Water Resources Management

, Volume 30, Issue 15, pp 5845–5859 | Cite as

Pumping Optimization of Coastal Aquifers Assisted by Adaptive Metamodelling Methods and Radial Basis Functions



The application of metamodelling frameworks is a popular approach to handle the computational cost arising from complex computer simulations and global optimization algorithms in simulation-optimization routines. In this paper, Radial Basis Functions (RBF) are used as metamodels for the computationally expensive variable-density flow and salt transport numerical simulations, in a pumping optimization problem of coastal aquifers. While RBF metamodels have been fairly utilized in many engineering optimization problems, their use is very limited in coastal aquifer management. Two adaptive metamodelling frameworks are employed, that is, the adaptive-recursive approach and the metamodel-embedded evolution strategy. In both frameworks, cubic RBF models are used to approximate the constraint functions imposed on the coastal aquifer pumping optimization problem. The optimal pumping rates are first calculated based on the variable-density and salt transport numerical models of seawater intrusion. The resulting optimal solutions and the computational times are set as benchmark values in order to assess the performance of the metamodelling optimization strategies. Results indicate that the metamodel-embedded evolution framework outperformed in terms of computational efficiency the adaptive-recursive approach while it successfully located the region of the global optimum. Furthermore, with the metamodel-embedded evolution strategy the computational time of the variable-density-based optimization was reduced by 96 %.


Coastal aquifers Pumping optimization Metamodels Radial basis functions Global optimization 


Compliance with ethical standards

Conflict of Interest

The authors declare that they have no conflict of interest


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© Springer Science+Business Media Dordrecht 2016

Authors and Affiliations

  1. 1.Laboratory of Reclamation Works and Water Resources Management, School of Rural and Surveying EngineeringNational Technical University of AthensAthensGreece

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