记忆原理的元胞自动机优化算法及其收敛性证明

为了求解大规模优化问题,根据记忆原理与元胞自动机的特点构造了求解优化问题的全局收敛算法。在该算法中,将优化问题的理论搜索空间划分为离散搜索空间,该空间定义为元胞空间,其中的每个元胞对应着一个候选解。将记忆原理的记忆、遗忘规律用于控制每个元胞的状态转移;元胞的状态由其空间位置、位置修正量以及记忆残留值构成,该值分为瞬时记忆、短时记忆和长时记忆3种状态类型,并依据元胞接受刺激的强度被加强或衰减;记忆残留值低于某个阈值的元胞时被遗忘,不再被处理。在元胞演化过程中,元胞从一个状态转移到另一个状态实现了元胞空间对理论搜索空间的搜索。应用可归约随机矩阵的稳定性条件证明了本算法具有全局收敛性。测试结果表明本算法是高效的。     

非线性方程组求解器全局优化求解能力对比研究

首次总结提出一套共14道低维但高难度非线性方程组案例题集,从效果与效率两方面对比测试了国内外目前认可度很高的5款优秀全局优化求解器Baron、Antigone、Couenne、Lingo和1stOpt,给出这5款求解器在非线性方程组全局优化求解能力方面的综合表现及排名,探讨了非线性方程组求解过程中“除法陷阱”和“冗余项影响”问题及解决方法,确定性优化算法的优缺点以及全局最优化求解器研发者的“卡耐基梅隆”及“跨行业”现象。     

元胞自动机可逆性研究

元胞自动机是对复杂适应系统建模的重要理论工具。可逆性是元胞自动机的一个重要属性,是模拟物理可逆空间的必要条件。本文介绍元胞自动机的基本概念、可逆性和可计算性,并介绍一维可逆元胞自动机可计算的证明思路。     

城市交通网元胞自动机全局流量预测方法*

面对城市交通的日益拥堵,针对交通管理中全局流量预测难的问题,通过将路口的各个方向的车流以不同的边表示,将双向道路的两侧分别拆分为两个端点。并提出了精准描述进入和离开交通道路各方向负载的方法,以节点作为元胞自动机的元胞,以边关系作为元胞的邻域,利用阻塞-转移方法,建立元胞自动机的局部规则,并采用递归算法计算每一时刻交通网中各个节点元胞上的交通流量,构建城市交通网络流量预测模型。最后以某市交通主干道的实测流量数据为例,验证了该预测模型的准确性和高效性,从而证实了该模型对于城市的交通管理能力有一定的提升的作用。     

基于元胞自动机的教与学优化算法

为解决教与学优化(TLBO)算法易陷入局部最优的问题,提出了一种基于元胞自动机的教与学优化算法(CATLBO)。算法建立了四边形网状元胞自动机模型并指定其邻域结构和规则。为保持种群多样性,在教学阶段提出以一定的概率接收退步个体的策略;为加快收敛并保证解的精度,在学习阶段制定不同学习规则,劣势个体向优势个体学习,优势个体执行混沌扰动进行自我学习。使用多个Benchmark测试函数和经典TSP问题对算法进行了仿真。结果表明:CATLBO算法全局搜索能力强,与基本TLBO等算法相比,在处理高维多峰问题上更具优势。     

基于元胞自动机的软件架构设计

探讨元胞自动机思想在软件架构设计领域内的应用。通过元胞抽象(Form、Controls、Operate、Process、Verify)和规则定义(显示加载规则、交互调用规则、提交卸载规则),构造出离散的可循环迭代的平行运算体系,实现普适各类业务的通用的软件架构设计。     

基于元胞自动机的交通流计算机模拟

元胞自动机是把复杂系统量化为简单的个体,在元胞自动机模型中.空间、时间都被离散化,每一个相互作用的单元仅为有限的状态.以元胞自动机理论为基础,把车辆在路段上交通流中运动的变化规律表述为元胞自动机的演化规则,建立了基于元胞自动机理论的交通流模拟模型,标定了元胞长度和最大速度等参数,分析了元胞变换的原则;详细探讨了元胞自动机在道路交通模拟中的应用,设计出了交通元胞自动机的结构,分析了交通元胞自动机所采取的状态变换原则,建立了一维(单车道)交通流模拟模型;并利用C语言编程实现模拟.模拟结果符合实际交通流的特点.     

