基于混沌粒子群优化算法的灰色GM(1,1)模型在地下水埋深预测中的应用

将混沌优化算法与粒子群优化算法相结合,形成新的混沌粒子群优化算法.利用混沌运动的遍历性,避免陷入局部最优.同时,粒子群算法能加快混沌优化算法的收敛速度,使搜索效率得到提高.用混沌粒子群优化算法优化灰色GM(1,1)模型中的参数,通过横向和纵向比较,优化效果良好,模型预测精度得到了提高.运用该模型对三江平原地下水埋深进行动态预测,预测结果可为有关决策部门提供参考.     

求解旅行商问题的一种改进粒子群算法

本文研究了求解旅行商问题的粒子群算法。针对标准粒子群算法在求解旅行商问题过程中容易出现早熟和停滞现象的缺点,提出了一种改进的粒子群算法。首先,在初始种群的选取过程中,利用改进的贪婪策略直接获得具有较高性能的初始种群以提高算法的搜索效率。其次,通过引入次优吸引子,使粒子在搜索过程中可以更加充分地利用群体的信息来提高自身的性能,有效抑制收敛过程中的停滞现象,提高算法的搜索能力。最后为了验证所提出的方法的有效性和可行性,对TSPLIB标准库中的多个实例进行了测试,并给出了数值结果。     

A multi-start opposition-based particle swarm optimization algorithm with adaptive velocity for bound constrained global optimization

In this paper we present a multi-start particle swarm optimization algorithm for the global optimization of a function subject to bound constraints. The procedure consists of three main steps. In the initialization phase, an opposition learning strategy is performed to improve the search efficiency. Then a variant of the adaptive velocity based on the differential operator enhances the optimization ability of the particles. Finally, a re-initialization strategy based on two diversity measures for the swarm is act in order to avoid premature convergence and stagnation. The strategy uses the super-opposition paradigm to re-initialize particles in the swarm. The algorithm has been evaluated on a set of 100 global optimization test problems. Comparisons with other global optimization methods show the robustness and effectiveness of the proposed algorithm.     

DSLC-FOA : Improved fruit fly optimization algorithm for application to structural engineering design optimization problems

In this study, we propose an improved fruit fly optimization algorithm (FOA) based on linear diminishing step and logistic chaos mapping (named DSLC-FOA) for solving benchmark function unconstrained optimization problems and constrained structural engineering design optimization problems. Based on comparisons with genetic algorithm, particle swarm optimization, FOA, LGMS -FOA, and chaotic FOA methods, we demonstrated that DSLC-FOA performed better at searching for the optimal solutions of four typical benchmark functions. The approximate optimal results were obtained using DSLC-FOA for three structural engineering design optimization problems as examples of applications. The numerical results demonstrated that the proposed DSLC-FOA algorithm is superior to the basic FOA and other metaheuristic or deterministic methods.     

超越方程的优化解法

针对粒子群算法局部搜索能力差,后期收敛速度慢等缺点,提出了一种改进的粒子群算法,该算法是在粒子群算法后期加入拟牛顿方法,充分发挥了粒子群算法的全局搜索性和拟牛顿法的局部精细搜索性,从而克服了粒子群算法的不足,把超越方程转化为函数优化的问题,利用该算法求解,数值实验结果表明,算法有较高的收敛速度和求解精度。     

PID control for chaotic synchronization using particle swarm optimization

In this paper, we attempt to use the proportional-integral-derivative (PID) controller to achieve the chaos synchronization for delayed discrete chaotic systems. Three PID control gains can be optimally determined by means of using a novel optimization algorithm, called the particle swarm optimization (PSO). The algorithm is motivated from the organism behavior of fish schooling and bird flocking, and involves the social psychology principles in socio-cognition human agents and evolutionary computations. It has a good numerical convergence for solving optimization problem. To show the validity of the PSO-based PID control for chaos synchronization, several cases with different initial populations are considered and some simulation results are shown.     

