In this paper, a tree-based encoding method is introduced to represent the Beta basis function neural network. The proposed model called Flexible Beta Basis Function Neural Tree (FBBFNT) can be created and optimized based on the predefined Beta operator sets. A hybrid learning algorithm is used to evolving FBBFNT Model: the structure is developed using the Extended Genetic Programming (EGP) and the Beta parameters and connected weights are optimized by the Opposite-based Particle Swarm Optimization algorithm (OPSO).

In this paper, we apply the Beta Basis Function Neural Network (BBFNN) trained with cuckoo search (CS) for time series predictions. The cuckoo search algorithm optimizes the network parameters. In order to evaluate the effectiveness of the proposed method, we have carried out some experiments on four data sets: Mackey Glass, Lorenz attractor, Henon map and Box-Jenkins. We give also simulation examples to compare the effectiveness of the model with the other known methods in the literature. The results show that the CS-BBFNN model produces a better generalization performance.