Memetic Algorithm with Normalized RBF ANN for Approximation of Objective Function and Secondary RBF ANN for Error Mapping

Abstract

Memetic algorithms (MAs) based on genetic algorithm (GAs) often require many evaluations of objective function. In applications like structural optimization a single evaluation of objective function can take from mere seconds to few hours or even days. Using artificial neural networks (ANN) to approximate the objective function can save computational time. To achieve required precision, certain number of training points has to be supplied. The time required to initialize and train the Radial Basis Function Artificial Neural Network (RBF ANN) depends on the number of training points and dimensionality, so it takes longer for more training points and more dimensions. More dimensions require more training points and so it is feasible to use the ANN approximation only for lower number of dimensions.To evaluate the objective function of a solution from population of GA or for local search, the algorithm chooses either FEM or ANN, depending on the estimated precision of ANN in the particular area of the optimization space. This algorithm is using two RBF ANNs, the primary ANN is used to approximate objective function and the secondary ANN maps precision of the primary ANN over the optimization space. This allows the algorithm to use the primary ANN to approximate objective function in areas where it is precise enough and helps to avoid false approximations in areas with low precision.