Due to the low pollution and sustainable properties, using electric buses for public transportation systems has attracted considerable attention, whereas how to recharge the electric buses with long continuous service hours remains an open problem. In this paper, we consider the problem of placing electric vehicle (EV) charging stations at selected bus stops, to minimize the total installation cost of charging stations. Specifically, we study two EV charging station placement cases, with and without considering the limited battery size, which are called ECSP_LB and ECSP problems, respectively. The solution of the ECSP problem achieves the lower bound compared with the solution of the ECSP_LB problem, and the larger the battery size of the EV, the lower the overall cost of the charging station installation. For both cases, we prove that the placement problems under consideration are NP-hard and formulate them into integer linear programming. Specifically, for the ECSP problem we design a linear programming relaxation algorithm to get a suboptimal solution and derive an approximation ratio of the algorithm. Moreover, we derive the condition of the battery size when the ECSP problem can be applied. For the ECSP_LB problem, we show that, for a single bus route, the problem can be optimally solved with a backtracking algorithm, whereas for multiple bus routes we propose two heuristic algorithms, namely, multiple backtracking and greedy algorithms. Finally, simulation results show the effectiveness of the proposed schemes.
['Xiumin Wang', 'Chau Yuen', 'Naveed Ul Hassan', 'Ning An', 'Weiwei Wu']
Electric Vehicle Charging Station Placement for Urban Public Bus Systems