An Alternating Direction Multiplier Method with Variable Neighborhood Search for Electric Vehicle Routing Problem with Time Windows and Battery Swapping Stations

This paper studies a real-world electric vehicle routing problem (EVRP). Specifically, it is an EVRP with time windows and battery swapping stations (EVRP_TWBSS). The EVRP_TWBSS considers the routing of electric vehicles (EVs), the determination of each electric vehicle’s battery level, and the selection of battery swapping stations. The criterion of EVRP_TWBSS is to minimize the operating costs. To simplify the structure of model, a time-discrete and multi-commodity flow model based on extended state-space-time network (TMFM_ESSTN) is established. Meanwhile, an alternating direction multiplier method with variable neighborhood search (ADMM_VNS) is presented to address the TMFM_ESSTN. In ADMM_VNS, the augmented lagrangian relaxation (ALR) model constructed from the TMFM_ESSTN is decomposed and linearized to a series of least cost vehicle routing subproblems through the linear augmented lagrangian relaxation (LALR) decomposed technique. Then, each subproblem is iteratively solved by using the dynamic programming and two special designed VNS strategies in ADMM_VNS iterative framework. The solution’s quality can be controlled to a certain extent through monitoring the gap between the lower and upper bounds obtained after each iteration. Test results on instances with different scales and a real-world instance based on partial road network in Kunming City demonstrate that ADMM_VNS can achieve smaller gaps and better solutions than several state-of-the-art algorithms. In which, ADMM_VNS can reduce the optimal gap by up to 2.27% compared to the other state-of-the-art algorithms in small-scale instances. The gap of ADMM_VNS is calculated based on the lower bound and the upper bound in the large-scale instances and the real-world instance are 10.36% and 1.57%, respectively.