Online Distributed Routing Problem of Electric Vehicles

Abstract

Considering the penetration of numerous electric vehicles (EV) into the transportation sector, the EV routing problem that jointly optimizes the charging and routing process of EVs is becoming increasingly popular, which should be solved in online fashion for the practical requirements. First, we start with an offline EVs routing and charging (EVRP) problem which is a large-scale mixed integer nonlinear program (MINLP). Considering the NP hardness of MINLP, solving the offline EVRP directly is a time-consuming task that is not suitable for the online setting. Hence, a Benders decomposition based method is proposed to decompose the offline EVRP into a master problem and a set of sub-problems which allows for distributed implementation. To further speed up the computation, we relax the mixed integer master problem to one that can be equivalently solved as a linear program. Moreover, a novel kind of valid cut is added to the relaxed master problem to further reduce the number of iterations. In order to adapt the offline EVRP to the online setting, by introducing the virtual depot, we utilize the rolling-horizon framework to tackle the uncertainty of future information, where the offline EVRP is solved in real-time repeatedly. Finally, simulations using real road map in Belgium are performed. Besides, numerical results validate that the computation speed of proposed algorithm is faster than the state-of-the-art algorithms by several orders of magnitude, and showcase the capability of proposed algorithm to solve large size instances up to 350 nodes with 35 EVs within 100 seconds.