Distributed learning particle swarm optimizer for global optimization of multimodal problems

Particle swarm optimizer (PSO) is an effective tool for solving many optimization problems. However, it may easily get trapped into local optimumwhen solving complex multimodal nonseparable problems. This paper presents a novel algorithm called distributed learning particle swarm optimizer (DLPSO) to solve multimodal nonseparable problems. The strategy for DLPSO is to extract good vector information from local vectors which are distributed around the search space and then to form a new vector which can jump out of local optima and will be optimized further. Experimental studies on a set of test functions show that DLPSO exhibits better performance in solving optimization problems with few interactions between variables than several other peer algorithms.     

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.     

一种求解复杂多峰问题的新型粒子群优化算法研究

为提升标准粒子群算法在求解多峰复杂问题时收敛速度慢和极易陷入局部最优解等缺点, 提出一种基于球形坐标的分类学习策略粒子群算法(CLPSO-HC)。该算法给出种群运行较差粒子的确定方法, 将运行较差的粒子进行分类, 并对每类粒子给出相应的学习策略, 保证种群跳出局部最优解的能力。为减少外界扰动, 将粒子速度和位置的更新在球形坐标中进行, 提升了种群向最优解飞行的概率。对三个典型测试函数进行仿真实验, 所得结果表明CLPSO-HC相比其他几种算法有较好的收敛性。因此, CLPSO-HC可以作为求解复杂多峰问题的有效算法。     

Cooperative particle swarm optimizer with depth first search strategy for global optimization of multimodal functions

This paper presents a Cooperative Particle Swarm Optimizer with Depth First Search Strategy (DFS-CPSO), which has better seacrch capality than classical Particle Swarm Optimizer (PSO) in solving multimodal optimization problems. In order to improve the quality of information exchange, the Depth First Search (DFS) strategy is hybridized to Cooperative Particle Swarm Optimization(CPSO), which makes information transfer more effectively and generates better quality solution. Specifically, DFS strategy enables different components of solution vector to exchange information separately with PSO and increases the diversity of the population, so that the information of solution components could be preserved by multiple iterations in CPSO. Confirmatory experiments are performed to prove the effectiveness of employing the DFS strategy to CPSO. The comparative results demonstrate superior performance of DFS-CPSO in solving high dimensional multimodal functions than CPSO and other advanced methods.

     

一种结合次梯度的粒子群全局优化算法

为优化不可微且非凸的连续目标函数,提出了结合次梯度的粒子群全局优化算法(SGPSO).在优化算法中,首次提出利用次梯度方向来更新粒子群算法中粒子的搜索速度方案.加上与粒子相互间的通信机制配合,改进方案提高了寻得全局最优的机率.进一步地,在次梯度迭代过程中,提出其中的步长函数需要满足关于次梯度幅值是低阶无穷小且关于迭代时刻是递减的充分条件保证序列稳定收敛.最后,针对标准库给出了SG-PSO的实验和比较以验证其有效性,结果表明提出的算法能很好地实现目标函数的全局优化,且收敛效果更好.     

一种有效的多峰函数优化算法

针对小生境粒子群优化技术中小生境半径等参数选取问题 ,提出了一种新颖的小生境方法 ,无须小生境半径等任何参数。通过监视粒子正切函数值的变化 ,判断各个粒子是否属于同一座山峰 ,使其追踪所在山峰的最优粒子飞行 ,进而搜索到每一座山峰极值。算法实现简单 ,不仅克服了小生境使用中需要参数的弊端 ,而且解决了粒子群算法只能找到一个解的不足。最后通过对多峰值函数的仿真实验 ,验证了算法可以准确地找到所有山峰。     

Adaptive fuzzy particle swarm optimization for global optimization of multimodal functions

This paper proposes an adaptive fuzzy PSO (AFPSO) algorithm, based on the standard particle swarm optimization (SPSO) algorithm. The proposed AFPSO utilizes fuzzy set theory to adjust PSO acceleration coefficients adaptively, and is thereby able to improve the accuracy and efficiency of searches. Incorporating this algorithm with quadratic interpolation and crossover operator further enhances the global searching capability to form a new variant, called AFPSO-QI. We compared the proposed AFPSO and its variant AFPSO-QI with SPSO, quadratic interpolation PSO (QIPSO), unified PSO (UPSO), fully informed particle swarm (FIPS), dynamic multi-swarm PSO (DMSPSO), and comprehensive learning PSO (CLPSO) across sixteen benchmark functions. The proposed algorithms performed well when applied to minimization problems for most of the multimodal functions considered.     

