Service network design of modular vehicles on general road networks considering passengers’ turning choices

The emergence of modular vehicles (MVs) opens the avenue to an entirely new urban transit system, in which a fleet of modular pods (MPs) circulates within the road network and collectively constitutes a dynamic MV service network, allowing transit passengers to freely make routing choices at each intersection by transferring to the appropriate pod. Provided feasible MP circulation patterns on the road network, this paper develops a novel mathematical model to depict passengers’ turning choices at user equilibrium in the MV service network. We establish the equivalence of this model to a linear optimization problem, which can be further transformed into a multi-commodity network flow problem on a revised network. Taking passengers’ turning choices as the lower-level problem, we then propose a bi-level problem to optimize the MP circulation pattern. We show that this bi-level problem can be transformed into a non-convex single-level problem with bi-convex property, and employ an alternating minimization (AM) algorithm to solve it by iteratively solving two convex subproblems. The convergence of the AM algorithm is established, and tailored algorithms are developed for solving each subproblem efficiently in large-scale networks. To mitigate the AM algorithm’s susceptibility to poor local optima in non-convex problems, an enhanced multi-start heuristic (MSAM) is proposed. Numerical experiments on small- to large-scale networks validate the effectiveness of the proposed model and demonstrate the computational efficiency of the developed algorithms.