A chaotic algorithm for providing a solution to the bi-level Discrete Equilibrium Network Design Problem （NDP） is discussed following an introduction of the Discrete Network Design Problem （DNDP） model and Chaos O...A chaotic algorithm for providing a solution to the bi-level Discrete Equilibrium Network Design Problem （NDP） is discussed following an introduction of the Discrete Network Design Problem （DNDP） model and Chaos Optimization Algorithms （COA）. A description of the chaotic approach for the DNDP model is described in details. Then a numerical example for the DNDP is carried out to investigate the chaotic approach. The results have been encouraging, indicating that the chaotic approach has great potential ability in finding the optimal solution of DNDP models.展开更多
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 ca...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.展开更多
基金This project is supported partly by National 0utstanding Young Investigation of National Natural Science Foundation of China（70225005,70471088,70501004 and 70501005）, the Special Research Found for Doctoral Programs in State Education Ministry （20050004005）, the 211 Project of Discipline Construction of Beijing Jiaotong University and Rencai Foundation of Beijing Jiaotong University （2003RC010）
文摘A chaotic algorithm for providing a solution to the bi-level Discrete Equilibrium Network Design Problem （NDP） is discussed following an introduction of the Discrete Network Design Problem （DNDP） model and Chaos Optimization Algorithms （COA）. A description of the chaotic approach for the DNDP model is described in details. Then a numerical example for the DNDP is carried out to investigate the chaotic approach. The results have been encouraging, indicating that the chaotic approach has great potential ability in finding the optimal solution of DNDP models.
基金Huang gratefully acknowledges the National Natural Science Foundation of China(Grant No. 79825001)and the Ministry of Educatio
文摘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.
