QoS multicast routing using a quantum-behaved particle swarm optimization algorithm

QoS multicast routing in networks is a very important research issue in networks and distributed systems. It is also a challenging and hard problem for high-performance networks of the next generation. Due to its NP-completeness, many heuristic methods have been employed to solve the problem. This paper proposes the modified quantum-behaved particle swarm optimization (QPSO) method for QoS multicast routing. In the proposed method, QoS multicast routing is converted into an integer programming problem with QoS constraints and is solved by the QPSO algorithm combined with loop deletion operation. The QPSO-based routing method, along with the routing algorithms based on particle swarm optimization (PSO) and genetic algorithm (GA), is tested on randomly generated network topologies for the purpose of performance evaluation. The simulation results show the efficiency of the proposed method on QoS the routing problem and its superiority to the methods based on PSO and GA.     

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 hybrid Improved Quantum-behaved Particle Swarm Optimization–Simplex method (IQPSOS) to solve power system load flow problems

This study proposes a new approach, based on a hybrid algorithm combining of Improved Quantum-behaved Particle Swarm Optimization (IQPSO) and simplex algorithms. The Quantum-behaved Particle Swarm Optimization (QPSO) algorithm is the main optimizer of algorithm, which can give a good direction to the optimal global region and Nelder Mead Simplex method (NM) which is used as a local search to fine tune the obtained solution from QPSO. The proposed improved hybrid QPSO algorithm is tested on several benchmark functions and performed better than particle swarm optimization (PSO), QPSO and weighted QPSO (WQPSO). To assess the effectiveness and feasibility of the proposed method on real problems, it is used for solving the power system load flow problems and demonstrated by different standard and ill-conditioned test systems including IEEE 14, 30 and 57 buses test systems, and compared with the conventional Newton–Raphson (NR) method, PSO and some versions of QPSO algorithms. Furthermore, the proposed hybrid algorithm is proposed for solving load flow problems with considering the reactive limits at generation buses. Simulation results prove the robustness and better convergence of IQPSOS under normal and critical conditions, when conventional load flow methods fail.     

量子粒子群算法在电力系统经济调度中的应用

量子粒子群算法以粒子群算法为基础,加入了量子波动理论,具有较好的全局收敛性.通过对电力系统经济调度问题中高维数、非线性、多约束等特点进行分析,运用具有量子行为的粒子群优化算法来解决电力系统经济调度问题,经过多组算例的测试:在满足电力系统各种约束的前提下,证明了新方法有效可行,能取得较好的收敛结果和鲁棒性.     

QPSO算法在训练支持向量机中的应用

训练支持向量机的本质问题就是求解二次规划问题，但对大规模的训练样本来说，求解二次规划问题困难很大。遗传算法和粒子群算法等智能搜索技术可以在较少的时间开销内给出问题的近似解。量子粒子群优化（QPSO）算法是在经典的微粒群算法的基础上所提出的一种有较高收敛性和稳定性的进化算法。将操作简单而收敛快速的QPSO算法运用于训练支持向量机，优化求解二次规划问题，为解决大规模的二次规划问题开辟了一条新的途径。     

基于QPSO算法的单阶段投资组合优化

投资组合优化问题是NP难解问题,通常的方法很难较好地接近全局最优.在经典微粒群算法(PSO)的基础上,研究了基于量子行为的微粒群算法(QPSO)的单阶段投资组合优化方法,具体介绍了依据目标函数如何利用QPSO算法去寻找最优投资组合.在具体应用中,为了提高算法的收敛性和稳定性对算法进行了改进.利用真实历史数据进行验证,结果表明在解决单阶段投资组合优化问题时,基于QPSO算法的投资组合优化的性能比PSO算法更加优越,且QPSO算法在投资组合优化领域具有很大的实际应用价值.     

An improved cooperative quantum-behaved particle swarm optimization

Particle swarm optimization (PSO) is a population-based stochastic optimization. Its parameters are easy to control, and it operates easily. But, the particle swarm optimization is a local convergence algorithm. Quantum-behaved particle swarm optimization (QPSO) overcomes this shortcoming, and outperforms original PSO. Based on classical QPSO, cooperative quantum-behaved particle swarm optimization (CQPSO) is present. This CQPSO, a particle firstly obtaining several individuals using Monte Carlo method and these individuals cooperate between them. In the experiments, five benchmark functions and six composition functions are used to test the performance of CQPSO. The results show that CQPSO performs much better than the other improved QPSO in terms of the quality of solution and computational cost.     

