摘要
为了更加准确地反映拥堵网络的交通流状态,必须在传统交通网络均衡模型中添加路段容量约束条件,限制路段交通流量的非现实的增长,因此构造了一个容量制约下的均衡交通网络流模型.在拥堵交通网络中,传统的路段特征函数不能反映拥堵的交通特性,修正路段的旅行费用表示为行车时间和因为拥堵而产生的等待延迟的总和,路段容量约束条件的拉格朗日乘子等于该路段的等待延迟.把外惩罚函数和牛顿法相结合构筑成增强拉格朗日乘子算法,用来求解拥堵网络的交通流状态.外惩罚函数通过调整惩罚参数,把容量约束下的网络均衡问题转化成传统网络均衡问题.牛顿法通过移动方向、修正矩阵和移动步长的组合来保证路径或路段交通流量解的可行性,同时获得转化后子问题的最优解.
The equilibrium network flow problem is formulated by adding the link capacity constraints as a mathematical programming, which is capable of describing the realistic traffic assignment problem. The travel cost on any congested link might be expressed in the sum of the running time and the waiting time occurred at the link end. The Lagrange multiplier associated with the link capacity constraint is equivalent to the waiting time of the link. The augmented Lagrange multiplier approach combines the exterior penalty with primal-dual and the Quasi-Newton method with the straight gradient to deal with the capacitated equilibrium network flow problem. The Quasi-Newton method employs the gradient of the objective function to obtain an improving feasible direction scaled by the secondorder derivatives, and makes line search to obtain an optimal step size to guarantee feasibility of either path or link flow.
出处
《管理科学学报》
CSSCI
北大核心
2006年第5期18-27,共10页
Journal of Management Sciences in China
基金
国家重点基础研究发展计划(973计划)资助项目(2006CB705500)
国家自然科学基金资助项目(50578037)
关键词
交通网络流
拥挤
堵塞
均衡
增强拉格朗日乘子
牛顿法
traffic network flow
congestion
jam
equilibrium
augmented Lagrange multiplier
Newton formula
