Genetic Algorithm (GA) for Optimizing BP Network Weights and Thresholds

The core concept of using Genetic Algorithm (GA) to train BP network weights and thresholds involves leveraging biological evolution mechanisms—selection, crossover, and mutation—to optimize neural network connection weights and node thresholds, thereby enhancing the convergence and prediction accuracy of BP networks. Below is a detailed breakdown of the implementation logic: Chromosome Encoding Design All weights and thresholds of the BP network are concatenated into a one-dimensional vector (chromosome). Real-value encoding directly represents parameters, while binary encoding requires conversion. The encoding length is determined by the network structure (number of input/hidden/output layer nodes). In MATLAB implementation, this can be achieved using vectorization operations, such as reshaping matrix parameters into a single array for genetic operations. Fitness Function Construction The prediction error of the BP network (e.g., Mean Squared Error, MSE) serves as the evaluation criterion. The fitness function typically takes the reciprocal or negative value of the error. Smaller errors result in higher individual fitness and a greater probability of retention. Code implementation involves calculating MSE after forward propagation and mapping it to a fitness score using 1/MSE or similar transformations. Genetic Operation Process Selection: Methods like roulette wheel or tournament selection filter high-quality individuals, preserving chromosomes with high fitness. Crossover: Single-point or uniform crossover operations blend parental genes to generate new parameter combinations. Mutation: Random perturbations are applied to genes selected with a small probability to avoid premature convergence. In algorithm design, crossover and mutation rates are key hyperparameters that require tuning for optimal performance. Weight Decoding and Network Training Optimized chromosomes from each generation are decoded back into weights/thresholds and substituted into the BP network to complete forward propagation and error calculation. This process iterates until termination conditions are met (e.g., maximum generations or error threshold). Implementation involves decoding the chromosome into weight matrices and bias vectors, then performing standard BP training steps. Advantages and Challenges Advantages: Helps BP networks escape local optima and is suitable for complex nonlinear problems. Challenges: Requires balancing search efficiency and precision, as the choice of crossover/mutation probabilities impacts convergence speed. This method can be implemented in MATLAB using the Global Optimization Toolbox combined with the Neural Network Toolbox, or by custom-coding fitness functions and genetic operators for specific application needs.