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。     

基于IAFSA-MUSIC算法的阵列信号DOA估计

针对传统MUSIC算法运算量过大以及低信噪比下分辨率差的问题,提出将改进人工鱼群算法与MUSIC的谱峰搜索相结合,利用鱼群觅食和追逐来对解空间进行高效搜索,从而保证算法收敛的快速性和全局性.聚群的存在促使少量陷于局部最优解的人工鱼向着全局最优解的方向靠拢,提高了鱼群对不利环境的自适应性,也增强了算法的稳定性.与此同时,改进人工鱼群算法在一定程度上加快了后期收敛速度,提高了算法的估计性能.实验结果表明在低信噪比时方法相较于MUSIC而言具有更好的估计性能,并且大大减少了运算量,保证了算法的实时性.     

施工网络计划优化的极值种群遗传算法

针对普通遗传算法用于施工网络计划优化的缺点,通过种群划分与极值搜索,建立了网络计划优化的极值种群改进遗传算法模型,有效地避免了陷入局部极值点,应用证明,该算法与普通遗传算法相比,具有优化速度快、求解精度高,全局寻优能力强等优点,尤其适合于大型复杂工程网络的优化计算。     

基于自适应均匀变异人工鱼群投资组合优化算法的研究

投资市场具有一定的风险,影响因素包括经济、政治、市场自身规律等,根据市场机制构建合适的投资组合模型,可以有效降低市场风险,提高投资回报率.人工鱼群算法是模仿自然界鱼类的一种人工智能优化算法,具有较好的优化能力,但有时会陷入局部最优解.首先将人工鱼群算法与均匀变异相结合,加入均匀变异随机数,使算法能够跳出局部最优解,得到全局最优,从而提高算法精度.然后采用改进人工鱼群算法对投资组合模型进行优化求解.实验表明,改进人工鱼群算法具有较好的收敛精度和收敛速度,对投资组合模型的求解效果更好,风险下降,收益增加、     

求解多维0-1背包问题的人工鱼群算法

对于多维0-1背包问题,国内外学者提出了诸如模拟退火、遗传算法、蚁群算法以及其他启发式算法.给出一种新的智能寻优方法——人工鱼群算法.算法通过各人工鱼的局部寻优,从而在群体中体现出全局最优.描述了人工鱼群算法的具体步骤并编程实现,通过多维背包算例进行了求解测试,获得了满意的效果.     

融合改进Tent混沌和模拟退火的灰狼算法

针对标准灰狼算法种群多样性差、后期收敛速度慢、易陷入局部最优的缺陷,提出一种改进灰狼算法.利用改进Tent混沌映射初始化种群,增加种群多样性;引入螺旋函数,提高算法收敛速度;融合模拟退火思想,避免陷入局部最优;设置搜索阈值,平衡全局搜索与局部搜索;利用改进Tent混沌映射产生新个体,替换性能较差个体并进行高斯扰动,增加寻优精度;将当前解和新解进行算术杂交,以保留当前解优点并减小扰动差异.使用基准测试函数和共享单车停车点选址及期初配置模型测试算法性能.结果表明,改进灰狼算法较标准灰狼算法、遗传算法和粒子群算法,收敛速度更快,寻优精度更高,性能更优越,并将该算法应用到共享单车停车选址上,验证了算法的有效性.     

基于统计引导和多项式差分学习的樽海鞘优化算法

樽海鞘优化算法相较于传统的群体智能优化算法,具有较好的鲁棒性和寻优能力。但仍存在全局寻优能力有限、执行效率不够高、易陷入局部极值的缺陷。针对上述问题,本文提出一种新的多项式差分学习策略,以区分和改进传统的线性差分方法;并设计一种随机种群划分方式,使得信息可以在邻域拓扑内均匀传递;另外,本文定义多项式差分学习的全局探索算子和局部开发算子,引入统计引导系数A,开启不同的多项式学习方法,从而进一步提高算法的全局搜索能力和寻优精度。最后,本文通过标准测试函数和实际应用问题的对比检验,证实了改进算法的优越性和鲁棒性,拓展和丰富了原算法的应用范围。     

基于PSO_Trainlm BP模型的图像去噪研究

针对在使用BP模型进行图像去噪时,模型存在的对初始权阈值敏感、易陷入局部极小值和收敛速度慢的问题.为了提高模型去噪效率,提出采用改进粒子群神经网络模型进行图像去噪.首先运用改进粒子群算法对BP神经网络权阈值进行初始寻优,再用trainlm BP算法对优化的网络权阈值进一步精确优化,随后建立基于粒子群算法的BP神经网络去噪模型,并将其应用到图像去噪研究中.仿真结果表明,新模型结合了粒子群算法的全局寻优能力和BP算法的局部搜索能力,减小了模型对初始权阈值的敏感性,有效防止了模型陷入局部极小值的可能,提高了图像去噪模型的速度和质量.     

