A BI-LEVEL FORMULATION AND QUASI-NEWTON ALGORITHM FOR STOCHASTIC EQUILIBRIUM NETWORK DESIGN PROBLEM WITH ELASTIC DEMAND

作     者：HUANG Haijun (School of Management, Beijing University of Aeronautics and Astronautics, Beijing 100083, China) WANG Shouyang (Institute of Systems Science, Academy of Mathematics and Systems Sciences, Chinese Academy of Sciences, Beijing 100080, China) Mi 

作者机构：北京航空航天大学 北京 100083 中科院系统科学所 北京 100080 University of Newcastle 英国 NE1 7RU 

出 版 物：《Journal of Systems Science & Complexity》 (系统科学与复杂性学报（英文版）)

年 卷 期：2001年第14卷第1期

页      面：40-53页

核心收录：

学科分类：07[理学] 070102[理学-计算数学] 0701[理学-数学] 

基　　金：Huang gratefully acknowledges the National Natural Science Foundation of China(Grant No. 79825001)and the Ministry of Educatio 

主　　题：Network design problem stochastic equilibrium assignment bi-level formulation quasi-Newton algorithm. 

摘      要：In this paper, a bi-level formulation of the continuous network design problem (NDP) is proposed on the basis of logit stochastic user equilibrium (SUE) assignment with elastic demand. The model determines the link capacity improvements by maximizing net economic benefit while considering changes in demand and traffic distribution in network. The derivatives of equilibrium link flows and objective function with respect to capacity expansion variables, which are analytically derived, can be computed without having to first find path choice information. These derivatives are employed to develop a quasi Newton algorithm with the BFG S (Broyden- Fletcher- Goldfarb-Shanno) formula for solving the nonlinear, nonconvex but differentiable SUE-constrained network design problem. The SUE assignment with elastic demand is solved by using the method of successive averages in conjunction with Bell’s matrix inversion logit assignment method. Simple and complex example networks are presented to illustrate the model and the algorithm.