量子粒子群优化算法在训练支持向量机中的应用

训练支持向量机的本质问题就是求解二次规划问题，但对大规模的训练样本来说，求解二次规划问题困难很大。遗传算法和粒子群算法等智能搜索技术可以在较少的时间开销内给出问题的近似解。量子粒子群优化（QPSO）算法是在经典的微粒群算法的基础上所提出的一种有较高收敛性和稳定性的进化算法。将操作简单而收敛快速的QPSO算法运用于训练支持向量机，优化求解二次规划问题．为解决大规模的二次规划问题开辟了一条新的途径。     

Image vector quantization algorithm via honey bee mating optimization

The vector quantization (VQ) was a powerful technique in the applications of digital image compression. The traditionally widely used method such as the Linde–Buzo–Gray (LBG) algorithm always generated local optimal codebook. Recently, particle swarm optimization (PSO) is adapted to obtain the near-global optimal codebook of vector quantization. An alternative method, called the quantum particle swarm optimization (QPSO) had been developed to improve the results of original PSO algorithm. In this paper, we applied a new swarm algorithm, honey bee mating optimization, to construct the codebook of vector quantization. The results were compared with the other three methods that are LBG, PSO–LBG and QPSO–LBG algorithms. Experimental results showed that the proposed HBMO–LBG algorithm is more reliable and the reconstructed images get higher quality than those generated from the other three methods.     

一种采用完全学习策略的量子行为粒子群优化算法

为了进一步提高量子行为粒子群优化（QPSO）算法的全局收敛性能,有效改善算法中存在的粒子早熟问题提出一种基于完全学习策略的改进QPSO算法（CLQPSO）.该学习策略改变了QPSO中局部吸引子的更新方式,充分利用了种群的社会信息.采用8个测试函数对算法性能进行比较分析.实验结果表明,所提出的改进算法不仅收敛速度快,而且全局收敛能力好,收敛精度优于PSO算法和QPSO算法.     

Training algorithm for radial basis function neural network based on quantum-behaved particle swarm optimization

Radial basis function (RBF) networks are widely applied in function approximation, system identification, chaotic time series forecasting, etc. To use a RBF network, a training algorithm is absolutely necessary for determining the network parameters. The existing training algorithms, such as orthogonal least squares (OLS) algorithm, clustering and gradient descent algorithm, have their own shortcomings respectively. In this paper, we propose a training algorithm based on a novel population-based evolutionary technique, quantum-behaved particle swarm optimization (QPSO), to train RBF neural network. The proposed QPSO-trained RBF network was tested on non-linear system identification problem and chaotic time series forecasting problem, and the results show that it can identify the system and forecast the chaotic time series more quickly and precisely than that trained by the particle swarm algorithm.     

Quantum-behaved particle swarm optimization: analysis of individual particle behavior and parameter selection

Quantum-behaved particle swarm optimization (QPSO), motivated by concepts from quantum mechanics and particle swarm optimization (PSO), is a probabilistic optimization algorithm belonging to the bare-bones PSO family. Although it has been shown to perform well in finding the optimal solutions for many optimization problems, there has so far been little analysis on how it works in detail. This paper presents a comprehensive analysis of the QPSO algorithm. In the theoretical analysis, we analyze the behavior of a single particle in QPSO in terms of probability measure. Since the particle's behavior is influenced by the contraction-expansion (CE) coefficient, which is the most important parameter of the algorithm, the goal of the theoretical analysis is to find out the upper bound of the CE coefficient, within which the value of the CE coefficient selected can guarantee the convergence or boundedness of the particle's position. In the experimental analysis, the theoretical results are first validated by stochastic simulations for the particle's behavior. Then, based on the derived upper bound of the CE coefficient, we perform empirical studies on a suite of well-known benchmark functions to show how to control and select the value of the CE coefficient, in order to obtain generally good algorithmic performance in real world applications. Finally, a further performance comparison between QPSO and other variants of PSO on the benchmarks is made to show the efficiency of the QPSO algorithm with the proposed parameter control and selection methods.     

基于全局层次的自适应QPSO算法

阐明了具有量子行为的粒子群优化算法理论（QPSO）,并提出了一种基于全局领域的参数控制方法。在QPSO中引入多样性控制模型,使PSO系统成为一个开放式的进化粒子群,从而提出了自适应具有量子行为的粒子群优化算法（AQPSO）。最后,用若干个标准函数进行测试,比较了AQPSO算法与标准PSO（SPSO）和传统QPSO算法的性能。实验结果表明,AQPSO算法具有强的全局搜索能力,其性能优于其它两个算法,尤其体现在解决高维的优化问题。     

基于高斯扰动的量子粒子群优化算法

针对量子粒子群优化（QPSO）算法在优化过程中面临早熟问题,提出了在粒子的平均位置或全局最优位置上加入高斯扰动的QPSO算法,可以有效地阻止粒子的停滞,因此较容易地使粒子避免陷入局部最优。为了评估算法的性能,利用标准测试函数对标准PSO算法、QPSO算法以及基于高斯扰动的QPSO算法进行了比较测试。其结果表明,该算法具有较强的全局搜索能力和较快的收敛速度。     

