# Lithium-Ion Battery Capacity Prediction with GA-Optimized CNN, RNN, and BP
## 3 Related Algorithms
### Genetic Algorithm  
The genetic algorithm is a computational method for solving optimization and search problems, inspired by natural selection and genetic processes. It is part of a sub-discipline called evolutionary computing. \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Battery Num.** & **HF1** & **HF2** & **HF3** & **HF4** \\ \hline B0005 & \(-0.9057\) & 0.9962 & 0.9824 & 0.9999 \\ B0006 & \(-0.9242\) & 0.9753 & 0.9379 & 0.9817 \\ B0007 & \(-0.8927\) & 0.0289 & 0.9611 & 0.9997 \\ B0018 & \(-0.4831\) & 0.7462 & 0.9856 & 0.9998 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Correlation Coefficient Between Battery Capacities and Extracted Features. Figure 5: Voltage–time chart during discharging. The genetic algorithm is based on the principle of natural selection. This principle suggests that better-matched individuals within a population, i.e., individuals who can solve the problem more effectively, are more likely to contribute more to the next generation. The genetic algorithm mimics this process of natural selection and aims to advance a solution space by allowing individuals within a population to interact with each other through various genetic operators, such as crossover, mutation, and selection. The genetic algorithm is particularly effective for complex, multidimensional, general search, or optimization problems. For instance, it can be applied to address challenges such as the traveling salesman problem, the optimization of machine learning models, or route planning. The working process of the genetic algorithm consists of the following steps:  
1. _Initial Population Generation:_ Generating the first-generation individuals using random or heuristic methods. 2. _Fitness Assessment:_ Calculating the fitness value of each individual, i.e., measuring how good the solution is. 3. _Selection:_ Selecting individuals based on their fitness values. Individuals with higher fitness have a greater probability of being selected. 4. _Crossover:_ The process of crossing over, which allows the exchange of genetic material between selected individuals, thus creating new individuals. 5. _Mutation:_ Introducing random genetic changes to newly created individuals. 6. _Creating New Population:_ The individuals resulting from crossover and mutation constitute the next generation population. 7. _Controlling the Termination Condition:_ Checking whether certain termination conditions have been met (e.g., reaching the maximum number of iterations or achieving a desired fitness level). 8. _Evaluation of Results:_ Analyzing the obtained results and assessing the proximity to the desired solution. The genetic algorithm functions used in this study are as follows:  
_Single Crossover:_ This is the simplest form of the crossover operator. In this method, the genetic material of two selected parental individuals is cut at a specific point and then the pieces are swapped. This process results in the creation of two offspring individuals. Figure 6 shows an example of a single crossover. _Uniform Mutation:_ A mutation operator that applies random changes to the genetic material of an individual. This operator ensures that each gene is replaced with random values with a certain probability. Uniform mutation helps the search process cover a wider area by increasing genetic diversity. In this way, the population of the genetic algorithm enhances its ability to discover and optimize potential solutions. Before Mutation: 01011011 After Mutation: 0111011  
_Roulette Selection Function:_ This function, used as a selection operator, allows the selection of individuals based on their fitness values. In this method, the probability of selecting each individual is determined by the ratio of its fitness value to the total fitness value. Thus, more suitable individuals are more likely to be selected. Consequently, fitter individuals are more likely to be passed on to the next generation. An example schematic of the roulette selection function is shown in Figure 7.  
Figure 6: Example of single crossover.