scheme is used for accurate local exploration. The global minimum is located by a process of finding progressively better local minima. The GPSO algorithm avoids the use of inertial weights and constriction coefficients which can cause the PSO algorithm to converge to a local minimum if improperly chosen. The De Jong test suite of benchmark optimization problems was used to test the new algorithm and facilitate comparison with the classical PSO algorithm. The GPSO algorithm is compared to four different refinements of the PSO algorithm from the literature and shown to converge faster to a significantly more accurate final solution for a variety of benchmark test functions.     

随机微粒群优化算法

微粒群优化算法是继蚁群算法之后又一种新的基于群体智能的启发式全局优化算法，其概念简单、易于实现，而且具有良好的优化性能，目前已在许多领域得到应用。但在求解高维多峰函数寻优问题时，算法易陷入局部最优。该文结合模拟退火算法的思想，提出了一种改进的微粒群优化算法——随机微粒群优化算法，该算法在运行初期具有更强的探索能力，可以避免群体过早陷入局部极值点。基于典型高维复杂函数的仿真结果表明，与基本微粒群优化算法相比，该混合算法具有更好的优化性能。     

Statistical learning makes the hybridization of particle swarm and differential evolution more efficient—A novel hybrid optimizer

This brief paper reports a hybrid algorithm we developed recently to solve the global optimization problems of multimodal functions, by combining the advantages of two powerful population-based metaheuristics—differential evolution (DE) and particle swarm optimization (PSO). In the hybrid denoted by DEPSO, each individual in one generation chooses its evolution method, DE or PSO, in a statistical learning way. The choice depends on the relative success ratio of the two methods in a previous learning period. The proposed DEPSO is compared with its PSO and DE parents, two advanced DE variants one of which is suggested by the originators of DE, two advanced PSO variants one of which is acknowledged as a recent standard by PSO community, and also a previous DEPSO. Benchmark tests demonstrate that the DEPSO is more competent for the global optimization of multimodal functions due to its high optimization quality. Supported by the National Natural Science Foundation of China (Grant No. 60374069), and the Foundation of the Key Laboratory of Complex Systems and Intelligent Science, Institute of Automation, Chinese Academy of Sciences (Grant No. 20060104)     

FRPSO: Fletcher–Reeves based particle swarm optimization for multimodal function optimization

Particle swarm optimization (PSO) is a population-based optimization tool that is inspired by the collective intelligent behavior of birds seeking food. It can be easily implemented and applied to solve various function optimization problems. However, relatively few researchers have explored the potential of PSO for multimodal problems. Although PSO is a simple, easily implemented, and powerful technique, it has a tendency to get trapped in a local optimum. This premature convergence makes it difficult to find global optimum solutions for multimodal problems. A hybrid Fletcher–Reeves based PSO (FRPSO) method is proposed in this paper. It is based on the idea of increasing exploitation of the local optimum, while maintaining a good exploration capability for finding better solutions. In FRPSO, standard PSO is used to update the particle’s current position, which is then further refined by the Fletcher–Reeves conjugate gradient method. This enhances the performance of standard PSO. The results of experiments conducted on seventeen benchmark test functions demonstrate that the proposed method shows superior performance on a set of multimodal functions when compared with standard PSO, a genetic algorithm (GA) and fitness distance ratio PSO (FDRPSO).     

Hybridizing particle swarm optimization with differential evolution for constrained numerical and engineering optimization

We propose a novel hybrid algorithm named PSO-DE, which integrates particle swarm optimization (PSO) with differential evolution (DE) to solve constrained numerical and engineering optimization problems. Traditional PSO is easy to fall into stagnation when no particle discovers a position that is better than its previous best position for several generations. DE is incorporated into update the previous best positions of particles to force PSO jump out of stagnation, because of its strong searching ability. The hybrid algorithm speeds up the convergence and improves the algorithm’s performance. We test the presented method on 11 well-known benchmark test functions and five engineering optimization functions. Comparisons show that PSO-DE outperforms or performs similarly to seven state-of-the-art approaches in terms of the quality of the resulting solutions.     