基于速度越界处理与高斯扰动的改进蝙蝠算法

蝙蝠算法(Bat algorithm,BA)是一种新型的、搜索全局最优解的元启发式算法.为解决蝙蝠算法局部搜索时易陷入局部极值的问题,提出一种基于速度越界处理与高斯扰动的改进蝙蝠算法(VGBA).该算法利用速度的越界处理控制蝙蝠位置更新的范围,利用高斯扰动增强蝙蝠算法的全局搜索能力.选取8个测试问题进行数值实验,实验结果表明,VGBA算法在收敛精度和稳定性上比BA算法有显著提升.     

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.     

RECENT PROGRESS ON SPHERICAL HARMONIC APPROXIMATION MADE BY BNU RESEARCH GROUP ——In memory of Professor Sun Yongsheng

As early as in 1990, Professor Sun Yongsheng, suggested his students at Beijing Normal University to consider research problems on the unit sphere. Under his guidance and encouragement his students started the research on spherical harmonic analysis and approximation. In this paper, we incompletely introduce the main achievements in this area obtained by our group and relative researchers during recent 5 years （2001-2005）. The main topics are： convergence of Cesaro summability, a.e. and strong summability of Fourier-Laplace series; smoothness and K-functionals; Kolmogorov and linear widths.     

Boundedness for commutators of multipliers on Hardy type spaces

In this paper, we study the commutators generalized by multipliers and a BMO function. Under some assumptions, we establish its boundedness properties from certain atomic Hardy space Hb^p（R^n） into the Lebesgue space L^p with p 〈 1.     

A unified approach to certain problems of best local approximation

In this paper we study best local quasi-rational approximation and best local approximation from finite dimensional subspaces of vectorial functions of several variables. Our approach extends and unifies several problems concerning best local multi-point approximation in different norms.     

Towards Excellence in Science Chinese Academy of Sciences

<正>May 26,2014,Beijing Science is a human enterprise in the pursuit of knowledge.The scientific revolution that occurred in the 17th Century initiated the advances of modern science.The scientific knowledge system created by     

THE 8~(th) INTERNATIONAL CONGRESS ON INDUSTRIAL AND APPLIED MATHEMATICS

<正>August 10-14,2015Beijing,ChinaThe International Congress on Industrial and Applied Mathematics(ICIAM)is the premier international congress in the field of applied mathematics held every four years under the auspices of the International Council for Industrial and Applied Mathematics.From August 10 to 14,2015,mathematicians,scientists     

Bounds for the zeros of polynomials

Let P(z)=∑↓j=0↑n ajx^j be a polynomial of degree n. In this paper we prove a more general result which interalia improves upon the bounds of a class of polynomials. We also prove a result which includes some extensions and generalizations of Enestrǒm-Kakeya theorem.     

Boundedness of commutators related to Marcinkiewicz integrals on hardy type spaces

In this paper, the authors study the boundedness of the operator [μΩ, b], the commutator generated by a function b ∈ Lipβ(Rn)(0 ＜β≤ 1) and the Marcinkiewicz integrals μΩ, on the classical Hardy spaces and the Herz-type Hardy spaces in the case Ω∈ Lipα(Sn-1)(0 ＜α≤ 1).     

Generalization of the interaction between Haar approximation and polynomial operators to higher order methods

In applications it is useful to compute the local average empirical statistics on u. A very simple relation exists when of a function f（u） of an input u from the local averages are given by a Haar approximation. The question is to know if it holds for higher order approximation methods. To do so, it is necessary to use approximate product operators defined over linear approximation spaces. These products are characterized by a Strang and Fix like condition. An explicit construction of these product operators is exhibited for piecewise polynomial functions, using Hermite interpolation. The averaging relation which holds for the Haar approximation is then recovered when the product is defined by a two point Hermite interpolation.     

Jacobi polynomials used to invert the laplace transform

Given the Laplace transform F(s) of a function f(t), we develop a new algorithm to find an approximation to f(t) by the use of the classical Jacobi polynomials. The main contribution of our work is the development of a new and very effective method to determine the coefficients in the finite series expansion that approximation f(t) in terms of Jacobi polynomials. Some numerical examples are illustrated.