A comparative analysis of modeling and solution methods for the en-route charging station location problems within uncongested and congested highway networks

This paper investigates a widely discussed class of charging station location problems for the en-route charging need of electric vehicles traveling in intercity highway networks. Due to the necessity for multiple charges along an intercity long-haul trip, this type of charging station location problems implies such an individual behavior that electric vehicle drivers make self-optimal route-and-charge decisions while ensuring the driving range of their vehicles to sustain trips without running out of charge. The main contribution of this paper is on analytically and computationally comparing the modeling and solution methods for the charging station location problems within uncongested and congested networks. Two distinct modeling frameworks are presented and analyzed: A metanetwork-based two-stage model for uncongested networks and a network-based bi-level model for congested networks. Both models are tackled by the classic branch-and-bound algorithm, which, however, resorts to different problem decomposition schemes, subregion bounding strategies, and network flow evaluation methods. Specifically, for uncongested networks, a two-phase procedure first employs a bi-criterion label-correcting algorithm for constructing a metanetwork and then implements the branch-and-bound algorithm on the metanetwork embedding a single-criterion label-setting algorithm for deriving network flows; on the other hand, for congested networks, the branch-and-bound algorithm is directly applied on the original network encapsulating a convex combinations method for deriving network flows. Finally, the two network scenarios and their modeling and solution methods are quantitatively evaluated with two real-world highway networks, in terms of implementation complexity, solution efficiency, and routing behavior.