A two-phase approach with a novel network representation for solving the multimodal traffic network equilibrium with multimode combinations

Abstract

The multimodal traffic network equilibrium problem (MTNEP) is a classical problem that can be modeled as a combined modal split and traffic assignment (CMSTA) problem to include both route and mode consideration. Recent studies were devoted to explicitly considering the combined travel modes in the MTNEP, as a significant portion of the daily travels in the modern urban metropolis are realized using multiple modes. To address the challenges of enumerating combined modes in existing multimodal traffic equilibrium models, this study proposes a novel two-phase approach for characterizing the combined travel modes in a multimodal transportation network. It converts the multimodal transportation network structure into a two-layered network representation, in which the upper-level network captures the mode combinations between the origin/transfer/destination nodes. Based on the two-layered network, we conduct the CMSTA problem by adopting the network generalized extreme value (NGEV) model, which effectively captures both underlying mode similarity and path correlation without explicitly listing all possible combinations of modes and paths. The existence and uniqueness of the proposed model are demonstrated by formulating the MTNEP as a fixed-point problem. Experimental results verify the capability of the two-phase method to avoid same-mode transfers, generate reasonable multimodal routes, and improve convergence efficiency. Particularly, the results show that the two-phase method outperforms the one-phase method which conducts both mode demand and path flow equilibration of all combinations of combined modes directly on the supernetwork. Incorporating the Barzilai-Borwein (BB) step-size strategy, the two-phase method reduces computation time by 32% in the Sioux-Falls network and by 50% in the Anaheim network, while maintaining stable convergence across different network scales.