Multiobjective training of artificial neural networks for rainfall-runoff modeling

This paper presents results on the application of various optimization algorithms for the training of artificial neural network rainfall-runoff models. Multilayered feed-forward networks for forecasting discharge from two mesoscale catchments in different climatic regions have been developed for this purpose. The performances of the multiobjective algorithms Multi Objective Shuffled Complex Evolution Metropolis-University of Arizona (MOSCEM-UA) and Nondominated Sorting Genetic Algorithm II (NSGA-II) have been compared to the single-objective Levenberg-Marquardt and Genetic Algorithm for training of these models. Performance has been evaluated by means of a number of commonly applied objective functions and also by investigating the internal weights of the networks. Additionally, the effectiveness of a new objective function called mean squared derivative error, which penalizes models for timing errors and noisy signals, has been explored. The results show that the multiobjective algorithms give competitive results compared to the single-objective ones. Performance measures and posterior weight distributions of the various algorithms suggest that multiobjective algorithms are more consistent in finding good optima than are single-objective algorithms. However, results also show that it is difficult to conclude if any of the algorithms is superior in terms of accuracy, consistency, and reliability. Besides the training algorithm, network performance is also shown to be sensitive to the choice of objective function(s), and including more than one objective function proves to be helpful in constraining the neural network training.