基于动态邻域和自适应惯性权重的微粒群算法

针对微粒群优化解决复杂优化问题时易陷入局部收敛、效率不高的缺点,提出一种基于动态邻域和自适应惯性权重的微粒群优化算法.通过定义动态邻域及其最优维值,提出种群个体的动态邻域最优维值学习策略,使微粒跟踪个体极值和邻域的最优维值进行搜索,以增加学习样本的多样性,避免局部收敛;提出一种基于个体适应度的惯性权重动态调整方法,提高算法的寻优效率.通过优化5个典型测试函数验证了本文所提方法的有效性.     

一种非线性改变惯性权重的粒子群算法

引入递减指数和迭代阈值对基本粒子群算法中线性递减权策略进行了改进,在优化遮代过程中,惯性权重随当前迭代次数、指数递减率和迭代阚值非线性变化。对三种具有代表性的测试函数进行了仿真实验,并与基本粒子群算法以及其他改进的粒子群算法进行了比较,结果表明,文中所提的改进粒子群算法在搜优精度、收敛速度以度稳定性等方面有明显优势。     

Simultaneous size,shape, and topology optimization of truss structures using integrated particle swarm optimizer

Modal transducers can be designed by optimizing the polarity of the electrode which covers the piezoelectric layers bonded to the host structure. This paper is intended as a continuation of our previous work (Donoso and Bellido J Appl Mech 57:434–441, 2009a) to make better the performance of such piezoelectric devices by simultaneously optimizing the structure layout and the electrode profile. As the host structure is not longer fixed, the typical drawbacks in eigenproblem optimization such as spurious modes, mode tracking and switching or repeated eigenvalues soon appear. Further, our model has the novel issue that both cost and constraints explicitly depend on mode shapes. Moreover, due to the physics of the problem, the appearance of large gray areas is another pitfall to be solved. Our proposed approach overcomes all these difficulties with success and let obtain nearly 0-1 designs that improve the existing optimal electrode profiles over a homogeneous plate.     

Dynamic particle swarm optimizer with escaping prey for solving constrained non-convex and piecewise optimization problems

This paper presents a novel meta-heuristic algorithm, dynamic particle swarm optimizer with escaping prey (DPSOEP), for solving constrained non-convex and piecewise optimization problems. In DPSOEP, the particles developed from two different species are classified into three different types, consisting of preys, strong particles and weak particles, to simulate the behavior of hunting and escaping characteristics observed in nature. Compared to other variants of particle swarm optimizer (PSO), the proposed algorithm takes account of an escaping mechanism for the preys to circumvent the problem of local optimum and also develops a classification mechanism to cope with different situations in the search space so as to achieve a good balance between its global exploration and local exploitation abilities. Simulation results obtained based on thirteen benchmark functions and two practical economic dispatch problems prove the effectiveness and applicability of the DPSOEP to deal with non-convex and piecewise optimization problem, considering the integration of linear equality and inequality constraints.     

Runtime analysis of a binary particle swarm optimizer

We investigate the runtime of a binary Particle Swarm Optimizer (PSO) for optimizing pseudo-Boolean functions f:{0,1}ⁿ→R. The binary PSO maintains a swarm of particles searching for good solutions. Each particle consists of a current position from {0,1}ⁿ, its own best position and a velocity vector used in a probabilistic process to update its current position. The velocities for a particle are then updated in the direction of its own best position and the position of the best particle in the swarm.We present a lower bound for the time needed to optimize any pseudo-Boolean function with a unique optimum. To prove upper bounds we transfer a fitness-level argument that is well-established for evolutionary algorithms (EAs) to PSO. This method is applied to estimate the expected runtime for the class of unimodal functions. A simple variant of the binary PSO is considered in more detail for the test function OneMax, showing that there the binary PSO is competitive to EAs. An additional experimental comparison reveals further insights.     

Dynamic multi-swarm particle swarm optimizer with harmony search

In this paper, the dynamic multi-swarm particle swarm optimizer (DMS-PSO) is improved by hybridizing it with the harmony search (HS) algorithm and the resulting algorithm is abbreviated as DMS-PSO-HS. We present a novel approach to merge the HS algorithm into each sub-swarm of the DMS-PSO. Combining the exploration capabilities of the DMS-PSO and the stochastic exploitation of the HS, the DMS-PSO-HS is developed. The whole DMS-PSO population is divided into a large number of small and dynamic sub-swarms which are also individual HS populations. These sub-swarms are regrouped frequently and information is exchanged among the particles in the whole swarm. The DMS-PSO-HS demonstrates improved on multimodal and composition test problems when compared with the DMS-PSO and the HS.     

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.     

