# Improved Ant Colony Algorithm for the Split Delivery Vehicle Routing Problem
## 5 Experimental Results
### Medium-Scale Dataset Experiments  
We conducted experiments on 14 instances and compared the results with those obtained by the traditional ant colony algorithm (TACA) to verify the effectiveness of the improved method proposed in this paper. ASGCT, ACGCT, and MMGCT were the recently proposed improved and colony algorithms [20]. To verify the performance of the algorithm, we also compared it with these three algorithms. The number of iterations of all algorithms was set to 180, and the number of ants was 40. Each algorithm was run 20 times, and the results were recorded in a table. The experimental results are shown in Table 9, where the numbers in the IACA column in bold indicate that the algorithm performs better than BKS. Table 9 indicates that both the best solution and the average solution of the IACA are superior to other algorithms. The path of the best solution obtained by the IACA is at most 16.70% shorter and at least 4.23% shorter than the path of the best solution obtained by the TACA. The path of the average solutions obtained by the IACA is at most 14.57% shorter and at least 3.36% shorter than the path of the average solutions obtained by the TACA. In addition, the IACA achieved better results than the other three improved ant colony \begin{table}
\begin{tabular}{l c c c c c c c c c c c c} \hline \hline \multirow{2}{*}{**Dataset**} & \multirow{2}{*}{**BKS**} & \multicolumn{8}{c}{**Best Solution**} & \multicolumn{8}{c}{**Average Solution**} \\ \cline{2-13}  & & **TACA** & **ASGCT \({}^{\star}\)** & **ACGCT \({}^{\star}\)** & **MMGCT \({}^{\star}\)** & **IACA** & **TACA** & **ASGCT \({}^{\star}\)** & **ACGCT \({}^{\star}\)** & **MMGCT \({}^{\star}\)** & **IACA** \\ \hline S51D1 & 458 & 545.84 & 520.94 & 516.26 & 492.34 & 466.25 & 551.32 & 526.55 & 525.63 & 507.75 & 480.30 \\ S51D2 & 726 & 841.20 & 833.25 & 816.11 & 808.92 & 727.00 & 847.13 & 838.63 & 825.65 & 817.81 & 741.47 \\ S51D3 & 972 & 116.38 & 1075.30 & 1065.46 & 1060.03 & 940.11 & 1126.52 & 1083.42 & 1075.53 & 1070.38 & 1024.40 \\ S51D4 & 1677 & 1729.55 & 1705.87 & 1697.93 & 1678.50 & 1493.69 & 1741.37 & 1709.36 & 1702.94 & 1690.17 & 1659.02 \\ S51D5 & 1440 & 1470.59 & 1431.80 & 1425.05 & 1421.95 & **1385.01** & 1482.30 & 1440.47 & 1438.78 & 1429.32 & 1407.64 \\ S51D6 & 2327 & 2409.84 & 2325.30 & 2310.76 & 2293.69 & **2261.11** & 4229.45 & 2330.89 & 2324.90 & 2308.66 & 2273.79 \\ S56D1D & 594 & 686.80 & 681.42 & 665.83 & 661.45 & 611.84 & 695.27 & 688.55 & 681.83 & 676.22 & 631.47 \\ S76D2 & 1147 & 1249.53 & 1241.94 & 1233.37 & 1228.70 & 1151.66 & 1252.24 & 1240.50 & 1240.26 & 1238.11 & 1190.20 \\ S76D3 & 1474 & 1655.48 & 1619.65 & 1611.79 & 1568.74 & 1540.38 & 1680.31 & 1627.20 & 1619.21 & 1607.64 & 1567.79 \\ S76D4 & 2257 & 2374.50 & 2306.21 & 2292.60 & 2279.72 & **2229.19** & 2391.05 & 2312.63 & 2302.74 & 2296.79 & 2268.51 \\ S101D1 & 716 & 883.14 & 868.54 & 835.38 & 793.77 & 735.65 & 892.01 & 877.22 & 876.39 & 842.56 & 760.50 \\ S101D2 & 1393 & 1642.72 & 1622.76 & 1606.94 & 1546.38 & 1510.85 & 1647.67 & 1631.83 & 1627.15 & 1602.27 & 1553.99 \\ S101D3 & 1975 & 2127.84 & 2110.99 & 2096.58 & 2082.30 & 2026.97 & 2137.85 & 2118.74 & 2103.45 & 2096.16 & 2063.99 \\ S101D5 & 2915 & 3088.61 & 3036.29 & 3025.76 & 3014.29 & 2957.87 & 3094.72 & 3053.90 & 3038.33 & 3029.32 & 2990.59 \\ \hline \hline \end{tabular}  
* Since the experimental parameter data are not given in the literature [20] and there is no data such as algorithm running time, we wrote test code according to the pseudo code in the literature [20] to obtain more comprehensive experimental data. The test code was applied to the medium-scale dataset experiments and large-scale dataset experiments.  
\end{table} 
Table 9: Comparison of the calculation results obtained on medium-scale datasets. optimization algorithms. Figure 4 shows the reduction rate of these algorithms compared to the TACA, which can more intuitively demonstrate the algorithm's solving performance. These results show that the improved method proposed in this paper improves solution quality.