数量调节用户均衡及OD分解算法  

User-equilibrium with Quantity Regulation and OD Decomposition Algorithm

作　　者：李志学 胡望欣[1] 黄中祥 LI Zhi-xue;HU Wang-xin;HUANG Zhong-xiang(School of Traffic&Transportation Engineering,Changsha University of Science&Technology,Changsha 410114,Hunan,China;Design and Research Institute Co.Ltd.,Hunan City University,Changsha 410205,Hunan,China;Hunan Provincial Urban and Rural Ecological Planning and Restoration Engineering Technology Research Center,Changsha 410205,Hunan,China)

机构地区：[1]长沙理工大学交通运输工程学院,湖南长沙410114 [2]湖南城市学院设计研究院有限公司,湖南长沙410205 [3]湖南省城乡生态规划与修复工程技术研究中心,湖南长沙410205

出　　处：《中国公路学报》2023年第5期220-230,共11页China Journal of Highway and Transport

基　　金：国家自然科学基金项目(51978082);国家自然科学基金重点项目(51338002);湖南省科技创新平台与人才计划项目(2017TP2006)。

摘　　要：城市居民出行过程中出行者的路径选择行为决定着道路网络交通流的分布模式,深刻影响着城市交通规划和网络设计方案的制定。传统交通分配依据最短路径时间选择出行路径,不能反映路径流量大小对出行者路径选择行为的直接影响。基于此,将出行起讫点间路径时间作为价格信号,路径流量作为数量信号,运用经济学非均衡理论中的价格-数量调节行为原理描述出行者的路径选择行为。在出行市场背景下,定义了数量调节用户均衡,建立了数量调节用户均衡条件和等价的非线性互补问题。运用GAP函数对非线性互补问题进行重新描述,最终建立了求解数量调节用户均衡的数学规划模型。鉴于路径流量不等于该路径中各路段流量之和,数量调节用户均衡问题需使用基于路径的算法求解,开发了基于OD分解的求解算法。OD分解算法与现有的基于路径的算法共享高斯-赛德尔分解方案,迭代过程中算法并不是顺序访问每个OD对,而是通过引入一个自适应方案来确定。针对未满足收敛条件的OD对,该算法将负梯度作为下降方向,运用Armijo类型的线性搜索确定步长,求解单OD子问题。最后分别对一简单网络和真实网络进行测试,计算结果表明:所开发的OD分解算法能将更多的计算成本投放在非均衡的OD对上,有效提升了计算效率和收敛性能,可应用于大规模网络计算。Route-choice behavior of urban residents during their travel processes determines the distribution pattern of traffic flow in a road network,which profoundly affects the formulation of urban traffic planning and network design schemes.Traditional traffic assignments select routes based on the shortest route travel time,which does not reflect the direct influence of route flow on travelers'route-choice behavior.In this study,travel time between the origin and destination as a price signal,and the route flow as a quantity signal are used to describe travelers'route choice behavior using the principles of price-quantity regulation behavior in economic disequilibrium theory.In the travel market context,the quantity regulation user equilibrium is defined,and the quantity regulation user equilibrium condition and equivalent nonlinear complementary problems are established.A mathematical programming model for solving the quantity regulation user equilibrium is established using the GAP function to redescribe the nonlinear complementary problem.As the route flow does not equal the sum of the flows on each link of the route,route-based algorithms are required to solve the quantity regulation user equilibrium problem.Thus,herein,a route-based algorithm based on OD decomposition is developed.The OD decomposition algorithm shares the Gaussian-Seidel decomposition scheme with the existing route-based algorithms.During the iterative process,the algorithm does not visit each OD pair sequentially but introduces an adaptive strategy.For OD pairs that do not satisfy the convergence criteria,the algorithm uses negative gradients in the descent direction and applies an Armijo-type linear search to determine the step size and solve a single OD subproblem.Finally,numerical computations are performed on a simple test network and real network,and the results reveal that the OD decomposition algorithm can allocate more computational energy to disequilibrium OD pairs,thereby effectively improving computational efficiency and convergence p

关 键 词：交通工程 数量调节用户均衡 价格调节 数量调节 不可加性 OD分解算法 

分 类 号：U491[交通运输工程—交通运输规划与管理]