## 7 Results and Discussions
 }} & \multirow{2}{*}{**MOEA**} & \multicolumn{8}{c}{**Uncertain Instances**} \\ \cline{3-14}  & & \multicolumn{3}{c}{**mIAQMSTP_Instances**} & \multicolumn{3}{c}{**mIAQMSTP_Instances**} & \multicolumn{3}{c}{**mIAQMSTP_Instances**} & \multicolumn{3}{c}{**mIAQMSTP_Instances**} \\ \cline{3-14}  & & \multicolumn{3}{c}{_HV_} & \multicolumn{3}{c}{_ICD_} & \multicolumn{3}{c}{_HV_} & \multicolumn{3}{c}{_ICD_} & \multicolumn{3}{c}{_HV_} & \multicolumn{3}{c}{_ICD_} & \multicolumn{3}{c}{_HV_} & \multicolumn{3}{c}{_ICD_} \\ \hline \hline \multirow{4}{*}{0.4} & \multirow{2}{*}{NCGAII} & \(\mathbf{6.17\times}\) & \(\mathbf{8.80\times}\) & \(\mathbf{6.24\times}\) & \(3.46\times\) & \(6.63\times\) & \(\mathbf{8.93\times}\) & \(\mathbf{4.45\times}\) & \(2.20\times\) & \(6.420\times\) & \(\  
Figure 8: Gardner–Altman plot for the HV generated by the MOEAs for the uncertain instances including \(mUAQMST\_Instance10\), \(mUAQMST\_Instance20\), \(mUAQMST\_Instance30\), and \(mUAQMST\_Instance40\) at confidence levels 0.4 (**–d**), and 0.9 (**–h**). Figure 9: Gardner-Altman plot for the IGD generated by the MOEAs for the uncertain instances including \(mUAQMST\_Instance10\), \(mUAQMST\_Instance20\), \(mUAQMST\_Instance30\), and \(mUAQMST\_Instance40\) at confidence levels 0.4 (**–d**), and 0.9 (**–h**). We have also compared the execution time of the algorithms used in this study, i.e., NSGAII and DENSEA, for all instances. Here, it is to be mentioned that we also considered another algorithm multi-objective cross generational elitist selection, heterogeneous recombination and cataclysmic mutation (MOCHC) ([PERSON] et al. [42]) from the literature. The parameter settings of the algorithms are the population size of 100, the 500-generation limit for each MOEA, and the crossover probability and the mutation probability, which are, respectively, set as 0.9 and 0.05. The test platform used for the simulation of our proposed study is a personal computer with Intel (R) Core TM [EMAIL_ADDRESS] GHz and 4 MB memory. The execution times of all the instances are shown in Table 6. Here, we can observe that for all the instances, DENSEA takes minimum computation time (highlighted in bold) to generate the solutions compared to its counterparts. Furthermore, considering all the four mUAQMSTP instances, we perform a two-level hypothesis testing on the performance metrics, HV and IGD. Here, at first, the null hypothesis (\(h_{0}\)) is tested for the two-sample parametric \(t\)-test for which the \(p\)-value is set as \(p^{+}\). Here, if the \(h_{0}\) is rejected, then we accept the value of \(p^{+}\). However, if \(h_{0}\) is accepted, then we conduct the two-sided nonparametric Wilcoxon signed-rank test for the same \(h_{0}\) and observe its corresponding \(p\)-value, which is represented as \(p^{-}\). In this context, it should be mentioned that as the distributions of the generation of the HV and IGD are unknown; therefore, we performed two-level hypothesis testing comprising both parametric and non-parametric tests. Accordingly, the \(h_{0}\) for the test is set as follow:  
\(h_{0}:\) Significantly equal performance metrics are engendered by NSGAII and DENSEA. Subsequently, in Table 7 we provide the result of the hypothesis testing, which is achieved at 5% level of significance. In this table, the column DENSEA+NSGAII conclude either of the following two conditions. 1. DENSEA\(\sim_{p^{+}or}p^{-}\)NSGAII: At 5% level of significance, DENSEA is significantly better than NSGAII, and \(h_{0}\) is not accepted at \(p^{+}or\)\(p^{-}\). 2. DENSEA\(\sim_{p^{+}or}p^{-}\)NSGAII: At 5% level of significance, DENSEA is significantly better than NSGAII, and \(h_{0}\) is accepted at \(p^{+}\)\(or\)\(p^{-}\).