## 3 Optimization Based on GA
### GA-Based Optimization  
As described in Section 1, GAs are a very popular choice for optimization problems. The GA is an evolutionary computing method for searching and optimizing complex problems, which is motivated by the evolution of animal populations on earth [7; 11]. Each possible solution of a problem is considered an \"individual\" with an encoded \"chromosome\". During the computation of a GA, different operators can typically be applied to the set of solutions to provide new evolutionary populations [25]. The flowchart of the GA mechanism is illustrated in Figure 4.  
Step 1: Identify design variables and then encode the required variables in the form of a fixed-length binary string. Binary encoding is used because of the following advantages: (a) simple coding and decoding operations; (b) genetic operations such as selection, crossover, and mutation are easy to implement; (c) it complies with the principle of minimum symbol set coding. In this paper, the positions of four hinge points of the two cylinders are taken as the design variables. However, the positions of cylinders will be applied to the actual structure. Given the assembly accuracy, we set the accuracy of the optimization results to four decimal places. Consequently, the length of the binary string is calculated according to Equation (18):  
\[2^{i-1}\leq(c_{m}-c_{n})\times 10^{4}\leq 2^{i}-1, \tag{18}\]  
\(i\): The length of the binary string;  
\(c_{m},c_{n}\): The top and bottom limits of the design variables. Step 2: Create a random initial population. The individuals within the population are digitized codes. Set the evolution algebraic counter and the maximum evolution algebra to 0 and T, respectively. Figure 4: Working mechanism flowchart of a genetic algorithm (GA). Step 3: Calculate their corresponding fitness values by means of the Equation (17) for the populations from Step 2 and those newly-bred populations after selection, crossover, and mutation from the next steps. Then, those individuals with relatively high calculated fitness are selected and kept in the procedure, which will be subsequently taken to reproduce a new generation with better adaptability than themselves in Step 5. As can be seen from Equation (17), the greater the fitness value, the smaller the stroke difference and arm difference. As a result, the optimal value is obtained when the fitness value reaches the maximum. Step 4: Check whether the iteration termination criterion for the GA has been reached. If the outputs of the GA do not satisfy the termination criteria, the next steps should be implemented. Step 5: Create new population through selection, crossover, and mutation. In GA, a method needs to be constructed to generate new species, in order to keep the objective function close to the optimal value. New species are generated via selection, crossover, and mutation. Selection is related to method and criteria, which are used to choose individuals with high fitness. Then, the selected individuals cross-pair with each other to generate new individuals, and these individuals are inserted into the parent population to generate more highly-adaptive populations, which is the offspring created by crossover. In other words, crossover creates new individuals through the recombination between string pairs of the selected individuals in the mating pool. Mutation refers to a new individual that resulted from a change in a gene of an individual's chromosome. **4. Case Study**  
This section takes the steering mechanism of a FW50 GL wheel loader as an example to verify the validation of the proposed optimization method in this paper, which is shown in Figure 5.  
A wheel loader is a typical articulated steering vehicle. The relevant parameters of the FW50 GL steering structure are shown in Table 1.