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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 Logit random user equilibrium model more efficiently, an improved truncated Newton algorithm is proposed, which has superlinear convergence speed. Firstly, variable elimination method is used to convert the Logit-type stochastic user equilibrium model into an unconstrained optimization problem, and truncated Newton algorithm to solve the optimization problem. On the Sioux Falls network, the gradient projection method is compared with the improved truncated Newton method. The calculation results show that in most cases, the improved truncated Newton method is more efficient than the gradient projection algorithm. The advantage of this algorithm is especially obvious under crowded conditions.