Design and implementation of a hybrid MLP-GSA model with multi-layer perceptron-gravitational search algorithm for monthly lake water level forecasting

  • Mohammad Ali GhorbaniEmail author
  • Ravinesh C. DeoEmail author
  • Vahid Karimi
  • Mahsa H. Kashani
  • Shahryar Ghorbani
Original Paper


Lakes are primitive water holding geographic structures containing most the fresh water on the Earth’s surface, but the recent trends show that climate change can potentially lead to a significant aberration in the Lake water level and its overall pristine state, and therefore, could also threaten the source of freshwater. The ability to forecast the lake water is a paramount decision-making and risk-reduction task, and this is required to retain the sustainability of the natural environment, and to reduce the risk to the local and global food chain, recreation activities, agriculture and ecosystems. In this study, we have designed and evaluated a new hybrid forecasting model, integrating the gravitational search algorithm (GSA), as a heuristic optimization tool, with the Multilayer Perceptron (MLP-GSA) algorithm to forecast water level in Winnipesaukee and Cypress Lakes in the United States of America. The performance of the resulting hybrid MLP-GSA model is benchmarked and compared with the traditional MLP trained with Levenberg–Marquadt back propagation learning algorithm, two other intelligent hybrid models (MLP-PSO and MLP-FFA) and also two stochastic models namely, ARMA and ARIMA models. In this case study, the monthly time scale water level data from 1938 to 2005 and 1942 to 2011 for the Lakes Winnipesaukee and Cypress, respectively, were applied to train and evaluate the MLP-GSA model. The best input combinations of the standalone (MLP) and the hybrid MLP-GSA forecasting models were determined by sensitivity analysis of historical water level training data for 1-month lead forecasting. The hybrid MLP-GSA model was evaluated independently with statistical score metrics: coefficient of correlation, coefficient of efficiency, the root mean square and relative root mean square errors, and the Bayesian Information Criterion. The results showed that the hybrid MLP–GSA4 and MLP-GSA5 model (where the ‘4 and 5 months’ of lagged input combinations of Lake water level data were utilized as the model inputs) performed more accurately than the ARIMA, ARMA, MLP4, MLP-PSO4 and MLP-FFA4 models for the Cypress Lake and ARIMA, ARMA, MLP5, MLP-PSO5 and MLP-FFA5 models for the Winnipesaukee lake, respectively. This study ascertained the robustness of hybrid MLP-GSA over ARMA, ARIMA, MLP, MLP-PSO and MLP-FFA for the forecasting of Lake water level. The high efficacy of the hybrid MLP-GSA model over the other applied models, indicate significant implications of its use in water resources management, decision-making tasks, irrigation management, management of hydrologic structures and sustainable use of water for agriculture and other necessities.


MLP Gravitational search algorithm Hybrid models ARMA ARIMA Lake Winnipesaukee Lake Cypress Water level 



The authors sincerely thank the Editor-In-Chief, the Associate Editor, and all the reviewers for their useful and gracious comments, which improved the clarity of the final manuscript.


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Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Department of Water Engineering, Faculty of AgricultureUniversity of TabrizTabrizIran
  2. 2.Engineering FacultyNear East UniversityNicosia, Mersin 10Turkey
  3. 3.School of Agricultural, Computational and Environmental Sciences, Centre for Sustainable Agricultural Systems & Centre for Applied Climate Sciences, Institute of Life Science and the EnvironmentUniversity of Southern QueenslandSpringfieldAustralia
  4. 4.Department of Water EngineeringUniversity of TabrizTabrizIran
  5. 5.Department of Water EngineeringUniversity of Mohaghegh ArdabiliArdabilIran
  6. 6.Graduate School of Social ScienceIstanbul Gedik UniversityIstanbulTurkey

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