## 7 Results and Discussions  
We have purposefully developed four arbitrary instances of mUAQMSTP for the sole purpose of this discussion. Instances \(mUAQMST\_Instance10\), \(mUAQMST\_Instance20\), \(mUAQMST\_Instance30\), and \(mUAQMST\_Instance40\) consist of ten, twenty, thirty and forty vertices, which eventually make up these instances, in that order. With \(n\) vertices and \({n\choose 2}\) edges, each of these instances is a UWCN and a complete graph. Here, we have expressed the edge weight of an edge, \(e_{i}\), for each occurrence as an imprecise linear cost, \(\xi_{i}\). In addition, for any one of these cases, there is an imprecise variable, \(\zeta_{ij}\), which represents a quadratic cost for any two neighboring edges, \(e_{i}\) and \(e_{j}\). In this context, \(\xi_{i}\) and \(\zeta_{ij}\) are viewed as zigzag uncertain variables. These variables are represented as \(\mathcal{Z}\left(l_{\xi_{i}},m_{\xi_{i}},n_{\xi_{i}}\right)\) and \(\mathcal{Z}\left(l_{\zeta_{ij}},m_{\zeta_{ij}},n_{\xi_{i}}\right)\) which are created at random to represent the related \(\xi_{i}\) and \(\zeta_{ij}\), respectively. In particular, the values of \(l_{\xi_{i}},m_{\xi_{i}}\), and \(n_{\xi_{i}}\) are generated at random from the interval \([700.5,150.5]\) for every edge, \(e_{i}\), of an instance, with the constraint that \(l_{\xi_{i}}<m_{\xi_{i}}<n_{\xi_{i}}\). Thereafter, \(l_{\zeta_{ij}},m_{\zeta_{ij}}\) and \(n_{\xi_{ij}}\) are chosen at random from the interval \([10.5,80.5]\) for each \(\zeta_{ij}\), with the condition that \(l_{\zeta_{ij}}<m_{\zeta_{ij}}<n_{\zeta_{ij}}\) is satisfied. Taking into account all four of the aforementioned mUAQMSTP instances, NSGAII and DENSEA, subsequently, solve the corresponding crisp equivalent Model (8) for the CCM at 0.4 and 0.9 confidence levels. The two most important performance measures that we use to evaluate the MOEAs on these four instances are hypervolume (HV) ([PERSON] et al. [38]) and inverted generational distance (IGD) ([PERSON] and [PERSON] [39]). A greater value is always preferred for HV. Nevertheless, lesser values are more likely to be attained for IGD. Consequently, HV and IGD, two performance measurements, corroborate each other that non-dominated solutions generated by an MOEA tend to ensure diversity and convergence. For each instance, at both confidence levels, a jMetal4.5 framework ([PERSON], [PERSON] [37]) is used to execute NSGAII and DENSEA on the Model (8). Because MOEAs are inherently stochastic, we have chosen to run each algorithm with 500 generations, 100 times, separately, with the population size of all the MOEAs considered as 100. Subsequently, for both the MOEAs, NSGAII, and DENSEA we employ _bit-flip mutation_, _single-point crossover_, and _binary tournament selection_ as genetic operators with their respective crossover probability as 0.9 and the mutation probability set to 0.05. Here, as indicated in Section 6, the genetic operators and their associated parameters are identical for both methods. The majority of real-world multi-objective scenarios typically make it impossible to obtain the collection of Pareto solutions indicated in a Pareto front (PF). To estimate the PF of an instance, a reference front is created that considers the non-inferior solutions from the first front. In this study, this front is constructed after each run of NSGAII and DENSEA on a specific instance. Following the establishment of the reference front, the solutions that constitute it are employed in the assessment of performance indicators. Figure 5: A possible bus route connecting all the cities for the compromise solution of \(G\) highlighted in bold, as reported in Tables 2 and 3, at the confidence level (**a**) 0.4 and (**b**) 0.9. By calculating the _mean_, standard deviation (_sd_), _median_, and interquartile range (_IQR_), we conduct the statistical analysis of the performance metrics.