## 4 Results and Discussion
### Multi-Objective Optimization  
Since the optimization direction of the objective function is not consistent, the use of multi-objective optimization algorithm can effectively obtain the optimal solution among the objective functions. However, discrete simulation results cannot be used for multi-objective optimization search, and the discrete results must be turned into objective functions. The 45 cases of simulation data of the heat exchanger are shown in Table 6, and the regression models of heat transfer quantity, oil pressure drop and oil outlet temperature with respect to fin angle, oil flow rate, and water flow rate are obtained by fitting these data with SVR. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline \multirow{3}{*}{**No. **} & \multicolumn{3}{c}{**Design Variables**} & \multicolumn{3}{c}{**Objective Function**} \\ \cline{2-7}  & **Fin Angle** & **Oil Flow** & **Water Flow** & **Heat Transfer** & **Oil** & **Oil Outlet** \\  & **(Degree)** & **Rate** & **Rate** & **Quantity** & **Pressure** & **Temperature** \\  & **(L/min)** & **(L/min)** & **(kW)** & **Drop (kPa)** & **(\({}^{\circ}\)C)** \\ \hline
1 & 30 & 5 & 5 & 5.04 & 7.11 & 65.00 \\
2 & 30 & 5 & 10 & 5.04 & 7.11 & 65.00 \\
3 & 30 & 5 & 15 & 5.04 & 7.12 & 65.00 \\
4 & 30 & 10 & 5 & 9.84 & 23.44 & 65.65 \\
5 & 30 & 10 & 10 & 10.07 The error of the SVR regression model regarding the 45 cases of simulation data is shown in Figure 7 and the maximum error did not exceed 2.5%. In fact, the boundary conditions of the simulation, i.e., oil flow and water flow (5-15 L/min), already covered the operating range of the heat exchanger. Therefore, the regression models did not need to predict the out-of-range data. These regression models would be used as the objective function for multi-objective optimization search. NSGA-II is a genetic algorithm that can minimize or maximize two or more objective functions under given constraints and boundary conditions. The three objective functions selected in this study were heat transfer quantity, oil pressure drop, and oil outlet temperature. In the process of heat exchanger operation, the smaller the oil pressure drop, the  
\begin{table}
\begin{tabular}{c c c c c c c} \hline \hline \multirow{3}{*}{**No. **} & \multicolumn{3}{c}{**Design Variables**} & \multicolumn{3}{c}{**Objective Function**} \\ \cline{2-7}  & \begin{tabular}{c} **Fin Angle** \\ **(Degree)** \\ \end{tabular}  & \begin{tabular}{c} **Oil Flow** \\ **Rate** \\ **(L/min)** \\ \end{tabular}  & \begin{tabular}{c} **Water Flow** \\ **Rate** \\ **(L/min)** \\ \end{tabular}  & \begin{tabular}{c} **Heat Transfer** \\ **(L/min)** \\ \end{tabular}  & \ \begin{tabular}{c} **Oil** \\ **(R/W)** \\ \end{tabular}  & \begin{tabular}{c} **Oil Outlet** \\ **Pressure** \\ **(R/Pa)** \\ \end{tabular}  \\ \hline
18 & 45 & 15 & 15 & 15.10 & 33.55 & 65.01 \\
19 & 60 & 5 & 5 & 5.04 & 4.13 & 65.00 \\
20 & 60 & 5 & 10 & 5.  
smaller the oil outlet temperature, and the larger the heat transfer quantity, the better. In other words, the optimization directions of the three objective functions were not consistent. Therefore, in the process of multi-objective optimization using NSGA-II, a negative sign was added before the objective function of heat transfer quantity to unify the optimization direction of objective functions to the minimum. The set of Pareto optimal solutions obtained by NSGA-II is shown in Figure 8, which contains a total of 2000 optimal solutions. After obtaining the optimal solution set, TOPSIS was used to evaluate the 2000 data comprehensively to decide the optimal solution and obtain the corresponding optimal parameters. In this study, the optimal fin angle for heat exchanger operation was 63.01\({}^{\circ}\), and the optimal oil flow rate and water flow rate were 9.7 L/min and 6.45 L/min, respectively.