Electric bus charging facility planning with uncertainties: Model formulation and algorithm design

This paper investigates the electric bus charging facility planning (EB-CFP) problem for a bus transit company operating a heterogeneous electric bus (EB) fleet to provide public transportation services, taking into account uncertainties in both EB travel time and battery degradation. The goal of the EB-CFP problem is to determine the number and type of EB chargers that should be deployed at bus terminals and depots to meet daily EB charging demand while minimizing total cost. The problem is formulated as a two-stage stochastic programming model, with the first stage determining the EB charger deployment scheme and the second stage estimating the EB daily operational cost with respect to a predetermined EB trip timetable for a given EB charger deployment scheme. To effectively address the second stage problem, a multi-agent EB transit simulation system that mimics the daily EB operation process is developed. We then design two heuristic methods, the reinforcement learning (RL)-based method and the surrogate-based optimization (SBO), that use the developed multi-agent EB transit simulation system to solve the two-stage stochastic programming model for large-scale instances. Lastly, we run a series of experiments on a fictitious EB transit network and a real-world EB transit network in Singapore to evaluate the performance of the models and algorithms. In order to improve the performance of the EB transit system, some managerial insights are also provided to urban bus transit companies.