This book proposes two novel algorithms for function classification and prediction that extends a three layered Feed Forward Neural Network (FFNN) and the standard Generalized Regression Neural Network (GRNN).In this book genetic algorithm(GA) is used inside the particle swarm optimization(PSO) algorithm to bring the worst particle in PSO search space nearer to the food. This helps in faster convergence of PSO algorithm and the possibility of the algorithm to get stuck at the local minima is eliminated.The detailed analysis of results and comparisons show that the proposed algorithms have effectively improved the performance of a neural network as a classifier and predictor and obtained the better accuracy with minimum mean square error than the non optimized neural networks.