## 3 Optimization Based on GA
### GA-Based Optimization
\begin{table}
\begin{tabular}{c c} \hline \hline
**Variables** & **Values** \\ \hline AP & 150 mm \\ CQ & 360 mm \\ PO & 1017 mm \\ QO & 13 mm \\ L & 3300 mm \\ b & 40\({}^{\circ}\) \\ \(l_{\text{max}}\) & 1040 mm \\ \(s\) & 800 mm \\ G & 3.8 t \\ \(\epsilon\) & 8 mm \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Parameters of the FW50 GL steering mechanism. Figure 5: Steering mechanism of a FW50 GL loader. According to the data listed in the table, the constraints can be obtained from Equations (5)-(13), and Equation (14) can be set as follows based on the frame structure of FW50 GL. \[ \begin{array}{c}310\leq CQ\leq 380\\ 0\leq QO\leq 40\\ 140\leq AP\leq 280\\ 980\leq PO\leq 1050\end{array} \]  
In the optimal design presented by this paper, the sus function (random traversal sampling) was used to select individuals with high fitness from the parent population to breed offspring. The probability that each individual is selected is the ratio between the individual fitness value and the sum of all individual fitness values in the population. In other words, the greater the individual fitness value, the greater the probability of being selected. The single-point cross function with a crossover ratio of 0.5 was selected for crossover. Mutant selects must function, and the mutation ratio selected was 0.02. The parameters related to the GA-based optimization algorithm are listed in Table 2.  
Based on the method and data proposed above, the steering mechanism of the FW50 GL is optimized in MATLAB based on GA. The curve of the fitness function is shown in Figure 6, which indicates that the maximum of the fitness was 1.55, and the maximum emerged in the 58 th generation. Based on the method and data proposed above, the optimized results are compared with the pre-optimization in Table 3. \begin{table}
\begin{tabular}{c c} \hline \hline
**Variables** & **Values** \\ \hline Population & 1000 \\ Mutation ratio & 0.02 \\ Crossover ratio & 0.5 \\ T (Genetic algebra) & 100 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Parameters related to the GA-based optimization algorithm. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Variables** & **AP** & **CQ** & **PO** & **QO** \\ \hline Pre-Opt & 150 mm & 360 mm & 1017 mm & 13 mm \\ After-GA-Opt & 258 mm & 300 mm & 1158 mm & 0.25 mm \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Data comparison between before and after optimization. Figure 6: The relationship between genetic algebra and maximum value of fitness function. As shown in Figures 7 and 8, the models of the FW50 GL-based steering mechanism were built in ADAMS (automatic dynamic analysis of mechanical systems) software according to the data in Table 3. As a result, the simulation curves describing the trend of stroke and arm force varying with the steering angle were obtained, and are shown in Figures 9 and 10. As can be seen from Figure 9, the stroke difference of the two steering hydraulic cylinders reached a maximum of 26 mm when the steering angle reached 40\({}^{\circ}\) before optimization. However, the maximum of stroke difference was reduced to 2 mm after optimizing by means of GA, and the maximum appeared at the steering angle of 29\({}^{\circ}\). As shown in Figure 10, the maximum arm difference was reduced from 56 mm to 12 mm after optimizing. Therefore, the stroke difference of steering hydraulic cylinders