Some numerical results on the diagonalization algorithm for network assignment with asymmetric interactions between cars and trucks

Abstract

Numerical experiments are performed to test the applicability of the diagonalization algorithm to problems involving asymmetric interactions between passenger cars and trucks in highway networks. Three test networks are considered, including a representation of the Texas highway network, thus providing a realistic case application. The main aspects of the algorithm's performance addressed in these experiments are its convergence characteristics as well as the effectiveness of some computational streamlining strategies. Although convergence is not guaranteed a priori, it was actually achieved in all test cases. Furthermore, it was shown that shortcut strategies can considerably reduce the algorithm's computational requirements. These strategies involve performing only a few “internal” Frank-Wolfe iterations in solving the sequence of diagonalized subproblems. The results suggest the use of less than four internal iterations, with the use of two such iterations exhibiting the highest frequency of best performance in the tests conducted, followed by one and three internal iterations, respectively.