动态分阶段蚁群算法及其收敛性分析

为了提高蚁群算法的收敛速度和求解精度，根据仿生优化算法在不同阶段的特点，提出一种改进的蚁群算法．该算法对参数和选择策略进行了分阶段设计，而且参数的分阶段是根据寻优状态动态划分的．通过对蚁群系统马尔科夫过程进行分析，证明了该算法的全局收敛性．针对典型的TSP问题进行仿真对比实验，验证了该算法在速度和精度方面优于传统蚁群算法．     

蚁群算法的收敛性分析及其在TSP上的求解

根据基本蚁群算法的特点对其收敛性进行分析,给出寻找最短路径的蚁群算法收敛的充分条件.并把算法运用到旅行商问题上,试验结果表明该算法在求解TSP问题上解的精度优于组合优化算法以及遗传算法且收敛速度比较快.     

模糊相关机会规划的蚁群优化算法及收敛性分析

模糊相关机会规划(Fuzzy dependent-chance programming, FDCP)因其非线性、非凸性及模糊性,对经典的优化理论提出了极大的挑战. 本文为解决复杂的模糊相关机会规划问题设计了一种基于模糊模拟的蚁群优化算法, 证明了该算法的收敛性,并通过估算期望收敛时间以分析蚁群优化算法的收敛速度. 数值案例研究验证了该算法的有效性、稳定性及准确性.     

一类自适应蚁群算法及其收敛性分析

为了克服蚁群算法易陷入局部最小点的缺点,同时提高算法的收敛速度,提出一类自适应蚁群算法.该算法利用自适应改变信息激素的挥发系数改善传统蚁群算法的全局搜索能力和收敛速度.通过马尔科夫过程对算法的全局收敛性进行分析,得出该类蚁群算法全局收敛性条件.并构造出该类算法的一种信息激素更新策略,证明了这种算法全局收敛性.利用提出的算法对典型的TSP问题进行仿真研究,结果表明比典型蚁群算法在收敛速度和解的性能上都有较大改善.     

基于粗粒度模型的蚁群优化并行算法

为了改进蚁群优化算法的收敛速度,研究了一种基于粗粒度模型的并行蚁群优化算法,该算法将搜索任务划分给q个子群,由这些子群并行地完成搜索,可使搜索速度大幅度提高。实验结果表明,用该算法求解TSP问题,收敛速度比最新的改进算法快百倍以上。     

蚁群算法及其在路由优化中的应用综述

蚁群算法(ACO)是一类新型的机器学习技术,根据蚁群算法的正反馈原理和启发式原理的特点,针对目前国内国际的研究情况,对蚁群算法在最优路径的搜寻上从收敛性,收敛算法的改进以及收敛速度等方面的研究分别进行了分析综述,并对蚁群算法的一些应用,如:LEO卫星网络和无线传感等方面进行了阐述.对蚁群算法在路由优化和负载平衡上的研究进行了对比分析,发现了它们存在的不足,指出了在该领域需要进一步研究的热点问题.     

一种混沌蚁群优化的多约束QoS算法*

蚁群算法提高算法了精度,但易陷入局部寻优过程,本文利用混沌算法随机性、规律性和遍历性来优化蚁群算法,充分考虑两种算法的优点,并将其结合求解最短QoS路由问题,提高了蚁群算法的搜索范围,仿真实验表明,该算法避免了系统的早熟收敛,并具有较好的稳定性和收敛性。     

改进的模糊C-均值算法在医学图像分割中的应用

针对随机选取聚类中心易使得迭代过程陷入局部最优解的缺点,提出了一种混合优化蚁群和动态模糊C-均值的图像分割方法,该方法利用蚁群算法较强处理局部极值的能力,并能动态确定聚类中心和数目.针对传统的分阶段结合遗传算法和蚁群算法的策略存在收敛速度慢,聚类精度差的问题,提出在整个优化过程综合遗传算法和蚁群算法,并在蚁群算法中引入拥挤度函数,利用遗传算法的快速性、全局收敛性提高了蚁群算法的收敛速度,同时利用蚁群算法的并行性和正反馈性提高了聚类的精确度.最后将该算法应用到医学图像分割,对比实验表明,混合算法具有很强的模糊边缘和微细边缘分割能力.     

