A Sequential Approximation Method Using Neural Networks for Nonlinear Discrete-Variable Optimization with Implicit Constraints

Abstract

This paper presents a sequential approximation method that combines a back-propagation neural network with a search algorithm for nonlinear discrete-variable engineering optimization problems with implicit constraints. This is an iteration process. A back-propagation neural network is trained to simulate the feasible domain formed by the implicit constraints. A search algorithm then searches for the “optimal point” in the feasible domain simulated 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 progressively form a better approximation for the feasible domain. This iteration process continues until the approximate model insists the same “optimal” point in consecutive iterations. In each iteration, only one evaluation of the implicit constraints is needed to see whether the current design point is feasible. No precise function value or sensitivity calculation is required. Several engineering design examples are used to demonstrate the practicality of this approach.