Evolutionary Learning of BMF Fuzzy-Neural Networks Using a Reduced-Form Genetic Algorithm

In this paper, a novel approach to adjust both the control points of B-spline membership functions (BMFs) and the weightings of fuzzy-neural networks using a reduced-form genetic algorithm (RGA) is proposed. Fuzzy-neural networks are traditionally trained by using gradient-based methods, which may fall into local minimum during the learning process. To overcome the problems encountered by the conventional learning methods, genetic algorithms are adopted because of their capabilities of directed random search for global optimization. It is well known, however, that the searching speed of the conventional genetic algorithms is not desirable. Such conventional genetic algorithms are inherently incapable of dealing with a vast number (over 100) of adjustable parameters in the fuzzy-neural networks. In this paper, the RGA is proposed by using a sequential-search-based crossover point (SSCP) method in which a better crossover point is determined and only the gene at the specified crossover point is crossed, serving as a single gene crossover operation. Chromosomes consisting of both, the control points of BMFs and the weightings of the fuzzy-neural network are coded as an adjustable vector with real number components that are searched by the RGA. Simulation results have shown that faster convergence of the evolution process searching for an optimal fuzzy-neural network can be achieved. Examples of nonlinear functions approximated by using the fuzzy-neural network via the RGA are demonstrated to illustrate the effectiveness of the proposed method.