An evaluation of back-propagation neural networks for the optimal design of structural systems: Part II. Numerical evaluation

Abstract In the companion paper the neural network training procedures used in the present evaluation were described in detail. Also, in the companion paper, two new training methods that used the derivative information to build global approximations, and a mixed local-global approximation scheme were proposed in addition to the common function-based training method. In this paper, we carry out an exhaustive numerical evaluation of the proposed and existing methods using five test problems with varying complexity. Approximately 1100 test cases were run as part of the numerical evaluations. First, the efficiency of three different optimization algorithms used for training including a sequential quadratic programming algorithm, a Levenberg–Marquardt algorithm and a genetic algorithm is evaluated. The developed training schemes were next evaluated by comparing with the classical structural optimization methods. The two new derivative-based training methods were found to be more accurate but less efficient than function-based training. Further, compared with classical structural optimization by non-linear programming algorithms, including design sensitivity analysis, global approximation and mixed local-global approximation using neural networks were found to be far less efficient. With careful training, the neural networks were found capable of predicting the exact solution, but this ability depended considerably on the complexity of the original problem. In general, the accuracy of the network, which is a function of the training effort, suffered considerably in large problems. The most surprising observation of the present study was that the training process required over 90% of the total solution time, even when considerable effort was exercised at using the most efficient training procedure. As expected, the use of neural network approximations (once training was complete) speeded up the optimal design process significantly.