带有弧容量约束的鲁棒交通网络均衡问题的计算

Calculation for Robust Traffic Network Equilibrium Problems with Capacity Constraints of Arcs

文章主要研究具有弧容量约束的费用函数不确定的交通网络均衡问题.借助ReLU函数和向量值Heaviside函数分别构造了求解弱向量均衡流和向量均衡流的等价优化问题,并对目标函数进行了Moreau邻近光滑化.另外,引入鲁棒向量均衡流的概念,构造与之等价的优化问题.同时,提出光滑化算法求解.最后,通过数值算例阐述该算法在计算速度以及获得鲁棒向量均衡流个数两个方面具有的优势.

In this paper,a traffic network equilibrium problem with uncertain cost functions and arc capacity constraints is studied.This paper adopts the ReLU function and the vector version of Heaviside function to construct two optimal problems that their solutions are equivalent to weak vector equilibrium flows and vector equilibrium flows,respectively.Then,the objective functions are smoothed by using Moreau proximal smoothing technique.In addition,the concept of robust vector equilibrium flows is introduced,and an equivalent optimization problem is also established.Simultaneously,a smoothing algorithm is proposed.Finally,compared with other state-of-the-art algorithms,the advantages of the computational speed and obtaining more robust vector equilibrium flows for our algorithm are illustrated by numerical examples.