求解基于专用道设置的动态交通规划问题的启发式算法

基于专用道设置的策略,该文提出了一个新的动态交通规划问题。大型运动会要求主办方在规定时间内将指定人员从运动员村运送到指定地点。该问题便是源自2010年广州亚运会的交通需求。其要求在保证30分钟内将运动员从运动员村运送到指定场馆的条件下,最小化设置专用通道的总成本。由于该问题的规模较大,本文提出了三种启发式算法用以求解已提出的线性整数规划模型。计算结果表明,通过该文提出的启发式算法得到的解与相对应的采用数学规划软件Lingo8．0得到的解之间的平均误差均小于1．89％。同时,启发式算法的计算时间远小于Lingo8．0所需的计算时间。     

城市地铁专用车厢模型建立及拥挤敏感性分析

处于城市化进程中的我国城市,交通拥堵问题日益严重.作为社会弱势群体的老幼孕人群,对公共交通的安全性与舒适性要求相对更高,但是这类人群中相当一部分需要在上下班高峰期与通勤人群一起出行.如果能够依据城市的具体情况设立专用车厢,把这一部分出行者引导到公共交通中,可以减少部分交通流,缓解交通拥堵.对建立专用车厢的可行性进行了分析,并建立了数学模型.     

现代城市公共交通系统运营社会效益的模糊综合评价

城市公共交通属于社会公共产品,其建设与运营不仅要考虑经济效益,还需要考虑社会效益.从公共服务水平、乘客满意度和可持续发展三个大方面考虑,构建了公共交通运营社会效益的评价指标体系.通过层次分析法确定了各指标的权重,从而建立了基于层次分析法的模糊综合评价模型.然后运用该指标体系和模型对上海市公共交通情况进行算例分析,结果表明,该评价方法科学合理、可操作性强,并指出上海公共交通运营社会效益处于中等水平,提高"安全水平"和"平均出行时间"等指标水平将显著的提高其社会效益.     

城市公共交通线路的优化设计

本文以成都市的公共交通为背景,在给定的道路网、车站分布及行驶的车辆数等条件下,以减少乘客使用公共交通工具所花时间为目标,提出了城市公共交通线路的优化设计问题.本文参考[1]中的基本思路,把优化设计分为两个步骤,首先建立符合营运要求的初始线路网,然后以总交通时间作为判别准则进行线路的调优改进,并结合实际情况及计算过程中发现的问题,在总交通时间的算法及初始线路网的建立方面作了重大改进.文中所用数学工具主要是网络最优化.     

多用户多准则随机系统最优与最优收费

针对固定交通需求量和出行者的时间价值为离散分布的多准则随机交通均衡,分别研究了依费用度量和依时间度量的多用户多准则随机系统最优和最优收费问题.分别建立了基于费用和基于时间的随机系统最优的最优化模型,阐述了该模型解的唯一性条件及等价的变分不等式问题.运用变分不等式方法,研究了一阶最优收费的可行性,即能否依边际定价原则,通过收取与出行者类别无关的道路收费使多用户多准则随机均衡流与随机系统最优流一致.一阶最优收费不适用于依时间度量的随机系统最优情况,因而建立了一个最优化模型来得到此时的非歧视性道路收费.最后给出了具体算例.     

城市非高峰期动态出行交通网络均衡

我国在城市化进程中,许多城市交通部门为了缓解城市交通拥堵问题,制订了大力发展公共交通的政策,而城市公共交通非高峰期的出行人群交通方式选择是一个值得讨论的问题.在此基础上通过分析几种不同的交通出行方式的分路段成本,建立了具有非高峰期特点的多方式出行路网模型,并对模型进行了计算求解,依据结果对非高峰期公共交通出行的特点进行了讨论.     

考虑城市住房分布的二维连续型动态交通分配模型及其污染物排放估计

将城市交通路网抽象为二维连续的平面,提出一个考虑城市住房分布的二维连续型动态交通分配模型,并估计了城市交通污染物排放水平.该模型中,住房分布影响交通需求,出行者根据用户最优准则选择出发时间和路径,可以用于模拟城市交通运行的动态演化过程,得到密度、速度和流量等物理量.采用基于车辆速度和加速度的微观污染物排放模型VT-micro估计城市交通CO2动态排放水平.基于三角网格,采用有限体积法、投影算法和相继平均法进行数值求解,给出一个数值算例验证了模型和算法的有效性.     

考虑禁左条件的用户均衡交通配流模型与算法

交叉口处左转车流是对车流量影响较大的一个流向,也是造成城市交通拥挤和交通事故的关键因素之一,所以越来越多的城市路网选择在交叉口禁止左转来保障主干路车流通畅.在禁左的情况下,出行者究竟如何选择出行路径,究竟应该在哪些交叉口采取禁左管理可以使网络总旅行时间最小?针对以上两个问题,将根据用户均衡(UE)原理,建立考虑交叉口禁左条件的交通配流双层规划模型.利用Frank-Wolfe算法,对下层模型中的出行车辆进行配流,并返回到上层模型计算网络总旅行时间,通过遗传算法确定设置禁左交叉口位置,使得网络总旅行时间达到最小.根据数值算例,展现合理设置禁左交叉口的位置,可以使得交通网络总费用减小.     

