Multi-objective management of saltwater intrusion in coastal aquifers using genetic programming and modular neural network based surrogate models
Introduction
Optimization of pumping from coastal aquifers is a challenging groundwater management problem as excessive extraction of water from aquifers hydraulically connected to the sea often results in salinity intrusion. Salinity intrusion in coastal aquifers is a highly non-linear and complex process (Bear et al., 1999). Once salinity intrusion occurs, it involves long-term measures incurring huge costs to remediate these contaminated aquifers. Hence, carefully planned strategies of groundwater extraction are required to prevent the eventual contamination of the valuable resource.
Salinity intrusion management models are used to prescribe management strategies for the sustainable use of coastal aquifers by controlling salt water intrusion. Developing an optimal management model involves integrating a groundwater flow and transport simulation model within an optimization framework. Flow and transport equations for salinity intrusion are coupled together by the density variation occurring during the mixing process, requiring simultaneous solution of both the equations. The numerical model for the density dependent flow and transport simulation would be computationally expensive, especially when used in a simulation–optimization framework. Trained and tested surrogate models are capable of approximating the numerical simulation model for simulating flow and transport process in the aquifer. Such a surrogate model when linked to an optimal decision model can evolve multi-objective optimal management strategies for the aquifer with the least computational burden. The use of genetic programming (GP) and modular neural networks (MNN) as the surrogate models is presented in this study. Trained and tested GP and MNN models are linked with a multi-objective genetic algorithm to derive optimal management strategies for a coastal aquifer.
Simulation–optimization models have been extensively used in solving groundwater pumping management problems (Gorelick, 1983, Gorelick et al., 1984, Ahlfeld and Heidari, 1994, Hallaji and Yazicigil, 1996, Emch and Yeh, 1998, Wang and Zheng, 1998, Das and Datta, 1999a, Das and Datta, 1999b, Cheng et al., 2000, Mantoglou, 2003, Mantoglou et al., 2004, Katsifarakis and Petala, 2006, Ayvaz and Karahan, 2008). Sharp-interface models and variable density models are the two modelling approaches used for simulating salinity intrusion in coastal aquifers. A number of studies have used sharp interface salinity intrusion models in the simulation–optimization framework (Iribar et al., 1997, Dagan and Zeitoun, 1998, Mantoglou, 2003, Park and Aral, 2004, Mantoglou and Papantoniou, 2008). Sharp-interface models are relatively simple and are easier to be incorporated within optimization models. Using a 3D density dependent model within an optimization framework is constrained by the CPU time taken by the model. Different techniques like response matrix method (Gorelick, 1983), embedding technique (Das and Datta, 1999a, Das and Datta, 1999b), and externally linking the flow and transport simulation model to the optimization model (Dhar and Datta, 2009) have been used in the past studies. In an externally linked simulation–optimization framework the optimization model calls the simulation model each time a candidate solution is evaluated. Thus the simulation model is run thousands of times before the optimal solution are obtained, adding to the computational complexity of the management model. Dhar and Datta (2009) reported a 30-day run time, on a 2.4 GHZ Oeptron AMD machine with 4 GB RAM, for a linked simulation–optimization model applied to a small aquifer system to find optimal solution.
Surrogate models are used to approximate the numerical simulation model in order to reduce the computational burden imposed by large scale numerical simulation models, especially within a linked simulation–optimization framework. Different methods like Artificial Neural Networks, radial-basis-function network, support vector machine etc. are used for constructing surrogate models. Extensive discussion of surrogate models can be seen in Jin (2005).
