Journal
TRANSPORTATION RESEARCH PART B-METHODOLOGICAL
Volume 42, Issue 4, Pages 339-354Publisher
PERGAMON-ELSEVIER SCIENCE LTD
DOI: 10.1016/j.trb.2007.09.005
Keywords
origin-destination matrix; user-equilibrium; sensitivity analysis
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In this paper we consider the estimation of an origin-destination (OD)-matrix, given a target OD-matrix and traffic counts on a subset of the links in the network. We use a general nonlinear bilevel minimization formulation of the problem, where the lower level problem is to assign a given OD-matrix onto the network according to the user equilibrium principle. After reformulating the problem to a single level problem, the objective function includes implicitly given link flow variables, corresponding to the given OD-matrix. We propose a descent heuristic to solve the problem, which is an adaptation of the well-known projected gradient method. In order to compute a search direction we have to approximate the Jacobian matrix representing the derivatives of the link flows with respect to a change in the OD-flows, and we propose to do this by solving a set of quadratic programs with linear constraints only. If the objective function is differentiable at the current point, the Jacobian is exact and we obtain a gradient. Numerical experiments are presented which indicate that the solution approach can be applied in practice to medium to large size networks. (C) 2007 Elsevier Ltd. All rights reserved.
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