A two-stage quantum-behaved particle swarm optimization with skipping search rule and weight to solve continuous optimization problem

Quantum-behaved particle swarm optimization (QPSO) is a recently developed heuristic method by particle swarm optimization (PSO) algorithm based on quantum mechanics, which outperforms the search ability of original PSO. But as many other PSOs, it is easy to fall into the local optima for the complex optimization problems. Therefore, we propose a two-stage quantum-behaved particle swarm optimization with a skipping search rule and a mean attractor with weight. The first stage uses quantum mechanism, and the second stage uses the particle swarm evolution method. It is shown that the improved QPSO has better performance, because of discarding the worst particles and enhancing the diversity of the population. The proposed algorithm (called ‘TSQPSO’) is tested on several benchmark functions and some real-world optimization problems and then compared with the PSO, SFLA, RQPSO and WQPSO and many other heuristic algorithms. The experiment results show that our algorithm has better performance than others.     

A modified particle swarm optimization with multiple subpopulations for multimodal function optimization problems

In this paper, a modified particle swarm optimization (PSO) algorithm is developed for solving multimodal function optimization problems. The difference between the proposed method and the general PSO is to split up the original single population into several subpopulations according to the order of particles. The best particle within each subpopulation is recorded and then applied into the velocity updating formula to replace the original global best particle in the whole population. To update all particles in each subpopulation, the modified velocity formula is utilized. Based on the idea of multiple subpopulations, for the multimodal function optimization the several optima including the global and local solutions may probably be found by these best particles separately. To show the efficiency of the proposed method, two kinds of function optimizations are provided, including a single modal function optimization and a complex multimodal function optimization. Simulation results will demonstrate the convergence behavior of particles by the number of iterations, and the global and local system solutions are solved by these best particles of subpopulations.     

改进的变尺度混沌粒子群算法及其应用

针对粒子群算法(PSO)存在局部最优及后期收敛速度慢等问题,提出一种改进的变尺度混沌粒子群算法(IMCPSO).该算法初期,在整个解空间对最优粒子进行变尺度混沌扰动,以防止陷入局部最优;算法后期,则以最优粒子为中心引入变尺度混沌扰动,以提高算法收敛速度.当算法一旦陷入局部最优时,采用混沌粒子替代部分种群粒子以增加粒子多样性,使算法尽快跳出局部最优.基于benchmark测试函数的仿真结果表明,所提算法与基本粒子群算法(SPSO)和变尺度混沌粒子群算法(MCPSO)相比,具有明显好的搜索精度和收敛速度.最后,将该算法应用于电路故障诊断实验中的支持向量机参数优化问题,实验结果说明了其应用价值.     

A novel abstraction for swarm intelligence: particle field optimization

Particle swarm optimization (PSO) is a popular meta-heuristic for black-box optimization. In essence, within this paradigm, the system is fully defined by a swarm of “particles” each characterized by a set of features such as its position, velocity and acceleration. The consequent optimized global best solution is obtained by comparing the personal best solutions of the entire swarm. Many variations and extensions of PSO have been developed since its creation in 1995, and the algorithm remains a popular topic of research. In this work we submit a new, abstracted perspective of the PSO system, where we attempt to move away from the swarm of individual particles, but rather characterize each particle by a field or distribution. The strategy that updates the various fields is akin to Thompson’s sampling. By invoking such an abstraction, we present the novel particle field optimization algorithm which harnesses this new perspective to achieve a model and behavior which is completely distinct from the family of traditional PSO systems.     

粒子群优化算法分析及研究进展

粒子群优化算法是一类基于群体智能的启发式全局优化技术,群体中的每一个微粒代表待解决问题的一个候选解,算法通过粒子间信息素的交互作用发现复杂搜索空间中的最优区域。本文介绍了粒子群优化算法的基本原理,并通过建立记忆表,详尽描述了粒子群优化算法中个体极优和全局极优的搜寻求解过程。同时,文章给出了多种改进形式以及研究现状,并提出了未来可能的研究方向。     

Parameter extraction for PSP MOSFET model using hierarchical particle swarm optimization

The particle swarm optimization (PSO) algorithm is applied to the problem of MOSFET parameter extraction for the first time. It is shown to perform significantly better than the genetic algorithm (GA). Several modifications of the basic PSO algorithm have been implemented: (a) Hierarchical PSO (HPSO) in which particles are hierarchically arranged and influenced by the positions of the local and global leaders, (b) memory loss operation due to which a particle forgets its past best position, (c) intensive local search in which the solution space around the global leader is searched with a high resolution, and (d) adaptive inertia which causes the inertia of the particles to change adaptively, depending on the fitness of the population. It is demonstrated that the above features improve the performance of the basic PSO algorithm both for the MOSFET parameter extraction problem and for benchmark functions.     

