非对称弹性需求网络容量限制交通分配有效算法

在非对称交通网络中,针对路段容量限制下弹性需求用户均衡分配模型计算困难,提出了一种路段容量限制弹性需求用户均衡交通分配问题的有效算法.该算法在迭代时,排队延误因子、误差因子与交通需求通过自适应调节来逼近真实路段车辆行驶时间和出行者交通需求,促使各路段交通流量逐步满足限制条件,最终达到弹性需求广义用户均衡.方法克服了容量限制弹性需求用户均衡分配计算量大及随机分配法要求枚举所有路径的困难.随后证明了算法的收敛性,并对一个小型路网进行了数值试验.     

双模式网络停车限制交通需求管理模型与方法研究

在轨道网和公路网并存的双模式交通网络, 合理设计出行终点的停车容量可优化汽车出行需求, 改善路网交通环境。本文通过分析私家车与城市轨道两种交通模式的出行需求, 并考虑私家车模式的终点停车收费服务, 建立了一种带路段环境容量和终点停车需求容量共同约束的交通需求管理模型。模型中路网使用者的出行模式采用二元Logit模型来计算, 而私家车的路线选择行为服从Logit随机用户均衡, 因此该模型是一个带不动点约束的数学规划问题。针对模型求解困难, 文中采用灵敏度分析来获取各路段流量和需求量关于终点容量波动的梯度信息, 进而设计了一种新的灵敏度分析求解算法.最后通过数值仿真实验, 验证了算法的有效性, 同时分析了不同停车收费参数对模型各指标变化趋势的影响。     

弹性需求下路段相互影响的交通网络均衡模型

本文利用网络用户均衡原理,对弹性需求下路段相互影响的交通配流问题进行研究,给了弹性需求下路段相互影响的网络均衡条件,建立了与均衡条件等价的变分不等式模型,论证了模型解的存在性和唯一性.     

基于Stackelberg博弈的时变双层交通分配模型

提出一个时变双层交通分配模型,其中上层网络管理者设立了一个路段的最大排队长度,其目标是使由网络流和排队长度定义的总出行时间最小.目标函数在离散时段内以路段流量和排队长度作为决策变量,同时考虑不同类型的信号交叉口延误的影响.下层网络用户的反应依赖于上层管理者的决策,其选择是使自身感知阻抗最小的路径,服从一个基于成对组合Logit的路径选择模型,构成一个成对组合Logit的均衡分配问题.结合了交通分配和流传播方法,将其表示为一个均衡约束下的双层数学规划问题,形成了一个Stackelberg非合作博弈.使用遗传算法求解该双层规划问题,并采用实证分析来表现模型的特征和算法的计算表现.结果表明路径重叠、路段流量、路段排队长度等因素对网络均衡流分布均有显著影响.     

基于ATIS的多用户混合交通均衡分配模型

提出一个ATIS影响下的混合交通均衡分配模型,模型中考虑多类不同的用户.不同类型用户产生的出行阻抗互相影响,且阻抗影响不对称.考虑ATIS影响下的三个不同的交通系统目标:使装备用户自身的阻抗最小化、使网络中所有装备用户的出行阻抗最小化以及使网络中所有用户的出行阻抗最小化,建立了三种情形下的路段非对称干扰的多用户混合交通分配模型.将模型表示成等价的变分不等式的形式,并分析了解的存在性和唯一性条件,结果表明解虽然存在,但并非一定唯一.提出一个对角化算法来求解混合交通均衡分配模型·最后用一个简单算例表明了模型和算法的有效性.     

随机需求下UE-CN混合交通均衡分配的效率损失

在交通网络中,用户的出行需求通常是随机的,而且不同类型用户的路径选择原则存在着差异.基于UE用户和CN用户路径选择原则的异质性,对随机需求下该类混合交通均衡分配的效率损失进行研究.构建了随机需求下UE-CN混合交通均衡分配的变分不等式模型;其次,运用非线性规划方法得到了路段出行时间成本为单项式函数时的效率损失上界表达式,进而探讨了需求还服从对数正态分布时的效率损失上界情况;最后,给出了数值算例.研究结果表明,单项式成本函数时的效率损失上界依赖于其最高次幂和CN用户的数目;当需求为对数正态分布时还和最大变异系数相关.数值算例表明解析方法是可行的.     

