# Structural Optimization of Combine Harvester Plate-Shell Undergoing Multi-Source Excitation
## 2 Materials and Methods
### Optimization Algorithm  
The multi-objective genetic algorithm (MOGA) [33] is essentially an improvement of the parallel distributed genetic algorithm, and it has better global solving ability and computational efficiency than the traditional genetic algorithm. Genetic Algorithm [34] (GA) was proposed by [PERSON] in the 1960s, mainly relying on the law of \"survival of the fittest\" in the process of biological evolution, imitating the genetic reproduction mechanism in the process of biological evolution, and encoding the individual in the solution space of the optimization problem (Binary or other bases), and then perform genetic operations (such as: selection, crossover, mutation, etc.) on the encoded individual population, and find the combination containing the optimal solution or better solution from the new population through iteration. The process of implementing a genetic algorithm has the following aspects:  
(1) Gene coding  
When using a genetic algorithm, the solution to the problem needs to be encoded into a genetic chain code. Each gene chain code is also called an individual and is sometimes called a chromosome. The length of chromosomes using binary coding can be determined according to the precision required by the problem. Commonly used encoding methods include: binary encoding, Gray code encoding, real number encoding, and symbol encoding algorithms. [PERSON]'s MOGA algorithm uses Gray coding as follows:  
\[\left\{ \begin{array}{l}g_{m}=b_{m}\\ g_{i}=b_{i+1}\oplus b_{i}\,i=m-1,m-2,\ldots 1\end{array} \right. \tag{6}\]  
(2) Fitness function  
For the initial variable and updated variable, the pros and cons of an individual in the group compared with other individuals need to be a unified evaluation index, which is individual fitness. Individuals with higher fitness indicate that they are close to or reach the optimal solution, and the probability of one cycle to the next generation is relatively high. The index designed according to the optimization objective function to judge whether the individual is good or bad is called the fitness function. (3) Genetic manipulation  
Similar to the process of genetic inheritance and mutation of biological evolution, the basic operations of genetic algorithm to update variables can be divided into three categories: selection, crossover, and mutation. (1) Select operation  
The purpose of selection is to select excellent individuals from the current population so that they have the opportunity to produce offspring individuals as parents. The criterion for judging whether an individual is good or not is the respective fitness value, as a kind of operator, there are many ways to realize the selection operation in the genetic algorithm, and the simplest one is to use the fitness proportional method for selection. Specifically, it is to first calculate the sum of the fitness of all individuals in the group, and then calculate the proportion of the fitness of each individual and take the next as the corresponding selection probability. (2) Crossover operation  
The reproduction of many organisms is accomplished by the crossing of chromosomes. This concept is used in genetic algorithms, with crossover as an operator. Moreover, the crossover operator occurs with a certain crossover probability. The realization process of the crossover operator is as follows: two individuals in the population are selected, and the two individuals are used as parents to cross the gene chain code, thereby producing two new individuals as their offspring. The simple crossover algorithm is: randomly select a truncation point, cut the gene chain code of the parents at the truncation point, and exchange the second half to form two new individuals. (3) Mutation operation  
Variation is an important step in the evolution of organisms. The newly created individual is differentiated from other individuals by creating mutations in certain gene locations on the chromosome.