Refueling station location problem for renewable energy in a transportation network with multiple time periods, nonlinear delay, and autonomous users
Construction of renewable energy refueling stations in a transportation network is a major step toward the promotion of alternative fuel vehicles among the customers. In this thesis, we aim to determine the locations of refueling stations in a transportation network through mathematical modeling. Two optimization models are established with a centralized planner. The objective of the models is to minimize the sum of total cost of constructions, system travel time, and delay at refueling stations. The main difference between these models lies in the modeling of traveler's behaviors. In the first model, we assume that travelers fully comply with the planner's guidance about the routes and stations selection, while the second model is formulated based on independent behaviors of travelers. The first model is a mixed-integer model with constant link travel time and staircase delay at refueling stations. Two well-known solution algorithms, branch-and-bound and Lagrangian relaxation, are employed to solve the model. The second model is a mixed-integer nonlinear model with link travel time and refueling delay both as functions of link flow. To capture users' independent travel behaviors, this model is formulated as a bi-level program, where the lower level problem describes the user equilibrium traffic distribution parameterized by the locations of refueling stations. These models are tested on networks of different sizes to evaluate their effectiveness. Computational studies indicate that these two models can lead to different results. Refueling station location pattern can change completely by using the second model, which considers the autonomous drivers in selecting the stations and paths. It is shown that optimal location pattern for the first model leads to higher overall cost of construction and total system travel time in comparison to the determined location pattern by the second model.