## 6 Numerical Illustrations
Subsequently, it is important to note that by adjusting the the chance (confidence) level to 0.4 and 0.9, we may solve Model (9). Consequently, Table 1 reports the compromise solutions of Model (9), where we can observe that with 0.4 and 0.9 confidence levels for both the model's objective functions, respectively, two distinct quadratic minimum spanning trees are produced. Here, in Table 1, \(\overline{F}_{1}\) represents the total possible expense for providing bus services between all the cities and \(\overline{F}_{2}\) determines the total possible discount to be offered by the company at two different confidence levels (i.e., 0.4 and 0.9) as set by the decision makers (project managers). Figure 2: An undirected weighted connected network, \(G\). It should be noted that the project managers aim to find the most efficient bus route by taking into account (i) the entire cost of running the service between all cities and (ii) the total discount that may be provided on ticket fares of the customers who will avail two successive buses of the company. The associated deterministic multi-objective Model (8) is solved using the two MOEAs, NSGAII, and DENSEA, to determine multiple non-dominated solutions of the CCM of \(G\) at confidence levels 0.4 and 0.9. The population size of all the MOEAs is considered as 100 and there is a 500-generations limit for each MOEAs. In this case, NSGAII and DENSEA both employ _bit-flip mutation_, _single-point crossover_, and _binary tournament selection_ as genetic operators. On top of that, the crossover probability is 0.9, and the mutation probability is 0.05 for both MOEAs. Furthermore, the non-dominated solutions of Model (8) for \(G\) are generated using a \(\mathrm{j}\)Metal4.5 framework (Durillo and Nebro [37]). Tables 2 and 3 detail these solutions that did not dominate each other, meaning they are not inferior. Here, each solution represents a possible bus route, which the decision makers can select. In this situation, we find that for both the 0.4 and 0.9 confidence levels of CCM, one of the non-inferior solutions generated by the MOEAs is the same as the solution generated by the global criterion approach (see Table 1). The bold solutions stand out. It can be shown from Tables 2 and 3 that DENSEA produces a higher number of non-dominated solutions for the CCM of \(G\) rather than NSGAII. Figures 3 and 4 provide a visual depiction of the non-dominated solutions that are created for the CCM. Additionally, Figure 5a, and Figure 5b also provide graphical illustrations of the possible bus routes corresponding to the nondominated solutions which are highlighted in bold as reported, respectively, in Tables 2 and 3. \begin{table}
\begin{tabular}{c c c c c} \hline \multicolumn{4}{c}{**CCM**} \\ \hline \multicolumn{4}{c}{**Confidence Level at 0.4**} & \multicolumn{3}{c}{**Confidence Level at 0.9**} \\ \hline \(-\) & \(-\) & \(-\) & \(-\) \\ \(\mathbf{F_{1}}\) & \(\mathbf{F_{2}}\) & **Minimum Spanning Tree of \(G\)** & \(\mathbf{F_{1}}\) & \(\mathbf{F_{2}}\) & **Minimum Spanning Tree of \(G\)** \\ \hline
1289.46 & 194.28 & \(\{e_{5},e_{8},e_{10},e_{11},e_{19},e_{21}\}\) & 1323.18 & 196.38 & \(\{e_{4},e_{5},e_{8},e_{13},e_{18},e_{21}\}\) \\ \hline \end{tabular}
\end{table} 
Table 1: The mUAQMSTs of \(G\) as obtained by solving the compromise deterministic equivalents of CCM at confidence levels of 0.4 and 0.9.