## 4 Results
More detailed data are contained in the Tables 2 and 4 together with the results of the Mann-Whitney test. According to the Mann-Whitney test results (column **T**), the EA algorithm was worse than the ABC algorithm only for NetworkSize = 5, 7 for BLP and ELP variants. For each bigger size of network \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**Network** & \multicolumn{2}{c}{**EA**} & \multicolumn{2}{c}{**ABC**} & \multirow{2}{*}{**MIP**} & \multicolumn{2}{c}{**Wilcoxon–Mann–Whitney Test**} \\
**\#Node** & **Mean** & & & **Best** & & **Mean** & **Best** \\ \hline
5 & 206 & 206 & 167 & 165 & 153 & \(-\) \\
7 & 402 & 401 & 362 & 354 & 341 & \(-\) \\
10 & 935 & 930 & 923 & 911 & 855 & \(=\) \\
12 & 1296 & 1284 & 1325 & 1293 & 1156 & \(+\) \\
15 & 2135 & 2104 & 2241 & 2191 & 1947 & \(+\) \\
17 & 2746 & 2688 & 2850 & 2762 & 2489 & \(+\) \\
20 & 4134 & 4080 & 4201 & 4054 & 3601 & \(+\) \\
22 & 5134 & 5170 & 5111 & 5187 & 4464 & \(+\) \\
25 & 7182 & 7262 & 7154 & 7331 & 6280 & \(=\) \\
30 & 11,378 & 11,260 & 11,331 & 11,113 & 9379 & \(=\) \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Comparison of the average and the best value of the objective function evaluation for each test case together with the outcomes of the paired Wilcoxon test, for the BLP model. Symbols \(+\), \(-\) and \(=\), in the last column, indicate whether the EA algorithm was better (\(+\)), worse (\(-\)) or equal (\(=\)) to the ABC algorithm. Figure 2: Convergence curves plotted for the algorithms considered, for a logistic network of different sizes, for the ELP model. Each curve is an average of 20 independent runs. (**a**) 5-node. (**b**) 10-node. (**c**) 15-node. (**d**) 20-node. (**e**) 25-node. (**f**) 30-node. considered in conducted experiments, the EA outperformed the ABC heuristic. The bigger the size of the network, the more noticeable the difference between heuristics. It is still worth emphasising that, despite the fact that the proposed heuristics do not find an optimal solution, suboptimal solutions are acceptable in the practical problems considered, especially as the calculations are not so time-consuming. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**Network** & \multicolumn{2}{c}{**EA**} & \multicolumn{2}{c}{**ABC**} & \multicolumn{2}{c}{**Wilcoxon–Mann–Whitney Test**} \\
**\#Node** & **Mean** & **std** & **Mean** & **std** & **MIP** & \multicolumn{1}{c}{**Whitney Test**} \\ \hline
5 & 14 & 0.2 & 2 & 0.1 & 11 & – \\
7 & 26 & 0.9 & 7 & 0.2 & 121 & – \\
10 & 76 & 1.93 & 75 & 11 & 43,200 & \(=\) \\
12 & 132 & 3.6 & 161 & 13 & 43,200 & \(+\) \\
15 & 317 & 4.7 & 533 & 23 & 43,200 & \(+\) \\
17 & 440 & 8.4 & 682 & 45 & 43,200 & \(+\) \\
20 & 1355 & 60 & 2580 & 149 & 43,200 & \(+\) \\
22 & 1355 & 60 & 2588 & 150 & 43,200 & \(+\) \\
25 & 2281 & 80 & 3908 & 528 & 43,200 & \(+\) \\
30 & 4963 & 86 & 11,212 & 1213 & 43,200 & \(+\) \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Comparison of the computation time (sec.) together with the outcomes of the paired Wilcoxon test, for the ELP model. Symbols \(+\), \(-\) and \(=\) indicate whether the EA algorithm was better (\(+\)), worse (\(-\)) or equal (\(=\)) to the ABC algorithm. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**Network** & \multicolumn{2}{c}{**EA**} & \multicolumn{2}{c}{**ABC**} & \multicolumn{2}{c}{**Wilcoxon–Mann–Whitney Test**} \\
**\#Node** & **Mean** & **std** & **Mean** & **std** & **MIP** & \multicolumn{1}{c}{**Whitney Test**} \\ \hline
5 & 12 & 0.3 & 1.98 & 0.1 & 4 & – \\
7 & 26 & 1.3 & 7 & 0.3 & 83 & – \\
10 & 83 & 1.1 & 129 & 8.2 & 83 & \(+\) \\
12 & 132 & 1.54 & 162 & 16.4 & 43,200 & \(+\) \\
15 & 325 & 3.35 & 518 & 37.5 & 43,200 & \(+\) \\
17 & 463 & 10 & 773 & 53.1 & 43,200 & \(+\) \\
20 & 1023 & 22 & 1816 & 155 & 43,200 & \(+\) \\
22 & 1392 & 16 & 2568 & 230 & 43,200 & \(+\) \\
25 & 2813 & 44.4 & 5353 & 298 & 43,200 & \(+\) \\
30 & 5885 & 84 & 12,146 & 1949 & 43,200 & \(+\) \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Comparison of the computation time (sec.)