Adjustment of origin–destination trip matrices from observed volumes: An algorithmic approach based on conjugate directions

This paper presents a new algorithmic alternative to the O–D matrix adjustment problem from observed link volumes when it is formulated as a mathematical programming problem with a bilevel structure. The algorithmic approach presented is based on a method for nondifferentiable optimization due to Wolfe that can be interpreted as a conjugate directions method with better convergence properties as shown with a set of computational tests. Closely related to the algorithm presented, the problem of approximating gradients of the upper level function is discussed and a new and consistent approach is presented and analyzed with a detailed description of the algorithmic aspects involved.