Fuzzy Neural Networks Learning by Variable- dimensional Quantum-behaved Particle Swarm Optimization

The evolutionary learning of fuzzy neural networks (FNN) consists of structure learning to determine the proper number of fuzzy rules and parameters learning to adjust the network parameters. Many optimization algorithms can be applied to evolve FNN. However the search space of most algorithms has fixed dimension, which cannot suit to dynamic structure learning of FNN. We propose a novel technique, which is named variable-dimensional quantum-behaved particle swarm optimization algorithm (VDQPSO), to address the problem. In the proposed algorithm, the optimum dimension, which is unknown at the beginning, is updated together with the position of swarm. The optimum dimension converged at the end of the optimization process corresponds to a unique FNN structure where the optimum parameters can be achieved. The results of the prediction of chaotic time series experiment show that the proposed technique is effective. It can evolve to optimum or near-optimum FNN structure and optimum parameters.