QPSO算法与PSO算法求解二维热传导反问题

热传导反问题在国内研究起步较晚,研究方法有很多,但通常方法很难较好地接近全局最优.在介绍经典的微粒群优化算法(PSO)的基础上,研究基于量子行为的微粒群优化算法(QPSO)的二维热传导参数优化方法,具体介绍依据目标函数如何利用上述的算法去寻找最优参数组合.为了提高算法的收敛性和稳定性,在具体应用中对算法进行了改进,并进行了大量实验,结果显示在解决热传导反问题优化问题中,基于QPSO算法的性能比经典PSO算法更加优越,证明QPSO在热传导领域具有很大的实际应用价值.     

基于量子粒子群算法的复杂函数参数估计

数理统计中在处理回归的问题时,常用的传统参数估计方法存在着一些严重不足之处.为解决此问题,提出了将基于量子行为的微粒群优化(QPSO)算法应用于复杂函数的参数估计中.通过仿真实验,表明了该算法不仅可以准确地估计出复杂函数的参数,并且具有计算简便、收敛速度快等特点.通过与传统微粒群(PSO)算法的比较,证明了QPSO算法的优越性.     

Integration of Artificial Immune System and K-Means Algorithm for Customer Clustering

This study proposes a novel artificial immune system (AIS)-based clustering algorithm, which integrates with a K-means (AISK) algorithm for a customer clustering problem. Computational results using Iris, Glass, Wine, and Breast Cancer benchmark datasets indicate that the proposed AIS-based clustering algorithm is more accurate than some particle swarm optimization (PSO)-based clustering algorithms. In addition, the model evaluation results using a daily transaction database provided by a cyberstore also show that the proposed AISK algorithm is superior to PSO-based clustering algorithms.     

Leaf constrained minimal spanning trees solved by modified quantum-behaved particle swarm optimization

Given an undirected, connected, weighted graph, the leaf-constrained minimum spanning tree (LCMST) problem seeks a spanning tree of minimum weight among all the spanning trees of the graph with at least l leaves. In this paper, we have proposed an approach based on Quantum-Behaved Particle Swarm Optimization (QPSO) for the LCMST problem. Particle swarm optimization (PSO) is a well-known population-based swarm intelligence algorithm. Quantum-behaved particle swarm optimization (QPSO) is also proposed by combining the classical PSO philosophy and quantum mechanics to improve performance of PSO. In this paper QPSO has been modified by adding a leaping behavior. When the modified QPSO (MQPSO), falls in to the local optimum, MPSO runs a leaping behavior to leap out the local optimum. We have compared the performance of the proposed method with ML, SCGA, ACO-LCMST, TS-LCMST and ABC-LCMST, which are reported in the literature. Computational results demonstrate the superiority of the MQPSO approach over all the other approaches. The MQPSO approach obtained better quality solutions in shorter time.     

具有适应性突变和惯性权重的粒子群优化(PSO)算法及其在动态系统参数估计中的应用

An important problem in engineering is the unknown parameters estimation in nonlinear systems. In this paper, a novel adaptive particle swarm optimization (APSO) method is proposed to solve this problem. This work considers two new aspects, namely an adaptive mutation mechanism and a dynamic inertia weight into the conventional particle swarm optimization (PSO) method. These mechanisms are employed to enhance global search ability and to increase accuracy. First, three well-known benchmark functions namely Griewank, Rosenbrock and Rastrigrin are utilized to test the ability of a search algorithm for identifying the global optimum. The performance of the proposed APSO is compared with advanced algorithms such as a nonlinearly decreasing weight PSO (NDWPSO) and a real-coded genetic algorithm (GA), in terms of parameter accuracy and convergence speed. It is confirmed that the proposed APSO is more successful than other aforementioned algorithms. Finally, the feasibility of this algorithm is demonstrated through estimating the parameters of two kinds of highly nonlinear systems as the case studies.     

QPSO算法优化的非线性观测器设计方法研究

具有量子行为的粒子群优化算法(Quantum-behavedParticleSwarmOptimization,简称QPSO)是继粒子群优化算法(ParticleSwarmOptimization,简称PSO)后,最新提出的一种新型、高效的进化算法。论文在研究基于PSO算法的非线性观测器基础上,提出了一种基于QPSO算法的非线性观测设计方法。以vanderPol系统为例进行了仿真实验,其基本思想是将非线性连续时间系统的状态估计问题转换为非线性函数的在线优化问题,然后利用PSO或QPSO算法获得系统状态的最优估计。仿真结果显示了基于QPSO算法的非观测器比基于PSO算法的非线性观测器的性能更优越。