Efficient Algorithm for the Nonadditive Traffic Assignment Problem With Link Capacity Constraints

Abstract

This paper presents an insightful examination of the modeling and efficient solution algorithm for the link capacitated nonadditive traffic assignment problem (CNaTAP) to provide highly accurate flow solutions for large-scale networks. Despite the increasing significance of the CNaTAP, the ability to efficiently solve it for satisfactory accuracy in practical applications remains inadequate. Given that existing CNaTAP models and algorithms are typically limited to small experimental networks, the CNaTAP model is formulated as a variational inequality (VI) problem in this paper. This formulation is decomposed into two VI subproblems that involve equilibrium and capacity constraints, utilizing the Karush–Kuhn–Tucker (KKT) conditions. The Lagrangian multipliers for the capacity constraints are treated as fixed costs for the links in the equilibrium subproblem, ensuring the stability of the Cartesian product structure within the feasible set. This approach facilitates the decomposition of OD pairs, enabling the efficient solution of CNaTAP in large-scale networks. In addition, an algorithmic framework is developed that incorporates high-frequency updates of these Lagrangian multipliers, along with an adaptive Barzilai–Borwein (ABB) step-size calculation method applied to expedite convergence in the equilibrium subproblem. Extensive numerical experiments confirm the efficacy of the proposed algorithm in efficiently solving large-scale networks with high convergence accuracy.