Training Fuzzy Neural Network via Multiobjective Optimization for Nonlinear Systems Identification

The design of fuzzy neural network (FNN) has long been a challenging problem since most methods rely on approximation error to train FNN, which may easily occur overfitting phenomenon to degrade the generalization performance. To improve the generalization performance, a fuzzy neural network with multi-objective optimization algorithm (MOO-FNN) is proposed in this paper. First, the multi-level learning objectives are designed around the generalization performance to guide the training process of FNN. Then, the method utilizes the approximation error, the structure complexity, and the output smoothness indicators instead of a single indicator to improve the evaluation accuracy of generalization performance. Second, a MOO algorithm with continuous-discrete variables is developed to optimize FNN. Then, MOO is able to use a novel particle update method to adjust both the structure and parameters rather than adjust them separately, thereby achieving suitable generalization performance of FNN. Third, the convergence of MOO-FNN is analyzed in detail to guarantee its successful applications. Finally, the experimental studies of MOO-FNN have been performed on model identification of nonlinear systems to verify the effectiveness. The results illustrate that MOO-FNN has a significant improvement over some state-of-the-art algorithms.