Abstract
Artificial neural networks in general and radial basis function in particular are known for high accuracies in function approximation, nonlinear system identification, and pattern classification problems; however, they pose numerous challenges with regards to the optimality of parameters involved. This paper proposes the use of a classical Nelder-Mead simplex method to optimize the parameters of activation function implicit in the design of radial basis function network. The key advantage of using Nelder-Mead simplex method lies in the fact that it provides a simple yet effective derivative-free approach for the numerical optimization of scalar variables such as spread and learning rate for Kernels of the radial basis function network. We thus present a novel hybrid algorithm in which weights of neurons are updated using gradient decent approach, while spread and learning rate is updated, viz. the Nelder-Mead simplex method. In results, the efficiency of proposed algorithm is statistically compared with the existing algorithms in different applications such as classification of digital signals in noise-limited wireless communication system, synthesis of microstrip patch antenna, and curve fitting problem. Lastly, we consider a two-variable function approximation problem to pedagogically express contrasting features of the hybrid algorithm, thereby pointing toward its potential usage in some engineering design problems.