Multiobjective criteria for neural network structure selection and identification of nonlinear systems using genetic algorithms

An approach to model selection and identification of nonlinear systems via neural networks and genetic algorithms is presented based on multiobjective performance criteria. It considers three performance indices or cost functions as the objectives, which are the Euclidean distance (L₂-norm) and maximum difference (L∞-norm) measurements between the real nonlinear system and the nonlinear model, and the complexity measurement of the nonlinear model, instead of a single performance index. An algorithm based on the method of inequalities, least squares and genetic algorithms is developed for optimising over the multiobjective criteria. Genetic algorithms are also used for model selection in which the structure of the neural networks is determined. The Volterra polynomial basis function network and the Gaussian radial basis function network are applied to the identification of a liquid-level nonlinear system