Heuristic algorithms for the bilevel origin-destination matrix estimation problem

Recently, a bilevel programming approach has been used for estimation of origin-destination (O-D) matrix in congested networks. This approach integrates the conventional generalized least squares estimation model and the standard network equilibrium model into one process. We extend this approach and develop a more general model and efficient heuristic algorithms to handle more realistic situation where link flow interaction cannot be ignored. The extended model is formulated in the form of a bilevel programming problem with variational inequality constraints. The upper-level problem seeks to minimize the sum of error measurements in traffic counts and O-D matrices, while the lower-level problem represents a network equilibrium problem formulated as variational inequalities, which guarantees that the estimated O-D matrix and corresponding link flows satisfy the network equilibrium conditions. Two computational techniques are presented for solving the bilevel O-D matrix estimation model. One is a heuristic iterative algorithm between traffic assignment and O-D matrix estimation and the other one is a sensitivity analysis based heuristic algorithm. Properties of the two algorithms are analyzed theoretically and compared numerically with small network examples. It is concluded that both algorithms can be used as efficient approaches for the bilevel O-D matrix estimation problems.