## 3 Optimization Algorithm  
### Genetic Algorithm  
The genetic algorithm (GA) [44] is a single population algorithm. Individuals in the population evolve their excellent genes through selection, crossing, and mutation operations, and enrich the gene pool of each generation to form a new generation of populations. Better individuals emerge with improved individual fitness. When the immature convergence occurs randomly, which drastically reduces the diversity of individuals in the population, and the viable new individuals are difficult to generate by the constant cross and mutation operators to break the limits, the result is easy to fall into a local solution. Therefore, both retaining good individuals and maintaining the diversity of the group should be considered to avoid falling into a local solution prematurely. The basic flow of GA is shown in Figure 6. The GA algorithm steps are as follows:  
1. The population is initialized to generate individuals carrying specific genetic information;
2. The first generation individuals are real-coded to keep them within the specified range;
3. The fitness function is determined and the fitness value of each individual is calculated;
4. According to the select operator \(P_{\mathrm{g}}\), individuals with better fitness values are selected for the next generation;
5. According to the cross operator \(P_{\mathrm{c}}\), the genes \(a_{lz}\) and \(a_{lz}\) at the \(z\) position of the \(k\) and \(l\) two individuals in the population are selected for cross operation by Equation (4); \[\left\{\begin{array}{l}a_{kz}=a_{kz}(1-b)+a_{lz}b\\ a_{lz}=a_{lz}(1-b)+a_{lz}b\\ \end{array}\right.,\] (4) where \(b\) is a random number between 0 and 1.
6. According to the mutation operator \(P_{m}\), the gene \(a_{uzz}\) at the \(z\) position of the \(u\) individual in the population is selected for mutation operation by Equations (5) and (6); \[a_{uz}=\left\{\begin{array}{l}a_{uz}+(-a_{uz}+a_{\mathrm{max}})*f(num)\qquad v >0.5\\ a_{uz}-(-a_{\mathrm{min}}+a_{uz})*f(num)\qquad v\leq 0.5\\ \end{array}\right.\] (5) \[f(num)=\left(v_{2}(1-num/G_{\mathrm{max}})\right)^{2},\] (6)  
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Factors** & **Sum of Square** & **Degree of Freedom** & **Mean of Square** & **F Value** & **\(p\)-Value** \\ \hline \(p\) & 6.797138188 & 3 & 2.265712729 & 277.754054 & 5.58571E-06 \\ \(\alpha\) & 0.153397188 & 3 & 0.051132396 & 6.268327865 & 0.037961183 \\ \(t\) & 0.234307187 & 3 & 0.078102396 & 9.5745841 & 0.016302002 \\ \(s\) & 0.014340063 & 1 & 0.014340063 & 1.757950354 & 0.242221652 \\ error & 0.040786312 & 5 & 0.008157262 & & \\ total & 7.239968938 & 15 & & & \\ \hline \hline \end{tabular}
\end{table}
Table 5: Variance analysis table of orthogonal erosion test.  
where \(a_{max}\) and \(a_{min}\) are the upper and lower limits of the gene \(a_{uz}\) respectively; \(v_{2}\) is a random number; \(num\) is the current iteration number; \(G_{max}\) is the maximum iteration number; \(v\) is a random number between 0 and 1.
* Update fitness values for all individuals in the population;
* Calculate the individual with the best fitness value in the current generation;
* If the termination condition \"maximum iteration number\" is satisfied, the calculation proceeds to the next step, otherwise, it returns to Step 4;
* Output the best individual and its fitness value as the optimal solution.