# AAGA: A Priori Adaptive Splitting Algorithm for the Split Delivery Vehicle Routing Problem
## 3 Performance Evaluation
### Numerical Results  
#### 3.4.1 CVRP Instance Attributes Comparison: AASA vs. VRPHAS  
As illustrated in Section 2.3.1, one of the promises of our proposed splitting algorithm is generating smaller size CVRP instances that can be solved consistently faster. To show this, we present the size of the CVRP instances and the number of routes (i.e., vehicles) in the generated CVRP solution obtained by the splitting strategies of VRPHAS and AASA for the evaluation sets SET-1 to SET-4 in Tables 2-5, respectively. It is observed that for all the benchmarking datasets, AASA reduces the size of the CVRP problem compared to the VRPHAS method. Moreover, the number of routes in the solution obtained by AASA is less than or equal to the VRPHAS solution except for a few instances. Although the reduced number of routes indicates the potential of AASA in producing better solutions compared to VRPHAS, it does not provide sufficient evidence for cost-efficiency since the actual routes taken by the vehicles determine the total cost. However, together with the solution gap results shown in the next section, we can conclude that AASA performs better than VRPHAS in terms of both solution quality and runtime and that is a result of the adaptive splitting approach we proposed.  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Instance** & \multicolumn{2}{c}{**CVRP Size**} & \multicolumn{2}{c}{**Number of Routes**} \\ \hline  & **VRPHAS** & **AASA** & **VRPHAS** & **AASA** \\ \hline p01\_110 & 121 & 92 & 3 & 3 \\ p01\_1030 & 176 & 148 & 11 & 11 \\ p01\_1050 & 207 & 193 & 17 & 17 \\ p01\_1090 & 268 & 204 & 33 & 33 \\ p01\_3070 & 257 & 198 & 33 & 33 \\ p01\_7090 & 326 & 240 & 50 & 50 \\ p02\_110 & 182 & 168 & 5 & 5 \\ p02\_1030 & 204 & 231 & 17 & 17 \\ \hline \hline \end{tabular}
\end{table}
Table 4: CVRP instance attributes: VRPHAS vs. AASA on SET-3.  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Instance** & \multicolumn{2}{c}{**CVRP Size**} & \multicolumn{2}{c}{**Number of Routes**} \\ \hline  & **VRPHAS** & **AASA** & **VRPHAS** & **AASA** \\ \hline SD1 & 32 & 18 & 8 & 7 \\ SD2 & 64 & 42 & 14 & 13 \\ SD3 & 64 & 36 & 13 & 13 \\ SD4 & 96 & 54 & 19 & 20 \\ SD5 & 128 & 84 & 26 & 26 \\ SD6 & 128 & 72 & 29 & 28 \\ SD7 & 160 & 110 & 34 & 34 \\ SD8 & 192 & 134 & 41 & 41 \\ SD9 & 192 & 126 & 39 & 39 \\ SD10 & 256 & 168 & 55 & 56 \\ SD11 & 320 & 222 & 68 & 68 \\ SD12 & 320 & 220 & 68 & 68 \\ SD13 & 384 & 272 & 80 & 83 \\ SD14 & 480 & 330 & 103 & 100 \\ SD15 & 576 & 403 & 123 & 121 \\ SD16 & 576 & 324 & 128 & 129 \\ SD17 & 640 & 444 & 138 & 140 \\ SD18 & 640 & 440 & 141 & 139 \\ SD19 & 768 & 535 & 167 & 165 \\ SD20 & 960 & 666 & 210 & 208 \\ SD21 & 1152 & 756 & 259 & 259 \\ \hline \hline \end{tabular}
\end{table}
Table 2: CVRP instance attributes: VRPHAS vs. AASA on SET-1.  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Instance** & \multicolumn{2}{c}{**CVRP Size**} & \multicolumn{2}{c}{**Number of Routes**} \\ \hline  & **VRPHAS** & **AASA** & **VRPHAS** & **AASA** \\ \hline SD1 & 32 & 18 & 8 & 7 \\ SD2 & 64 & 42 & 14 & 13 \\ SD3 & 64 & 36 & 13 & 13 \\ SD4 & 96 & 54 & 19 & 20 \\ SD5 & 128 & 84 & 26 & 26 \\ SD6 & 128 & 72 & 29 & 28 \\ SD7 & 160 & 110 & 34 & 34 \\ SD8 & 192 & 134 & 41 & 41 \\ SD9 & 192 & 126 & 39 & 39 \\ SD10 & 256 & 168 & 55 & 56 \\ SD11 & 320 & 222 & 68 & 68 \\ SD12 & 320 & 220 & 68 & 68 \\ SD13 & 384 & 272 & 80 & 83 \\ SD14 & 480 & 330 & 103 & 100 \\ SD15 & 576 & 403 & 123 & 121 \\ SD16 & 576 & 324 & 128 & 129 \\ SD17 & 640 & 444 & 138 & 140 \\ SD18 & 640 & 440 & 141 & 139 \\ SD19 & 768 & 535 & 167 & 165 \\ SD20 & 960 & 666 & 210 & 208 \\ SD21 & 1152 & 756 & 259 & 259 \\ \hline \hline \end{tabular}
\end{table}
Table 3: CVRP instance attributes: VRPHAS vs. AASA on SET-2.