Multiclass bi-criteria traffic assignment without class-specific variables: An alternative formulation and a subgradient projection algorithm

In this paper, we focus on the multiclass bi-criteria (time and toll) traffic assignment (MBTA) problem. The conventional MBTA model keeps multiple copies of class-specific variables to model user heterogeneity, which puts a great burden on memory storage and computational speed when dealing with real transportation networks. This paper proposes an alternative formulation for the MBTA problem without class-specific variables by exploiting the order information of paths and travelers, i.e., high value of time (VOT) travelers will prefer fast but expensive paths, while low VOT travelers will prefer slow but cheap paths. We prove the equivalence of the alternative formulation to the conventional MBTA model. To solve the alternative formulation with a nondifferentiable convex objective function, a path-based subgradient projection algorithm is developed utilizing the subgradient and available second-order information. We adopt a small network and several large networks to examine the detailed features and the computational performance of the proposed formulation and algorithm, respectively. The results show that the alternative formulation provides the same link flow pattern as that of the conventional MBTA model but uses much fewer variables, which can greatly relieve the burden on computer memory and computational speed in solving real transportation networks.