## 4 Experimental Study
### Tested Benchmarks
#### 4.3.3 Taguchi Method for Orthogonal Experimental Design
\begin{table}
\begin{tabular}{l c c c} \hline
**DMOPs** & **D** & **M** & **Properties** \\ \hline FDA1 & 20 & 2 & Type I, convex, POS: sinusoidal and vertical shift \\ \hline FDA2 & 15 & 2 & Type II, POP: convex to concave, dynamic density, POS: sinusoidal and vertical shift \\ \hline FDA3 & 30 & 2 & Type II, POP: convex, dynamic spread, POS: sinusoidal and vertical shift \\ \hline FDA4 & 12 & 3 & Type I, POP: concave, dynamic spread, POS: sinusoidal and vertical shift \\ \hline FDA5 & 12 & 3 & Type II, POP: concave, dynamic spread, POS: sinusoidal and vertical shift \\ \hline dMOP1 & 10 & 2 & Type III, POP: convex to concave, POS: no change \\ \hline Muli & dMOP2 & 10 & 2 & Type II, POP: convex to concave, POS: sinusoidal and vertical shift \\ \hline Optimization & dMOP3 & 10 & 2 & Type I, POP: convex, dynamic spread, POS: sinusoidal and vertical shift \\ \hline F5, F6, F7 & 20 & 2 & Type II, POP: convex to concave, POS: sinusoidal and vertical shift \\ \hline F9, F10 & 20 & 2 & Type II, POP: convex to concave, POS: sinusoidal and vertical shift \\ \hline F8 & 20 & 3 & Trigonometric and vertical \\ \hline UDF1 & 10 & 2 & Type I, POP: linear continuous, POS: trigonometric and vertical shift \\ \hline UDF2 & 10 & 2 & Type I, POP: linear continuous, POS: polynomial and vertical shift \\ \hline UDF3 & 10 & 2 & Type III, POP: discontinuous, POS: trigonometric and no variation \\ \hline UDF4 & 10 & 2 & Type II, convex to concave, POS: trigonometric and horizontal shift \\ \hline UDF5 & 10 & 2 & Type II, convex to concave, POS: polynomial + vertical shift \\ \hline UDF6 & 10 & 2 & Type III, discontinuous, POS: trigonometric and no variation \\ \hline UDF7 & 10 & 3 & Type III, POP :3D radius concave, POS: trigonometric and no variation \\ \hline \end{tabular}
\begin{tabular}{l c c c} \hline  & MaF1 & & Linear \\ \hline MaF2 & 11 & 2 & Concave \\ \hline MaF3 & 12 & 3 & Convex, multimodal \\ \hline MaF4 & 16 & 7 & Concave, multimodal \\ \hline MaF5 & & & Convex, biased \\ \hline MaF6 & & & Concave, degenerate \\ \hline \multirow{4}{*}{MaF7} & 21 & 2 & Mixed \\ \cline{2-4}  & 22 & 3 & Disconnected \\ \cline{1-1} \cline{2-4}  & 26 & 7 & Multimodal \\ \hline \end{tabular}
\end{table} 
Table 5: Properties of the tested benchmarks: DMOPs and MaOPsFigure 4 presents a different data distribution according to the configurations of parameters \(p\) and \(q\) of the Beta function, which are fixed to 5 or 50. As mentioned in Table 6, the application of the Taguchi orthogonal arrays identified an array of \(L_{8}(2^{6})\) with only eight best runs for a different combination of parameter designs, with a two-level design for six control factors. The sensitivity of parameter design of the proposed DB-CSA algorithm was confirmed using the Taguchi method. As shown in Table 7, the parameters of Beta1 function with p1 and q1 are equal to 5, and those of Beta2 function with p2 and q2 are equal to 50, to achieve the smallest mean values for MIGD, IGD and HVD metrics and solve DMOPs with severe and moderate changes and MaOPs with seven objectives. However, the experimental study was carried out using the best configuration, obtained using the Taguchi method. \begin{table}
\begin{tabular}{c c c c} \hline
**DMOPs** & & **D** & **M** & **Properties** \\ \hline  & WFG1 & 11 & 2 & Convex, unimodal \\ \hline WFG2 & 12 & 3 & Convex, disconnected \\ \hline WFG3 & 16 & 7 & Linear, unimodal \\ \hline WFG4 & & & Concave, multimodal \\ \hline WFG5 & 12 & 3 & Concave, deceptive \\ \hline WFG6 & 14 & 5 & Concave, unimodal \\ \hline WFG7 & 17 & 8 & Concave, unimodal \\ \hline WFG8 & 19 & 10 & Concave, unimodal \\ \hline WFG9 & 24 & 15 & Concave, multimodal \\ \hline  & & 7 & 3 \\ \cline{2-4} Problems & & 9 & 5 \\ \cline{2-4}  & DTLZ1 & 12 & 8 \\ \cline{2-4}  & & 14 & 10 \\ \cline{2-4}  & & 19 & 15 \\ \hline DTLZ2 & 12 & 3 & Concave \\ \hline DTLZ3 & 14 & 5 & Concave \\ \hline DTLZ4 & 17 & 8 & Concave \\ \hline DTLZ5 & 19 & 10 & Degenerate \\ \hline DTLZ7 & 22 & 3 & Disconnected \\ \hline \end{tabular}
\end{table}