In this paper, we present MLEANN (Meta-Learning Evolutionary Artificial Neural Network), an automatic computational framework for the adaptive optimization of artificial neural networks wherein the neural network architecture, activation function, connection weights; learning algorithm and its parameters are adapted according to the problem. We explored the performance of MLEANN and conventionally designed artificial neural networks for function approximation problems. To evaluate the comparative performance, we used three different well-known chaotic time series. We also present the state of the art popular neural network learning algorithms and some experimentation results related to convergence speed and generalization performance. We explored the performance of backpropagation algorithm; conjugate gradient algorithm, quasi-Newton algorithm and Levenberg-Marquardt algorithm for the three chaotic time series. Performances of the different learning algorithms were evaluated when the activation functions and architecture were changed. We further present the theoretical background, algorithm, design strategy and further demonstrate how effective and inevitable is the proposed MLEANN framework to design a neural network, which is smaller, faster and with a better generalization performance.