# SVD Enhanced Metaheuristic for Plug-In Hybrid Electric Vehicle Routing Problem
## 4 Methodology
### Memetic Algorithm
As shown in Table 4, in the cases of E0F0, the maximum cost Error is 4.2% and the minimum cost Error is 0.8%, the SD values of cost are between 0.35 and 3.46, in the cases of E2F2, the cost SD values and cost error values are between 0.51 and 0.38, 0.8% and 4.8% respectively, in the cases of E4F4, the cost SD values are from 0.2 to 4.39, the cost error values are from 0.3% to 5.4%. In this study, our aim is to minimize the total cost, the value of mile is the total distance of the solution which has the minimum cost value. The total distance is not the considered point of our problem; therefore, the stability of mile values for the tested instances is less than that of the cost value. In a special case of the B-n35-K5 in E4F4, the mile error is \(-1.6\%\), this is because the related mile is greater than the average value in this case. The standard deviation and the error could be used to express the degree of data dispersion. The smaller the two values are, the more centralized distribution of experimental results is, on the contrary, the more decentralized the distribution is. \begin{table}
\begin{tabular}{c c c c c c c c c c c c} \hline \hline  & \multicolumn{4}{c}{E0F0} & \multicolumn{4}{c}{E2F2} & \multicolumn{4}{c}{E4F4} \\ \cline{2-13}
**Instances** & \multicolumn{2}{c}{**SA\_RS\_CF**} & \multicolumn{2}{c}{**HMA\_SVND**} & \multicolumn{2}{c}{**SA\_RS\_CF**} & \multicolumn{2}{c}{**HMA\_SVND**} & \multicolumn{2}{c}{**SA\_RS\_CF**} & \multicolumn{2}{c}{**HMA\_SVND**} \\ \cline{2-13}  & **Cost** & **Mile** & **Cost** & **Mile** & **Cost** & **Mile** & **Cost** & **Mile** & **Cost** & **Mile** & **Cost** & **Mile** \\ \hline A-n33-k5 & 113.70 & 521 & 96.45 & 439 & 111.36 & 527 & 90.51 & 398 & 103.98 & 512 & 77.98 & 417 \\ A-n46-k7 & 157.68 & 720 & 133.94 & 597 & 154.08 & 750 & 123.58 & 585 & 150 & 754 & 115.42 & 597 \\ A-n60-k9 & 205.50 & 944 & 150.44 & 667 & 201.84 & 979 & 136.45 & 681 & 195.90 & 970 & 127.46 & 664 \\ B-n35-k5 & 166.80 & 758 & 88.45 & 390 & 155.58 & 778 & 78.03 & 402 & 144.06 & 814 & 65.34 & 408 \\ B-n45-k5 & 138.72 & 641 & 109.92 & 496 & 132.66 & 678 & 100.74 & 488 & 123.66 & 768 & 86.20 & 520 \\ B-n68-k9 & 187.32 & 875 & 92.19 & 406 & 186.30 & 981 & 81.98 & 420 & 174 & 914 & 69.03 & 439 \\ B-n78-k10 & 196.50 & 929 & 136.10 & 607 & 183.84 & 952 & 112.83 & 566 & 171.18 & 996 & 102.66 & 603 \\ E-n30-k3 & 100.26 & 465 & 84.49 & 388 & 97.38 & 522 & 74.98 & 376 & 86.82 & 556 & 63.58 & 333 \\ E-n51-k5 & 102.48 & 490 & 99.99 & 454 & 93.24 & 534 & 88.44 & 449 & 81.78 & 574 & 75.77 & 451 \\ E-n76-k7 & 133.98 & 637 & 127.46 & 570 & 132.90 & 754 & 116.22 & 592 & 113.82 & 775 & 104.44 & 619 \\ F-n72-k4 & 44.40 & 248 & 45.60 & 208 & 29.76 & 322 & 37.37 & 218 & 22.2 & 349 & 30.82 & 215 \\ F-n135-k7 & 319.08 & 1487 & 190.63 & 852 & 317.64 & 1481 & 166.85 & 930 & 313.14 & 1616 & 158.49 & 892 \\ P-n76-k4 & 138.84 & 673 & 128.84 & 575 & 125.46 & 726 & 118.30 & 650 & 114.84 & 741 & 104.41 & 624 \\ P-n101-k4 & 168.86 & 813 & 157.80 & 699 & 155.88 & 870 & 142.97 & 780 & 154.08 & 981 & 127.34 & 750 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Comparison results of HMA_SVND (proposed) and SA_RS_CF [8]. Figure 4: The comparative results of the proposed HMA_SVND method and SA_RS_CF method of [PERSON] et al. [8]