路票约束下的用户均衡网络流建模及其算法

为了缓解交通拥堵问题，在传统用户均衡模型的基础上，建立了带路票约束条件的用户均衡网络模型。本模型采用牛顿算法作为子算法，结合增强拉格朗日乘子法求解带路票约束的用户均衡网络流。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。算例分析表明，相对于传统的交通分配方法，添加路票约束能显著改变交通分配结果，使高流量路段的交通量减少了25％，能够有效地缓解交通拥堵。

Modeland algorithm of user equilibrium network with tradable credits

In order to ease traffic congestion problem,the new user equilibrium （UE）traffic network model has been established with tradable credits constraints.This model adopts Newton algorithm and augmented Lagrange multiplier to solve the above UE network.By adj usting the penalty parameter,the issue of network equilibrium under the restriction of capacity has been conver-ted to traditional network equilibrium issue.Through matrix correction,step movement and changing direction,Newton algorithm ensures the feasibility of the path or road traffic flow solution.Meanwhile,the optimal solution of subproblems has been a-chieved.The example shows that the new model can significantly transform traffic assignment results and reduce the traffic vol-ume by 25%,which can effectively alleviate traffic congestion.