Learning with multi-objective criteria

The paper presents a new algorithm for learning with neural networks based on multi objective performance criteria. It considers three performance indices (or cost functions) as the objectives, which are the Euclidean distance and maximum difference measurements between the real nonlinear system and the nonlinear model (L₂, L_∞ norms), and the complexity measure 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 multi objective criteria. Genetic algorithms are also used simultaneously for model selection in which the structure of the neural networks are 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