双层优化交通模型及其算法

Bi-level Optimization in Transportation Analysis

提出了一个用于交通工程实践的考虑用户路径选择行为的两层数学规划模型.该模型可以应用在交通网络 设计、道路收费、交通信号灯配时等方面.分析了两层规划模型的特性和求解难点所在.并提出了一种基于路段变 量的连续可导的边际函数和距离函数,从而把两层规划转化成单层规划问题.通过把距离函数罚到目标函数上,转 化后的单层规划问题可以方便求解.

This paper presented a unified description of the transportation bi-level optimization problems with user equilibrium constraints.Specifically,the network link capacity expansion problem,the road toll pricing problem and the optimal signal timing problem are discussed.The traditional bi-level model formulation of these problems is transformed into a single-level continuously differentiable problem using a marginal function approach.An efficient partially penalized method is used to solve the resulting single-level differentiable optimization problems.The methods are illustrated with simple analytical examples.The marginal function approach proves to be very promising in dealing with the transportation bi-level optimization problems with user equilibrium constraints.