## 2 PPCFP Problem Formulation
### Optimization Modeling
#### 2.2.1 Parameters and Variables  
The aim of process parameter optimization is to improve the global production efficiency of PPCFP through the synergistic mechanism model. The model consists of two optimization tasks of the polymerization process of a production line, in which each sub-model deals with a single task. The symbols and meanings of the model used in our formulation are described in Table 1.  
In order to ensure the safety and reliability of the polymerization process, every decision variable needs to satisfy a certain range in the actual industrial production. Table 2 shows the fixed parameters and their values. The ranges of every decision variable are presented in Table 3.  
\begin{table}
\begin{tabular}{c l l l} \hline \hline
**Symbol** & **Meaning** & **Symbol** & **Meaning** \\ \hline \(Q_{1,1}\) & Yield in PL 1\# & \(w_{1}\) & Weight factor \\ \(Q_{2,1}\) & Yield in PL 2\# & \(w_{2}\) & Weight factor \\ \(C_{1,2}\) & production capacity utilization in PL 1\# & \(w_{3}\) & Weight factor \\ \(C_{2,2}\) & production capacity utilization in PL 2\# & \(k\) & Tradeoff factor \\ \(M_{1}\) & Monomer concentration of kettle 1 & \(T_{s}\) & Temperature of material mass flow \\ \(M_{2}\) & Monomer concentration of kettle 2 & \(q_{M_{1}}\) & Material mass flow of kettle 1 \\ \(I_{1}\) & Initiator concentration of kettle 1 & \(q_{M_{2}}\) & Material mass flow of kettle 2 \\ \(I_{2}\) & Initiator concentration of kettle 2 & \(H\) & Specific heat capacity \\ \(N_{1}\) & Commoner concentration of kettle 1 & \(t\) & Production time \\ \(N_{2}\) & Commoner concentration of kettle 2 & \(\beta\) & Correction parameters \\ \(T_{1}\) & Temperature of kettle 1 & \(m\) & Material quality \\ \(T_{2}\) & Temperature of kettle 2 & \(R\) & Idea gas constant \\ \(M_{min}\) & Lower bound of monomer concentration & \(U_{tra}\) & Heat transfer coefficient \\ \(M_{max}\) & Upper bound of monomer concentration & \(A_{tra}\) & Heat exchange contact area \\ \(I_{min}\) & Lower bound of initiator concentration & \(T_{jac}\) & Jacket average temperature \\ \(I_{max}\) & Upper bound of initiator concentration & \(k_{p}\) & Chain growth rate constant \\ \(N_{min}\) & Lower bound of monomer concentration & \(f\) & Initiation efficiency \\ \(N_{max}\) & Upper bound of monomer concentration & \(k_{t}\) & Material mass flow \\ \(k_{t1}\) & Decomposition rate constant of kettle 1 & \(A_{d}\) & Pre-exponential factor \\ \(k_{t2}\) & Decomposition rate constant of kettle 2 & \(E_{d}\) & Activation energy \\ \hline \hline \end{tabular}
\end{table}
Table 1: Symbols and meanings.  
\begin{table}
\begin{tabular}{l l l l} \hline \hline
**Parameters** & **Value** & **Parameters** & **Value** \\ \hline \(w_{1}\) & 0.49315 & \(H\) & 4179 J/(kg\textless{}K) \\ \(w_{2}\) & 1 & \(\beta\) & 0.99 \\ \(w_{3}\) & 1 & \(f\) & 0.8 \\ \(k\) & 1 & R & 8.314 J/(mol\textless{}K) \\ \(A_{tra}\) & 1 m\({}^{2}\) & \(A_{d}\) & \(1\times 10^{13}\) \\ \(\overline{T_{jac}}\) & 333.15 K & \(E_{d}\) & 120 kJ/mol \\ \(k_{p}\) & 1960 L/(mol\textless{}S) & \(k_{t}\) & 7.82 \(\times\) 10\({}^{8}\) L/(mol\textless{}S) \\ \hline \hline \end{tabular}
\end{table}
Table 2: Fixed parameters and their values.