A sequential approximation method using neural networks for nonlinear discrete-variable optimization with implicit constraints

This paper presents a sequential approximation method that combines a back- propagation neural network with a search algorithm for nonlinear discrete-v ariable engineering optimization problems with implicit constraints. This i s an iteration process. A back-propagation neural network is trained to sim ulate the feasible domain formed by the implicit constraints. A search algo rithm then searches for the "optimal point" in the feasible domain simulate d by the neural network. This new design point is checked against the true constraints to see whether it is feasible, and is added to the training set . Then the neural network is trained again. With more design points in the training set, information about the whole search domain is accumulated to p rogressively form a better approximation for the feasible domain. This iter ation process continues until the approximate model insists the same "optim al" point in consecutive iterations. In each iteration, only one evaluation of the implicit constraints is needed to see whether the current design po int is feasible. No precise function value or sensitivity calculation is re quired. Several engineering design examples are used to demonstrate the pra cticality of this approach.