基于PSO-AFSA混合算法的模糊投资组合问题的研究

针对模糊不确定的证券市场,用可能性均值、下可能性方差和协方差分别替换了投资组合模型中概率均值、方差和协方差,构建了双目标均值-方差投资组合模型。然后采用线性加权法将双目标模型转化为单目标模型,进而提出了一个PSO-AFSA混合算法对其求解。该混合算法中,将粒子群算法搜索的结果作为人工鱼群算法初始鱼群,进一步搜索,这样能有效的避免粒子群算法陷入局部最优。同时,将人工鱼群中的最好位置反馈到粒子群算法的速度更新公式中,指引粒子运动,加快算法收敛。最后,进行实例分析,结果表明:PSO-AFSA混合算法是有效的,混合算法搜索到的全局最优值好于基本粒子群算法搜索到的全局最优值。     

Dynamic guiding particle swarm optimization with embedded chaotic search for solving multidimensional problems

The proposed approach incorporated dynamic guiding approach and chaotic search procedure into particle swarm optimization (PSO), named DCPSO. Chaotic search, enjoyed ergodicity, irregularity and pseudo-randomness in PSO, would refine global best position evidently. And, dynamic guiding approach with fluctuating property would easily conduct unpredictable migrations for PSO to break away from evolutionary stagnation. The experiment reports indicated that the proposed DCPSO approach could improve the evolution performance significantly, and present the superiority in solving complex multidimensional problems.     

免疫逃避型粒子群优化算法

针对基本粒子群优化算法容易陷入局部极值的缺陷,提出了一种免疫逃避型粒子群优化算法.其基本思想是将初始粒子群划分为寄生与宿主两个种群以模拟生物寄生行为,对寄生种群的粒子采用精英学习策略,对宿主群的粒子采用探索策略,再引入免疫系统的高频变异对寄生群采用相应的免疫逃避机制,以增强群体逃离局部极值、提高算法的全局寻优能力.采用标准测试函数的实验结果表明,该算法在收敛速度和求解精度方面均有显著改进.     

混合变异粒子群优化算法及其应用

为改善粒子群优化算法在解决复杂优化问题时收敛质量不高的不足,提出了一种改进的粒子群优化算法,即混合变异粒子群优化算法(HMPSO).HMPSO算法采用了带有随机因子的惯性权重取值更新策略,降低了标准粒子群优化算法中由于粒子飞行速度过大而错过最优解的概率,从而加速了算法的收敛速度.此外,通过混合变异进化环节的引入,缓解了粒子种群在进化过程中的多样性与收敛性这一矛盾,使得算法的全局探索与局部开发得到有效平衡.利用经典的基准测试函数和平面冗余机械臂逆运动学问题的求解来验证提出算法的有效性,试验结果表明:与其他算法相比,HMPSO算法具有更快的收敛速度、更高的收敛精度、更强的收敛稳定性以及更低的计算成本.     

Balanced fuzzy particle swarm optimization

In the present study an extension of particle swarm optimization (PSO) algorithm which is in conformity with actual nature is introduced for solving combinatorial optimization problems. Development of this algorithm is essentially based on balanced fuzzy sets theory. The classical fuzzy sets theory cannot distinguish differences between positive and negative information of membership functions, while in the new method both kinds of information “positive and negative” about membership function are equally important. The balanced fuzzy particle swarm optimization algorithm is used for fundamental optimization problem entitled traveling salesman problem (TSP). For convergence inspecting of new algorithm, method was used for TSP problems. Convergence curves were represented fast convergence in restricted and low iterations for balanced fuzzy particle swarm optimization algorithm (BF-PSO) comparison with fuzzy particle swarm optimization algorithm (F-PSO).     

一种改进粒子群优化算法及其在投资规划中的应用

粒子群优化算法(PSO)是模拟生物群体智能的优化算法,具有良好的优化性能.但是群体收缩过快和群体多样性降低导致早熟收敛.本文引入了多样性指标和收敛因子模型来改进PSO算法,形成多样性收敛因子PSO算法(DCPSO),并且对现代资产投资的多目标规划问题进行了优化,简化了多目标规划的问题,并且表现出了比传统PSO算法更好性能.     

