Multiobjective graph genetic programming with encapsulation applied to neural system identification

This paper presents two new encapsulation operators compatible with graph genetic programming. The approach is used for the evolvement of partially interconnected, feed-forward hybrid neural networks, within the framework of nonlinear system identification. The suggested encapsulations are targeted to protect valuable terminals and useful sub-graphs directly connected with the root node. To preserve a better balance between exploitation and exploration, the quality of the inner substructures is assessed in relation with the phenotypic properties of the individuals to whom they belong. The multiobjective optimization of accuracy and parsimony is adopted; for each generation, the requirements expressed by the decision block are progressively translated to the evolutionary algorithm, via a preliminary clustering of the individuals, performed before Pareto-ranking. The experimental results achieved on the identification of an industrial plant indicate that the proposed encapsulations are able to enforce the selection of accurate and simple models.