## 3 Orthogonal Experiments and Grey Relational Analysis
### Neural Network Genetic Algorithm Function Optimization
#### 4.3.2 Genetic Algorithm Optimization  
The genetic algorithm is a heuristic algorithm that is easy to implement, highly accurate, and fast-converging [20]. Therefore, this study utilized the genetic algorithm for optimization solving. In the optimization phase using the genetic algorithm, binary encoding composed of 0 and 1 is currently the most widely used encoding method. Therefore, this genetic algorithm adopts binary encoding. For the selection mechanism, the survival of the fittest was used to improve search efficiency and ensure the survival probability of excellent individuals. For the crossover method, multi-point crossover was used to increase the possibility of finding the global optimal solution. For the mutation method, random resetting was used to increase the genetic diversity of the population. Through multiple experiments, it was found that the best fitness no longer changed after about 80 iterations, so the number of iterations was set to 100. Based on the optimization objectives and data characteristics, the population size of this genetic algorithm was set to 50, with a crossover probability of 0.3, a mutation probability of 0.2, and an elite retention strategy size of 10. The mathematical model (formula (10)) was used as the fitness function, and (150, 600) and (0.90, 1.35) were used as the constraint conditions for the blank holder force and die clearance, respectively. Through 100 iterations of optimization, the minimum value of the fitness value was the minimum value of the comprehensive score, and the fitness convergence curve is shown in Figure 7.  
During the first 10 iterations, the fitness curve decreased rapidly, and then its rate of decline gradually reduced. Around the 20 th iteration, the fitness curve quickly stabilized, showing no significant upward or downward trend, indicating that the algorithm had found a relatively optimal solution. As the iterations continued, although the changes in fitness were very minor, there were still variations around the 67 th and 81 st iterations. This suggests that the algorithm is gradually converging to the optimal or near-optimal solution, confirming that the algorithm has good convergence characteristics.  
\begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline \multirow{2}{*}{**Serial Number**} & \multirow{2}{*}{\begin{tabular}{c} **Blank Holder** \\ **Force/KN** \\ \end{tabular} } & \multirow{2}{*}{\
\begin{tabular}{c} **Die Clearance** \\ **/mm** \\ \end{tabular} } & \multicolumn{2}{c}{**Maximum Thickening Rate/\%**} & \multicolumn{2}{c}{**Maximum Thinning Rate/\%**} & \multirow{2}{*}{
\begin{tabular}{c} **Average Error** \\ **Rate/\%** \\ \end{tabular} } \\ \cline{3-3} \cline{5-8}  & & & **Simulation** & **Predicted** & **Simulation** & **Predicted** & **Rate/\%** \\ \hline
1 & 177.65 & 0.98 & 5.18 & 5.14 & 32.36 & 31.97 & 0.99 \\
2 & 265.53 & 1.21 & 5.49 & 5.56 & 30.47 & 29.95 & 1.49 \\
3 & 169.74 & 1.06 & 5.71 & 5.77 & 29.68 & 28.96 & 1.74 \\
4 & 365.47 & 1.16 & 5.51 & 5.48 & 33.10 & 33.69 & 1.16 \\
5 & 401.70 & 0.93 & 5.13 & 5.17 & 36.16 & 35.96 & 0.67 \\
6 & 549.36 & 1.24 & 5.13 & 5.03 & 28.56 & 28.16 & 1.67 \\
7 & 489.75 & 1.19 & 4.81 & 4.78 & 37.63 & 37.24 & 0.83 \\
8 & 289.56 & 1.31 & 4.96 & 5.11 & 34.47 & 34.96 & 2.22 \\
9 & 349.63 & 1.27 & 5.01 & 4.94 & 36.19 & 36.93 & 1.72 \\ \hline \hline \end{tabular}
\end{table}
Table 7: Prediction error table.  
Figure 7: Convergence curve of adaptation.