# Electric-Vehicle Routing Planning Based on the Law of Electric Energy Consumption
## 7 Conclusions  
In this paper, we develop a nonlinear energy consumption model based on EVs' driving cycles, which incorporates driving phase, load, travel distance, and speed. This has a key influence on routing EVs, as energy consumption directly determines the maximal driving range and the recharging behavior of EVs. We then introduce the EVRPTW-DC and L-EVRPTW models to address the EVs' routing problem and utilize an adaptive PSO algorithm to solve it. Numerical analyses are performed for scenarios built from realistic operational data of Company J. Each scenario is solved by three approaches, which are EVRPTW-DC \begin{table}
\begin{tabular}{c c c c c c c c c c} \hline \hline  & \multicolumn{4}{c}{**Scenario 1**} & \multicolumn{4}{c}{**Scenario 2**} & \multicolumn{4}{c}{**Scenario 3**} \\ \cline{2-10}
**Model** & **EVRPTW- DC** & **EVRPTW- ENRPTW- ENRPTW- NL** & **EVRPTW- ENRPTW- NL** & **EVRPTW- ENRPTW- NL** & **EVRPTW- NL** & **L- ENRPTW- ENRPTW- NL** \\ \hline
**Total Cost (Yuan)** & 440.53 & 482.08 & 693.85 & 946.67 & 783.01 & 1022.25 & 1032.09 & 721.74 & 1114.72 \\ \hline
**Cost of Distance (\%)** & 40\% & 40\% & 29\% & 30\% & 35\% & 27\% & 30\% & 35\% & 27\% \\ \hline
**Recharging Cost (\%)** & 43\% & 37\% & 52\% & 54\% & 45\% & 48\% & 54\% & 45\% & 48\% \\ \hline
**Cost of Time Window Violation (\%)** & 17\% & 23\% & 19\% & 16\% & 20\% & 25\% & 16\% & 20\% & 25\% \\ \hline
**Number of Visits to Recharging Stations** & 2 & 2 & 4 & 6 & 4 & 5 & 5 & 4 & 7 \\ \hline
**Average Path Length (km)** & 73.08 & 82.43 & 84.13 & 87.91 & 85.79 & 86.34 & 81.16 & 77.31 & 79.91 \\ \hline \hline \end{tabular}
\end{table} 
Table 16: Cost compositions of EVRPTW-DC, L-EVRPTW, and L-EVRPTW-NL. with the driving-cycle-based nonlinear energy consumption model, L-EVRPTW using a linear energy consumption function, and L-EVRPTW-NL implementing nonlinear energy consumption on the optimal routes of L-EVRPTW. By comparing the optimal routes of EVRPTW-DC and L-EVRPTW, we find that the implementation of the driving-cycle-based energy consumption model effectively provides more realistic routing paths. The routing scheme obtained under linear energy consumption may not be able to proceed smoothly as the actual recharging needs may require more recharging time and possibly result in additional time window violation, leading to higher total cost than the theoretical plan. Moreover, when comparing L-EVRPTW-NL with EVRPTW-DC, it is found that the shorter the length of the paths and the fewer the customers on the paths obtained under the linear energy consumption rule, the lower the probability that the costs of recharging and time window violation will increase when the implementing nonlinear energy consumption model. It can therefore be considered that the L-EVRPTW model can be applied to such scenarios if the scale is small, the customer's time window is relaxed, the nodes in the distribution network are close, and the delivery paths are short in the resulting solution of the linear energy consumption function. Otherwise, EVRPTW-DC will be the better choice to provide a more realistic delivery plan. Several interesting aspects are available for future research. Even though our driving-cycle-based energy consumption model considered some main factors, the realistic driving cycles may be more complicated. Further research may consider more complex driving phases with additional external environmental conditions. Additionally, we would like to incorporate a partial recharging strategy in future research, which would allow EVs to be recharged to the necessary battery level rather than to full capacity. From the computational perspective, future research can focus on improving the efficiency of the adaptive PSO algorithm for a better quality of the optimal solution, and testing the algorithm on larger-scale problems. Conceptualization, N.D.; Formal analysis, Z.H. and J.H. ; Methodology, N.D. and J.Y. ; Supervision, N.D. and J.Y. ; Writing--original draft, N.D.; Writing--review and editing, J.Y. and J.H.