Handling multi-objective optimization problems with a multi-swarm cooperative particle swarm optimizer

This paper presents a new multi-objective optimization algorithm in which multi-swarm cooperative strategy is incorporated into particle swarm optimization algorithm, called multi-swarm cooperative multi-objective particle swarm optimizer (MC-MOPSO). This algorithm consists of multiple slave swarms and one master swarm. Each slave swarm is designed to optimize one objective function of the multi-objective problem in order to find out all the non-dominated optima of this objective function. In order to produce a well distributed Pareto front, the master swarm is developed to cover gaps among non-dominated optima by using a local MOPSO algorithm. Moreover, in order to strengthen the capability locating multiple optima of the PSO, several improved techniques such as the Pareto dominance-based species technique and the escape strategy of mature species are introduced. The simulation results indicate that our algorithm is highly competitive to solving the multi-objective optimization problems.     

Self-organizing hierarchical particle swarm optimizer with time-varying acceleration coefficients

This paper introduces a novel parameter automation strategy for the particle swarm algorithm and two further extensions to improve its performance after a predefined number of generations. Initially, to efficiently control the local search and convergence to the global optimum solution, time-varying acceleration coefficients (TVAC) are introduced in addition to the time-varying inertia weight factor in particle swarm optimization (PSO). From the basis of TVAC, two new strategies are discussed to improve the performance of the PSO. First, the concept of "mutation" is introduced to the particle swarm optimization along with TVAC (MPSO-TVAC), by adding a small perturbation to a randomly selected modulus of the velocity vector of a random particle by predefined probability. Second, we introduce a novel particle swarm concept "self-organizing hierarchical particle swarm optimizer with TVAC (HPSO-TVAC)". Under this method, only the "social" part and the "cognitive" part of the particle swarm strategy are considered to estimate the new velocity of each particle and particles are reinitialized whenever they are stagnated in the search space. In addition, to overcome the difficulties of selecting an appropriate mutation step size for different problems, a time-varying mutation step size was introduced. Further, for most of the benchmarks, mutation probability is found to be insensitive to the performance of MPSO-TVAC method. On the other hand, the effect of reinitialization velocity on the performance of HPSO-TVAC method is also observed. Time-varying reinitialization step size is found to be an efficient parameter optimization strategy for HPSO-TVAC method. The HPSO-TVAC strategy outperformed all the methods considered in this investigation for most of the functions. Furthermore, it has also been observed that both the MPSO and HPSO strategies perform poorly when the acceleration coefficients are fixed at two.     

A novel particle swarm optimizer hybridized with extremal optimization

Particle swarm optimization (PSO) has received increasing interest from the optimization community due to its simplicity in implementation and its inexpensive computational overhead. However, PSO has premature convergence, especially in complex multimodal functions. Extremal optimization (EO) is a recently developed local-search heuristic method and has been successfully applied to a wide variety of hard optimization problems. To overcome the limitation of PSO, this paper proposes a novel hybrid algorithm, called hybrid PSO–EO algorithm, through introducing EO to PSO. The hybrid approach elegantly combines the exploration ability of PSO with the exploitation ability of EO. We testify the performance of the proposed approach on a suite of unimodal/multimodal benchmark functions and provide comparisons with other meta-heuristics. The proposed approach is shown to have superior performance and great capability of preventing premature convergence across it comparing favorably with the other algorithms.     

Stability analysis of the particle dynamics in particle swarm optimizer

Previous stability analysis of the particle swarm optimizer was restricted to the assumption that all parameters are nonrandom, in effect a deterministic particle swarm optimizer. We analyze the stability of the particle dynamics without this restrictive assumption using Lyapunov stability analysis and the concept of passive systems. Sufficient conditions for stability are derived, and an illustrative example is given. Simulation results confirm the prediction from theory that stability of the particle dynamics requires increasing the maximum value of the random parameter when the inertia factor is reduced.     

An improved memetic algorithm using ring neighborhood topology for constrained optimization

This paper proposes an improved memetic algorithm relying on ring neighborhood topology for constrained optimization problems based on our previous work in Cai et al. (Soft Comput (in press), 2013). The main motivation of using ring neighborhood topology is to provide a good balance between effective exploration and efficient exploitation, which is a very important design issue for memetic algorithms. More specifically, a novel variant of invasive weed optimization (IWO) as the local refinement procedure is proposed in this paper. The proposed IWO variant adopts a neighborhood-based dispersal operator to achieve more fine-grained local search through the estimation of neighborhood fitness information relying on the ring neighborhood topology. Furthermore, a modified version of differential evolution (DE), known as “DE/current-to-best/1”, is integrated into the improved memetic algorithm with the aim of providing a more effective exploration. Performance of the improved memetic algorithm has been comprehensively tested on 13 well-known benchmark test functions and four engineering constrained optimization problems. The experimental results show that the improved memetic algorithm obtains greater competitiveness when compared with the original memetic approach Cai et al. in (Soft Comput (in press), 2013) and other state-of-the-art algorithms. The effectiveness of the modification of each component in the proposed approach is also discussed in the paper.     

