## 4 Experiments  
### Parameter Setting  
To test the performance of the proposed method in this work, numerical experiments are carried out. The GA presented in Procedure 1 is coded in MATLAB and runs on a laptop with eight Intel(R) Core(TM) i7-10750H CPU @2.60 GHz. In order to select a better group of parameters (including \(\gamma\), \(n\)-tournament, \(P_{c}\), and \(P_{m}\)) for the GA, experiments were performed with different parameter settings for 20 cases. Let \(\Gamma_{1}=(n_{1}\), \(n_{2}\ \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**Population** & \multirow{2}{*}{_n-_Tournament_} & \multirow{2}{*}{_Pc_} & \multirow{2}{*}{_Pm_} & \multirow{2}{*}{_No._} & \multirow{2}{*}{_TI\({}_{\
u}\)_,_ \(i\) \(\in\) {1, 2,..., 45} & \(\varphi_{\
u}\)_,_ \(i\) \(\in\) {1, 2,..., 45} \\ \hline  & & & 0.05 & 1 & 441 & 44.35 \\ \cline{3-6}  & & & 0.15 & 2 & 583 & 30.35 \\ \cline{3-6}  & & & 0.25 & 3 & 734 & 21.50 \\ \cline{3-6}  & & & 0.05 & 4 & 452 & 43.30 \\ \cline{3-6}
10 & 5 & 0.3 & 0.15 & 5 & 604 & 30.20 \\ \cline{3-6}  & & & 0.25 & 6 & 732 & 19.85 \\ \cline{3-6}  & & & 0.05 & 7 & 447 & 42.55 \\ \cline{3-6}  & & & 0.15 & 8 & 627 & 29.10 \\ \cline{3-6}  & & & 0.25 & 9 & 741 & 18.80 \\ \hline  & & & 0.05 & 10 & 513 & 39.60 \\ \cline{3-6}  & & & 0.15 & 11 & 682 & 24.70 \\ \cline{3-6}  & & & 0.25 & 12 & 834 & 12.40 \\ \cline{3-6}  & & & 0.05 & 13 & 531 & 36.55 \\ \cline{3-6}
5 & 0.3 & & 0.15 & 14 & 721 & 21.60 \\ \cline{3-6}  & & & 0.25 & 15 & 833 & 12.25 \\ \cline{3-6}  & & & 0.05 & 16 & 534 & 35.75 \\ \cline{3-6}  & & & 0.15 & 17 & 721 & 20.40 \\ \cline{3-6}
20 & & & 0.25 & 18 & 872 & 9.25 \\ \hline  & & & 0.05 & 19 & 525 & 39.55 \\ \cline{3-6}  & & & 0.15 & 20 & 667 & 22.15 \\ \cline{3-6}  & & & 0.25 & 21 & 815 & 12.40 \\ \cline{3-6}  & & & 0.05 & 22 & 513 & 38.85 \\ \cline{3-6}
10 & 0.3 & & 0.15 & 23 & 719 & 24.95 \\ \cline{3-6}  & & & 0.25 & 24 & 850 & 10.10 \\ \cline{3-6}  & & & 0.05 & 25 & 548 & 36.40 \\ \cline{3-6}  & & & 0.15 & 26 & 713 & 22.40 \\ \cline{3-6}  & & & 0.25 & 27 & 890 & 8.30 \\ \hline  & & & 0.05 & 28 & 558 & 34.30 \\ \cline{3-6}  & & & 0.15 & 29 & 772 & 19.90 \\ \cline{3-6}  & & & 0.25 & 30 & 909 & 6.85 \\ \cline{3-6}  & & & 0.05 & 31 & 576 & 32.40 \\ \cline{3-6}
5 & 0.3 & & 0.15 & 32 & 770 & 14.65 \\ \cline{3-6}  & & & 0.25 & 33 & 931 & 4.95 \\ \cline{3-6}  & & & 0.05 & 34 & 596 & 28.85 \\ \cline{3-6}  & & & 0.15 & 35 & 763 & 13.70 \\ \cline{3-6}  & & & 0.25 & 36 & 970 & 6 \\ \cline{3-6}
30 & & & 0.05 & 37 & 552 & 32.90 \\ \cline{3-6}  & & & 0.15 & 38 & 759 & 19.55 \\ \cline{3-6}  & & & 0.25 & 39 & 906 & 7.45 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Experimental results of the presented GA with different parameter settings. One way to measure a group of parameter settings of GA is introduced as follows. Let \(F_{\pi}(i,j,q)\) denote the fitness value obtained by GA with the \(i\)-th group of parameters for Case \(j\) under a PVS in which the number of wafers in a repeated wafer loading sequence is \(q\), \(i\in\{1,2,\,\ldots,\,45\}\), \(j\in\{1,2,\,\ldots,\,20\}\), and \(q\in\{2,\,3,\,\ldots,\,100\}\). Let \(I(u_{1},u_{2})=1\) if \(u_{1}=u_{2}\), and otherwise \(I(u_{1},u_{2})=0\). Then, \(I_{i}(max(F_{\pi}(i,j,q)\,|i\in\{1,2,\,\ldots,\,45\})\), \(F_{\pi}(i,j,q))\) is used to record if GA with the \(i\)-th group of parameters achieves the best solution among the 45 groups of parameter settings under the given \(j\) and \(q\). Let \(TI_{i}\) denote the total number of best solutions that GA with the \(i\)-th group of parameters achieves among the 45 group of parameter settings under different \(j\) and \(q\). Thus, we have  
\[TI_{i}=\sum_{j=1}^{20}\sum_{q=2}^{100}I_{i}(max(F_{\pi}(i,j,q)|i\{1,\,2,\, \ldots,\,45\}),F_{\pi}(i,j,q)),\,\,i\,\in\,\{1,\,2,\,\ldots,\,45\} \tag{8}\]  
\(TI_{i}\) reflects the capability of GA with the \(i\)-th group of parameters to search a better solution among the 45 different parameter settings to some extent.