# Improved Ant Colony Algorithm for the Split Delivery Vehicle Routing Problem
## 5 Experimental Results
### Setup of Experimental Parameters  
The settings of each parameter in the ant colony algorithm will affect the performance of the algorithm. In the existing related research [49], the parameter settings of the ant colony algorithm usually need to be determined based on past experience and comparative experiments.  
We determined the range of \(\alpha\) and \(\beta\) according to experience: \(\alpha\in\{\)1, 2, 3, 4\(\}\) and \(\beta\in\{\)4, 5, 6, 7, 8, 9\(\}\). Then, we selected [PERSON]'s dataset from the small-scale datasets; S51D1, S76D4 and S101D2 from the medium-scale datasets; and kelly02 from the large-scale datasets. On these datasets, the algorithm used different combinations of \(\alpha\) and \(\beta\) values for calculation. The experiment of each set of parameters was run 5 times, and the average path length was  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Name 1** & **N** & **Q** & **D(avg) 2** & **D(std) 3** & **BKS** \\ \hline kelly01 & 240 & 550 & 20 & 10 & 5646.46 \\ kelly02 & 320 & 700 & 20 & 10 & 8566.04 \\ kelly03 & 400 & 900 & 20 & 10 & 11,649.06 \\ kelly04 & 480 & 1000 & 20 & 10 & 14,639.32 \\ \hline \hline \end{tabular} 1
[FOOTNOTE:1]Footnote 1: “Name” denotes the instances’ name. These data can be found at [[https://www.bernabe.dorronsoro.es/vrp](https://www.bernabe.dorronsoro.es/vrp)]([https://www.bernabe.dorronsoro.es/vrp](https://www.bernabe.dorronsoro.es/vrp)) (accessed on 22 April 2024). 2
[ENDFOOTNOTE]  
\end{table}
Table 4: Information on large-scale instances.  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Name 1** & **N 2** & **D 3** & **Q 4** & **M 5** & **BKS 6** \\ \hline S51D1 & 50 & \(\lceil\)0.01Q\(\rfloor\), \(\lfloor\)0.1Q\(\rfloor\)] & 160 & 3 & 458 \\ S51D2 & 50 & \(\lceil\)0.1Q\(\rfloor\), \(\lfloor\)0.3Q\(\rfloor\)] & 160 & 9 & 726 \\ S51D3 & 50 & \(\lceil\)0.1Q\(\rfloor\), \(\lfloor\)0.5Q\(\rfloor\)] & 160 & 15 & 972 \\ S51D4 & 50 & \(\lceil\)0.1Q\(\rfloor\), \(\lfloor\)0.9Q\(\rfloor\)] & 160 & 27 & 1677 \\ S51D5 & 50 & \(\lceil\)0.3Q\(\rfloor\), \(\lfloor\)0.7Q\(\rfloor\)] & 160 & 23 & 1440 \\ S51D6 & 50 & \(\lceil\)0.7Q\(\lfloor\)0.9Q\(\rfloor\)] & 160 & 41 & 2327 \\ S76D1 & 75 & \(\lceil\)0.01Q\(\rfloor\), \(\lfloor\)0.1Q\(\rfloor\)] & 160 & 4 & 594 \\ S76D2 & 75 & \(\lceil\)0.1Q\(\rfloor\), \(\lfloor\)0.3Q\(\rfloor\)] & 160 & 15 & 1147 \\ S76D3 & 75 & \(\lceil\)0.1Q\(\rfloor\), \(\lfloor\)0.5Q\(\rfloor\)] & 160 & 23 & 1474 \\ S76D4 & 75 & \(\lceil\)0.1Q\(\rfloor\), \(\lfloor\)0.9Q\(\rfloor\)] & 160 & 37 & 2257 \\ S101D1 & 100 & \(\lceil\)0.01Q\(\rfloor\), \(\lfloor\)0.1Q\(\rfloor\)] & 160 & 5 & 716 \\ S101D2 & 100 & \(\lceil\)0.1Q\(\rfloor\), \(\lfloor\)0.3Q\(\rfloor\)] & 160 & 20 & 1393 \\ S101D3 & 100 & \(\lceil\)0.1Q\(\rfloor\), \(\lfloor\)0.5Q\(\rfloor\)] & 160 & 31 & 1975 \\ S101D5 & 100 & \(\lfloor\)0.3Q\(\rfloor\), \(\lfloor\)0.7Q\(\rfloor\)] & 160 & 48 & 2915 \\ \hline \hline \end{tabular}
\end{table}
Table 3: Information on medium-scale instances.  
calculated. Finally, when \(\alpha=2\) and \(\beta=8\), the average length of the path obtained by the algorithm was the shorter. The algorithm parameters are shown in Table 5. The maximum number of iterations is different due to the size of the experimental data set, which will be explained in the specific experiment.