# Improvement Technique for Group Search Optimization Using Experimental Design Method
## 2 Related Work
### Taguchi Method  
The Taguchi method proposed by [PERSON] [38] is a statistics-based experimental design method widely used to solve practical design issues, including parameter design, system design, and tolerance design [39]. Compared with the vast amount of experiments required for factorial experiments, the orthogonality of the Taguchi method substantially reduces experimental costs and simplifies data analysis. Taguchi method uses three static characteristics for evaluation indicators: the smaller-the-better characteristic, the nominal-the-best characteristic, and the larger-the-better characteristic. In this study, the Taguchi method is used to enhance the regional search capability of the GSO algorithm, and the smaller-the-better characteristic is used to analyze the factor response.  
The Taguchi method uses an \(L_{a}(b^{c})\) orthogonal table to arrange experiments, where \(a\) is the number of experiments, \(b\) is the number of levels for each factor, and \(c\) is the maximum of factors. Table 4 is an \(L_{8}(2^{7})\) orthogonal table.  
After the orthogonal table required for Taguchi method is established, the factor response table is established based on the SNR (signal-to-noise ratio, \(\eta\)) observed after the experiment [47] as shown in Equation (11):  
\[\eta_{i}=-10 log \tag{11}\]  
where \(y_{ii}\) is the \(t\)th result of the \(i\)th experimental combination.  
Table 5 is an example of the response table. The experimenter can determine whether a factor performs well and at which levels by comparing the response values at different levels.  
\begin{table}
\begin{tabular}{c c c c c c c c c c c} \hline \hline \multirow{2}{*}{**No.**} & \multicolumn{8}{c}{**Factors**} & \multirow{2}{*}{**Result**} & \multirow{2}{*}{**SNR**} \\ \cline{2-2} \cline{4-10}  & **A** & **B** & **C** & **D** & **E** & **F** & **G** & \\ \hline
1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & \(y_{11}\) & \(y_{12}\) & \(y_{13}\) & \(\eta_{1}\) \\
2 & 1 & 1 & 1 & 2 & 2 & 2 & 2 & \(y_{21}\) & \(y_{12}\) & \(y_{23}\) & \(\eta_{2}\) \\
3 & 1 & 2 & 2 & 1 & 1 & 2 & 2 & \(y_{31}\) & \(y_{32}\) & \(y_{33}\) & \(\eta_{3}\) \\
4 & 1 & 2 & 2 & 2 & 2 & 1 & 1 & \(y_{41}\) & \(y_{42}\) & \(y_{43}\) & \(\eta_{4}\) \\
5 & 2 & 1 & 2 & 1 & 2 & 1 & 2 & \(y_{51}\) & \(y_{52}\) & \(y_{53}\) & \(\eta_{5}\) \\
6 & 2 & 1 & 2 & 2 & 1 & 2 & 1 & \(y_{61}\) & \(y_{62}\) & \(y_{63}\) & \(\eta_{6}\) \\
7 & 2 & 2 & 1 & 1 & 2 & 2 & 1 & \(y_{71}\) & \(y_{72}\) & \(y_{73}\) & \(\eta_{7}\) \\
8 & 2 & 2 & 1 & 2 & 1 & 1 & 2 & \(y_{81}\) & \(y_{82}\) & \(y_{83}\) & \(\eta_{8}\) \\ \hline \hline \end{tabular}
\end{table}
Table 4: A usage table of the \(U_{11}\) uniform layout.  
\begin{table}
\begin{tabular}{c c} \hline \hline \multicolumn{1}{c}{**The Number of Factors**} & **Columns Need to Be Selected** \\ \hline
2 & 1 7 \\
3 & 1 5 7 \\
4 & 1 2 5 7 \\
6 & 1 2 3 5 7 8 \\ \hline \hline \end{tabular}
\end{table}
Table 3: A usage table of the \(U_{11}\) and \(U_{10}\) uniform layouts.  
\begin{table}
\begin{tabular}{c c c c c c c c c c} \hline \hline \multirow{2}{*}{**Terms**} & \multicolumn{8}{c}{**Factors**} \\ \cline{2-10}  & **A** & **B** & **C** & **D** & **E** & **F** & **G** & \\ \hline Level 1 & \(\eta_{A1}\) & \(\eta_{B1}\) & \(\eta_{C1}\) & \(\eta_{D1}\) & \(\eta_{E1}\) & \(\eta_{F1}\) & \(\eta_{G1}\) \\ Level 2 & \(\eta_{A2}\) & \(\eta_{B2}\) & \(\eta_{C2}\) & \(\eta_{D2}\) & \(\eta_{E2}\) & \(\eta_{F2}\) & \(\eta_{F2}\) \\ \hline \hline \end{tabular}
\end{table}
Table 5: A response table from the \(L_{8}(2^{7})\) orthogonal table.  
Here, factor A is taken as an example to illustrate how to calculate the response value of each level.  
\[\eta_{A1}=(\eta_{1}+\eta_{2}+\eta_{3}+\eta_{4})/4 \tag{12}\]  
\[\eta_{A2}=(\eta_{5}+\eta_{6}+\eta_{7}+\eta_{8})/4 \tag{13}\]  
Equations (12) and (13) can be used to evaluate the performance of each factor at different levels. First, \(\eta\) and the level of each factor should be collected and then averaged. The best factor level can then be obtained from the response table.