基于蚁群算法的多维0-1背包问题的研究

系统地阐述了蚁群算法,并对它进行改进、优化。将蚁群算法应用于求解多维0-1背包问题,提出一种求解多维0-1背包问题的算法——多维0-1背包问题蚁群算法。它大大减少了蚁群算法的搜索时间,有效改善了蚁群算法易于过早地收敛于非最优解的缺陷。仿真实验取得了较好的结果。     

基于感知模糊自适应蚁群算法的非线性PID控制

随着系统复杂度的提高和对象不确定性因素的增加,为克服线性PID动态性能和稳态性能差的缺陷,分析了非线性PID控制器各控制参数对误差的理想变化过程,构造非线性PID控制器。由于增益参数大量增加,传统参数优化方法不再适用,在分析蚁群算法的基础上,提出了基于感知自适应蚁群算法,并加入模糊自适应信息素更新机制,用于优化非线性PID控制器的设计方法。通过仿真实验将该控制器与基于蚁群算法的非线性PID控制器和基于蚁群算法、Z-N法的PID控制器进行对比,并对控制性能和收敛性能进行了分析,结果表明该算法有效克服了传统蚁群算法收敛速度较慢、容易陷入局部最优而停滞的缺陷,该控制器具有更好的动态性能和稳态性能。     

An optimal discrimination of two mixed qubit states with a fixed rate of inconclusive results

In this paper we consider the optimal discrimination of two mixed qubit states for a measurement that allows a fixed rate of inconclusive results. Our strategy is to transform the problem of two qubit states into a minimum error discrimination for three qubit states by adding a specific quantum state \(\rho _{0}\) and a prior probability \(q_{0}\), which behaves as an inconclusive degree. First, we introduce the beginning and the end of practical interval of inconclusive result, \(q_{0}^{(0)}\) and \(q_{0}^{(1)}\), which are key ingredients in investigating our problem. Then we obtain the analytic form of them. Next, we show that our problem can be classified into two cases \(q_{0}=q_{0}^{(0)}\) (or \(q_{0}=q_{0}^{(1)}\)) and \(q_{0}^{(0)}<q_{0}<q_{0}^{(1)}\). In fact, by maximum confidences of two qubit states and non-diagonal element of \(\rho _{0}\), our problem is completely understood. We provide an analytic solution of our problem when \(q_{0}=q_{0}^{(0)}\) (or \(q_{0}=q_{0}^{(1)}\)). However, when \(q_{0}^{(0)}<q_{0}<q_{0}^{(1)}\), we rather supply the numerical method to find the solution, because of the complex relation between inconclusive degree and corresponding failure probability. Finally we confirm our results using previously known examples.     

Scheduling Equal-Length Jobs with Delivery times on Identical Processors

The problem of scheduling n jobs of equal duration p with release and delivery times on m identical processors with the objective to minimize the maximal job completion time is considered. An algorithm is proposed that has the time complexity O ( mn log n ) if the maximal job delivery time q max is bounded by some constant. This is better than the earlier known best bound of O ( mn 2 log( np / m )) for the version of the problem with non-restricted q max . The algorithm has the time complexity O(q_{\max }^2 n\log n\max \{ m,\;q_{\max } \} ) without the restriction on q max . As the presented computational experiments show, practical behavior of the algorithm remains good without restriction on q max , i.e., for arbitrarily long delivery times, the running time of the algorithm, in practice, does not depend on q max .     

0-1背包问题的预期效率和线性拟合求解

为了进一步优化0-1背包问题的解,就背包容量、物体个数、物体重量、物体价格和物体性价比之间的关系进行深入的分析研究,构建了一个基于数学理论的线性拟合模型,与预期效率相结合,给出了一个解决0-1背包问题的混合算法。给出了三组实验,测试ρ<0.7时的算例,当背包容量改变时,与萤火虫群算法相比,该算法提高了目标函数值的收敛速度,同时节省了存储空间;与单纯的预期效率算法相比,该算法能够求得最优解,而单纯的预期效率算法则不能。实验结果表明,预期效率和线性拟合混合算法具有合理性及准确性,该算法能够应用于解决实际的0-1背包问题。     

Convergence of fuzzy-pyramid algorithms

Pyramid linking is an important technique for segmenting images and has many applications in image processing and computer vision. The algorithm is closely related to the ISODATA clustering algorithm and shares some of its properties. This paper investigates this relationship and presents a proof of convergence for the pyramid linking algorithm. The convergence of the hard-pyramid linking algorithm has been shown in the past; however, there has been no proof of the convergence of fuzzy-pyramid linking algorithms. The proof of convergence is based on Zangwill's theorem, which describes the convergence of an iterative algorithm in terms of a descent function of the algorithm. We show the existence of such a descent function of the pyramid algorithm and, further, show that all the conditions of Zangwill's theorem are met; hence the algorithm converges.This research was supported by the U.S. Army Research Office under contract DAAL 03-91-G0050.     

