基于改进正则化蝙蝠算法求解第一类Fredholm积分方程

本文提出了一种改进正则化蝙蝠算法来求解第一类Fredholm积分方程.对蝙蝠算法的速度惯性系数做出调整以增加种群多样性,添加高斯扰动来进一步优化集群,并采用Tikhonov正则化方法解决不适定性.计算实例表明:改进正则化蝙蝠算法的收敛速度和精度都优于传统正则化蝙蝠算法,并解决了严重偏离点的问题.     

非线性二维Volterra积分方程的一个高阶数值格式

对非线性二维Volterra积分方程构造了一个高阶数值格式.block-byblock方法对积分方程来说是一个非常常见的方法,借助经典block-by-block方法的思想,构造了一个所谓的修正block-by-block方法.该方法的优点在于除u(x_1,y),u(x_2,y),u(x,y_1)和u(x,y_2)外,其余的未知量不需要耦合求解,且保存了block-by-block方法好的收敛性.并对此格式的收敛性进行了严格的分析,证明了数值解逼近精确解的阶数是4阶。     

求解对称鞍点问题的修正Uzawa方法

本文基于两个非线性逼近逆的非线性Uzawa方法,给出了一种新的修正非线性Uzawa方法,并对其收敛性进行了分析以及与已有算法的收敛性进行了比较.最后由数值试验说明了算法的正确性和有效性.     

等腰三角形Mindlin板的自由振动分析

提出了一种新方法来对基于 Mindlin剪切变形理论的等腰三角形板进行自由振动分析 .此方法采用了一种新的基函数并利用 pb-2 Rayleigh-Ritz边界函数得到了一种新型的 Ritz方法 .这种方法的有效性通过收敛性和对比性分析得到了证实 .数值结果表明此方法相当精确有效 .     

广义KdV方程Fourier谱逼近的最优误差估计

分析了一类带周期边界条件的广义KdV方程Fourier谱方法,得到了L2范数下最优误差估计,改进了由Maday和Quarteroni给出的结果.还提出了一种修改Fourier拟谱方法,并且证明它享有与Fourier谱方法同样的收敛性.     

求解无容量设施选址问题的拉格朗日蝙蝠算法

无容量设施选址问题(Uncapacitated Facility Location Problem,UFLP)是一类经典的组合优化问题,被证明是一种NP-hard问题,易于描述却难于求解.首先根据UFLP的数学模型及其具体特征,重新设计了蝙蝠算法的操作算子,给出了求解UFLP的蝙蝠算法.其次构建出三种可行化方法,并将其与求解UFLP的蝙蝠算法和拉格朗日松弛算法相结合,设计了求解该问题的拉格朗日蝙蝠算法.最后通过仿真实例和与其他算法进行比较的方式,验证了该混合算法用来求解UFLP的可行性,是解决离散型问题的一种有效方式.     

非全局Lipschitz条件下跳适应向后Euler方法的强收敛性分析

本文研究跳适应向后Euler方法求解跳扩散随机微分方程在非全局Lipschitz条件下的强收敛性.通过克服方程非全局Lipschitz系数给收敛性分析带来的主要困难,我们成功地建立了跳适应后向Euler方法的强收敛性结果并得到相应的收敛率.最后,我们通过数值试验对前文所得理论结果做进一步的验证.     

利用远场模式的完全与不完全数据反演声波阻尼区域

提出一种方法,利用远场模式的完全数据与不完全数据反演声波阻尼区域,证明了方法的收敛性,并给出若干数值例子.     

一类四阶微积分方程的Legendre-Galerkin谱逼近

针对研究吊桥模型而建立的四阶微积分方程, 提出Legendre谱逼近法进行求解.构造迭代算法来求解得到的线性系统, 证明了迭代格式的收敛性, 对问题进行了误差分析.数值算例验证了迭代的收敛性和方法的高精度.     

混合序列部分和的若干收敛性质

本文研究了混合序列部分和的若干收敛性质.利用Serfling不等式推广情形,证明了一类随机变量序列部分和的一个收敛性结果,获得了混合序列部分和的收敛性,并进一步得到了混合序列加权和的强收敛性和完全收敛性,推广并改进了文[2]中有关结果.     

函数优化的小生境蝙蝠算法

针对蝙蝠算法易陷入局部最优解的缺点,利用小生境技术对蝙蝠算法进行了改进,提出一种小生境蝙蝠优化算法.算法基于小生境技术的适应度共享来分隔种群,引入了小生境排挤机制来保持种群多样性,在延续蝙蝠算法原有并行搜索等优势的基础上,提高了算法的金局搜索能力和局部收敛速度,具有可在不同邻域内发现多个解的特点.通过对一系列经典函数测试,并与已有算法进行比较,结果表明该算法在函数优化问题的求解中具有较高的计算效率和精度,以及较好的全局寻优能力.     

Chaos-enhanced synchronized bat optimizer

In this paper, a chaos-enhanced bat algorithm is proposed to tackle the global optimization problems. Bat algorithm is a relatively new stochastic optimizer inspired by the echolocation behavior of bats in nature. Due to its effectiveness, it has been applied to many fields such as engineering design, feature selection, and machine learning. However, the classical approach is often prone to falling into local optima. This paper proposes an enhanced bat algorithm to alleviate this problem observed in the original algorithm. The proposed method controls the steps of chaotic mapping by a threshold and synchronizes the velocity of agents using a velocity inertia weight. These mechanisms are designed to boost the stability and convergence speed of the bat algorithm, instantly. Eighteen well-established and the state-of-the-art meta-heuristic approaches are considered to validate the effectiveness of the developed algorithm. Experimental results reveal that the proposed chaos-enhanced bat algorithm is not only superior to the well-established algorithms such as the original method but also the latest improved approaches. Also, the proposed method is successfully applied to I-beam design problems, welded beam design, and pressure vessel design. The results show that chaos-enhanced bat algorithm can deal with unconstrained and constrained feature spaces, effectively.     

