A customized two-stage parallel computing algorithm for solving the combined modal split and traffic assignment problem

Efficiently solving the traffic assignment problem (TAP) for large-scale transport networks is a critical problem for transportation studies. Most of the existing algorithms for TAP are serial ones based on single-computer mode, which has inherently limited the computational efficiency, compared with parallel computing methods. Thus, this paper aims to propose an efficient distributed multi-computer cluster resource allocation method for the parallel computing of TAP. Previous studies on the parallel computing of TAP are mainly based on a single-mode, which is extended to a more complex combined modal split and traffic assignment (CMSTA) case in this paper. In order to decompose the CMSTA problem, we proposed a block-decomposed model for solving the CMSTA problem. Then we designed an optimal parallel computing resource schedule for solving each block problem more quickly on the huge transportation network. Therefore, we implemented a customized two-stage parallel (TP) algorithm that can fully use parallel resources. The first parallel stage of the TP algorithm is used in the path generation phase, and the second parallel stage is used in the path flow adjustment phase. Besides, the parallel slowdown is uncovered in calculating each block problem of the path flow adjustment phase by using parallel resources. Numerical examples are taken to validate the efficiency and robustness of the proposed TP algorithm.