Transit assignment is an important problem in the literature of transportation. Almost all competitive algorithms in this area are strategy based. For uncongested transit networks, the problem may be formulated into an optimization problem for which good solution algorithms exist. A variational inequality formulation of the problem with several solution methods is also presented in the literature for congested networks. This paper is devoted to solving a transit assignment problem based on complementarity formulation using path flows. The solution algorithm exploits the three concepts of decomposition, path generation, and linearization. The procedure has been applied on a large-scale real-case transit network under fixed travel times as well as flow-dependent dwell times. Computational experiments show rapid convergence of the algorithm. Moreover, for the limited experiments performed, the computational time for the flow-dependent problem is only about twice that of the case for the fixed travel times, without an appreciable excess memory requirement.
Abstract