## 2 Improved BP Neural Network Model Based on GA
### Principles of Genetic Algorithm  
Genetic algorithm imitates the evolutionary mechanisms of biological selection, crossover, and mutation to find the most suitable individuals. It is a random search algorithm that can solve optimization problems for both discrete and continuous functions. In genetic algorithms, the solution to each problem is called a string of chromosomes, typically represented as a bit string, and each chromosome is referred to as an individual. This algorithm adopts a population organization search method, where these populations (chromosome strings) are composed of several individuals, and the individuals are composed of units that control one or more genetic features. The genes for certain features are distributed along the chromosome, and the corresponding strings are called loci. Each genotype represents a potential solution to a problem, which is obtained by mapping chromosome representations to the decision variable space through fitness functions [19]. Algorithms usually preset four operating parameters: population size, evolutionary generation, crossover probability, and mutation probability. When the preset parameter limits are reached, the algorithm will automatically stop. The basic process of classical genetic algorithms is shown in Figure 2.  
The specific operation steps are as follows. (1) Genetic Algorithm Encoding  
In genetic algorithm optimization of BP neural network algorithm, each chromosome is decomposed into two parts: connecting genes and parameter genes, and different encoding methods are adopted for these two parts. Encoding is a method of transforming feasible solutions of a problem from its solution space to the search space that the algorithm can handle using genetic algorithms. It is the first problem to be solved when using genetic  
Figure 2: Genetic Algorithm flow chart. algorithms. Meanwhile, encoding also affects the operations of selection, crossover, and mutation operators during the operation of genetic algorithms. (2) Design of fitness function  
The fitness function, also known as the evaluation function, in genetic algorithms is the only method to determine the quality of solutions by judging the degree of superiority or inferiority of individuals in the population based on the objective function of the problem being solved. It has a direct impact on the convergence speed of the algorithm and the search for the optimal solution. In the process of searching evolution, genetic algorithms use fitness function values to measure the degree to which each individual in the population can achieve or approach finding the optimal solution in optimization calculations. The fitness function in this article is based on the total error of the neural network and is expressed as follows:  
\[f=\frac{1}{(1+E)}. \tag{15}\]  
Among them, \(E\) is the total error in the network structure, \(Z_{j}^{k}\) is the ideal output, \(Y_{j}^{k}\) is the actual output, and \(K\) is the number of sample sets. (3) Genetic operator design  
Genetic operations include three basic genetic operators: selection, crossover, and mutation. (1) The operation of finding excellent individuals from a group and eliminating inferior individuals is called selection. The purpose of selection is to directly pass on optimized individuals or solutions to the next generation or generate new individuals through paired crossover and then pass them on to the next generation. This operation is based on the assessment of individual fitness in the population. The selection operator in this article adopts the most commonly used and simplest roulette wheel selection in genetic algorithms. The roulette wheel selection first calculates the selection probability of each individual, and the steps are as follows. 1.