人工蜂群算法的收敛性分析

利用随机过程理论,对人工蜂群算法收敛性进行理论分析,给出人工蜂群算法的一些数学定义和蜜源位置的一步转移概率,建立人工蜂群算法的Markov链模型,分析此Markov链的一些性质,论证了人工蜂群状态序列是有限齐次Markov链,且状态空间是不可约的。结合随机搜索算法的全局收敛准则,证明了人工蜂群算法能够满足随机搜索算法全局收敛的两个假设,保证算法的全局收敛。     

Convergence of a New Evolutionary Computing Algorithm in Continuous State Space

A Markov chain on a new evolutionary computing algorithm is analyzed in continuous state space. By establishing transition probability density, the convergence of the similartaxis operator is proved. Meanwhile, the local property of the similartaxis operator is shown. To avoid its prematurity, a dissimilation operator need to be introduced. With the concept of P-absorbing field and P-optimal state, the convergence of the dissimilation operator is proved. We apply this new algorithm to a difficult problem for the accurate mixture ratio of raw materials of cement processing and make a comparison between GAs and the new algorithm. Finally, the functions of similartaxis and dissimilation operators are analyzed in a practical view.     

Mean-square error and stability analysis of a subband structure for the rapid identification of sparse impulse responses

In a context of supervised adaptive filtering, the sparsity of the impulse response to be identified can be employed to accelerate the convergence rate of the algorithm. This idea was first explored by the so-called proportionate NLMS (PNLMS) algorithm, where the adaptation step-sizes are made larger for the coefficients with larger magnitudes. Whereas fast initial adaptation convergence rate is obtained with the PNLMS algorithm for white-noise input, slow convergence is observed for colored input signals. The combination of the PNLMS approach and a subband structure results in an algorithm with better convergence rate for sparse systems and colored input signals. In this paper, the steady-state mean-square error (MSE) and the maximum value of the step-size β that allows convergence of the subband PNLMS-type algorithm are analyzed. Theoretical results are confirmed by simulations.     

思维进化算法的转移概率分析及几乎处处收敛性证明

思维进化算法已有的收敛性分析均是在依概率收敛意义下考虑的,而几乎处处收敛强于依概率收敛。在详细分析思维进化算法趋同算子和异化算子转移概率的基础上,利用种群最大适应度值函数描述思维进化算法的演化过程,将最大适应度值函数的进化过程转化为下鞅数列,并根据数学期望的性质和最大适应度值函数的特点,利用下鞅收敛定理严格证明了思维进化算法的几乎处处收敛性。     

多变量系统的耦合梯度辨识算法与性能分析

针对多变量系统维数大、参数多、一般的辨识算法计算量大的问题, 基于耦合辨识概念, 推导多变量系统的耦合随机梯度算法, 利用鞅收敛定理分析算法的收敛性能. 算法的主要思想是将系统模型分解为多个单输出子系统,在子系统的递推辨识过程中, 将每个子系统的参数估计值耦合起来. 所提出算法与最小二乘算法和耦合最小二乘算法相比, 具有较少的计算量, 收敛速度可以通过引入遗忘因子得到改善. 性能分析表明了所提出算法收敛, 仿真实例验证了算法的有效性.

     

The convergence analysis and specification of the Population-Based Incremental Learning algorithm

In this paper, we investigate the global convergence properties in probability of the Population-Based Incremental Learning (PBIL) algorithm when the initial configuration p⁽⁰⁾ is fixed and the learning rate α is close to zero. The convergence in probability of PBIL is confirmed by the experimental results. This paper presents a meaningful discussion on how to establish a unified convergence theory of PBIL that is not affected by the population and the selected individuals.