Mixed constrained image filter design using particle swarm optimization

This article describes an evolutionary image filter design for noise reduction using particle swarm optimization (PSO), where mixed constraints on the circuit complexity, power, and signal delay are optimized. First, the evaluated values of correctness, complexity, power, and signal delay are introduced to the fitness function. Then PSO autonomously synthesizes a filter. To verify the validity of our method, an image filter for noise reduction was synthesized. The performance of the resultant filter by PSO was similar to that of a genetic algorithm (GA), but the running time of PSO is 10% shorter than that of GA.     

A learning method for dynamic Bayesian network structures using a multi-objective particle swarm optimizer

In this article, we present a multi-objective discrete particle swarm optimizer (DPSO) for learning dynamic Bayesian network (DBN) structures. The proposed method introduces a hierarchical structure consisting of DPSOs and a multi-objective genetic algorithm (MOGA). Groups of DPSOs find effective DBN sub-network structures and a group of MOGAs find the whole of the DBN network structure. Through numerical simulations, the proposed method can find more effective DBN structures, and can obtain them faster than the conventional method.     

Interior ballistic charge design based on a modified particle swarm optimizer

According to the limitation of the interior ballistic charge design with genetic algorithms and some other direct optimization methods, which has complex evolution operators such as crossover and mutation or has poor perferance in solution accuracy and speed, a modified particle swarm optimizer is proposed which is based on a geometrical way and a fuzzy multi-objective optimization. The modified particle swarm optimizer is used to both single-objective and multi-objective optimization problems of interior ballistic charge design for a guided projectile. The solution results show that the modified particle swarm optimizer has a better convergence rate and accuracy than the original particle swarm optimizer and other ever used optimization methods. Combined with deterred propellant technique, the interior ballistic charge design for a guided projectile is optimized by the modified particle swarm optimizer. The optimization results improve the interior ballistic performance and launch safety and provide theoretical direction for the interior ballistic charge design of guided projectile.     

Common model analysis and improvement of particle swarm optimizer

Particle swarm optimizer （PSO）, a new evolutionary computation algorithm, exhibits good performance for optimization problems, although PSO can not guarantee convergence of a global minimum, even a local minimum. However, there are some adjustable parameters and restrictive conditions which can affect performance of the algorithm. In this paper, the algorithm are analyzed as a time-varying dynamic system, and the sufficient conditions for asymptotic stability of acceleration factors, increment of acceleration factors and inertia weight are deduced. The value of the inertia weight is enhanced to （-1, 1）. Based on the deduced principle of acceleration factors, a new adaptive PSO algorithm- harmonious PSO （HPSO） is proposed. Furthermore it is proved that HPSO is a global search algorithm. In the experiments, HPSO are used to the model identification of a linear motor driving servo system. An Akaike information criteria based fitness function is designed and the algorithms can not only estimate the parameters, but also determine the order of the model simultaneously. The results demonstrate the effectiveness of HPSO.     

基于微粒群算法的非线性系统建模方法研究

针对非线性系统多模型自适应控制中的模型覆盖问题,提出一种基于微粒群算法的多模型建模方法.首先,对非线性系统定义了基于混合逻辑模型的多模型描述,建立了非线性系统的混合线性多模型;然后,基于微粒群优化算法对非线性系统进行优化建模,在保证建模准确性的同时采用最少的子模型逼近非线性系统;最后,通过一个仿真算例表明了该建模方法的有效性.     

A particle swarm optimizer with chaotic self-feedback for global optimization of multimodal functions

This paper proposes an improved particle swarm optimization （PSO） with iterative chaotic map with infinite collapses （ICMIC） perturbations （ICMICPSO） for global optimization of multimodal functions. The chaotic perturbation generated by the ICMIC is incorporated into the particle＇s velocity updating rule as self-feedback to make the particles have a larger potential space to fly. With the coefficient of chaotic perturbation decaying, the dynamics of ICMICPSO algorithm is a chaotic dynamics first and then a steepest descent dynamics. The proposed ICMICPSO method as hybrid optimization is tested on several widely used multimodal functions. Numerical results of the proposed algorithm are compared with that of some other Chaotic PSO variants available in the existing literature. The performance studies demonstrate that the effectiveness and efficiency of the proposed ICMICPSO approach are comparably to or better than that of the other CPSO variants for solving the global optimization of multimodal functions.     

PSO混合DE算法求解约束优化问题

提出了一个全新的混合算法并命名为微粒群差分算法,该算法在标准微粒群算法的基础上结合了差分进化算法用于求解约束的数值和工程优化问题。传统的标准微粒群算法由于其种群单一性容易陷入局部最优值,针对这一缺点利用差分进化算法中的变异、交叉、选择3个算子来更新每次迭代每个粒子新生产的位置以使粒子跳出局部优值。融合了标准微粒群算法和差分进化算法优点的混合算法加速了粒子的收敛速度。为了避免惩罚因子的选择对实验结果的影响,采取了可行规则法来处理约束优化问题。最后将微粒群差分算法用于5个基准函数和两个工程问题,并与其他算法作了比较,试验结果表明,微粒群差分算法算法具有很好的精准性、鲁棒性和有效性。