稳健交通均衡模型的SDP松弛  

SDP Relaxation of Robust Traffic Equilibrium Model

作　　者：张倩[1] 张超[1] 修乃华[1] 

机构地区：[1]北京交通大学数学系,北京100044

出　　处：《运筹与管理》2013年第1期1-8,共8页Operations Research and Management Science

基　　金：国家自然科学基金资助项目(70871008;11001011);教育部留学回国人员基金资助项目(教外司留[010]609号)

摘　　要：交通均衡问题在城市交通管理中具有重要意义.研究均衡交通的目的是通过对稳定交通流进行量化分析,为决策者提供交通规划及管理的依据.Wardrop交通均衡原理是描述交通均衡问题的基石,本文在其扩展之一的稳健Wardrop(Robust Wardrop,简记为RW)互补均衡模型的基础上,将不确定因素的盒子约束改进为球约束,以改善原有模型的保守度.其次给出带有不确定因素的稳健Wardrop极小化形式及其确定性稳健对应模型(Robust Counterpart,简记为RC).最后通过SDP松弛手段将稳健对应模型(RC)松弛为容易的线性半定规划问题进行求解,并给出实例说明,为不确定因素影响下的交通均衡问题提供了一种新的有效模型及解法.Traffic equilibrium problem plays an important role in management of urban transportation. Research on traffic equilibrium aims to analyse the stable traffic flow pattern and hence provides a solid basis for transport managers making decision. Wardrop＇ s equilibrium principal is the foundation of describing equilibrium state in transportation. This paper is based on one of its extensions, called the robust Wardrop equilibrium（RW）. We replace the box constrains representing uncertain factors for the RW model in traffic network by the ball constrains to improve the degree of conservation. We further propose the minimization formulation for RW concerning uncertain factors and its correspondingly deterministic Robust Counterpart（RC）model. Through a semi-definite programming（SDP） relaxation, we relax the RC model to a SDP. Finally by numerical experiments, we show that the RC model with SDP relaxation proposed in this paper provides a new effective way for traffic equilibrium under uncertainty.

关 键 词：运筹学 SDP交通均衡模型 半定松弛 交通均衡流 

分 类 号：O224.0[理学—运筹学与控制论]