A column generation algorithm for the estimation of origindestination matrices in congested traffic networks ?
The general problem of estimating origindestination (OD) matrices in congested traffic networks is formulated as a mathematical programme with equilibrium constraints, referred to as the demand adjustment problem (DAP). This approach integrates the OD matrix estimation and the network equilibrium assignment into one process. In this paper, a column generation algorithm for the DAP is presented. This algorithm iteratively solves a deterministic user equilibrium model for a given OD matrix and a DAP restricted to the previously generated paths, whose solution generates a new OD trip matrix estimation. The restricted DAP is formulated via a single level optimization problem. The convergence on local minimum of the proposed algorithm requires only the continuity of the link travel cost functions and the gauges used in the definition of the DAP. In order to analyze the convergence and performance of the proposed algorithm, various numerical tests were carried out on small scale problems.
traffic adjustment of origindestination trip matrix mathematical programming with equilibrium constraints large scale optimization robustness and sensitivity analysis