## 4 Experimental Study
### Results Analysis and Discussion
#### 4.4.1 Analysis of the Comparative Study (1) for FDA and dMOP Problems  
The comparative study (1) is first considered to compare the proposed DB-CSA-II algorithm to six transfer learning-based methods, the standard CSA algorithm and the first variant DB-CSA and solve FDA and dMOP test beds with severe (\(\tau_{t}=5\), \(n_{t}=10\)), moderate (\(\tau_{t}=n_{t}=10\)) and slight (\(\tau_{t}=20\), \(n_{t}=10\)) environmental changes. The MIG \begin{table}
\begin{tabular}{l c c c c c c c c} \hline \hline \multirow{2}{*}{**Problems**} & \multicolumn{3}{c}{**Population Size**} & \multicolumn{3}{c}{**Max-Iteration**} & \multicolumn{3}{c}{**Parameters of Beta Function**} & \multicolumn{3}{c}{**Best Mean Values**} \\ \cline{3-10}  & & & **p1** & **p2** & **q1** & **q2** & **MIGD** & **IGD** & **HYD** \\ \hline \multirow{8}{*}{DMOPs with Severe Change} & FDA1 & 100 & 250 & 5 & 50 & 5 & \(6.37\times 10^{-7}\) & \(5.73\times 10^{-4}\) & \(2.22\times 10^{-2}\) \\  & FDA2 & 100 & 250 & 5 & 50 & 5 & \(3.33\times 10^{-6}\) & \(2.99\times 10^{-3}\) & \(7.96\times 10^{-1}\) \\  & FDA3 & 100 & 250 & 5 & 50 & 5 & \(2.63\times 10^{-4}\) & \(2.36\times 10^{-4}\) & \(4.89\times 10^{-1}\) \\  & FDA4 & 100 & 250 & 5 & 50 & 5 & \(50\) & \(1.60\times 10^{-6}\) & \(1.44\times 10^{-3}\) & \(7.92\times 10^{-2}\) \\  & FDA5 & 200 & 250 & 50 & 5 & 50 & \(5\) & \(3.14\times 10^{-6}\) & \(2.83\times 10^{-3}\) & \(1.48\times 10^{-1}\) \\  & dMOP1 & 100 & 250 & 5 & 50 & 5 & \(50\) & \(7.28\times 10^{-7}\) & \(6.55\times 10^{-4}\) & \(4.14\times 10^{-3}\) \\  & dMOP2 & 200 & 250 & 50 & 50 & 5 & \(50\) & \(1.26\times 10^{-6}\) & \(1.13\times 10^{-3}\) & \(3.80\times 10^{-2}\) \\  & dMOP3 & 200 & 250 & 50 & 50 & 5 & \(50\) & \(5.21\times 10^{-5}\) & \(4.69\times 10^{-2}\) & \(4.23\times 10^{+0}\) \\ \hline \multirow{8}{*}{DMOPs with Moderate change} & FDA1 & 100 & 350 & 5 & 50 & 5 & 50 & \(6.35\times 10^{-7}\) & \(5.71\times 10^{-4}\) & \(1.96\times 10^{-2}\) \\  & FDA2 & 100 & 350 & 5 & 50 & 5 & 50 & \(4.19\times 10^{-6}\) & \(3.77\times 10^{-3}\) & \(4.33\times 10^{+0}\) \\  & FDA3 & 100 & 350 & 5 & 50 & 50 & \(4.69\times 10^{-4}\) & \(4.22\times 10^{-1}\) & \(6.24\times 10^{-1}\) \\  & FDA4 & 100 & 350 & 5 & 50 & 5 & \(50\) & \(1.43\times 10^{-6}\) & \(1.29\times 10^{-3}\) & \(3.67\times 10^{-2}\) \\  & FDA5 & 100 & 350 & 5 & 50 & 5 & \(50\) & \(3.90\times 10^{-6}\) & \(3.51\times 10^{-3}\) & \(1.61\times 10^{-1}\) \\  & dMOP1 & 100 & 350 & 5 & 50 & 5 & 50 & \(5.95\times 10^{-7}\) & \(5.35\times 10^{-4}\) & \(1.99\times 10^{-2}\) \\  & dMOP2 & 100 & 350 & 50 & 5 & 5 & 50 & \(1.02\times 10^{-6}\) & \(9.18\times 10^{-4}\) & \(3.13\times 10^{-2}\) \\  & dMOP3 & 200 & 350 & 5 & 50 & 5 & 50 & \(3.36\times 10^{-5}\) & \(3.02\times 10^{-2}\) & \(1.68\times 10^{-1}\) \\ \hline \multirow{8}{*}{MaOPs with 7 objectives} & WFG1 & 100 & 25,000 & 5 & 50 & 5 & \(0\) & - & \(2.42\times 10^{-4}\) & - \\  & WFG2 & 100 & 25,000 & 5 & 5 & 50 & - & \(2.53\times 10^{-4}\) & - \\  & WFG3 & 100 & 25,000 & 5 & 50 & 5 & \(50\) & - & \(5.87\times 10^{-5}\) & - \\  & WFG4 & 100 & 25,000 & 50 & 5 & 5 & 50 & - & \(4.09\times 10^{-4}\) & - \\  & WFG5 & 100 & 25,000 & 50 & 5 & 5 & 50 & - & \(1.54\times 10^{-4}\) & - \\  & WFG6 & 100 & 25,000 & 50 & 5 & 5 & 50 & - & \(3.57\times 10^{-4}\) & - \\  & WFG7 & 100 & 25,000 & 50 & 5 & 5 & 50 & - & \(3.87\times 10^{-4}\) & - \\  & WFG8 & 100 & 25,000 & 5 & 50 & 5 & 50 & - & \(1.91\times 10^{-3}\) & - \\  & WFG9 & 100 & 25,000 & 5 & 50 & 5 & 50 & - & \(7.93\times 10^{-4}\) & - \\ \hline \hline \end{tabular}
\end{table} 
Table 7: Best Experimental Design using Taguchi Method for MIGD, IGD, HVD Metric for DMOPs (FDA, dMOP) with Severe and Moderate Dynamic Changes and MoAps with 7 Objectives (WFG). metric aims to measure the mean value of the obtained IGD values and is used to measure the convergence and diversity of the obtained POF compared to the true one.