基于元胞自动机的城市交通流仿真系统

利用元胞自动机理论，建立了单车道及交叉路口交通流模型。为了使用户直观的了解交通运行状况，以便采取有效的优化措施对交通进行管理，设计并实现了城市交通流仿真系统。该系统具有优化功能，能够通过对数据的分析，产生交通管理的优化策略，对优化城市交通提出可供借鉴的措施。     

海岸线遥感信息提取的元胞自动机方法及其应用

从遥感资料中准确提取海岸线信息,是海岛海岸带遥感调查与海岸带综合管理的重要内容。为了对多类型海岸线进行准确提取,基于"自下而上"演化的元胞自动机方法,结合遥感图像方向信息权重,构建了一种新的岸线提取算法,并在Matlab环境下开发实现包括均值平滑、海陆分离、离散地物去除和目标追踪的功能。以Landsat ETM+遥感影像作为数据源,分别对人工海岸上海市长兴岛-横沙岛和淤泥质海岸上海市崇明东滩岸线进行了检测,验证了该岸线信息提取的元胞自动机算法。研究表明,基于元胞自动机的岸线提取方法,能够以较高精度提取人工海岸和淤泥质海岸的岸线信息。     

一种基于元胞自动机的图像拼接方法

描述了一种基于元胞自动机的图像拼接方法,采用元胞自动机提取图像特征点,然后以特征点邻域灰度互相关法进行特征点匹配,最后根据匹配的特征点对得到图像间的变换参数。实验结果表明,本方法不仅准确实现了图像拼接,而且降低了图像重叠度的要求。     

A new trust-region method with line search for solving symmetric nonlinear equations

A new trust-region method is proposed for symmetric nonlinear equations. In this given algorithm, if the trial step is unsuccessful, one line search will be used instead of repeatedly solving the subproblem of the normal trust-region method. Moreover, the global convergence is established under mild conditions by a new way. The quadratic convergence of the presented method is also proved. Numerical results show that the method is interesting for the given problems.     

A new cubic convergent method for solving a system of nonlinear equations

We present a new cubic convergent method for solving a system of nonlinear equations. The new method can be viewed as a modified Chebyshev's method in which the difference of Jacobian matrixes replaces three order tensor. Therefore, the new method reduces the storage and computational cost. The new method possesses the local cubic convergence as well as Chebyshev's method. A rule is deduced to ensure the descent property of the search direction, and a nonmonotone line search technique is used to guarantee the global convergence. Numerical results indicate that the new method is competitive and efficient for some classical test problems.     

The global convergence analysis of a class of nonlinear network systems

In this paper, the global convergence for a class of nonlinear network systems with multiple equilibriums was studied, which can be viewed as interconnected systems composed of nonlinear systems through linear input and output interconnections. Frequency-domain conditions were established for global convergence and convergence of bounded solutions. The effects of the input and output interconnections can be studied through a nonsingular inner coupling matrix and nonzero scales, representing the interconnection, which takes values according to the eigenvalues of the nonsingular outer coupling matrix. Then, the design method based on linear matrix inequality was presented by using the KYP Lemma and Schur complement.     

Global convergence of a filter-trust-region algorithm for solving nonsmooth equations

In this paper, we present a new algorithm for solving nonsmooth equations, where the function is locally Lipschitzian. The algorithm attempts to combine the efficiency of filter techniques and the robustness of trust-region method. Global convergence for this algorithm is established under reasonable assumptions.     