多用户类多准则交通分配的势博弈与拥挤定价

交通管理者在解决路网拥挤问题时,并不知道出行者的出行效用,同时管理者难以对出行者的路径选择行为做出准确的观测.运用势博弈理论分析多用户类多准则交通行为的演化过程,得到了固定需求和弹性需求情形下的可容许动态(一种刻画出行者通过转换路径增加当前效用的近似调整行为的演化动态),证明当路段时间函数和逆需求函数为严格单调、连续、可微时,所对应的交通分配是势博弈问题的惟一Nash均衡点.进一步研究了固定需求下的可变拥挤道路收费问题,得到了在当前系统状态下实现系统最优交通分配的拥挤收费水平.     

软容量约束带随机需求的设施选址问题的近似算法

文考虑了软容量约束带随机需求的设施选址问题,根据此问题构造出一个无容量约束带随机需求的设施选址问题,通过求解无容量约束情形给出软容量情形的一个可行解,分析出近似比为6。     

收费机制下一类随机需求混合交通均衡分配的非合作代价

运用算法博弈论探讨一类随机需求混合交通均衡分配在收费机制下的非合作代价.首先,构建了收费机制下随机需求UE-CN混合交通均衡分配的变分不等式模型.其次,运用解析推导法分别得到单项式出行成本函数下是否将收费作为系统总成本一部分时,该类混合交通均衡分配的非合作代价上界表达式.在此基础上,探讨了出行需求服从对数正态分布时的非合作代价上界表达式.并以数值算例验证所得结论.     

非线性互补约束均衡问题的一个滤子SQP算法

提出了—个求解非线性互补约束均衡问题的滤子SQP算法.借助Fischer-Burmeister函数把均衡约束转化为—个非光滑方程组,然后利用逐步逼近和分裂思想,给出—个与原问题近似的一般的约束优化.引入滤子思想,避免了罚函数法在选择罚因子上的困难.在适当的条件下证明了算法的全局收敛性,部分的数值结果表明算法是有效的.     

A column generation algorithm for the estimation of origin–destination matrices in congested traffic networks

The general problem of estimating origin–destination (O–D) matrices in congested traffic networks is formulated as a mathematical programme with equilibrium constraints, referred to as the demand adjustment problem (DAP). This approach integrates the O–D matrix estimation and the network equilibrium assignment into one process. In this paper, a column generation algorithm for the DAP is presented. This algorithm iteratively solves a deterministic user equilibrium model for a given O–D matrix and a DAP restricted to the previously generated paths, whose solution generates a new O–D trip matrix estimation. The restricted DAP is formulated via a single level optimization problem. The convergence on local minimum of the proposed algorithm requires only the continuity of the link travel cost functions and the gauges used in the definition of the DAP.     

Fixed-point fast sweeping weighted essentially non-oscillatory method for multi-commodity continuum traffic equilibrium assignment problem

This work presents a fixed-point fast sweeping weighted essentially non-oscillatory method for the multi-commodity continuum traffic equilibrium assignment problem with elastic travel demand. The commuters’ origins (i.e. home locations) are continuously dispersed over the whole city with several highly compact central business districts. The traffic flows from origins to the same central business district are considered as one commodity. The continuum traffic equilibrium assignment model is formulated as a static conservation law equation coupled with an Eikonal equation for each commodity. To solve the model, a pseudo-time-marching approach and a third order finite volume weighted essentially non-oscillatory scheme with Lax–Friedrichs flux splitting are adopted to solve the conservation law equation, coupled with a third order fast sweeping numerical method for the Eikonal equation on rectangular grids. A fixed-point fast sweeping method that utilizes Gauss–Seidel iterations and alternating sweeping strategy is designed to improve the convergence for steady state computations of the problem. A numerical example is given to show the feasibility of the model and the effectiveness of the solution algorithm.     

