A heuristic for the OD matrix adjustment problem in a congested transport network

•An approximation of the gradient of the objective function in DAP is built.•An effective descent scheme to numerically solve DAP is presented.•An actualization scheme for the penalization parameters improves the approximation.

We study the Demand Adjustment Problem (DAP) associated to the urban traffic planning. The framework for the formulation of the DAP is mathematical programming with equilibrium constraints. In particular, if we consider the optimization problem equivalent to the equilibrium problem, the DAP becomes a bilevel optimization problem. In this work we present a descent scheme based on the approximation of the gradient of the objective function of DAP.