An efficient adaptive trust-region method for systems of nonlinear equations

We present an adaptive trust-region algorithm to solve systems of nonlinear equations. Using the nonmonotone technique of Grippo, Lampariello and Lucidi, we introduce a new adaptive radius to decrease the total number of iterations and function evaluations. In contrast with the pervious methods, the new adaptive radius ensures that the size of radius is not too large or too small. We show that the sequence generated by the proposed adaptive radius is decreasing, so it prevents the production of too large radius as possible. Furthermore, it is shown that this sequence is reduced slowly, so it prevents the production of the intensely small radius. The global and quadratic convergence of the proposed approach are proved. Preliminary numerical results of our algorithm are also reported which indicate the promising behaviour of the new procedure to solve systems of nonlinear equations.     

求解非线性方程重根的区间牛顿法

讨论了求解非线性方程重根问题,针对此时Moore区间牛顿法不再适用,以及Hansen改进的区间牛顿法收敛速度慢的情况,通过引入原方程的一种相关方程,建立了求解非线性方程重根的区间牛顿法;证明了其局部平方收敛的性质,给出了数值算例。验证了新算法比Hansen改进的区间牛顿法具有更快的收敛速度,且算法是有效和可靠的。     

Conjugate direction particle swarm optimization solving systems of nonlinear equations

Solving systems of nonlinear equations is a difficult problem in numerical computation. For most numerical methods such as the Newton’s method for solving systems of nonlinear equations, their convergence and performance characteristics can be highly sensitive to the initial guess of the solution supplied to the methods. However, it is difficult to select a good initial guess for most systems of nonlinear equations. Aiming to solve these problems, Conjugate Direction Particle Swarm Optimization (CDPSO) was put forward, which introduced conjugate direction method into Particle Swarm Optimization (PSO)in order to improve PSO, and enable PSO to effectively optimize high-dimensional optimization problem. In one optimization problem, when after some iterations PSO got trapped in local minima with local optimal solution , conjugate direction method was applied with as a initial guess to optimize the problem to help PSO overcome local minima by changing high-dimension function optimization problem into low-dimensional function optimization problem. Because PSO is efficient in solving the low-dimension function optimization problem, PSO can efficiently optimize high-dimensional function optimization problem by this tactic. Since CDPSO has the advantages of Method of Conjugate Direction (CD) and Particle Swarm Optimization (PSO), it overcomes the inaccuracy of CD and PSO for solving systems of nonlinear equations. The numerical results showed that the approach was successful for solving systems of nonlinear equations.     

Generalized newton multi-step iterative methods GMNp,m for solving system of nonlinear equations

A generalization of the Newton multi-step iterative method is presented, in the form of distinct families of methods depending on proper parameters. The proposed generalization of the Newton multi-step consists of two parts, namely the base method and the multi-step part. The multi-step part requires a single evaluation of function per step. During the multi-step phase, we have to solve systems of linear equations whose coefficient matrix is the Jacobian evaluated at the initial guess. The direct inversion of the Jacobian it is an expensive operation, and hence, for moderately large systems, the lower-upper triangular factorization (LU) is a reasonable choice. Once we have the LU factors of the Jacobian, starting from the base method, we only solve systems of lower and upper triangular matrices that are in fact computationally economical. The developed families involve unknown parameters, and we are interested in setting them with the goal of maximizing the convergence order of the global method. Few families are investigated in some detail. The validity and numerical accuracy of the solution of the system of nonlinear equations are presented via numerical simulations, also involving examples coming from standard approximations of ordinary differential and partial differential nonlinear equations. The obtained results show the efficiency of constructed iterative methods, under the assumption of smoothness of the nonlinear function.     

Collocation method for solving systems of Fredholm and Volterra integral equations

In this paper, a numerical method based on based quintic B-spline has been developed to solve systems of the linear and nonlinear Fredholm and Volterra integral equations. The solutions are collocated by quintic B-splines and then the integral equations are approximated by the four-points Gauss-Turán quadrature formula with respect to the weight function Legendre. The quintic spline leads to optimal approximation and O(h⁶) global error estimates obtained for numerical solution. The error analysis of proposed numerical method is studied theoretically. The results are compared with the results obtained by other methods which show that our method is accurate.