Multi-objective model for architecture optimization and training of radial basis function neural networks

Radial Basis Function Neural Network (RBFNN) is a type of artificial neural networks used for supervised learning. They rely on radial basis functions (RBFs), nonlinear mathematical functions employed to approximate complex nonlinear data. Determining the architecture of the network is challenging, impacting the achievement of optimal learning and generalization capacities. This paper presents a multi-objective model for optimizing and training RBFNN architecture. The model aims to fulfill three objectives: the first is the summation of distances between the input vector and the corresponding center for the neurons in the hidden layer. The second objective is the global error of the RBFNN, defined as the discrepancy between the calculated output and the desired output. The third objective is the complexity of the RBFNN, quantified by the number of neurons in the hidden layer. This innovative approach utilizes multiple objective simulated annealing to identify optimal parameters and hyperparameters for neural networks. The numerical results provide accuracy and reliability of the theoretical results discussed in this paper, as well as advantages of the proposed approach.