## 3 Proposed Algorithm
### Framework of Tr-EGT  
The flowchart of the proposed Tr-EGT algorithm for operational indices optimizations of the polymerization process is shown in Figure 3.  
First, for each optimization problem, i.e., \(OP_{1}\) and \(OP_{2}\), we assign it a single-task evolutionary solver with an independent population. Next, to establish the connections between different optimization problems, two sets of solutions are randomly sampled from the corresponding search space as the source domain and target domain of the  
Figure 3: Flow chart of the proposed Tr-EGT.  
domain adaptation approach, and a transformation mapping matrix across tasks is obtained. Further, the explicit genetic transfer occurs when the two evolutionary solvers performed at a certain interval. In particular, during the execution of both solvers, a good solution sought by one solver is injected into the population of the other through a domain adaptation approach.  
Algorithm 1 demonstrates the framework of Tr-EGTto help the readers better understand the flowchart.  
```
0:\(G_{max}\), maximum generation; \(G\), interval of explicit solution transfer across tasks; \(F_{1}(.)\), the optimization function for \(OP_{1}\); \(F_{2}(.)\), the optimization function for \(OP_{2}\); solver1, a single-task evolutionary solver for \(OP_{1}\); solver2, a single-task evolutionary solver for \(OP_{2}\); \(\kappa(\cdot,\cdot)\), kernel function.
0:\(\textit{{POF}}_{s}\) of each task.
1: Initialization two populations and set g = 0.
2: Calculate \(F_{OP_{1}}\) and \(F_{OP_{2}}\) to get the \(\textit{{POF}}_{1}\) and \(\textit{{POF}}_{2}\), respectively via use solver1 and solver2.
3:for g = 1 to \(G_{max}\)do
4:if mod (g, G) = 0 then
5: Next-Offspring\({}_{1}\) = Tr-OG(\(F_{1}(.)\), \(\textit{{POF}}_{2}\), \(\kappa(\cdot,\cdot)\)).
6: Next-Offspring\({}_{2}\) = Tr-OG(\(F_{2}(.)\), \(\textit{{POF}}_{1}\), \(\kappa(\cdot,\cdot)\)).
7:else
8: Generate Next-Offspring\({}_{1}\) and Next-Offspring\({}_{2}\), respectively using assortative mating.
9:endif
10:\(\textit{{POP}}1_{g+1}=\textit{{POP}}1_{g}\cup\{\text{Next-Offspring}_{1}\}\).
11:\(\textit{{POP}}2_{g+1}=\textit{{POP}}2_{g}\cup\{\text{Next-Offspring}_{2}\}\).
12: Update the \(\textit{{POP}}1_{g+1}\) and \(\textit{{POP}}2_{g+1}\).
13:\(\textit{{POF}}1_{g+1}\)=solver1(\(\textit{{POP}}1_{g+1}\)).
14:\(\textit{{POF}}2_{g+1}\)=solver2(\(\textit{{POP}}2_{g+1}\)).
15:\(\texttt{g}=\texttt{g}+1\).
16:endfor
```  
**Algorithm 1** Framework of Tr-EGT  
Tr-EGT follows the general framework of EMT-EGT, except that the transfer learning-based offspring generator (Tr-OG) is adopted to conduct efficient knowledge transfer across tasks. \(F_{1}\) and \(F_{2}\) are the optimization functions with respect to \(OP_{1}\) and \(OP_{2}\), respectively, and \(\textit{{POF}}1_{g}\) and \(\textit{{POF}}2_{g}\) represent their POF, which has already been found. Next-Offspring\({}_{1}\) and Next-Offspring\({}_{2}\) are the offspring for \(F_{1}\) and \(F_{2}\) at the next generation. When the interval conditions are met, Tr-OG generates an offspring population using the POF of domain adaption approach. A new generation is chosen from the joint of the offspring population and its parent population via environment selection, which can be used to evolve at generation \(g+1\). Specifically, we can get two types of knowledge transfer; in general, one is \(OP_{1}\to OP_{2}\), and the other is \(OP_{2}\to OP_{1}\). For \(OP_{1}\to OP_{2}\), the obtained \(\textit{{POF}}1_{g}\) and \(F_{2}(.)\). In general, the feasible solutions of \(OP_{2}\), are used as the source domain and target domain, respectively. A mapping function \(\varphi\) is got using the domain adaptation approach, which maps source and target data with different distributions into the latent space. Next, a good offspring population is generated, which accelerates convergence of the population.