**5. GP as surrogate model for simulation-optimization**

A very important application of data intensive modelling approaches is to develop surrogate models to computationally complex numerical simulation models. As detailed elsewhere in this article, the authors have utilized GP in developing potential surrogates to a complex density dependent groundwater flow and transport simulation model. The potential utility of the surrogates is to replace the numerical simulation model in simulationoptimization frameworks. Simulation-optimization models are used to derive optimal management decisions using optimization algorithms in which a numerical simulation

models is run to predict the outcome of implementing the alternative management options. For example, the authors developed simulation-optimization models to develop optimal management decisions for coastal aquifers. The optimal pumping from the coastal aquifer can be decided only by considering the impact of any alternative pumping strategy on saltwater intrusion. For this the numerical simulation model needs to be integrated with the optimization algorithm and the impact of each candidate pumping strategy is predicted by using the simulation model iteratively. This involve a lot of computational burden as thousands of numerical model runs are required before an optimal pumping strategy is identified.

Genetic Programming: Efficient Modeling Tool in Hydrology and Groundwater Management 239

1. Genetic programming is able to develop simple models for developing the time series forecast models. When compared to the complex architecture of neural networks the GP models are simpler and easy to analyse. This is particularly relevant in developing transparent models for predicting natural phenomena. Complex neural network architectures make ANN model more or less "black-box" in nature, where as simpler GP models makes it easy to analyse the physical significance of each input in the model

2. In GP modeling, the optimum model architecture is evolved by GP after testing, most often, millions of alternate model structures and parameters as against the trial and error approach being followed by other artificial intelligence modeling approaches like neural networks. This helps in converging to global optimal solutions in minimizing the error criteria used for model development. Thus GP is able to develop global optimum

3. Genetic programming has the capability of parsimoniously selecting the variables for model development from the potential inputs. This helps to prevent redundancy in model development in terms of unnecessary inputs and parameters. In course of the model development GP determines the significance of each input in the model development in an efficient way so that the totally insignificant inputs are eliminated from the model. As shown in the results approaches like neural network models are also able to identify the relative significance of the inputs, they are less efficient in achieving this because of the rigidity of the model structure and connection weights. These key advantages of GP modeling are illustrated using realistic example in the broad area of hydrology and groundwater management for time series model development and conclusions are drawn which establishes the potential of genetic programming as a

models for predicting/forecasting hydrological processes and time series.

modeling and prediction tool for hydrology and water resources application.

*School of Engineering and Physical Sciences, James Cook University, Townsville, Australia* 

*3CRC for Contaminant Assessment and Remediation of the Environment, Mawson Lakes, Australia* 

[1] Koza, J.R., 1994. Genetic programming as a means for programming computers by

[2] Babovic, V., Keijzer, M., 2002. Rainfall runoff modelling based on genetic programming.

development.

**Author details** 

**7. References** 

J. Sreekanth1,2,3 and Bithin Datta1,2

*1CSIRO Land and Water, Ecosciences Precinct, Australia 2Discipline of Civil and Environmental Engineering,* 

Nordic Hydrology, 33(5): 331-346.

natural selection. Statistics and Computing, 4(2): 87-112.

GP was used a surrogate model within the optimization algorithm as a substitute of the numerical simulation model in our study (Sreekanth and Datta, 2010). Previous studies have used artificial neural networks as surrogate models to replace groundwater numerical simulation models. Emily et a1 (2005) used genetic programming based surrogate models for groundwater pollution source identification. In our study (Sreekanth and Datta, 2010), it was found that genetic programming could be used as a superior surrogate model in such application with definite advantages. The study intended to develop optimal pumping strategies for coastal aquifers in which the total pumping could be maximized and at the same time limiting the saltwater intrusion at pre-specified limits. In doing so, the effect of pumping on the salinity levels was predicted using trained and tested GP models. The GP models were externally coupled to a genetic algorithm based optimization model to derive the optimal management strategies. The results of the GP based simulation-optimization was then compared to the results obtained using an ANNbased simulation-optimization model. The ability of GP in parsimoniously identifying the model inputs helped in reducing the dimension of the decision space in which modelling and optimization was carried out. The smaller dimension of the modelling space helped in reducing the training and testing required to develop the surrogate models. The study identified that GP has potential applicability in developing surrogate models with potential application in simulation-optimization methodology to solve environmental management problems.

### **6. Conclusion**

The aim of this chapter is to introduce genetic programming as a potential modelling tool for hydrology and water resources applications. Genetic programming belongs to the broad class of evolutionary computational tools developed in recent years. Compared to the vast number of data mining and artificial intelligence applications in hydrology and water resources, the application of GP has been limited in spite of its potential applicability in a wide range of modelling applications. This chapter illustrates a few applications of GP as a modelling tool in the broad area of water resources modelling and management. The studies have found GP to be a useful tool for such applications with some advantages over other artificial intelligence techniques. The major findings reported in this chapter are enumerated as follows;


These key advantages of GP modeling are illustrated using realistic example in the broad area of hydrology and groundwater management for time series model development and conclusions are drawn which establishes the potential of genetic programming as a modeling and prediction tool for hydrology and water resources application.
