# Variable Neighborhood Search for the Two-Echelon Electric Vehicle Routing Problem with Time Windows
## 2 Related Literature  
Recent decades have witnessed considerable research efforts concerning the vehicle routing problem and its variations. Researchers and practitioners have put great effort into modeling and designing efficient routing strategies considering requirements and conditions that arise in real-life scenarios. Various extensions of vehicle routing problems as well as recent advances and challenges are defined and presented in [4; 5]. Moreover, a broad taxonomy and a classification of publications available in the VRP literature are provided in [6]. Apart from introducing new problem variations, researchers also focused on developing solution methodologies to solve already existing problem extensions efficiently. A taxonomic review of metaheuristic solution approaches for vehicle routing problems and their variations is presented in [7]. The problem we address in this study combines two main research lines: the one on electric vehicle routing problems (EVRPs) and the one on two-echelon vehicle routing problems (2E-VRPs). Therefore, before presenting works related to our 2E-EVRP-TW problem, we will first summarize the literature on the EVRP and on the 2E-VRP. Driven by environmental considerations and a growing interest in the use of alternative fuel in logistics, the related literature has focused on developing optimal routing plans considering the limited driving range and en-route charging necessity of electric vehicles. Respective publications either call the tackled problem an EVRP or, more generally, a green vehicle routing problem. A systematic review of green vehicle routing problems is presented in [8; 9]. The study presented in [10] is regarded as the pioneering work that introduced route optimization of rechargeable vehicles to the literature. After this preliminary work, several researchers presented variations of electric vehicle routing problems together with solution methodologies. [PERSON] et al. [11] proposed a mixed-integer programming model as well as two heuristic solution techniques for the generation of routing plans for alternative fueling vehicles. [PERSON] et al. [12] extended the EVRP by including time window constraints into the model. Moreover, they proposed a metaheuristic algorithm based on VNS and tabu search (TS). Aiming to develop more realistic models and applications, [PERSON] et al. [13] and [PERSON] and [PERSON] [14] analyzed and utilized multiple charging technologies with regard to different charging speeds and the partial recharging of electric vehicles. Moreover, [PERSON] et al. [15] introduced a new model that takes into account the non-linear charging time of batteries. They reported that the time spent for charging batteries is non-linear, and ignoring this fact may cause the generation of infeasible and/or costly solutions. [PERSON] and [PERSON] [16] recently introduced a multi-depot green vehicle routing problem and developed a mixed-integer linear programming model. They proposed a solution method based on VNS and TS and reported on the computational properties of the algorithm. [PERSON] et al. [17] proposed exact and heuristic algorithms based on branch-and-price-and-cut and on column generation to solve the EVRP with TWs. After [PERSON] et al. [18] introduced the concept of two echelons in the context of the 2E-VRP as a new concept to the literature, this line of research developed into one of the most popular ones in the context of urban freight transportation [19]. The idea of developing sustainable cities and transportation systems further increases the interest in this field of research. [PERSON] et al. [20] proposed a mathematical model and math-based heuristics for the 2E-VRP. Various researchers proposed exact solution approaches such as branch-and-cut (see [21; 22]) and branch-and-price methods (see [23; 24]) as well as dynamic programming [25] to solve various extensions of the 2E-VRP. However, with growing instance size and problem complexity, researchers focused on approximate techniques to solve these problems. [PERSON] et al.