Feasibility study of using artificial neural networks for approximation of n-dimensional obj ective functions in memetic algorithms for structural optimization

摘要

Evaluation of objective function for problems of structural optimization is generally considered as computationally expensive and can take from few seconds to hours or even days. After certain number of solutions has been evaluated during optimization, artificial neural networks (ANNs) can be trained and used to approximate the objective function. The number of training points depends on the character and topology of objective function, but the most important factor is the dimensionality of objective function. Similarly as the performance of optimization algorithms, requirements on training data for ANNs are affected by so called "curse of dimensionality". To achieve the same precision of ANN approximation over n-dimensional space, the number of training points grows exponentially with the number of dimensions. This paper presents a feasibility study of using ANNs for approximation of objective function for problems solved by structural optimization with respect to the number of optimization variables. The goal of this study was to find the maximum number of dimensions, where it is feasible to use ANNs for approximation of objective function. Test problem with varying number of optimization variables was used to assess the feasibility of using ANN.