Evolutionary Multiobjective Neural Network Models Identification: Evolving Task-Optimised Models Pedro M. Ferreira and Ant ´ onio E. Ruano Abstract In the system identification context, neural networks are black-box mod- els, meaning that both their parameters and structure need to be determined from data. Their identification is often done iteratively in an ad-hoc fashion focusing the first aspect. Frequently the selection of inputs, model structure, and model order are underlooked subjects by practitioners, because the number of possibilities is com- monly huge, thus leaving the designer at the hands of the curse of dimensionality. Moreover, the design criteria may include multiple conflicting objectives, which gives to the model identification problem a multiobjective combinatorial optimisa- tion character. Evolutionary multiobjective optimisation algorithms are particularly well suited to address this problem because they can evolve optimised model struc- tures that meet pre-specified design criteria in acceptable computing time. In this article the subject is reviewed, the authors present their approach to the problem in the context of identifying neural network models for time-series prediction and for classification purposes, and two application case studies are described, one in each of these fields. 1 Introduction In most practical applications of Artificial Neural Networks (ANN), they are used to perform a non-linear mapping between an input space, X, and an output space, y, in order to model complex relationships between these or to detect patterns in input-output data. These functionalities correspond mostly to function approxima- Pedro M. Ferreira Algarve Science & Technology Park, University of Algarve, Campus de Gambelas - Pav. A5, 8005- 139 Faro, Portugal, e-mail: pfrazao@ualg.pt Ant´ onio E. Ruano and Pedro M. Ferreira Centre for Intelligent Systems, University of Algarve - FCT, Campus de Gambelas, 8005-139 Faro, Portugal e-mail: aruano@ualg.pt 1