OPSO: Orthogonal Particle Swarm Optimization and Its Application to Task Assignment Problems

This paper proposes a novel variant of particle swarm optimization (PSO), named orthogonal PSO (OPSO), for solving intractable large parameter optimization problems. The standard version of PSO is associated with the lack of a mechanism responsible for the process of high-dimensional vector spaces. The high performance of OPSO arises mainly from a novel move behavior using an intelligent move mechanism (IMM) which applies orthogonal experimental design to adjust a velocity for each particle by using a systematic reasoning method instead of the conventional generate-and-go method. The IMM uses a divide-and- conquer approach to cope with the curse of dimensionality in determining the next move of particles. It is shown empirically that the OPSO performs well in solving parametric benchmark functions and a task assignment problem which is NP-complete compared with the standard PSO with the conventional move behavior. The OPSO with IMM is more specialized than the PSO and performs well on large-scale parameter optimization problems with few interactions between variables.     

A parallel boundary search particle swarm optimization algorithm for constrained optimization problems

During the past decade, considerable research has been conducted on constrained optimization problems (COPs) which are frequently encountered in practical engineering applications. By introducing resource limitations as constraints, the optimal solutions in COPs are generally located on boundaries of feasible design space, which leads to search difficulties when applying conventional optimization algorithms, especially for complex constraint problems. Even though penalty function method has been frequently used for handling the constraints, the adjustment of control parameters is often complicated and involves a trial-and-error approach. To overcome these difficulties, a modified particle swarm optimization (PSO) algorithm named parallel boundary search particle swarm optimization (PBSPSO) algorithm is proposed in this paper. Modified constrained PSO algorithm is adopted to conduct global search in one branch while Subset Constrained Boundary Narrower (SCBN) function and sequential quadratic programming (SQP) are applied to perform local boundary search in another branch. A cooperative mechanism of the two branches has been built in which locations of the particles near boundaries of constraints are selected as initial positions of local boundary search and the solutions of local boundary search will lead the global search direction to boundaries of active constraints. The cooperation behavior of the two branches effectively reinforces the optimization capability of the PSO algorithm. The optimization performance of PBSPSO algorithm is illustrated through 13 CEC06 test functions and 5 common engineering problems. The results are compared with other state-of-the-art algorithms and it is shown that the proposed algorithm possesses a competitive global search capability and is effective for constrained optimization problems in engineering applications.     

Non-parametric particle swarm optimization for global optimization

In recent years, particle swarm optimization (PSO) has extensively applied in various optimization problems because of its simple structure. Although the PSO may find local optima or exhibit slow convergence speed when solving complex multimodal problems. Also, the algorithm requires setting several parameters, and tuning the parameters is a challenging for some optimization problems. To address these issues, an improved PSO scheme is proposed in this study. The algorithm, called non-parametric particle swarm optimization (NP-PSO) enhances the global exploration and the local exploitation in PSO without tuning any algorithmic parameter. NP-PSO combines local and global topologies with two quadratic interpolation operations to increase the search ability. Nineteen (19) unimodal and multimodal nonlinear benchmark functions are selected to compare the performance of NP-PSO with several well-known PSO algorithms. The experimental results showed that the proposed method considerably enhances the efficiency of PSO algorithm in terms of solution accuracy, convergence speed, global optimality, and algorithm reliability.     

一种混合粒子群算法的贝叶斯网络优化模型

传统的粒子群优化算法通过群体中粒子间的合作和竞争进行群体智能指导优化搜索,算法收敛速度快,但较易陷入局部较优值,进入早熟状态。为了解决这个问题,提出了一种混合粒子群算法的贝叶斯网络优化模型,它可以通过当前所选择的较优解群构造一个贝叶斯网络和联合概率分布模型,利用这个模型进行采样得到更优解,用其可随机替换掉PSO中的一些粒子或个体最优解;同时利用粒子群算法对当前选择出的较优解群进行深度搜索,并将得到的最优解融入到较优解群中。分析可知,该方法可以提高算法有效性和可靠性。     

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.     

