Training Fuzzy Neural Network via Multiobjective Optimization for Nonlinear Systems Identification

The design of a fuzzy neural network (FNN) has long been a challenging problem since most methods rely on approximation error to train an FNN, which may easily result in overfitting phenomenon to degrade the generalization performance. To improve the generalization performance, an FNN with a multiobjective optimization algorithm (MOO-FNN) is proposed in this article. First, the multilevel learning objectives are designed around the generalization performance to guide the training process of an 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, an MOO algorithm with continuous-discrete variables is developed to optimize the FNN. Then, MOO is able to use a novel particle update method to adjust both the structure and parameters rather than adjusting them separately, thereby achieving suitable generalization performance of the 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.

Automated summary

This article proposes an FNN with a multiobjective optimization algorithm (MOO-FNN) to improve the generalization performance. It utilizes multilevel learning objectives and multiple indicators for evaluating the generalization performance accurately. The MOO algorithm is applied to adjust both the structure and parameters of the FNN, resulting in significant improvements compared to other algorithms.