基于交通收费配流的随机均衡双层规划

发布时间：2018-04-26 17:50

本文选题：随机均衡双层规划 + 交通收费配流　；参考：《大连理工大学》2012年硕士论文

【摘要】：本文以公路交通收费配流模型为背景,随机均衡双层规划问题为研究对象,阐明了公路交通收费配流问题可表示成为一个双层的随机用户均衡模型,并探讨了其最优化条件及SAA方法解的收敛性质。论文的第一部分介绍了随机用户均衡问题出现的由来以及其研究的现状,并说明了为什么要引入公路交通收费配流模型作为应用。第二部分介绍了本文相关的主要数学背景,如凸规划问题,变分不等式以及要用到的定理及其证明过程,为后面的模型推导与定理证明做理论铺垫。第三部分是在弹性需求条件下对带有随机用户均衡条件的城市交通收费配流模型进行的数学描述,证明了弹性配流均衡条件可以表示成一个变分不等式问题,并以此为基础给出了交通收费配流问题的广义纳什均衡态定义。第四部分是在固定流量条件下进行数学建模,具体刻画了一个随机均衡双层规划模型,并给出了退化的收费决策问题。最后针对该收费决策问题,在目标函数非光滑的情况下用样本平均估计方法对问题的解的收敛性质进行了探讨。第五部分对固定流量条件问题利用光滑化SAA方法进行的实例分析,并给出相应的数值结果,证明光滑化SAA方法对非光滑随机规划问题是可行的。
[Abstract]:In this paper, based on highway traffic toll allocation model and stochastic equilibrium bilevel programming problem, it is clarified that highway traffic toll allocation problem can be expressed as a two-tier stochastic user equilibrium model. The optimization conditions and the convergence properties of the solution of SAA method are discussed. The first part of the paper introduces the origin of stochastic user equilibrium problem and its research status, and explains why the highway traffic toll allocation model should be used as an application. The second part introduces the main mathematical background of this paper, such as convex programming problems, variational inequalities, the theorems to be used and their proofs, which provide a theoretical basis for the following model derivation and theorem proof. The third part is the mathematical description of the urban traffic toll allocation model with random user equilibrium under the condition of elastic demand. It is proved that the elastic distribution equilibrium condition can be expressed as a variational inequality problem. On this basis, the generalized Nash equilibrium state definition of traffic toll allocation problem is given. In the fourth part, a stochastic equilibrium bilevel programming model is modeled under the condition of fixed flow, and the problem of degenerate pricing decision is given. Finally, the convergence property of the solution of the problem is discussed by using the method of sample average estimation under the condition that the objective function is not smooth. In the fifth part, an example of the fixed flow condition problem using smooth SAA method is analyzed, and the corresponding numerical results are given. It is proved that smooth SAA method is feasible for non-smooth stochastic programming problems.
【学位授予单位】：大连理工大学
【学位级别】：硕士
【学位授予年份】：2012
【分类号】：F224;F540.4

【相似文献】