Artificial Neural Networks (ANN) have been widely used as surrogates for groundwater models (Ranjithan et al., 1993, Rogers et al., 1995, Aly and Peralta, 1999). Substantial research work has been done on using Artificial Neural Networks as surrogate models for simulation–optimization studies. Bhattacharjya, 2003, Rao et al., 2004, Bhattacharjya and Datta, 2005, Bhattacharjya and Datta, 2009, Kourakos and Mantoglou, 2006 and Dhar and Datta (2009) have used Neural Network surrogate models for developing salinity intrusion management models. Arndt et al. (2005) developed a neural network surrogate model implementing search interval adaptation. The adaptive neural network model was used as a surrogate for a finite element groundwater model and was used with an optimization algorithm to solve an optimal design problem. Yan and Minsker (2006) developed an Adaptive Neural Network Genetic Algorithm (ANGA) where the network was trained with search interval adaptation and genetic algorithm used to solve the optimization model. Behzadian et al. (2009) used adaptive neural networks in combination with multi-objective genetic algorithm NSGA-II to locate pressure loggers for a stochastic sampling design. Kourakos and Mantoglou (2009) developed a modular neural network (MNN) with a number of sub-networks replacing a global ANN. Salinity concentration in each monitoring well was predicted using a modular neural network and the intrusion is controlled by relatively few pumping wells falling within certain control distance from the monitoring wells. The networks were trained adaptively as optimization progresses. The computational time could be reduced considerably by using the modular neural networks.
A few studies in the broad area of hydrology and water resources have used GP models (Dorado et al., 2002, Makkeasorn et al., 2008, Parasuraman and Elshorbagy, 2008, Wang et al., 2009). GP has been used to develop prediction models run-off, river stage and real-time wave forecasting. (Babovic and Keijzer, 2002, Sheta and Mahmoud, 2001, Gaur and Deo, 2008). Zechman et al. (2005) developed a GP based surrogate model for use in a groundwater pollutant source identification problem. The chemical signals at the observation wells were used to reconstruct the pollution loading scenario. The inverse problem was solved using a simulation–optimization approach using GA to conduct the search. The numerical model was replaced by a surrogate model developed using genetic programming to reduce the computational burden.
The present study uses two surrogate models, GP and MNN, linked with multi-objective genetic algorithm to solve the pumping optimization problem. Genetic programming (GP) models are developed as surrogates for the variable density flow and transport simulation model, FEMWATER, which is used to simulate the salinity concentration at each monitoring well location. The GP models are then coupled with a Multi-objective Genetic Algorithm, Non-dominated Sorted Genetic Algorithm- II (NSGA-II) (Deb, 2001) to derive optimal pumping strategies. Modular neural network models were also developed for predicting the salinity concentrations at these locations and linked with NSGA II to solve the same problem. Both GP and MNN models are trained with search space adaptation in two stages to increase the accuracy of prediction in a search space near the entire Pareto-optimal set of solutions.
The governing equations for the simulation of variable density flow and transport are described in Section 2. The framework of the management model and the optimization formulation are presented in Section 3. The GP-MOGA and MNN-MOGA models are presented in Sections 3.3 GP-MOGA model, 3.4 MNN-MOGA model respectively. The methodology of search space adaptation and retraining the surrogate models for a multi-objective problem framework is described in Section 4. Section 5 presents the application of the developed methodologies to a small coastal aquifer and the relevant results and discussions. The conclusions are presented in Section 6.
Section snippets
Density dependent flow and transport simulation model
The three dimensional density dependent flow and transport simulation model FEMWATER (Lin et al., 1997) was chosen to simulate the coupled flow and transport process in the coastal aquifer system. The relevant equations for the density dependent flow and transport are as follows (Lin et al., 1997).
Coastal aquifer management model
The coastal aquifer management model developed in the present study essentially has two components. First component is a surrogate model for predicting the salinity levels in the specified monitoring locations, as a result of the groundwater extraction from the aquifer. Second component is an optimization algorithm based model to evolve optimal management strategies satisfying the imposed managerial constraints and other system constraints.
Search space modifications and adaptive training of the surrogate models
The optimization algorithm searches for optimal solutions in an N-dimensional search space, where N is the number of variables of the problem. Each variable in the optimization problem adds a dimension to the search space. The search process begins with random evaluations of candidate solutions uniformly distributed over the entire search space. Progressively better solutions are identified and the search process is confined to the space near to the optimal solutions in the variable space.