基于时间价值及基尼系数的拥挤收费设计

城市道路交通拥挤日益严重,交通拥挤收费是解决城市道路交通拥挤的手段之一,双层规划模型是研究交通拥挤收费问题的一个有力工具.然而,对时间价值不同的出行者收取拥挤费用将产生社会不公平问题.基尼系数是衡量资源分配是否公平的一个重要指标.以出行费用为公平指标,利用基尼系数改进传统双层模型的上层模型,加入基尼系数函数,构造一个管理者收益尽量大而基尼系数尽量小的目标函数.同时加入控制基尼系数的参数,通过选择适当的参数,可满足不同公平性的要求.算例表明,基于时间价值及基尼系数的拥挤收费设计,达到缓解交通拥挤的目的,且兼顾了管理者收益与交通公平.     

带柔性时间窗车辆路径问题的混沌蚁群算法

带柔性时间窗的开放式车辆路径问题(Opening Vehicle Routing Problem with Flexible Time Windows,OVRPFTW)对物流配送中的延迟或者提早具有一定程度的容忍.本文首先建立了OVRPFTW的数学模型,然后分别将Sine映射,Chebyshev映射和Logistic映射引入基本蚁群算法,构建了三种混沌蚁群算法,并将其用于求解OVRPFTW.算例测试表明:Sine映射和Chebyshev映射能够明显地改进基本蚁群算法的优化性能,基于Sine映射和Chebyshev映射的混沌蚁群算法的求解性能优于基本蚁群算法和基于Logistic映射的混沌蚁群算法.     

On a class of self-similar processes with stationary increments in higher order Wiener chaoses

We study a class of self-similar processes with stationary increments belonging to higher order Wiener chaoses which are similar to Hermite processes. We obtain an almost sure wavelet-like expansion of these processes. This allows us to compute the pointwise and local Hölder regularity of sample paths and to analyse their behaviour at infinity. We also provide some results on the Hausdorff dimension of the range and graphs of multidimensional anisotropic self-similar processes with stationary increments defined by multiple Wiener–Itô integrals.     

A REPRESENTATION FORMULA RELATED TO SCHR(O)DINGER OPERATORS

Schr(o)dinger operator is a central subject in the mathematical study of quantum mechanics.Consider the Schrodinger operator H = -△ V on R, where △ = d2/dx2 and the potential function V is real valued. In Fourier analysis, it is well-known that a square integrable function admits an expansion with exponentials as eigenfunctions of -△. A natural conjecture is that an L2 function admits a similar expansion in terms of "eigenfunctions" of H, a perturbation of the Laplacian (see [7], Ch. Ⅺ and the notes), under certain condition on V.     

On a class of Riemann surfaces

It is considered the class of Riemann surfaces with dimT1 = 0, where T1 is a subclass of exact harmonic forms which is one of the factors in the orthogonal decomposition of the spaceΩH of harmonic forms of the surface, namely The surfaces in the class OHD and the class of planar surfaces satisfy dimT1 = 0. A.Pfluger posed the question whether there might exist other surfaces outside those two classes. Here it is shown that in the case of finite genus g, we should look for a surface S with dimT1 = 0 among the surfaces of the form Sg\K , where Sg is a closed surface of genus g and K a compact set of positive harmonic measure with perfect components and very irregular boundary.     

CONTENTS OF VOLUME 30

正~~     

Instructions for contributions

正Applied Mathematics-A Journal of Chinese Universities,Series B(Appl.Math.J.Chinese Univ.,Ser.B)is a comprehensive applied mathematics journal jointly sponsored by Zhejiang University,China Society for Industrial and Applied Mathematics,and Springer-Verlag.It is a quarterly journal with     

Journal of Mathematical Research with Applications Guide for Authors

正Journal overview:Journal of Mathematical Research with Applications(JMRA),formerly Journal of Mathematical Research and Exposition(JMRE)created in 1981,one of the transactions of China Society for Industrial and Applied Mathematics,is a home for original research papers of the highest quality in all areas of mathematics with applications.The target audience comprises:pure and applied mathematicians,graduate students in broad fields of sciences and technology,scientists and engineers interested in mathematics.     

Staircase transportation problems with superadditive rewards and cumulative capacities

A cumulative-capacitated transportation problem is studied. The supply nodes and demand nodes are each chains. Shipments from a supply node to a demand node are possible only if the pair lies in a sublattice, or equivalently, in a staircase disjoint union of rectangles, of the product of the two chains. There are (lattice) superadditive upper bounds on the cumulative flows in all leading subrectangles of each rectangle. It is shown that there is a greatest cumulative flow formed by the natural generalization of the South-West Corner Rule that respects cumulative-flow capacities; it has maximum reward when the rewards are (lattice) superadditive; it is integer if the supplies, demands and capacities are integer; and it can be calculated myopically in linear time. The result is specialized to earlier work of Hoeffding (1940), Fréchet (1951), Lorentz (1953), Hoffman (1963) and Barnes and Hoffman (1985). Applications are given to extreme constrained bivariate distributions, optimal distribution with limited one-way product substitution and, generalizing results of Derman and Klein (1958), optimal sales with age-dependent rewards and capacities.To our friend, Philip Wolfe, with admiration and affection, on the occasion of his 65th birthday.Research was supported respectively by the IBM T.J. Watson and IBM Almaden Research Centers and is a minor revision of the IBM Research Report [6].