广义粒子群优化模型

粒子群优化算法提出至今一直未能有效解决的离散及组合优化问题．针对这个问题,文中首先回顾了粒子群优化算法在整数规划问题的应用以及该算法的二进制离散优化模型,并分析了其缺陷．然后,基于传统算法的速度一位移更新操作,在分析粒子群优化机理的基础上提出了广义粒子群优化模型（GPSO）,使其适用于解决离散及组合优化问题．GPSO模型本质仍然符合粒子群优化机理,但是其粒子更新策略既可根据优化问题的特点设计,也可实现与已有方法的融合．该文以旅行商问题（TSP）为例,针对遗传算法（GA）解决该问题的成功经验,使用遗传操作作为GPSO模型中的更新算子,进一步提出基于遗传操作的粒子群优化模型,并以Inverover算子作为模型中具体的遗传操作设计了基于GPSO模型的TSP算法．与采用相同遗传操作的GA比较,基于GPSO模型的算法解的质量与收敛稳定性提高,同时计算费用显著降低．     

一种催化粒子群算法及其性能分析

针对粒子群算法（PSO）在解决高维、多模复杂问题时容易陷入局部最优的问题,提出了一种新颖的混合算法—催化粒子群算法（CPSO）。在CPSO优化过程中,种群中的粒子始终保持其个体历史最优值pbests。CPSO种群更新由改造PSO、横向交叉以及垂直交叉三个搜索算子交替进行,其中,每个算子产生的中庸解均通过贪婪思想产生占优解pbests,并作为下一个算子的父代种群。在CPSO中,纵横交叉算法（CSO）作为PSO的加速催化剂,一方面通过横向交叉改善PSO的全局收敛性能,另一方面通过纵向交叉维持种群的多样性。对6个典型benchmark函数的仿真结果表明,相比其它主流PSO变体,CPSO在全局收敛能力和收敛速率方面具有明显优势。     

基于梯度粒子群算法的细菌觅食算法

针对细菌觅食算法在优化过程中环境感知能力较弱且容易陷入局部极值的缺陷,将梯度粒子群算法的基本思想引入细菌觅食算法中,改进原算法的收敛速度和收敛能力,并据此提出了基于梯度粒子群算法的细菌觅食算法GPSO-BFA。该算法既利用了细菌觅食算法出色的全局搜索能力,又借助梯度粒子群算法的快速局部寻优能力,很好地将两者的优势结合在一起。基于六个高维Benchmark函数的实验结果显示,该算法在收敛速度和精度方面都优于其他四种细菌觅食算法。     

Binary optimization using hybrid particle swarm optimization and gravitational search algorithm

The PSOGSA is a novel hybrid optimization algorithm, combining strengths of both particle swarm optimization (PSO) and gravitational search algorithm (GSA). It has been proven that this algorithm outperforms both PSO and GSA in terms of improved exploration and exploitation. The original version of this algorithm is well suited for problems with continuous search space. Some problems, however, have binary parameters. This paper proposes a binary version of hybrid PSOGSA called BPSOGSA to solve these kinds of optimization problems. The paper also considers integration of adaptive values to further balance exploration and exploitation of BPSOGSA. In order to evaluate the efficiencies of the proposed binary algorithm, 22 benchmark functions are employed and divided into three groups: unimodal, multimodal, and composite. The experimental results confirm better performance of BPSOGSA compared with binary gravitational search algorithm (BGSA), binary particle swarm optimization (BPSO), and genetic algorithm in terms of avoiding local minima and convergence rate.     

自适应扩散混合变异机制微粒群算法

为了避免微粒群算法(particle swarm optimization,简称PSO)在全局优化中陷入局部极值,分析了标准PSO算法早熟收敛的原因,提出了自适应扩散混合变异机制微粒群算法(InformPSO).结合生物群体信息扩散的习性,设计了一个考虑微粒分布和迭代次数的函数,自适应调整微粒的"社会认知"能力,提高种群的多样性;模拟了基因自组织和混沌进化规律,引入克隆选择使群体最佳微粒gBest实现遗传微变、局部增值,具有变异确定性;利用Logistic序列指导gBest随机漂移,进一步增强逃离局部极值能力.基于种群的随机状态转移过程,证明了新算法具有全局收敛性.与其他几种PSO变种相比,复杂基准函数仿真优化结果表明,新算法收敛速度快,求解精度高,稳定性好,能够有效抑制早熟收敛.