**4. Multiple predictive model structures using GP**

236 Genetic Programming – New Approaches and Successful Applications

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**Figure 4.** Impact factors of input variables in predicting Salinity at location 1.

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**Figure 5.** Impact factors of input variables in predicting Salinity at location 2.

From these figures it can be observed that all the variables considered has a non-zero impact in the developed ANN models. Whereas, GP is able to assign zero impact factor to those inputs which are not significant and thus able to eliminate them from the model. This helps in developing simpler models and reducing the predictive uncertainty. In figure 4 it can be seen that GP identified 13 inputs with zero impact factor. This implies that the pumping values corresponding to these inputs have negligible effect on the salinity levels at the observation location. Thus 13 out of the 33 inputs considered are eliminated from the GP models resulting in much simpler models compared to the ANN models where all the 33 inputs take part in predicting the salinity even though some of them are having very less impact on the predictions made. The ability of GP to eliminate insignificant variables is because of the evolutionary nature of model structure optimization. By performing crossover, mutation and selection of candidate models over a number of generations GP is able to derive the optimum model structure with the most important input variables which are

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The advent of GP as a modelling tool has paved the way for researches exploring the possibility of multiple optimal models for predicting hydrological processes. Genetic programming, in its evolutionary approach to derive optimal model structures and parameters, tests millions of model structures which can mimic the physical process under consideration. Researches have found that multiple models can be identified using GP which are considerably different in model structures but able to make consistently good predictions. Parasuraman and Elshorbagy [8] developed genetic programming based models for predicting the evapo-transporation. In doing so, multiple optimal GP models were trained and tested and they were applied to quantify the uncertainty in those models. Another study by the authors [9] developed ensemble surrogate models for predicting the aquifer responses to pumping in terms of salinity levels at observation locations. An ensemble of surrogate models based on GP was developed and the ensemble was used to get model predictions with improved reliability levels. The variance of the model predictions were used as the measure of uncertainty in the modelling process.
