求解基于路径的Logit型随机用户均衡模型的新算法

A New Algorithm for Path-based Logit Stochastic User Equilibrium Model

为了更高效地求解Logit型随机用户均衡模型,提出了一种改进的截断牛顿算法,该算法具有超线性的收敛速度。首先运用变量消去法,将Logit型随机用户均衡模型转化为一个无约束的最优化问题,再运用截断牛顿算法求解该最优化问题。在Sioux Falls网络上,对梯度投影法与改进的截断牛顿法进行了对比。计算结果表明:多数情况下,改进的截断牛顿法的计算效率高于梯度投影算法;在拥挤条件下,该算法的优势尤为明显。

In order to solve the path-based Logit stochastic user equilibrium （SUE） model more efficiently, a modified truncated Newton （MTN） algorithm was proposed, which has a superlinear convergence rate. Firstly, the variable elimination method was used to transform the SUE model into an unconstrained minimization problem, and then the truncated Newton method was used to solve this problem. The MTN algorithm was compared with the gradient projection （GP） algorithm on the Sioux Falls network. The results indicate that in most cases, MTN is more efficient than GP. When the congestion level is high, its advantage is more obvious.