# SVD Enhanced Metaheuristic for Plug-In Hybrid Electric Vehicle Routing Problem
## 4 Methodology
### Memetic Algorithm
\begin{table}
\begin{tabular}{c c c c c c c c c c c c} \hline \hline  & \multicolumn{6}{c}{**Standard Deviation**} & \multicolumn{6}{c}{**Error**} \\ \cline{2-13}
**Instances** & \multicolumn{2}{c}{**E0F0**} & \multicolumn{2}{c}{**E2F2**} & \multicolumn{2}{c}{**E4F4**} & \multicolumn{2}{c}{**E0F0**} & \multicolumn{2}{c}{**E2F2**} & \multicolumn{2}{c}{**E4F4**} \\ \cline{2-13}  & **Cost** & **Mile** & **Cost** & **Mile** & **Cost** & **Mile** & **Cost** & **Mile** & **Cost** & **Mile** & **Cost** & **Mile** \\ \hline A-n33-k5 & 2.44 & 10.40 & 3.38 & 26.69 & 3.75 & 9.94 & 2.8\% & 2.6\% & 2.9\% & 7.8\% & 5.4\% & 3.1\% \\ A-n46-k7 & 2.84 & 11.88 & 0.86 & 7.14 & 1.10 & 10.19 & 2.4\% & 2.4\% & 1.1\% & 1.0\% & 1.1\% & 1.3\% \\ A-n60-k9 & 2.68 & 11.22 & 2.18 & 21.42 & 2.37 & 22.16 & 2.4\% & 2.3\% & 2.7\% & 2.0\% & 2.5\% & 0.8\% \\ B-n35-k5 & 1.81 & 7.57 & 0.51 & 10.96 & 0.20 & 8.36 & 1.7\% & 1.5\% & 0.8\% & 0.9\% & 0.3\% & -1.6\% \\ B-n45-k5 & 0.95 & 3.98 & 2.99 & 28.67 & 1.60 & 11.76 & 1.2\% & 1.1\% & 4.8\% & 10.5\% & 2.3\% & 2.4\% \\ B-n68-k9 & 2.32 & 13.09 & 2.38 & 27.11 & 2.38 & 28.22 & 3.3\% & 3.5\% & 4.0\% & 9.2\% & 5.2\% & 4.5\% \\ B-n78-k10 & 3.46 & 14.52 & 2.99 & 10.32 & 4.04 & 7.47 & 3.6\% & 3.3\% & 4.3\% & 2.7\% & 1.9\% & 0.5\% \\ E-n30-k3 & 0.65 & 2.93 & 1.20 & 4.03 & 1.42 & 12.47 & 0.8\% & 0.8\% & 2.6\% & 0.6\% & 3.6\% & 0.8\% \\ E-n51-k5 & 2.97 & 12.84 & 2.45 & 16.74 & 2.40 & 20.03 & 2.4\% & 2.2\% & 2.7\% & 4.0\% & 3.7\% & 1.8\% \\ E-n76-k7 & 2.39 & 10.02 & 1.55 & 21.02 & 0.84 & 15.38 & 4.2\% & 4.0\% & 2.3\% & 6.9\% & 1.0\% & 3.2\% \\ F-n72-k4 & 0.35 & 1.66 & 0.69 & 2.32 & 0.95 & 8.75 & 0.8\% & 0.8\% & 1.5\% & 0.2\% & 4.8\% & 1.9\% \\ F-n135-k7 & 3.29 & 14.36 & 2.75 & 13.18 & 3.79 & 8.65 & 2.2\% & 2.2\% & 2.9\% & 1.8\% & 3.4\% & 0.2\% \\ P-n76-k4 & 3.35 & 14.51 & 1.40 & 7.04 & 1.83 & 22.49 & 3.3\% & 3.3\% & 1.7\% & \(-1.7\%\) & 2.2\% & 3.3\% \\ P-n101-k4 & 2.81 & 11.98 & 3.36 & 14.63 & 4.39 & 24.45 & 2.3\% & 2.1\% & 4.8\% & 0.6\% & 5.3\% & 5.4\% \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Standard deviation and Error on tested instances. In terms of the robustness, Figure 5a,b graphically illustrate the box plot of the standard deviation and error of cost for different power station configurations. It can be observed that, in the case of E0F0 and E2F2, the stability of the algorithm is better when the number of energy stations increases, the robustness of the algorithm will become slightly worse. In summary, compared to SA_RS_CF algorithm, our proposed HMA_SVND algorithm obtained a better performance in terms of precision and the robustness. ## 6 Conclusions

In this paper, we focused on solving the routing problem for PHEV, a new hybrid optimization algorithm which merges the memetic algorithm and the sequential variable neighborhood descent is proposed. The proposed approach exhibits a competitive performance in terms of precision and robustness, achieving superior results to prevalent algorithms. However, our studied problem is still based on some simplified assumptions. For example, the charging time of the charging station was not considered and the electric station is set to be always available. In real life, charging time and mode should be considered, and there may be queues at stations; vehicles may need to wait for charging and refilling in energy stations, so the cost of waiting should also be considered. At the same time, each customer may have a time window for their services. Therefore, in future research, we will concentrate on more comprehensive problems for real-life PHEV routing. The research work was conducted in collaboration with all authors. [PERSON], [PERSON] and [PERSON] defined the research theme and designed the proposed method. [PERSON], [PERSON] and [PERSON] implemented the prototype and wrote the article. [PERSON] and [PERSON] discussed and evaluated the data test. Both authors have thoroughly contributed to reading and validating the manuscript. All authors have read and agreed to the published version of the manuscript.