## 4 Experimental Results
### Computational Results
\begin{table}
\begin{tabular}{c c c c c c c c c c} \hline \hline \multirow{2}{*}{**Instance**} & \multirow{2}{*}{**Current**} & \multicolumn{3}{c}{**PSO**} & \multicolumn{2}{c}{**Time**} & \multicolumn{2}{c}{**DE**} & \multirow{2}{*}{**Time**} \\ \cline{3-6}  & & **Best** & **Average** & **SD** & & & **(s)** & **Best** & **Average** & **SD** & **(s)** \\ \hline
35 & 35.12 & 20.7 & 22.09 & 0.7 & 166.5 & 17.49 & 17.89 & 0.37 & 174.06 \\
36 & 34.74 & 20.72 & 21.66 & 0.55 & 180.39 & 16.98 & 17.91 & 0.38 & 185.7 \\
37 & 30.19 & 19.34 & 20.57 & 0.48 & 164.51 & 14.54 & 16.33 & 0.95 & 164.86 \\
38 & 31.82 & 18.49 & 19.36 & 0.46 & 155.19 & 15.56 & 16.55 & 0.55 & 162.95 \\
39 & 31.39 & 17.82 & 18.84 & 0.48 & 152.59 & 14.74 & 15.28 & 0.4 & 155.57 \\
40 & 29.36 & 18.68 & 19.59 & 0.41 & 148.9 & 14.19 & 14.91 & 0.47 & 147.4 \\
41 & 31.88 & 18.53 & 19.21 & 0.4 & 157.6 & 14.53 & 15.13 & 0.39 & 156.06 \\
42 & 32.20 & 19.32 & 20.33 & 0.44 & 200.58 & 15.15 & 16.23 & 0.53 & 203.92 \\
43 & 30.42 & 18.77 & 19.46 & 0.29 & 132.47 & 15.16 & 15.86 & 0.4 & 124.59 \\
44 & 33.57 & 18.64 & 19.31 & 0.43 & 163.96 & 15.72 & 15.95 & 0.16 & 172.84 \\
45 & 30.40 & 17.99 & 18.65 & 0.42 & 129.07 & 15.66 & 16 & 0.3 & 137.2 \\
46 & 38.38 & 21.45 & 22.05 & 0.41 & 220.58 & 16.74 & 17.48 & 0.53 & 216.86 \\
47 & 28.97 & 17.31 & 19.16 & 0.67 & 157.94 & 15.34 & 15.64 & 0.29 & 153.27 \\
48 & 30.18 & 19.46 & 20.37 & 0.46 & 190.09 & 15.69 & 16.34 & 0.4 & 202.63 \\
49 & 33.70 & 20.81 & 21.44 & 0.27 & 177.48 & 16.57 & 16.95 & 0.44 & 201.89 \\
50 & 31.68 & 18.19 & 18.85 & 0.38 & 172.02 & 14.32 & 14.85 & 0.52 & 163.4 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: \(Cont.\)According to the results in Table 3, it is obvious that both the PSO and DE algorithms performed very well in generating solutions with less distance, compared with those obtained from the current practices for all instances, with fast computing times. Both algorithms were able to provide robust solutions with small standard deviations. However, it was observed that DE clearly outperformed PSO, since DE was able to generate the better solution quality for the best and average travel distances in all instances. In Table 4, DE shows its superiority to PSO for all instances by providing higher _PD_ values from the current practice solutions. The percentage deviation (_PD_) of the distance ranged from 33.34 to 45.91 with an average of 39.93 for the PSO algorithm and from 42.92 to 57.88 with an average of 51.62 for the DE algorithm. Moreover, the performance differences between PSO and DE are visually demonstrated in Figure 8, showing box plots of the total travel distance from 10 replicated runs of the PSO and DE algorithms, which used solutions from instances 1, 20, 40 and 50. According to the results in Figure 8, it is clearly seen that the solutions obtained from DE were significantly better than those obtained by PSO. Lastly, the behavior of the algorithms was investigated in terms of time and space complexity (i.e., how the algorithm runtime and space requirements scaled when the inputs grew). Specifically, the plots of the algorithm runtimes and memory usages versus the number of visited locations (customers plus the post office) were constructed as shown in Figures 9 and 10. The number of locations ranged from 10 to 100, with the distance matrix randomly generated specifically for the complexity examination of those algorithms. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline \multirow{2}{*}{**Instance**} & \multirow{2}{*}{**Current Practice**} & \multicolumn{3}{c}{**PSO**} & \multicolumn{2}{c}{**DE**} \\ \cline{3-6}  & & **Best** & _PD_ & **Best** & _PD_ \\ \hline  
\hline \multicolumn{6}{c}{_Average_} & \multicolumn{3}{c}{39.93} & \multicolumn{3}{c}{_51.62_} \\ \hline \hline \end{tabular}
\end{table} 
Table 4: _Cont._Figure 8: Box plot comparison of the total travel distance (km) from 10 replicated runs between the PSO and DE algorithms (instances 1, 20, 40 and 50). Figure 10: Plot between the algorithm memory usage (DE and PSO) and the visited locations.