New algorithmic alternatives for the O-D matrix adjustment problem on traffic networks

For demand estimation on traffic networks, a source of information of relatively moderate cost are traffic counts on a subset of links of the network and this fact has motivated the development of bilevel mathematical programming formulations for adjusting O-D trip matrices that reproduce the observed traffic volumes. In the algorithmic field several methods have been developed specifically for the problem that, although can be viewed as heuristics, adopt approaches common to the general methods in optimization. Many of these methods can be viewed as a descent direction methods because in a step of the algorithm, an heuristic approximation of the steepest descent direction for the upper level objective function is evaluated. This paper compares some of the existing methods for the OD matrix adjustment problem, such as the method of Spiess in [7], the method of Chen in [2], the method of Yang in [8], and the method of Codina and Barceló in [3] with two new algorithmic alternatives developed by the authors. The first alternative is an adaptation of the proximal point algorithm that is based on a development of Codina in [4] for the approximation of the steepest descent direction of the upper level function and the second alternative developed by Garćıa and Maŕın in [5] consists in the linearization at each iteration of the lower level problem.