A Novel Bat Algorithm based on Cross Boundary Learning and Uniform Explosion Strategy

Population-based algorithms have been used in many real-world problems. Bat algorithm(BA) is one of the states of the art of these approaches. Because of the super bat,on the one hand, BA can converge quickly; on the other hand, it is easy to fall into local optimum. Therefore, for typical BA algorithms, the ability of exploration and exploitation is not strong enough and it is hard to find a precise result. In this paper, we propose a novel bat algorithm based on cross boundary learning(CBL) and uniform explosion strategy(UES),namely BABLUE in short, to avoid the above contradiction and achieve both fast convergence and high quality. Different from previous opposition-based learning, the proposed CBL can expand the search area of population and then maintain the ability of global exploration in the process of fast convergence. In order to enhance the ability of local exploitation of the proposed algorithm, we propose UES, which can achieve almost the same search precise as that of firework explosion algorithm but consume less computation resource. BABLUE is tested with numerous experiments on unimodal, multimodal, one-dimensional, high-dimensional and discrete problems, and then compared with other typical intelligent optimization algorithms.The results show that the proposed algorithm outperforms other algorithms.     

Forme confluente de l'ε-algorithme topologique

This paper deals with a confluent form of the topological ε-algorithm which is a method to accelerate the convergence of a sequence of elements of a topological vector space. After giving the rules of the algorithm it is related to some generalizations of the functional Hankel determinants. Some properties and some results about it are proved. An interpretation of the algorithm is given. The last paragraph is devoted with convergence results about the confluent form of the topological ε-algorithm. A parameter is introduced in the algorithm to accelerate the convergence. The optimal value of this parameter is caracterized. By estimating this optimal value, the confluent form of the ?-algorithm is obtained. The paper ends with a remark about the confluent form of the topological ?-algorithm.     

Parametric Inference for imperfectly observed Gibbsian fields

Summary This paper presents a maximum likelihood estimation method for imperfectly observed Gibbsian fields on a finite lattice. This method is an adaptation of the algorithm given in Younes [28]. Presentation of the new algorithm is followed by a theorem about the limit of the second derivative of the likelihood when the lattice increases, which is related to convergence of the method. Some practical remarks about the implementation of the procedure are eventually given.     

双目标消防救援站选址模型的元胞阴阳平衡优化算法

为衡量消防救援站在不同时间内提供的救援服务质量,基于火灾风险等级引入时效性评价函数,构建考虑时效性和经济性的双目标选址模型。针对新模型属于NP难问题特点,设计元胞阴阳平衡优化算法进行求解。寻优个体既在阴阳平衡优化算法搜索空间进行全局探索,又在元胞空间利用演化规则在邻居范围内进行局部开发。实验证明了新模型的可行性和有效性,与蝙蝠算法、蜂群算法、和声搜索算法、NGSA-Ⅱ和元胞蚁群优化算法的比较表明,新算法在非劣解集的收敛性、多样性、分布均匀性以及计算速度方面优势显著。     

Monte Carlo EM加速算法

EM算法是近年来常用的求后验众数的估计的一种数据增广算法, 但由于求出其E步中积分的显示表达式有时很困难, 甚至不可能, 限制了其应用的广泛性. 而Monte Carlo EM算法很好地解决了这个问题, 将EM算法中E步的积分用Monte Carlo模拟来有效实现, 使其适用性大大增强. 但无论是EM算法, 还是Monte Carlo EM算法, 其收敛速度都是线性的, 被缺损信息的倒数所控制, 当缺损数据的比例很高时, 收敛速度就非常缓慢. 而Newton-Raphson算法在后验众数的附近具有二次收敛速率. 本文提出Monte Carlo EM加速算法, 将Monte Carlo EM算法与Newton-Raphson算法结合, 既使得EM算法中的E步用Monte Carlo模拟得以实现, 又证明了该算法在后验众数附近具有二次收敛速度. 从而使其保留了Monte Carlo EM算法的优点, 并改进了Monte Carlo EM算法的收敛速度. 本文通过数值例子, 将Monte Carlo EM加速算法的结果与EM算法、Monte Carlo EM算法的结果进行比较, 进一步说明了Monte Carlo EM加速算法的优良性.     

The quadratic convergence of the topological epsilon algorithm for systems of nonlinear equations

In this work we consider the topological epsilon algorithm for solving systems of nonlinear equations. In section 2, a sufficient condition for its quadratic convergence is given. In section 3, some geometrical remarks about this condition are made.     

一种新的双模式盲均衡算法研究

针对恒模算法(CMA)收敛速度较慢、收敛后均方误差较大的缺点,提出一种新的双模式盲均衡算法.在算法初期,利用能快速收敛的归一化恒模算法(NCMA)进行冷启动,在算法收敛后切换到判决引导(DD-LMS)算法,减少误码率.计算机仿真表明,提出的新算法有较快的收敛速度和较低的误码率.