An efficient hyperpath-based algorithm for the capacitated transit equilibrium assignment problem

This paper studied the capacitated transit equilibrium assignment problem (CTEAP), which particularly accounts for the capacity effect that impacts passengers' route choices in a transit network. Specifically, we impose strict capacity constraints on line segments to ensure that the passenger flow does not exceed the line capacity. By introducing associated Lagrange multipliers, we derived the generalised hyperpath cost function and established an equivalent variational inequality formulation. A solution framework is developed to solve CTEAP based on the Method of Multipliers. To handle destroyed Cartesian product structures, we transformed the master problem into a sequence of uncapacitated subproblems, which can be tackled by two modified Newton-type hyperpath-based algorithms. Numerical analyses were performed for a small Gentile network and a large Shenzhen transit network to evaluate the impacts of the capacity constraint on passenger flows and computation costs. Our results demonstrate the superiority of the proposed CTEAP model to prevent over-loaded flows, and show the promise of applying the hyperpath-based algorithm in the implementation of real-world networks.