An evaluation of back-propagation neural networks for the optimal design of structural systems: Part I. Training procedures Original Research Article

Design optimization using approximations based on feed-forward back-propagation neural network is the topic of much recent research. The neural network schemes that have been proposed in the literature for optimal design of structural systems differ in their architecture and training procedures. Furthermore, their utility vis-a-vis classical optimization techniques is not always clear. A systematic comparison of the efficiency and accuracy of the neural network-based solution schemes to classical structural optimization techniques is the aim of this and the companion paper. In this paper, the neural network training procedures used in the present evaluation are described in detail. When using first-order nonlinear programming algorithms with neural networks, the ability to approximate derivatives is important. Therefore, mainly for completeness of evaluation, two new training methods that use the derivative information are proposed in addition to the now common function-based training method. The first method uses the derivatives to create additional training points in the vicinity of the original points, based on Taylorʹs series expansion. The second method attempts to minimize the error in derivatives while imposing the error in output functions as constraint. Expressions for analytical derivatives are derived for both function-based and derivative-based training. Significant savings in computational time are reported when calculating derivatives using built-in analytical derivatives instead of using finite difference derivatives. In the companion paper the proposed methods are applied to solve five optimization problems with varying degree of complexity. Approximately 1100 test cases are executed in the companion paper to compare the accuracy and efficiency of neural network-based optimization with the classical approaches.