交通分配中的梯度投影算法及其改进模型

最近的研究表明基于路径的交通分配算法具有很强的生命力和广阔的应用前景。在这些算法中,梯度投影算法(GP)由于其极高的计算效率引起了研究者极大的兴趣。但是研究同样表明GP算法在求高精度分配解时遇到了收敛问题。文章首先介绍了GP算法的理论基础及算法步骤,然后分析了算法产生收敛问题的关键原因,针对其高精度解不能很好收敛的问题,采用二分法改进了其中关键的步长确定策略,提出了改进的GP算法(IGP,Improved GP),并通过计算实例比较了GP和IGP的表现,分析了IGP的优势。并用计算实例证明IGP在求解高精度分配解和整体收敛速度两方面都优于GP。

The Gradient Projection Algorithm for Traffic Assignment and its Improvement

Recent researches have indicated the viability and prospect of path-based algorithms in the solution of traffic assignment(problem.)And much attention has been paid to gradient projection(GP) algorithm for its high converge rate.But there are problems in(obtaining) high-level accuracy.This paper introduces the GP algorithm firstly,and then analyzes the structure drawback of the GP leading to this problem is analyzed.To improve the GP,bisection method is employed to find an optimal step size so as to improve its (performance) in accuracy level and convergence rate.A numerical example is provided to compare the performances of the GP and the(improved) GP (IGP).The example also shows that the IGP performs better than the GP in terms of both convergence rate and accuracy level for the traffic assignment.