具有拓扑时变和搜索扰动的混合粒子群优化算法

粒子群优化（PSO）算法在求解复杂多峰函数时极易早熟,陷入局部最优无法跳出。研究表明改变粒子间的拓扑结构和调整算法的迭代机制有助于改善种群的多样性,提高算法的寻优能力。因此,提出一种具有拓扑时变和搜索扰动的混合粒子群优化（HPSO-TS）算法。该算法采用K-medoids聚类算法对粒子群进行动态分簇,形成多个异构子群,以利于子群内粒子间进行信息流通。在速度更新中,增加簇最优粒子的引导,并引入非线性变化极值扰动,帮助粒子搜索更多的区域。而后在位置迭代中引入花授粉算法（FPA）中的转换概率,使粒子在全局搜索和局部搜索之间转换。在全局搜索时结合狮群算法中的母狮觅食机制对粒子的位置进行更新;在局部搜索时引入正弦扰动因子,帮助粒子跳出局部最优。实验结果表明所提算法在求解精度和鲁棒性方面明显优于FPA、PSO、改进粒子群算法（IPSO）、具有动态拓扑结构的粒子群算法（PSO-T）;并且随着测试维度和次数的增加,这种优势更加明显。HPSO-TS算法所引入的拓扑时变策略和搜索扰动机制能有效地提高种群的多样性和粒子的活性,从而改善寻优能力。     

基于精英克隆选择的粒子群优化算法研究与应用

粒子群算法(PSO)是一种基于迭代的智能算法,具有较好的全局搜索能力,但局部搜索能力较弱.针对粒子群算法容易陷入局部最优不足这一问题,本文提出了一种精英克隆选择的方法.该算法在基本粒子群算法的基础上保留了种群中的若干个精英粒子,然后将这些精英粒子进行克隆复制,并将复制之后的粒子进行变异操作,再将变异之后的粒子与变异前的粒子进行亲和度的比较,保留下来亲和度提高的粒子并替换之前适应值较差的粒子,通过这种方式增强了种群的多样性,从而避免了粒子陷入局部最优的问题.此外,本文引入了新的改进惯性权重的机制,根据粒子位置和速度的情况自适应地改变惯性权重,这样避免了粒子盲目运动,更有针对性的寻找最优解.对4个高维复杂函数寻优测试,分别从平均精度和标准差这两方面进行分析,结果表明改进之后的算法在寻优精度和稳定性方面都超过了基本PSO,从仿真图像中可以看出改进之后的算法在迭代末期跳出了局部最优更接近全局最优值.最后将这种改进的算法应用到优化乙烯、丙烯的收率模型中,应用结果表明当裂解原料属性发生改变时,本文提出的算法可以很快完成对操作变量的寻优,显著提高了“双烯”收率.     

求解工程约束优化问题的PSO-ABC混合算法*

针对包含约束条件的工程优化问题,提出了基于人工蜂群的粒子群优化PSO-ABC算法。将PSO中较优的粒子作为ABC算法的蜜源,并使用禁忌表存储其局部极值,克服粒子群优化算法易陷入局部最优的缺陷。采用可行性规则进行约束处理,将粒子种群分为可行子群和不可行子群,并在ABC算法产生蜜源的过程中保留部分较优的可行解和不可行解的信息,弥补了可行性规则处理最优点位于约束边界附近的问题时存在的不足。四个典型工程优化设计的实验结果表明,该算法能够寻得更优的约束最优化解,且稳健性更强。     

结合梯度法的混合微粒群优化算法

在微粒群优化算法PSO中引入梯度算法,提出了一种新型的混合微粒群优化算法——GPSO。该混合优化算法是对PSO每一次进化后的所有微粒进一步执行梯度法寻优操作,并以寻找到的更优个体替代当前个体参与群体的下一代进化。GPSO既利用了PSO出色的全局搜索能力,又借助梯度法的快速局部寻优能力,很好地将两者的优势结合在一起。数值实验表明：无论是对于低维的多峰函数,还是高维的多峰和单峰病态函数,GPSO都表现出很强的优化效率、适用性和鲁棒性。     

