# PSO-SVM Based Performance-Driving Scheduling Method for Semiconductor Manufacturing Systems
## 4 Empirical Study
### Experimental Design  
To test the availability of our proposed method, we designed multiple simulation-based case studies. Because the proposed method was a prototype system, which contained multiple methodologies, we designed different case studies for different methodologies and the whole proposed method. In Section 4.3.1, we conduct case studies and comparisons between the proposed composite dispatching rules (CDR) and the other three widely used heuristic dispatching rules, FIFO (first in, first out), EDD (earliest due date), and CR, to determine if CDR is preferable (critical ratio). In Section 4.3.2, we conduct case studies and comparisons between CDR and the proposed scheduling method to evaluate the efficacy of the proposed \"performance-driving\" and \"feedback\" concepts. Different dispatching parameters will lead to different performances, so we randomly set the parameters' values and gathered nearly twenty groups of experimental data to avoid experimental coincidence. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Kernel Type** & **RBF** & **Polynomial** & **Linear** \\ \hline \(C\) & 18.7 & 183.78 & 1500 \\ \(\varepsilon\) & 0.0827 & 0.0000538 & 0.0885 \\ \(\gamma\) & 2.6 & - & - \\ \(d\) & - & 3 & - \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Optimal parameters of the PSO-SVM. \begin{table}
\begin{tabular}{c c} \hline \hline
**NO. ** & **Selected Features** \\ \hline \(1\) & the number of WIPs in a 5” production line. \\ \(2\) & the ratio of the WIP quantity in the oxidation area to that in the whole manufacturing system. \\ \(3\) & the ratio of the WIP quantity in the photolithography area to that in the whole manufacturing system. \\ \(4\) & the ratio of the WIP quantity in the dry-etching area to that in the whole manufacturing system. \\ \(5\) & the ratio of the number of bottleneck equipment to that of the whole manufacturing system. \\ \(6\) & the ratio of the number of available bottleneck equipment in the oxidation and diffusion area to that in the whole manufacturing system. \\ \(7\) & the ratio of the number of available bottleneck equipment in the photolithography area to that in the whole manufacturing system. \\ \(8\) & the ratio of the number of workpieces processed by the manufacturing system to the throughput. \\ \(9\) & average remaining processing time of workpieces. \\ \(10\) & number of urgent workpieces (hot lots) in the whole manufacturing system. \\ \(11\) & number of urgent workpieces in the oxidation and photolithography area. \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Kernel Type** & **RBF** & **Polynomial** & **Linear** \\ \hline \(C\) & 18.7 & 183.78 & 1500 \\ \(\varepsilon\) & 0.0827 & 0.0000538 & 0.0885 \\ \(\gamma\) & 2.6 & - & - \\ \(d\) & - & 3 & - \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Optimal parameters of the PSO-SVM. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**Kernel Type** & **RBF** & \multicolumn{2}{c}{**Polynomial**} & \multicolumn{2}{c}{**Linear**} \\ \hline  & Train & Test & Train & Test & Train & Test \\ CC & 0.911 & 0.902 & 0.932 & 0.925 & 0.870 & 0.849 \\ RMSE & 0.048 & 0.064 & 0.024 & 0.035 & 0.075 & 0.076 \\ MAE & 0.040 & 0.052 & 0.016 & 0.028 & 0.064 & 0.065 \\ SI & 0.129 & 0.173 & 0.082 & 0.096 & 0.204 & 0.204 \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Statistical parameters for different kernel types of PSO-SVM. In this research, to carry out \"performance-driving\", we selected six kinds of performances from three aspects: equipment-related (EU_P and EU_O), fab-wide (MOV and PR), and wafer-related (PCSR and ODR). To investigate scheduling effects generated by different \"performance-driving\", in Section 4.3.2, we make multiple case studies with \"equipment-related performance-driving method\", \"fab-wide performance-driving method\", \"wafer-related performance-driving method\", and \"all six kinds of performance-driving method\". Like Section 4.3.1, we randomly set the parameters' values and gathered nearly twenty groups of experimental data to avoid experimental coincidence.