Abstract
This paper proposes a hierarchical multi-dimensional differential evolution (HMDDE) algorithm, which is an automatic computational frame work for the optimization of beta basis function neural network (BBFNN) wherein the neural network architecture, weights connection, learning algorithm and its parameters are adapted according to the problem. In the HMDDE-designed neural network, the number of individuals of the population multi-dimensions is the number of beta neural networks. The population of HMDDE forms multiple beta networks with different structures at the higher level and each individual of the previous population is optimized at a lower hierarchical level to improve the performance of each individual. For the beta neural network consisting of m neurons, n individuals (different lengths) are formed in the upper level to optimize the structure of the beta neural network. In the lower level, the population within the same length is to optimize the free parameters of the beta neural network. To evaluate the comparative performance, we used benchmark problems drawn from identification system and time series prediction area. Empirical results illustrate that the HMDDE produces a better generalization performance. (C) 2012 Elsevier B.V. All rights reserved.