基于随机变异的粒子群优化算法及其应用研究

提出了一种改进粒子群优化算法,对标准粒子群优化算法中影响粒子移动方向的4个因子进行了讨论及优化设定,并设计了一种基于随机变异思想的选择操作,在粒子陷入局部极值点时,重新部署粒子,有利于粒子跳出局部极值点,快速搜寻到最优解.该算法继承了标准粒子群优化算法计算简洁的特点,对经典的测试函数计算表明,该算法的收敛精度和鲁棒性均优于标准粒子群优化算法.将该算法应用于组播路由优化问题,仿真试验表明,该算法能快速、准确地构建满足时延要求,链路代价最小的组播树.     

一种双态免疫微粒群算法

针对基本微粒群算法的缺陷,提出了一种双态免疫微粒群算法.把微粒群分为捕食与探索两种状态,处于捕食状态的精英粒子采用精英学习策略,指导精英粒子逃离局部极值;处于探索状态的微粒采用探索策略,扩大解的搜索空间,抑制早熟停滞现象.同时引入免疫系统的克隆选择和受体编辑机制,增强群体逃离局部极值及多模优化问题全局寻优能力.实验表明...     

Individualism of particles in particle swarm optimization

The particle swarm optimization (PSO) method is an effective, nature-inspired, computational algorithm for optimization problems. However, the influence of individuals’ cultural orientations is neglected in particle swarms. Individualist and collectivist orientations have an important influence on optimization. In order to improve the performance of PSO in nature, particularly with respect to the balance of exploitation and exploration in the search process, and in view of the inherent characteristics of particles, a few particles in the swarm was regarded as having an individualistic orientation, which may be beneficial to group creativity from a cultural psychology perspective. The particles holding individualistic orientations were named individualism particles (I-particles). To simulate the divisive and unruly features of I-particles, a random term was introduced to the velocity updating formula to simulate the creative behavior. The experiment was performed with and without I-particles in the PSO algorithm. The presence of I-particles produced better performance in terms of solution accuracy and convergence speed. Furthermore, when added to one of the PSO variants, the I-particles could also contribute to improve the performance of the PSO variant. Further, even for complex CEC2013 benchmark functions, good results were achieved in most problems when I-particles were added to the PSO. Besides, the study is not focused on a PSO variant algorithm, but on the nature of the PSO. Thus, The findings of the nature indicated that I-particles in a particle swarm might be regarded as a supplement to the basic structure of PSO.     

一种基于竞选领导策略的改进粒子群算法

针对标准粒子群算法由于粒子多样性的大量丧失而导致的算法易陷入局部最优解,收敛精度不高的问题,提出一种基于竞选领导策略的改进粒子群算法,该算法在全局最优粒子的领导能力丧失时,通过引进细菌觅食算法的趋化算子对精英粒子进行优化,然后选出更具领导能力的粒子作为新的领导粒子来带领种群跳出局部最优解,以增强算法的全局搜索能力。通过四个典型函数的测试,结果表明改进算法在较好保留了标准粒子群算法快速收敛优点的前提下,有效地预防了早熟现象的产生,提高了收敛精度。     

Gradient-based adaptive particle swarm optimizer with improved extremal optimization

Most real-world applications can be formulated as optimization problems, which commonly suffer from being trapped into the local optima. In this paper, we make full use of the global search capability of particle swarm optimization (PSO) and local search ability of extremal optimization (EO), and propose a gradient-based adaptive PSO with improved EO (called GAPSO-IEO) to overcome the issue of local optima deficiency of optimization in high-dimensional search and reduce the time complexity of the algorithm. In the proposed algorithm, the improved EO (IEO) is adaptively incorporated into PSO to avoid the particles being trapped into the local optima according to the evolutional states of the swarm, which are estimated based on the gradients of the fitness functions of the particles. We also improve the mutation strategy of EO by performing polynomial mutation (PLM) on each particle, instead of on each component of the particle, therefore, the algorithm is not sensitive to the dimension of the swarm. The proposed algorithm is tested on several unimodal/multimodal benchmark functions and Berkeley Segmentation Dataset and Benchmark (BSDS300). The results of experiments have shown the superiority and efficiency of the proposed approach compared with those of the state-of-the-art algorithms, and can achieve better performance in high-dimensional tasks.