Pumping optimization of coastal aquifers based on evolutionary algorithms and surrogate modular neural network models George Kourakos, Aristotelis Mantoglou * Department of Rural and Surveying Engineering, National Technical University of Athens, 9, Iroon Polytechniou Str., Athens 15 780, Greece article info Article history: Received 14 May 2008 Received in revised form 31 December 2008 Accepted 2 January 2009 Available online 22 January 2009 Keywords: Modular neural networks Surrogate models Seawater intrusion Coastal aquifers Variable density models Pumping optimization Evolutionary algorithms abstract Pumping optimization of coastal aquifers involves complex numerical models. In problems with many decision variables, the computational burden for reaching the optimal solution can be excessive. Artificial Neural Networks (ANN) are flexible function approximators and have been used as surrogate models of complex numerical models in groundwater optimization. However, this approach is not practical in cases where the number of decision variables is large, because the required neural network structure can be very complex and difficult to train. The present study develops an optimization method based on mod- ular neural networks, in which several small subnetwork modules, trained using a fast adaptive proce- dure, cooperate to solve a complex pumping optimization problem with many decision variables. The method utilizes the fact that salinity distribution in the aquifer, depends more on pumping from nearby wells rather than from distant ones. Each subnetwork predicts salinity in only one monitoring well, and is controlled by relatively few pumping wells falling within certain control distance from the monitoring well. While the initial control area is radial, its shape is adaptively improved using a Hermite interpola- tion procedure. The modular neural subnetworks are trained adaptively during optimization, and it is possible to retrain only the ones not performing well. As optimization progresses, the subnetworks are adapted to maximize performance near the current search space of the optimization algorithm. The mod- ular neural subnetwork models are combined with an efficient optimization algorithm and are applied to a real coastal aquifer in the Greek island of Santorini. The numerical code SEAWAT was selected for solv- ing the partial differential equations of flow and density dependent transport. The decision variables cor- respond to pumping rates from 34 wells. The modular subnetwork implementation resulted in significant reduction in CPU time and identified an even better solution than the original numerical model. Ó 2009 Elsevier Ltd. All rights reserved. 1. Introduction Seawater intrusion in coastal aquifers is one of the most com- mon forms of groundwater contamination since about 70% of the world population lives in coastal areas [8]. Thus pumping manage- ment of coastal aquifers is a very important problem nowadays. For optimal management of water extraction from coastal aqui- fers, it is essential to simulate the movement of water and disper- sion of salts in response to different pumping strategies. Two modelling approaches for simulating seawater intrusion in coastal aquifers are based on the sharp interface approximation and on variable density dispersion. The sharp interface approximation as- sumes a thin transition zone between fresh and seawater and is applicable in regional scale problems when the transition zone is narrow relative to the scale of the problem [39]. The sharp inter- face approximation has been extensively employed in the past be- cause of its simplicity in terms of required parameters and computational burden [36,39,38,47,46,43,35,40,26,12]. Variable salt concentration in the mixing zone, constitutes a highly complex system where changes in concentration affect den- sity which affects velocity which in turn affects concentrations. Although variable density models better describe real coastal aqui- fers, they are difficult to implement because of high computational demands, lack of measurements of 3D aquifer properties and lack of reliable estimates of dispersion coefficients [43]. Nonetheless, an increasing number of researchers are adopting disperse inter- face models [27,57,60,5,7]. These models require solution of a cou- pled set of two partial differential equations, i.e. the equation of fluid flow and the equation of solute mass transport [25,60]. Das and Datta [14] proposed a sequential iterative solution using a nonlinear optimization method for solving the governing equa- tions. Several numerical codes such as SEAWAT [24] based on finite differences, FEFLOW [15], SUTRA [61] based on finite elements, 0309-1708/$ - see front matter Ó 2009 Elsevier Ltd. All rights reserved. doi:10.1016/j.advwatres.2009.01.001 * Corresponding author. Tel.: +30 2107722763. E-mail addresses: giorgk@gmail.com (G. Kourakos), mantog@central.ntua.gr (A. Mantoglou). Advances in Water Resources 32 (2009) 507–521 Contents lists available at ScienceDirect Advances in Water Resources journal homepage: www.elsevier.com/locate/advwatres