2005 Volume 6 Pages 1455-1470
This paper deals with a class of transportation network optimization problems with user equilibrium constraints, which can be formulated by the bilevel programming models. It first shows that the linear independent constraint qualification at any feasible path flow does hold for the user equilibrium traffic assignment problem with parameters. Accordingly, the fact that the transportation network optimization problems with user equilibrium constraints have a single level continuously differentiable optimization model is verified again. In view of the unique characteristics of a transportation network problem, a novel trust region method for the transportation network optimization problems with user equilibrium constraints is then developed. Compared to the typical trust region methods in operations research, the trust region method solves a series of sub-problems with linear objective functions and the customized trust regions for the link flows. However, it is still a convergent algorithm. Finally, this study employs an origin-destination matrix estimation problem as a numerical example to test the proposed trust region method.
