Solving the combined modal split and traffic assignment problem considering the equilibrium on transit networks

In previous studies on using the gradient projection (GP) algorithm to solve the combined modal split and traffic assignment (CMSTA) problem, the transit network of each origin destination (OD) is simplified as a link on the super-network. This simplification ignores the equilibrium of flow on the transit network, which should be included in the CMSTA problem for big cities which have transit networks. In this paper, a GP algorithm is presented for solving the CMSTA problem considering the equilibrium on a metro network. The GP algorithm in this study can solve the flow of two modes simultaneously and thus obviate the mode split stage. First, the CMSTA problem with a full metro network is converted into a new user equilibrium (UE) problem by constructing a new super-network. Second, the GP algorithm is modified for it to apply to the new UE problem on the super-network. The CMSTA problem considering equilibrium on the metro network and the GP algorithm for solving it overcomes the drawback of the previous studies on the CMSTA problem taking the transit network as a link. It is useful in transportation planning and management.