Improved particle swarm optimization-based artificial neural network for rainfall-runoff modeling

This paper presents the application of an improved particle swarm optimization (PSO) technique for training an artificial neural network (ANN) to predict water levels for the Heshui watershed, China. Daily values of rainfall and water levels from 1988 to 2000 were first analyzed using ANNs trained with the conjugate-gradient, gradient descent and Levenberg-Marquardt neural network (LM-NN) algorithms. The best results were obtained from LM-NN and these results were then compared with those from PSO-based ANNs, including conventional PSO neural network (CPSONN) and improved PSO neural network (IPSONN) with passive congregation. The IPSONN algorithm improves PSO convergence by using the selfish herd concept in swarm behavior. Our results show that the PSO-based ANNs performed better than LM-NN. For models run using a single parameter (rainfall) as input, the root mean square error (RMSE) of the testing dataset for IPSONN was the lowest (0.152 m) compared to those for CPSONN (0.161 m) and LM-NN (0.205 m). For multi-parameter (rainfall and water level) inputs, the RMSE of the testing dataset for IPSONN was also the lowest (0.089 m) compared to those for CPSONN (0.105 m) and LM-NN (0.145 m). The results also indicate that the LM-NN model performed poorly in predicting the low and peak water levels, in comparison to the PSO-based ANNs. Moreover, the IPSONN model was superior to CPSONN in predicting extreme water levels. Lastly, IPSONN had a quicker convergence rate compared to CPSONN