Inspired grey wolf optimizer for solving large-scale function optimization problems

Grey wolf optimizer algorithm was recently presented as a new heuristic search algorithm with satisfactory results in real-valued and binary encoded optimization problems that are categorized in swarm intelligence optimization techniques. This algorithm is more effective than some conventional population-based algorithms, such as particle swarm optimization, differential evolution and gravitational search algorithm. Some grey wolf optimizer variants were developed by researchers to improve the performance of the basic grey wolf optimizer algorithm. Inspired by particle swarm optimization algorithm, this study investigates the performance of a new algorithm called Inspired grey wolf optimizer which extends the original grey wolf optimizer by adding two features, namely, a nonlinear adjustment strategy of the control parameter, and a modified position-updating equation based on the personal historical best position and the global best position. Experiments are performed on four classical high-dimensional benchmark functions, four test functions proposed in the IEEE Congress on Evolutionary Computation 2005 special session, three well-known engineering design problems, and one real-world problem. The results show that the proposed algorithm can find more accurate solutions and has higher convergence rate and less number of fitness function evaluations than the other compared techniques.     

An improved particle swarm optimizer for parametric optimization of flexible satellite controller

Parametric optimization of flexible satellite controller is an essential for almost all modern satellites. Particle swarm algorithm is a global optimization algorithm but it suffers from two major shortcomings, that of, premature convergence and low searching accuracy. To solve these problems, this paper proposes an improved particle swarm optimization (IPSO) which substitute “poorly-fitted-particles” with a cross operation. Based on decision possibility, the cross operation can interchange local optima between three particles. Thereafter the swarm is split in two halves, and random number (s) get generated by crossing the dimension of particle from both halves. This produces a new swarm. Now the new swarm and old swarm are mixed, and based on relative fitness a half of the particles are selected for the next generation. As a result of the cross operation, IPSO can easily jump out of local optima, has improved searching accuracy and accelerates the convergence speed. Some test functions with different dimensions are used to analyze the performance of IPSO algorithm. Simulation results show that the IPSO has more advantages than standard PSO and Genetic Algorithm PSO (GAPSO). In that it has a more stable performance and lower level of complexity. Thus the IPSO is applied for parametric optimization of flexible satellite control, for a satellite having solar wings and antennae. Simulation results shows that the IPSO can effectively get the best controller parameters vis-a-vis the other optimization methods.     

Chaos-enhanced accelerated particle swarm optimization

There are more than two dozen variants of particle swarm optimization (PSO) algorithms in the literature. Recently, a new variant, called accelerated PSO (APSO), shows some extra advantages in convergence for global search. In the present study, we will introduce chaos into the APSO in order to further enhance its global search ability. Firstly, detailed studies are carried out on benchmark problems with twelve different chaotic maps to find out the most efficient one. Then the chaotic APSO (CAPSO) will be compared with some other chaotic PSO algorithms presented in the literature. The performance of the CAPSO algorithm is also validated using three engineering problems. The results show that the CAPSO with an appropriate chaotic map can clearly outperform standard APSO, with very good performance in comparison with other algorithms and in application to a complex problem.     

A dynamic global and local combined particle swarm optimization algorithm

Particle swarm optimization (PSO) algorithm has been developing rapidly and many results have been reported. PSO algorithm has shown some important advantages by providing high speed of convergence in specific problems, but it has a tendency to get stuck in a near optimal solution and one may find it difficult to improve solution accuracy by fine tuning. This paper presents a dynamic global and local combined particle swarm optimization (DGLCPSO) algorithm to improve the performance of original PSO, in which all particles dynamically share the best information of the local particle, global particle and group particles. It is tested with a set of eight benchmark functions with different dimensions and compared with original PSO. Experimental results indicate that the DGLCPSO algorithm improves the search performance on the benchmark functions significantly, and shows the effectiveness of the algorithm to solve optimization problems.     

