A methodology for increasing convergence speed of traffic assignment algorithms based on the use of a generalised averaging function

In this paper, we propose a generalisation of the Method of Successive Averages (MSA) for solving traffic assignment problems. The generalisation consists in proposing a different step sequence within the general MSA framework to reduce computing times. The proposed step sequence is based on the modification of the classic 1/k sequence for improving the convergence speed of the algorithm. The reduction in computing times is useful if the assignment problems are subroutines of algorithms for solving Network Design Problems—such algorithms require estimation of the equilibrium traffic flows at each iteration, hence, many thousands of times for real-scale cases. The proposed algorithm is tested with different parameter values and compared with the classic MSA algorithm on a small and on two real-scale networks. A test inside a Network Design Problem is also reported. Numerical results show that the proposed algorithm outperforms the classic MSA with reductions in computing times, reaching up to 79%. Finally, the theoretical properties are studied for stating the convergence of the proposed algorithm.