Evaluation of the developed methodology
The proposed methodology was evaluated by applying it to an illustrative study area comprising of a portion of a coastal aquifer. Fig. 3 illustrates the aquifer system with the pumping and barrier wells and the monitoring locations. All the boundaries of the aquifer were taken as no-flow boundaries, except the sea-side boundary. The sea-side boundary is a constant head and constant concentration boundary with a concentration of 35 kg/m3. The study area was discretized into triangular finite
Conclusion
Multi-objective pumping optimization models for coastal aquifers were developed in the simulation–optimization framework with genetic programming and modular neural networks as surrogate models for simulating the salinity levels. A multi-objective genetic algorithm NSGA II was used to solve the optimization problem. Individual surrogate models were developed for predicting the salinity concentrations at each monitoring location, for both GP-MOGA and MNN-MOGA approach. This approach is effective
Acknowledgements
The research was supported by CRC for the Contamination Assessment and Aemediation of the Environment. Also we acknowledge the efforts of unknown reviewers whose suggestions helped us to improve the presentation of this paper, considerably.
References (50)
- et al.
Approximating a finite element model by neural network prediction for facility optimization in groundwater engineering
European Journal of Operational Research
(2005) - et al.
A stochastic sampling design using a multi-objective genetic algorithm and adaptive neural networks
Environ Model Software
(2009) - et al.
Seawater-freshwater interface in a stratified aquifer of random permeability distribution
Journal of Contaminant Hydrology
(1998) - et al.
Real-time wave forecasting using genetic programming
Ocean Engineering
(2008) - et al.
Review and comparison of methods to study the contribution of variables in artificial neural network models
Ecological Modelling
(2003) Back-propagation neural networks for modelling complex systems
Artificial Intelligence in Engineering
(1995)- et al.
Inverse modelling of seawater intrusion in the Llobregat delta deep aquifer
Journal of Hydrology
(1997) - et al.
Combining genetic algorithms and boundary elements to optimize coastal aquifers’ management
Journal of Hydrology
(2006) - et al.
Pumping optimization of coastal aquifers based on evolutionary algorithms and surrogate modular neural network models
Advances in Water Resources
(2009) - et al.
Short-term streamflow forecasting with global climate change implications – a comparative study between genetic programming and neural network models
Journal of Hydrology
(2008)
Optimal design of pumping networks in coastal aquifers using sharp interface models
Journal of Hydrology
Management of coastal aquifers based on nonlinear optimization and evolutionary algorithms
Journal of Hydrology
Illuminating the “black box”: a randomization approach for understanding variable contributions in artificial neural networks
Ecological Modelling
Multi-objective optimization of pumping rates and well placement in coastal aquifers
Journal of Hydrology
A comparison of performance of several artificial intelligence methods for forecasting monthly discharge time series
Journal of Hydrology
Applications of optimal hydraulic control to groundwater systems
Journal of Water Resources Planning and Management-Asce
Optimal design of aquifer cleanup systems under uncertainty using a neural network and a genetic algorithm
Water Resources Research
A simulation/optimization model for the identification of unknown groundwater well locations and pumping rates
Journal of Hydrology
Rainfall runoff modeling based on genetic programming
Nordic Hydrology
Seawater Intrusion in Coastal Aquifers – Concepts, Methods and Practices
Optimal management of coastal aquifer using linked simulation optimization approach
Water Resources Management
ANN-GA-based model for multiple objective management of coastal aquifers
Journal of Water Resources Planning and Management-Asce
Pumping optimization in saltwater-intruded coastal aquifers
Water Resources Research
Development of management models for sustainable use of coastal aquifers
Journal of Irrigation and Drainage Engineering-Asce
Cited by (168)
Review of machine learning-based surrogate models of groundwater contaminant modeling
2023, Environmental ResearchCausal interpretation for groundwater exploitation strategy in a coastal aquifer
2023, Science of the Total EnvironmentSteady-state density-driven flow and transport: Pseudo-transient parameter continuation
2023, Advances in Water ResourcesOptimal utilization of groundwater resources and artificial recharge system of Shahriar plain aquifer, Iran
2023, Physics and Chemistry of the EarthMapping and monitoring seasonal and tidal effects on the salt-freshwater interface using electrical resistivity tomography techniques
2022, Estuarine, Coastal and Shelf Science