The block diagram method for designing the particle swarm optimization algorithm

In this paper, the block diagram method of the dispersed control system is proposed for designing or improving the normal particle swarm optimization algorithms (PSO), that is, it uses the Jury-test of the control theory to compare the block diagrams getting from existing particle swarm optimization methods and finds out some defects of the existing particle swarm optimization methods, for example, the premature convergence of PSO algorithm, and so on. Thus a new particle swarm algorithm is also proposed for improving these defects, that is, the speed iteration and position iteration formulas of PSO are revised for both adjusting its convergence speed and jumping out of the local minimum points. To show effectiveness of the proposed method, the simulations of 13 benchmark examples are carried out, as a result, it indicates that the proposed method is very useful.     

Enhanced speciation in particle swarm optimization for multi-modal problems

In this paper, we present a novel multi-modal optimization algorithm for finding multiple local optima in objective function surfaces. We build from Species-based particle swarm optimization (SPSO) by using deterministic sampling to generate new particles during the optimization process, by implementing proximity-based speciation coupled with speciation of isolated particles, and by including “turbulence regions” around already found solutions to prevent unnecessary function evaluations. Instead of using error threshold values, the new algorithm uses the particle’s experience, geometric mean, and “exclusion factor” to detect local optima and stop the algorithm. The performance of each extension is assessed with leave-it-out tests, and the results are discussed. We use the new algorithm called Isolated-Speciation-based particle swarm optimization (ISPSO) and a benchmark algorithm called Niche particle swarm optimization (NichePSO) to solve a six-dimensional rainfall characterization problem for 192 rain gages across the United States. We show why it is important to find multiple local optima for solving this real-world complex problem by discussing its high multi-modality. Solutions found by both algorithms are compared, and we conclude that ISPSO is more reliable than NichePSO at finding optima with a significantly lower objective function value.     

A balanced whale optimization algorithm for constrained engineering design problems

In this study, two novel effective strategies composed of Lévy flight and chaotic local search are synchronously introduced into the whale optimization algorithm (WOA) to guide the swarm and further promote the harmony between the inclusive exploratory and neighborhood-informed capacities of the conventional technique and investigate the core searching capabilities of WOA in dealing with optimization tasks. However, the conventional WOA may simply be stuck at local optima or the global best may not be obtained successfully when tackling more complex optimization landscapes, including the multimodal and high dimensional scenarios. To substantiate the efficacy of the enhanced method, it is compared to a set of well-regarded variants of particle swarm optimization and differential evolution. The used benchmark problems are composed of unimodal, multimodal, and fixed-dimensions multimodal functions. Additionally, the proposed balanced method is applied to realize three practical, well-known mathematical models such as tension/compression spring, welded beam, pressure vessel design, three-bar truss design, and I-beam design problems. The experimental results and analysis reveal that the proposed algorithm can outperform other competitors in terms of the convergence speed and the quality of solutions. Promisingly, the proposed method can be treated as an effective and efficient auxiliary tool for more complex optimization models and scenarios.     

Chaotic catfish particle swarm optimization for solving global numerical optimization problems

Chaotic catfish particle swarm optimization (C-CatfishPSO) is a novel optimization algorithm proposed in this paper. C-CatfishPSO introduces chaotic maps into catfish particle swarm optimization (CatfishPSO), which increase the search capability of CatfishPSO via the chaos approach. Simple CatfishPSO relies on the incorporation of catfish particles into particle swarm optimization (PSO). The introduced catfish particles improve the performance of PSO considerably. Unlike other ordinary particles, the catfish particles initialize a new search from extreme points of the search space when the gbest fitness value (global optimum at each iteration) has not changed for a certain number of consecutive iterations. This results in further opportunities of finding better solutions for the swarm by guiding the entire swarm to promising new regions of the search space and accelerating the search. The introduced chaotic maps strengthen the solution quality of PSO and CatfishPSO significantly. The resulting improved PSO and CatfishPSO are called chaotic PSO (C-PSO) and chaotic CatfishPSO (C-CatfishPSO), respectively. PSO, C-PSO, CatfishPSO, C-CatfishPSO, as well as other advanced PSO procedures from the literature were extensively compared on several benchmark test functions. Statistical analysis of the experimental results indicate that the performance of C-CatfishPSO is better than the performance of PSO, C-PSO, CatfishPSO and that C-CatfishPSO is also superior to advanced PSO methods from the literature.