Optimizing neural networks for river flow forecasting – Evolutionary Computation methods versus the Levenberg–Marquardt approach

Abstract

Summary Although neural networks have been widely applied to various hydrological problems, including river flow forecasting, for at least 15 years, they have usually been trained by means of gradient-based algorithms. Recently nature inspired Evolutionary Computation algorithms have rapidly developed as optimization methods able to cope not only with non-differentiable functions but also with a great number of local minima. Some of proposed Evolutionary Computation algorithms have been tested for neural networks training, but publications which compare their performance with gradient-based training methods are rare and present contradictory conclusions. The main goal of the present study is to verify the applicability of a number of recently developed Evolutionary Computation optimization methods, mostly from the Differential Evolution family, to multi-layer perceptron neural networks training for daily rainfall–runoff forecasting. In the present paper eight Evolutionary Computation methods, namely the first version of Differential Evolution (DE), Distributed DE with Explorative–Exploitative Population Families, Self-Adaptive DE, DE with Global and Local Neighbors, Grouping DE, JADE, Comprehensive Learning Particle Swarm Optimization and Efficient Population Utilization Strategy Particle Swarm Optimization are tested against the Levenberg–Marquardt algorithm – probably the most efficient in terms of speed and success rate among gradient-based methods. The Annapolis River catchment was selected as the area of this study due to its specific climatic conditions, characterized by significant seasonal changes in runoff, rapid floods, dry summers, severe winters with snowfall, snow melting, frequent freeze and thaw, and presence of river ice – conditions which make flow forecasting more troublesome. The overall performance of the Levenberg–Marquardt algorithm and the DE with Global and Local Neighbors method for neural networks training turns out to be superior to other Evolutionary Computation-based algorithms. The Levenberg–Marquardt optimization must be considered as the most efficient one due to its speed. Its drawback due to possible sticking in poor local optimum can be overcome by applying a multi-start approach.