Optimizing BP Neural Networks Using Differential Evolution (DE) Algorithm

The optimization of BP neural network weights and thresholds using the Differential Evolution (DE) algorithm significantly improves model performance in PM2.5 concentration forecasting. Traditional BP neural networks often suffer from local minima convergence and slow training speeds, while DE serves as a global optimization technique that adaptively adjusts network parameters through population mutation, crossover, and selection operations, enabling more effective exploration of the solution space. In PM2.5 data validation experiments, DE-optimized BP neural networks consistently demonstrate superior prediction accuracy and stability. Implementation requires encoding neural network connection weights and thresholds as individual vectors in DE's population structure, where prediction errors serve as the fitness function. Through multiple evolutionary generations, the algorithm progressively approximates optimal parameter combinations. Compared to gradient descent methods, DE optimization eliminates the need for manual learning rate tuning and exhibits lower sensitivity to initial parameters, making it particularly suitable for handling highly nonlinear air quality data. This approach combines the powerful fitting capability of neural networks with DE's global search advantages, providing a more robust solution for modeling complex environmental data. The implementation typically involves: 1) Defining the parameter encoding scheme where each DE vector represents all weights and thresholds; 2) Implementing a fitness function that calculates mean squared error between predictions and actual PM2.5 values; 3) Configuring DE operations including mutation factor (F) and crossover rate (CR) for balanced exploration-exploitation; 4) Setting termination criteria based on fitness improvement or maximum generations. Future research could explore adaptive DE variants or hybrid optimization strategies to handle higher-dimensional parameter spaces more efficiently.