求解交通均衡问题的光滑化方法

发布时间：2018-04-14 13:30

本文选题：双层规划 + 互补约束数学规划　；参考：《大连理工大学》2015年博士论文

【摘要】：在大多数居住城市中,交通拥挤已经成为城市交通的核心问题和具有挑战性的问题。在传统的Stackelberg博弈中,带有两个局中人(领导-下属)的交通网络设计问题可被描述为一双层规划问题。其中领导是制定交通规则的控制中枢,下属代表道路使用者,他们按Wardrop用户均衡条件极小化行走时间／费用。这些问题要求交通规划者处理控制交通系统的涉及费用,道路连通性,用户交通工具选择与道路收费等因素的分片光滑变量。本研究关注求解各类道路网络设计问题的新的数值方法。本文考虑的三类用户均衡交通问题均可以表示为双层规划问题。我们提出基于F-B函数的光滑化方法求解与双层规划等价的互补约束优化(MPCC)司题.证明了当参数μ＼0时,光滑化方法具有全局收敛性质。我们采用Newton方法求解光滑化的子问题。在交通网络中考虑添加道路连接或删除道路连接的交通网路设计模型是网络扩容问题,其目的是确定连接的容量增扩集合,以及相应的均衡流量,使得交通系统的效率得到提高。可以用涉及两个局中人的一双层规划模型来表示这一问题。我们把扩容双层规划问题转化为一互补约束的上学规划问题(MPCC).我们把第3章提出的扰动方法用于得到的问题,并用变分分析工具证明其收敛性质。将扰动方法用于交通文献中出现的若干个不同的问题,得到的解优于以前的方法得到的解。比较重要地,本论文研究了将网络扩容与道路收费相结合的策略,这一策略可使交通系统获得极大的收益。我们将这一问题表达为—MPCC问题,它可以用一个光滑函数表达为一单层的连续可微优化问题。我们用一简单的数值例子来说明该方法。与城市交通问题密切相关的问题中,空气污染是一主要的问题,需要交通规划者或研究者在考虑其它因素的同时,也要将它考虑到被优化的目标中去。正是由于这一原因,各种各样的环境函数被集成到城市网络设计的目标函数中。本论文将考虑排放因素的连续网络设计(CNDP)问题表达为一双层优化问题。我们把考虑排放因素的双层CNDP优化问题转化为一MPCC问题。用扰动方法把这—MPCC问题用一单层的非线性规划(NLP)问题来近似。序列二次规划方法用来求解得到的单层可微优化问题。我们给出一简单的数值例子用于说明该方法,得到的数值结果是可接受的。
[Abstract]:In most cities, traffic congestion has become the core and challenging problem of urban traffic.In the traditional Stackelberg game, the traffic network design problem with two players (leader-subordinate) can be described as a bilevel programming problem.The leaders are the control center for making traffic rules, and their subordinates represent the road users. They minimize the walking time / cost according to the Wardrop user equilibrium conditions.These problems require traffic planners to deal with piecewise smooth variables that control the cost of traffic systems, road connectivity, user choice of vehicles and road pricing.This study focuses on new numerical methods for solving various road network design problems.The three classes of user equilibrium traffic problems considered in this paper can be expressed as bilevel programming problems.We propose a smoothing method based on F-B function to solve the problem of complementary constrained optimization which is equivalent to bilevel programming.It is proved that the smoothing method has the global convergence property when the parameter 渭\ 0.We use the Newton method to solve the subproblem of smoothing.The traffic network design model that considers adding or deleting road connections in traffic networks is a problem of network capacity expansion, which aims to determine the capacity expansion set of connections and the corresponding equilibrium flow.The efficiency of the transportation system is improved.This problem can be represented by a bilevel programming model involving two players.We transform the extended bilevel programming problem into a complementary constrained school planning problem.We apply the perturbation method proposed in Chapter 3 to the obtained problem and prove its convergence by using variational analysis tools.The perturbation method is applied to several different problems in traffic literature, and the solutions obtained are superior to those obtained by the previous methods.More importantly, this paper studies the strategy of combining network expansion with road pricing, which can greatly benefit the traffic system.We express this problem as a MPCC problem, which can be expressed as a single layer continuous differentiable optimization problem by a smooth function.We use a simple numerical example to illustrate the method.Among the problems closely related to urban traffic problems, air pollution is a major problem, which requires traffic planners or researchers to take other factors into account as well as the optimized objectives.For this reason, various environmental functions are integrated into the objective functions of urban network design.In this paper, the problem of continuous network design with emission factors is expressed as a bilevel optimization problem.We transform the two-level CNDP optimization problem considering emission factors into a MPCC problem.The perturbation method is used to approximate the MPCC problem with a single layer nonlinear programming (NLP) problem.The sequential quadratic programming method is used to solve the single layer differentiable optimization problem.A simple numerical example is given to illustrate the method and the results are acceptable.
【学位授予单位】：大连理工大学
【学位级别】：博士
【学位授予年份】：2015
【分类号】：U491

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