# Ant-Balanced Multiple Traveling Salesmen: ACO-BmTSP
## 3 Experimental Results and Analysis
### Computational Results  
In order to evaluate the proposed algorithm's performance, several benchmark mTSP instances were tested. All of the experiments were performed on the Google Colab platform, which allowed code in the Python language to be run. The instances used considered several numbers of cities and \(m=\{3,5,10,15\}\) salesmen, leading to 19 different problems. Each instance was run, and the results are presented in Table 2. Columns 1 and 2 indicate the numbers of cities and salesmen. Column 3 presents the total cost of each solution. In the next columns, Avg and Std present the average and standard deviation, respectively. The following five columns indicate each tour's cost in descending order. The first five tours are in black in the line, and for the ten- and fifteen-salesman problems, the next five and last five are in gray in the second and third lines, respectively. For the problem with 51 cities and three salesmen, a total cost of 468.09 and tour costs of \(\{160.73,154.69,152.68\}\) were obtained. The tours had a difference of 8.05 between the maximum and the minimum cost, leading to an average of 156.03 and a standard \begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline  & & & & & & \multicolumn{3}{c}{**TSP N.\({}^{*}\) (\(\mathbf{l=\{0,1,2,3\}}\))**} \\ \cline{5-10} _Name_ & \(m\) & **Total** & **Avg.** & **Std.** & \(\mathbf{1+\texttt{SI}}\) & \(\mathbf{2+\texttt{SI}}\) & \(\mathbf{3+\texttt{SI}}\) & \(\mathbf{4+\texttt{SI}}\) & \(\mathbf{5+\texttt{SI}}\) \\ \hline mTSP51 & 3 & 468.09 & 156.03 & 4.19 & 160.73 & 154.69 & 152.68 & – & – \\  & 5 & 523.78 & 104.75 & 7.41 & 117.36 & 105.00 & 101.91 & 100.92 & 98.58 \\  & 10 & 765.83 & 76.58 & 9.30 & 93.44 & 88.11 & 82.39 & 79.43 & 76.61 \\  & & & & & 74.41 & 70.36 & 68.39 & 66.64 & 66.06 \\ \hline mTSP100 & 3 & 24,455.04 & 8151.69 & 579.15 & 8580.49 & 8381.72 & 7492.87 & – & – \\  & 5 & 27,309.44 & 5461.89 & 311.23 & 5772.65 & 5664.10 & 5591.60 & 5255.97 & 5025.12 \\  & 10 & 43,824.70 & 4382.47 & 689.43 & 5264.51 & 5136.02 & 4942.60 & 4870.01 & 4508.78 \\  & & & & & 4148.68 & 4119.31 & 4086.25 & 3619.29 & 3129.26 \\ \hline mTSP150 & 3 & 39,471.09 & 13,157.03 & 76.97 & 13,211.62 & 13,190.47 & 13,069.00 & – & – \\  & 5 & 44,322.33 & 8864.47 & 146.69 & 9082.80 & 8922.60 & 8845.47 & 8763.26 & 8,708.21 \\  & 10 & 58,298.47 & 5829.85 & 508.42 & 6221.31 & 6188.45 & 6125.01 & 6103.19 & 5,974.78 \\  & & & & & 5957.49 & 5936.46 & 5700.35 & 5587.74 & 4503.69 \\ \hline
11a & 3 & 224.18 & 74.73 & 5.12 & 78.17 & 77.17 & 68.85 & – & – \\ \hline
11b & 3 & 265.09 & 88.36 & 10.80 & 96.31 & 92.71 & 76.07 & – & – \\ \hline
12a & 3 & 226.53 & 75.51 & 3.77 & 78.17 & 77.17 & 71.20 & – & – \\ \hline
12b & 3 & 3073.08 & 1024.36 & 108.56 & 1100.77 & 1072.21 & 900.10 & – & – \\ \hline
16 & 3 & 271.79 & 90.60 & 4.38 & 93.89 & 92.28 & 85.62 & – & – \\ \hline mTSP128 & 10 & 47,256.11 & 4725.61 & 1268.96 & 6304.43 & 6247.17 & 6163.11 & 5954.47 & 3967.22 \\  & & & & 3954.17 & 3904.04 & 3902.46 & 3765.28 & 3093.76 \\  & 15 & 75,394.28 & 5026.29 & 1187.69 & 6190.42 & 6143.34 & 6127.44 & 6020.33 & 5995.13 \\  & & & & & 5954.85 & 5886.04 & 5655.69 & 5006.01 & 5001.86 \\  & & & & & 3601.67 & 3600.24 & 3565.89 & 3382.81 & 3262.55 \\ \hline kroD100 & 3 & 26,009.03 & 8669.68 & 1077.89 & 9828.23 & 8484.31 & 7696.49 & – & – \\  & 5 & 32,808.35 & 6561.67 & 926.92 & 7929.75 & 6918.62 & 6528.11 & 5770.61 & 5661.26 \\  & 10 & 47,256.09 & 4725.61 & 1268.96 & 6304.43 & 6247.17 & 6163.11 & 5954.47 & 3967.22 \\  & & & & & 3954.16 & 3904.04 & 3902.46 & 3765.27 & 3093.76 \\ \hline rat783 & 20 & 25,089.70 & 1254.55 & 136.22 & 1413.45 & 1374.56 & 1365.69 & 1353.25 & 1347.03 \\  & & & & 1345.72 & 1338.38 & 1322.84 & 1313.55 & 1303.64 \\  & & & & 1299.97 & 1289.81 & 1276.78 & 1231.01 & 1221.94 \\  & & & & 1201.95 & 1157.57 & 1023.50 & 1005.08 & 903.99 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Total and partial distance traveled by salesmen when using the ACO-BmTSP algorithm. deviation of 4.19.