A sequential approximation method using neural networks for engineering design optimization problems

There are three characteristics in engineering design optimization problems: (1) the design variables are often discrete physical quantities; (2) the constraint functions often cannot be expressed analytically in terms of design variables; (3) in many engineering design applications, critical constraints are often ‘pass–fail’, ‘0–1’ type binary constraints. This paper presents a sequential approximation method specifically for engineering optimization problems with the three characteristics. In this method a back-propagation neural network is trained to simulate a rough map of the feasible domain formed by the constraints using a few representative training data. A training data point consists of a discrete design point and whether this design point is feasible or infeasible. Function values of the constraints are not required. 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 then added to the training set. The neural network is trained again with this added information, in the hope that the network will better simulate the boundary of the feasible domain of the true optimization problem. Then a further search is made for the optimal point in this new approximated feasible domain. This process continues in an iterative manner until the approximate model locates the same optimal point in consecutive iterations. A restart strategy is also employed so that the method may have a better chance to reach a global optimum. Design examples with large discrete design spaces and implicit constraints are solved to demonstrate the practicality of this method.