A novel algorithm for area traffic capacity control with elastic travel demands

A non-linear area traffic control system with limited capacity is considered in this paper. Optimal signal settings and link capacity expansions can be determined while trip distribution and network flow are in equilibrium. This problem can be formulated as a non-linear mathematical program with equilibrium constraints. For the objective function a non-linear constrained optimization program for signal settings and link capacity expansion is determined. For the constraint set the elastic user equilibrium traffic assignment obeying Wardrop’s first principle can be formulated as a variational inequality. Since the constrained optimization problem is non-convex, only local optima can be obtained. In this paper, a novel algorithm using a non-smooth trust region approach is proposed. Numerical tests are performed using a real data city network and various example test networks in which the effectiveness and robustness of the proposed method are confirmed as compared to other well-known solution methods.     

Parking Capacity and Pricing in Park'n Ride Trips: A Continuous Equilibrium Network Design Problem

In this paper we consider the problem of designing parking facilities for park'n ride trips. We present a new continuous equilibrium network design problem to decide the capacity and fare of these parking lots at a tactical level. We assume that the parking facilities have already been located and other topological decisions have already been taken.The modeling approach proposed is mathematical programming with equilibrium constraints. In the outer optimization problem, a central Authority evaluates the performance of the transport network for each network design decision. In the inner problem a multimodal traffic assignment with combined modes, formulated as a variational inequality problem, generates the share demand for modes of transportation, and for parking facilities as a function of the design variables of the parking lots. The objective is to make optimal parking investment and pricing decisions in order to minimize the total travel cost in a subnetwork of the multimodal transportation system.We present a new development in model formulation based on the use of generalized parking link cost as a design variable.The bilevel model is solved by a simulated annealing algorithm applied to the continuous and non-negative design decision variables. Numerical tests are reported in order to illustrate the use of the model, and the ability of the approach to solve applications of moderate size.     

弹性需求下城市公交网络服务的优化

对具有弹性需求的城市公交网络系统进行了票价结构与发车频率组合的优化。考虑到公交定价和发车频率会影响乘客需求以及乘客对路径的选择行为,将这一问题描述为一个双层规划问题,上层是寻求社会福利最大的优化问题;下层考虑了乘客的出行选择行为,为弹性需求下乘客在城市公交网络上流量分布的随机用户平衡分配模型。鉴于双层规划问题的非凸性,运用模拟退火算法对模型进行求解,并给出一个仿真算例说明提出的模型和算法的合理性。     

Solving the bicriteria traffic equilibrium problem with variable demand and nonlinear path costs

In this paper, we present an algorithm for solving the bicriteria traffic equilibrium problem with variable demand and nonlinear path costs. The path cost function considered is comprised of two attributes, travel time and toll, that are combined into a nonlinear generalized cost. Travel demand is determined endogenously according to a travel disutility function. Travelers choose routes with the minimum overall generalized costs. The algorithm involves two components: a bicriteria shortest path routine to implicitly generate the set of non-dominated paths and a projection and contraction method to solve the nonlinear complementarity problem (NCP) describing the traffic equilibrium problem. Numerical experiments are conducted to demonstrate the feasibility of the algorithm to this class of traffic equilibrium problems.     

多方式弹性需求下公交定价双层规划模型

为描述多方式城市交通网络下公交定价与出行选择行为的相互作用与影响,将出行方式选择与路径选择涵盖于同一网络,建立了上层模型分别以企业利润最大化、乘客出行成本最小化和社会福利最大化为目标函数,下层模型为多方式弹性需求随机用户配流模型的公交定价双层规划模型。运用改进遗传算法对模型整体进行求解,下层模型采用综合对角化算法和MSA算法的组合求解算法。最后,设计了一个算例以说明模型应用。结果表明:运用双层规划模型所确定的公交票价较传统静态票价可使政府、企业及出行者三方都获得更高收益,且上层模型以社会福利最大化为目标函数能代表社会群体中多数人利益,优化效果最为理想。