## 4 Experimental Study
### Results Analysis and Discussion
#### 4.4.3 Analysis of the Comparative Study (2) for MaF and WFG Problems with 2, 3 and 7 Objectives
\begin{table}
\begin{tabular}{l c c c c c} \hline
**DB-CSA vs.** & **QI** & **Prob.** & **R\(-\)** & **R+** & \(p\)**-Value** & **Best Method** \\ \hline MSOPS-II & & & 378 & 0 & 0.000006 & \\ MOEA/D & & & 378 & 0 & 0.000006 & \\ HypE & & & 374 & 4 & 0.000009 & \\ PICEA-g & & & 378 & 0 & 0.000006 & \\ SPEA/SDE & & & 376 & 2 & 0.000007 & \\ GrEA & & & 378 & 0 & 0.000006 & \\ NSGA-III & & & 378 & 0 & 0.000010 & DB-CSA \\ KnEA & & & 378 & 0 & 0.000006 & \\ RVEA & & & 378 & 0 & 0.000006 & \\ Two\_Arch2 & & & 374 & 4 & 0.000009 & \\ \(\theta\)-DEA & & & 376.5 & 1.5 & 0.000007 & \\ MOEA/DD & & & 377 & 1 & 0.000006 & \\ AnD & & & 378 & 0 & 0.000006 & \\ CSA & & & 378 & 0 & 0.000006 & \\ \hline MSOPS-II & & & 231 & 0 & 0.000060 & \\ PMEA*-MA & & & 1035 & 0 & 0.000006 & \\ MOEA/D & & & 231 & 0 & 0.000060 & \\ HypE & & & 231 & 0 & 0.000060 & \\ PICEA-g & & & 231 & 0 & 0.000060 & \\ SPEA/SDE & & & 231 & 0 & 0.000060 & \\ GrEA & & & 231 & 0 & 0.000060 & DB-CSA \\ NSGA-III & & & 231 & 0 & 0.000060 & \\ KnEA & & & 231 & 0 & 0.000060 & \\ RVEA & & & 231 & 0 & 0.000060 & \\ Two\_Arch2 & & & 231 & 0 & 0.000060 & \\ \(\theta\)-DEA & & & 231 & 0 & 0.000060 & \\ MOEA/DD & & & 231 & 0 & 0.000060 & \\ AnD & & & 231 & 0 & 0.000060 & \\ CSA & & & 231 & 0 & 0.000060 & \\ \hline PMEA-MA & & & 1035 & 0 & \(5.179\times 10^{-9}\) & \\ PMEA*-MA & & & 1035 & 0 & \(5.179\times 10^{-9}\) & \\ SPEA2/SDE & & & 1035 & 0 & \(5.179\times 10^{-9}\) & \\ NSGA-II/SDR & & & 1035 & 0 & \(5.179\times 10^{-9}\) & DB-CSA \\ VaEA & & & 1035 & 0 & \(5.179\times 10^{-9}\) & \\ SPEA & & & 1035 & 0 & \(5.179\times 10^{-9}\) & \\ CSA & & & 1035 & 0 & \(5.179\times 10^{-9}\) & \\ \hline PMEA-MA & & & 629 & 1 & \(2.70\times 10^{-7}\) & \\ PMEA*-MA & & & 1035 & 0 & \(2.70\times 10^{-7}\) & \\ PMEA*-MA & & & 629 & 1 & \(2.70\times 10^{-7}\) & \\ SPEA2/SDE & & & 630 & 0 & \(2.48\times 10^{-7}\) & DB-CSA \\ NSGA-II/SDR & & & 630 & 0 & \(2.48\times 10^{-7}\) & \\ MaOEA/IGD & & & 630 & 0 & \(2.48\times 10^{-7}\) & \\ VaEA & & & 629 & 1 & \(2.70\times 10^{-7}\) & \\ SPEA & & & 630 & 0 & \(2.48\times 10^{-7}\) & \\ \hline \end{tabular}
\end{table} 
Table 10: Non-parametric statistical analysis based on Wilcoxon signed rank test of DB-CSA vs. thirteen peer MAOEAs over the IGD metric for WFG, MaF and DTLZ functions. DB-CSA approach to solve a set of complex DTLZ and WFG test suites with 3, 5, 8, 10 and 15 objectives. Figure 13 presents the box-plots of all comparable approaches based on the one-way ANOVA test and the obtained figures show the importance of the DB-CSA algorithm for solving the WFG tests with 3, 5 and 15 objectives. Some qualitative results are presented in Figures 14 and 15 to present the estimated POF of the true optimal solutions for both WFG and DTLZ, with 10 and 15 objectives, respectively. However, all quantitative results are given in Tables S8 and S9 of the Supplementary File, presenting the efficiency of the new DB-CSA approach compared to  
Figure 9: The plots of MIGD values for FDA, dMOP functions with (**a**) severe, (**b**) moderate and (**c**) slight environmental changes using the DB-CSA algorithm. Figure 10: The plots of IGD values for FDA, dMOP functions with (**a**) severe, (**b**) moderate and (**c**) slight environmental changes using the DB-CSA algorithm. Figure 11: The plots of HVD values for FDA, dMOP functions with (**a**) severe, (**b**) moderate and (**c**) slight environmental changes using the DB-CSA algorithm. As a global conclusion and based on comparative studies (1) and (2), all quantitative results showed the efficiency of DB-CSA and DB-CSA-II variants and their flexibility in solving eight DMOPs (FDA and dMOP) with 2 and 3 objectives, including several types of time-varying POF and POS, compared to the seven transfer-learning based methods (MMTL-MOEA/D, KF-MOEA/D, PPS-MOEA/D, SVR-MOEA/D, Tr-MOEA/D, and RI-MOEA/D) using the MIGD metric.