Optimizing Center Values and Widths of RBF (Radial Basis Function) Neural Network Using Genetic Algorithm (GA_RBF)

Genetic Algorithm Optimization of RBF Neural Network Center Values and Widths

RBF neural network is an efficient function approximation tool, particularly suitable for modeling and predicting nonlinear systems. However, traditional RBF neural networks typically rely on empirical or random selection when determining the center values and widths of the hidden layer, which can affect network performance. Using genetic algorithm (GA) to optimize these parameters can significantly improve model accuracy and stability.

Integration Approach of Genetic Algorithm with RBF Genetic algorithm simulates natural selection and genetic mechanisms, continuously optimizing individuals in the population through selection, crossover, and mutation operations. In GA_RBF, each individual represents a set of center values and widths for the RBF network. The fitness function is typically set as the network's error on the training set (such as mean squared error), where smaller errors correspond to higher individual fitness.

Key Steps in the Optimization Process Encoding: Center values and widths are encoded into chromosomes using real-value encoding or binary encoding schemes Initial Population: Randomly generate multiple sets of center values and widths as initial solutions Fitness Evaluation: Calculate the RBF network output error for each set as selection criteria using methods like MSE calculation Genetic Operations: Generate new solutions through roulette wheel selection, crossover with specified probability, and mutation operations Termination Condition: Stop optimization when preset iteration count or error threshold is reached

Advantages and Applications GA_RBF can automatically search for optimal network parameters, avoiding the blindness of manual parameter tuning. It demonstrates excellent performance in nonlinear approximation, time series prediction, and pattern recognition tasks, particularly suitable for scenarios with complex data distributions where traditional methods struggle with modeling.

The RBF neural network optimized through genetic algorithm not only improves approximation accuracy but also enhances model generalization capability, providing more reliable solutions for practical engineering problems.