A self-learning particle swarm optimizer for global optimization problems

Particle swarm optimization (PSO) has been shown as an effective tool for solving global optimization problems. So far, most PSO algorithms use a single learning pattern for all particles, which means that all particles in a swarm use the same strategy. This monotonic learning pattern may cause the lack of intelligence for a particular particle, which makes it unable to deal with different complex situations. This paper presents a novel algorithm, called self-learning particle swarm optimizer (SLPSO), for global optimization problems. In SLPSO, each particle has a set of four strategies to cope with different situations in the search space. The cooperation of the four strategies is implemented by an adaptive learning framework at the individual level, which can enable a particle to choose the optimal strategy according to its own local fitness landscape. The experimental study on a set of 45 test functions and two real-world problems show that SLPSO has a superior performance in comparison with several other peer algorithms.     

解决约束优化问题的改进粒子群算法

针对约束优化问题的求解,提出一种改进的粒子群算法（CMPSO）。在CMPSO算法中,为了增加种群多样性,提升种群跳出局部最优解的能力,引入种群多样性阈值,当种群多样性低于给定阈值时,对全局最优粒子位置和粒子自身最优位置进行多项式变异;并根据粒子违背约束条件的程度,提出一种新的粒子间比较准则来比较粒子间的优劣,该准则可以保留一部分性能较优的不可行解;为提升种群向全局最优解飞行的概率,采取一种广义学习策略。对经典测试函数的仿真结果表明,所提出的算法是一种可行的约束优化问题的求解方法。     

求解多目标优化问题的自适应粒子群算法

提出了一种基于自适应惯性权重的多目标粒子群优化算法AWMOPSO,采用新的适应值分配机制,在搜索过程中根据粒子的适应值对粒子进行分类,动态调整粒子的惯性权重以控制粒子的开发和探索能力。用外部精英集保存非支配解,并通过拥挤距离维持解的多样性。引入精英迁移和局部扰动策略,提高收敛的速度和精度。典型的测试函数的计算结果表明了算法能够快速逼近Pareto最优前沿,是求解多目标优化问题的有效方法。     

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.     

用于多峰函数优化的改进小生境微粒群算法

针对小生境微粒群算法在处理复杂多峰函数优化问题中存在的一些缺陷,提出一种改进的小生境SNPSO算法。SNPSO算法将顺序小生境的思想引入其中,首先在主群体中应用Stretching技术,其次对子群体采用解散策略,即当在子群体中找到一个极值点后把子群体解散回归主群体,最后设置子群体创建时的半径阈值,避免子群体半径过大。该算法解决了标准的NichePSO算法在处理多峰函数时,极值点的个数依赖于子群体个数及极值点容易出现重复、遗漏等问题。对3个常用的基本测试函数的实验表明,新算法（SNPSO）在多峰函数寻优中解的稳定性、收敛性和覆盖率均优于标准NichePSO。     

一种快速多种群的粒子群多模优化算法

针对粒子群多模优化问题中存在的易早熟、收敛速度慢及寻优精度低等问题,提出了一种快速多种群的粒子群多模优化算法。首先采用动态半径及种群划分策略,避免了多种群区域重叠问题;然后引入拓扑机制,使种群内粒子在速度上保持同步,以群落为单位在解空间上飞行,加快进化速度;同时增加种群之间的交流,在多样性和快速收敛之间达到平衡;最后采用随机权重、异步变化因子及种群淘汰策略,提高算法的搜索能力和学习能力。通过几个典型测试函数的实验结果表明,该算法具有较好的多模态寻优率,在收敛速度和精度等方面均有提高。     

A new multi-function global particle swarm optimization

In this paper, we introduce the concept of population density in PSO, and accordingly, we discuss the relationship between the search capability of PSO and the population density. From related numerical experiments, we find that the search capability of PSO becomes saturated when the population density exceeds a certain value. Accordingly, we propose a strategy that divides the particles into two parts for different functions. Thus, we propose an approach called multi-function global particle swarm optimization (MFPSO) on the basis of this strategy. Further, we carry out a series of numerical experiments to verify that MFPSO has high global convergence capability, high convergence speed, and highly reliable performance when it is used to solve complex problems.     

