Integrated optimisation of electric bus scheduling and top-up charging at bus stops with fast chargers

Proper vehicle scheduling and charging scheduling play an essential role in an efficient, effective and economical (3E) operation of electric bus fleet. An optimal vehicle scheduling can minimise the number of required electric buses and deadhead trips. Compared to normal plug-in charging at depot, fast charging at stops can reduce the required battery capacity, the number of deadhead trips, and further save energy consumption. In this paper, we introduce the integrated problem of vehicle scheduling and charging scheduling with fast chargers at selected bus stops to support electric bus operation. Multiple practical considerations are incorporated into the model, including penalty cost for the extra waiting due to charging activity, time-varying electricity price and various battery capacities. A genetic algorithm based heuristic approach is proposed to solve the integrated optimisation problem. Multiple education operators are proposed to improve the vehicle and charging scheduling. Numerical results show that the electric bus fleet can complete all the assigned trips with top-up charging at selected bus stops, and the charging time keeps in line with passengers' boarding and alighting time at most stops when the bus loads and unloads passengers.