عنوان مقاله [English]
Introduction: Precise prediction of river flows is the key factor for proper planning and management of water resources. Thus, obtaining the reliable methods for predicting river flows has great importance in water resource engineering. In the recent years, applications of intelligent methods such as artificial neural networks, fuzzy systems and genetic programming in water science and engineering have been grown extensively. These mentioned methods are able to model nonlinear process of river flows without any need to geometric properties. A huge number of studies have been reported in the field of using intelligent methods in water resource engineering. For example, Noorani and Salehi (23) presented a model for predicting runoff in Lighvan basin using adaptive neuro-fuzzy network and compared the performance of it with neural network and fuzzy inference methods in east Azerbaijan, Iran. Nabizadeh et al. (21) used fuzzy inference system and adaptive neuro-fuzzy inference system in order to predict river flow in Lighvan river. Khalili et al. (13) proposed a BL-ARCH method for prediction of flows in Shaharchay River in Urmia. Khu et al. (16) used genetic programming for runoff prediction in Orgeval catchment in France. Firat and Gungor (11) evaluated the fuzzy-neural model for predicting Mendes river flow in Turkey. The goal of present study is comparing the performance of genetic programming and M5 model trees for prediction of Shaharchay river flow in the basin of Lake Urmia and obtaining a comprehensive insight of their abilities.
Materials and Methods: Shaharchay river as a main source of providing drinking water of Urmia city and agricultural needs of surrounding lands and finally one of the main input sources of Lake Urmia is quite important in the region. For obtaining the predetermined goals of present study, average monthly flows of Shaharchay River in Band hydrometric station has been gathered from 1951 to 2011. Then, two third of mentioned data were used for calibration and the rest were used for validation of study models including genetic programming and M5 model trees. It should be noted that for prediction of Shaharchay river flows, previous data of mentioned river in 1, 2 and 3 months ago (Q, Q, Q) were used.
Genetic programming: was first proposed by Koza (17). It is a generalization of genetic algorithms. The fundamental difference between genetic programming and genetic algorithm is due to the nature of the individuals. In genetic algorithm, the individuals are linear strings of fixed length (chromosomes). In genetic programming, the individuals are nonlinear entities of different sizes and shapes (parse trees). Genetic programming applies genetic algorithms to a “population” of programs, typically encoded as tree-structures. Trial programs are evaluated against a “fitness function”. Then the best solutions are selected for modification and re-evaluation. This modification-evaluation cycle is repeated until a “correct” program is produced.
Model trees generalize the concepts of regression trees, which have constant values at their leaves. So, they are analogous to piece-wise linear functions. M5 model tree is a binary decision tree having linear regression function at the terminal nodes, which can predict continuous numerical attributes. Tree-based models are constructed by a divide-and-conquer method.
Results and Discussion: In order to investigate the probability of using different mathematical functions in genetic programming method, three combinations of the functions were used in the current study. The results showed that in the case of predicting river flows with Q, M5 model trees with root mean squared error of 4.7907 in comparison with genetic programming by the best mathematical functions and root mean squared error of 4.8233 had better performances. Obtained results indicated that adding more mathematical functions to the genetic programming and producing more complicated analytical formulations did not have positive effect in reducing prediction error. Unlike the previous observed trend, in case of predicting river flows with Q Q, the genetic programming method with root mean squared error of 3.3501 in comparison with M5 model trees with error of 3.8480 had more satisfied performance. Finally, in the case of predicting river flows with Q, Q,Q, the genetic programming method with root mean squared error of 3.3094 in comparison with M5 model trees with error of 3.5514 presented better predictions. As a result, it can be stated that genetic programming by the best mathematical functions and considering the input parameters of Q,Q,Q, by resulting less root mean squared error and high correlation coefficients had the best performances among others. Also, the results showed that adding more trigonometric functions did not improve the precisions of the predictions.
Conclusion: In this research, the intelligent models such as genetic programming and M5 model trees have been used for prediction of monthly flows of Shaharchay River located in East Azerbaijan, Iran. The obtained results showed that the genetic programming by the best mathematical functions and M5 model trees in case of considering the input parameters of Q,Q,Q, by less root mean squared error had the best performances in river flow predictions. As a conclusion, the genetic programming method by specific mathematical functions including four basic operations, logarithm, power and using input parameters of Q,Q,Q, has been proposed as the best and precise model for predicting Shaharchay River flows.