# A Two-Echelon Electric Vehicle Routing Problem with Time Windows and Battery Swapping Stations
## 6 Conclusions  
In this research, a novel two-echelon vehicle routing problem including mixed vehicles considering battery swapping stations (2E-EVRPTW-BSS) is considered, in which the integration of optimization for the two echelons is implemented by restricting the latest arrival time of ICVs at satellites in the first echelon to meet the requirement of EVs in the second echelon. The objective of the 2E-VERPTW-BSS aims to minimize the total cost. Various constraints related to vehicle capacity, battery capacity, time windows, and battery swapping stations are considered based on the requirements from real operations.  
As a variant of the VRP, this problem is obviously NP hard and untractable by using exact algorithms. In addition, the integration optimization for a two-echelon transportation system inevitably increases the difficulty in solving this problem. Hence, a kind of VNS algorithm is proposed for solving the 2E-EVRPTW-BSS problem in this paper. To evaluate the performance of the proposed VNS, the algorithm developed by [PERSON] et al. [37] is adapted according to the requirements of 2E-VERPTW-BSS for comparison. The extensive numerical experiments on different sizes of instances are conducted to examine the effectiveness and efficiency of the proposed VNS in this paper. It is found that the proposed VNS can easily achieve the optimal solutions for the small-sized instances. For larger instances, the proposed VNS demonstrates a higher efficiency in searching for the solutions of high performance compared with the algorithm of [PERSON] et al. [37] and can find better solutions in the same running time.  
The research of this paper is a kind of extension to the existing investigations. Of course, there are some other factors from the real demands worthy of being considered. For example, uncertainties are almost everywhere in the real world. Hence, in future studies, uncertainties in elements such as transportation time, electric power consumption, etc., can be included in the models, and the optimization under uncertainty can be considered.  
Conceptualization, D.W.; investigation, D.W. and H.Z.; methodology, D.W.; validation, D.W.; writing--original draft preparation, D.W. and H.Z. All authors have read and agreed to the published version of the manuscript.  
This research was funded by the National Natural Science Foundation of China, grant numbers 71471007.  
Not applicable.  
**Data Availability Statement:** Publicly available datasets were analyzed in this study. This data can be found here: [[https://www.univie.ac.at/prolog/research/TwoEVRP/](https://www.univie.ac.at/prolog/research/TwoEVRP/)]([https://www.univie.ac.at/prolog/research/TwoEVRP/](https://www.univie.ac.at/prolog/research/TwoEVRP/)) (accessed on 11 November 2021).  
The authors declare no conflict of interest.  
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline \multirow{2}{*}{**Inst**} & \multicolumn{2}{c}{**Instance Size**} & \multirow{2}{*}{**EV**} & \multirow{2}{*}{**ICV**} & \multirow{2}{*}{**Gap** (EV/ICV)**} \\ \cline{2-2} \cline{5-6}  & **m** & & & & \\ \hline
1–6 & 2 & 10 & 86.21 & 107.12 & \(-19.52\%\) \\
1–10 & 2 & 10 & 58.47 & 82.66 & \(-29.26\%\) \\
2–10 & 2 & 50 & 559.22 & 694.88 & \(-19.52\%\) \\
2–11 & 2 & 50 & 513.77 & 638.41 & \(-19.52\%\) \\
3–1 & 5 & 100 & 752.01 & 934.45 & \(-19.52\%\) \\ \hline \hline \end{tabular}
\end{table}
Table 6: Results of emissions of ICVs and EVs in the second echelon.