求解动态交通配流问题的快速投影梯度算法  

A fast projection gradient method for solving the dynamic traffic assignment problem

作　　者：吴中明 李敏 徐红利[2] WU Zhongming;LI Min;XU Hongli(School of Management Science and Engineering,Nanjing University of Information Science and Technology,Nanjing 210044,China;School of Management and Engineering,Nanjing University,Nanjing 210093,China)

机构地区：[1]南京信息工程大学管理工程学院,南京210044 [2]南京大学工程管理学院,南京210093

出　　处：《系统工程理论与实践》2021年第10期2696-2709,共14页Systems Engineering-Theory & Practice

基　　金：国家自然科学基金(11771078,71571097,12001286);江苏省自然科学基金(BK20181258);江苏高校哲学社会科学研究一般项目(2020SJA0163)。

摘　　要：针对同时考虑出行者出发时间和出行路径选择的动态交通配流问题,文中首先基于用户均衡理论,给出了均衡条件下的变分不等式模型.接着,对于给定模型提出了一种带松弛和外推的快速投影梯度算法进行求解,新算法能有效提高模型的求解效率.同时借助优化理论给出了新算法的收敛性结果.最后,将新算法应用于求解不同规模实际路网的动态交通配流问题,通过数值仿真实验验证了模型的有效性和新算法的优越性,并得到了均衡状态下不同时刻各路网的路径出发流量模式.这有助于交通网络动态配流的快速模拟和实现,给交通管理部门及时有效反馈,为制定管理措施和规划出行方案提供保障.Based on the user equilibrium theory,this paper firstly presents a variational inequality(VI)model to characterize the equilibrium conditions for the dynamic traffic assignment problem where the users consider route-and-departure-time choice simultaneously.Then,we propose a fast projection gradient method with relaxation and extrapolation to solve the constructed VI model.The theoretical convergence of the new method is established based on the optimization theory.Finally,applying the proposed method to solve the actual dynamic traffic assignment problems on several different scale transportation networks.According to some numerical simulations,the effectiveness of the model and the advantages of the new method are illustrated,and the departure flow pattern of all routes for each tested transportation network can be obtained under user equilibrium state.This work is helpful to achieve and simulate the dynamic traffic assignment rapidly in the transportation network and provide timely and effectively feedback to the traffic management department,which can provide assurance for taking management measures and travel planning.

关 键 词：动态交通配流问题 用户均衡 变分不等式模型 投影梯度算法 

分 类 号：F505[经济管理—产业经济]