A hybrid evolutionary algorithm to train neural networks as time-series predictors

Design of a non-parametric time-series predictor is an exercise in functional approximation. This work proposes a novel approach to the development of artificial neural network models for time-series predictors. The approach involves a hybrid genetic algorithm that simultaneously encodes both the structure and the magnitude of the weights of the neural network into a compound genotype representation. Modified genetic crossover and mutation operators then act on the population to simultaneously discover the appropriate network structure and weight magnitudes.; This approach was validated experimentally on a number of time-series applications, including an adaptive optics application. The imaging resolution of large, ground-based telescopes is restricted to a fraction of the maximum resolution at the diffraction limit due to the distortion caused by the atmosphere. The phase of an incoming optical wavefront is distorted by passing through regions of differing indices of refraction that are caused largely by differential solar heating of the surface of the earth. Adaptive optics systems are capable of dynamically correcting for the distortion before imaging takes place by correcting the shape of the incoming wavefront with a deformable mirror. For optimal correction, the deformable mirror must apply the conjugate of the current distortion affecting the wavefront.; Real atmospheric distortion data from the European Southern Observatory at La Silla, Chile was employed to evaluate the prediction scheme. The neural networks discovered by the genetic algorithm consist exclusively of linear elements and provide a marginal performance improvement over conventional techniques, including linear prediction. The topology of the resultant neural networks discovered using data with a variety of signal-to-noise characteristics is shown to be consistent with a filtered fractional Brownian motion model of the wavefront slope distortion process that has been recently suggested by McGaughey and Aitken.; The capabilities of the proposed genetic algorithm technique to develop neural networks to perform other time-series prediction techniques is also demonstrated. Time-series predictors with good performance are automatically generated by the genetic algorithm to predict the observed magnitude of a star and on a complex, non-linear time-series that was used as a prediction problem in the 1998 K. U. Leuven time-series prediction competition.; While the present work has been limited to discovering feedforward neural network architectures, the technique is readily extensible to feature maps and recurrent networks. A fundamental advantage over the popular error-backpropagation network training technique is that the objective function employed to discover the networks is not limited to mean-squared error.