变步长自适应萤火虫群多模态函数优化算法

针对萤火虫群优化（GSO）算法优化多模态函数存在收敛速度慢和求解精度不高等缺陷,提出一种变步长自适应萤火虫群优化算法（CSGSO）。该算法主要思想是在GSO算法中引入搜索成功与失败概念,在每次迭代中萤火虫个体据其搜索成功或失败,加大或减小其搜索步长,使算法具有动态自适应性。实验结果表明,该算法可有效地解决GSO算法优化多模态函数存在收敛速度慢和求解精度不高的问题,增强了GSO算法优化多模态函数的性能;与其他算法相比,提出的算法具有操作简单、容易理解、收敛速度快和求解精度高等优点。     

A tree-structured random walking swarm optimizer for multimodal optimization

This paper develops a novel tree structured random walking swarm optimizer for seeking multiple optima in multimodal landscapes. First, we show that the artificial bee colony algorithm has some distinct advantages over the other swarm intelligence algorithms for accomplishing the multimodal optimization task, from analytical and experimental perspectives. Then, a tree-structured niching strategy is developed to assist the algorithm in exploring multiple optima simultaneously. The strategy constructs a weighted complete graph based on the positions of the food sources (candidate solutions). A minimum spanning tree that encodes the distribution of the food sources is built upon the complete graph to guide the search of the bee swarm. Each artificial bee sets out from a food source and flies along the edges of the tree to gather information about the search space. The dance trajectories of bees are simulated by a random walk model considering both distance and fitness information. Then, mutant vectors are selected from the trajectories to update the food source. This graph-based search method is introduced to simultaneously promote the progress of exploitation and exploration in multimodal environments. Extensive experiments indicate that our proposed algorithm outperforms several state-of-the-art algorithms.     

一种小生境技术的微粒群优化器

提出了一种基于聚类的小生境技术,可以有效地解决多模态问题并获得多个最优解,并且有较快的收敛速度。认知模式微粒群优化器只利用了每个粒子的认知信息从而在局部区域进行搜索,每个粒子在局部区域寻优并趋向区域最优解,且存在收敛速度慢等问题。为此,提出了一种改进算法,可以让粒子迅速收敛到局部最优解附近。最终每个粒子经历过的最优位置形成了若干个簇．通过对其聚类获得每个簇中的粒子信息。此时问题已转化为多个簇的单模态问题,在各个簇中再利用保收敛微粒群优化器获得每个簇的最优解。最后给出了实验,证明了该方法在圆形拓扑环境中的有效性。     

A hierarchical particle swarm optimizer for noisy and dynamic environments

New Particle Swarm Optimization (PSO) methods for dynamic and noisy function optimization are studied in this paper. The new methods are based on the hierarchical PSO (H-PSO) and a new type of H-PSO algorithm, called Partitioned Hierarchical PSO (PH-PSO). PH-PSO maintains a hierarchy of particles that is partitioned into several sub-swarms for a limited number of generations after a change of the environment occurred. Different methods for determining the best time when to rejoin the sub-swarms and how to handle the topmost sub-swarm are discussed. A standard method for metaheuristics to cope with noise is to use function re-evaluations. To reduce the number of necessary re-evaluations a new method is proposed here which uses the hierarchy to find a subset of particles for which re-evaluations are particularly important. In addition, a new method to detect changes of the optimization function in the presence of noise is presented. It differs from conventional detection methods because it does not require additional function evaluations. Instead it relies on observations of changes that occur within the swarm hierarchy. The new algorithms are compared experimentally on different dynamic and noisy benchmark functions with a variant of standard PSO and H-PSO that are both provided with a change detection and response method.

A hybrid genetic algorithm and particle swarm optimization for multimodal functions

Heuristic optimization provides a robust and efficient approach for solving complex real-world problems. The focus of this research is on a hybrid method combining two heuristic optimization techniques, genetic algorithms (GA) and particle swarm optimization (PSO), for the global optimization of multimodal functions. Denoted as GA-PSO, this hybrid technique incorporates concepts from GA and PSO and creates individuals in a new generation not only by crossover and mutation operations as found in GA but also by mechanisms of PSO. The results of various experimental studies using a suite of 17 multimodal test functions taken from the literature have demonstrated the superiority of the hybrid GA-PSO approach over the other four search techniques in terms of solution quality and convergence rates.     

一种基于距离行为模型的改进微粒群算法

提出一种基于距离行为模型的改进微粒群算法,根据微粒所处区域来调整其飞行的速度。在吸引区域微粒加速飞向群体最优位置,在排斥区域按正常速度飞行。为了研究算法的性能,对几种典型高维非线性函数进行了测试。研究结果表明,与基本微粒群算法相比,改进后的微粒群算法提高了算法的收敛速度和收敛精度,改善了算法的性能。