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 funct ions as the objectives, which are the euclidean distance (L-2-norm) and max imum difference (L-infinity-norm) measurements between the real nonlinear s ystem and the nonlinear model, and the complexity measurement of the nonlin ear 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 als o used for model selection in which the structure of the neural networks is determined. The Volterra polynomial basis function network and the gaussia n radial basis function network are applied to the identification of a liqu id-level nonlinear system.