مدل‌سازی جریان روزانۀ رودخانه با استفاده از برنامه‌ریزی ژنتیک و شبکۀ عصبی (مطالعۀ موردی: حوضۀ آبخیز معرّف امامه)

Introduction
Rainfall-runoff relationship is one the most complicated issues in hydrological cycle and its accurate estimation is one the most important concerns in water resources engineering and management. In addition, Rainfall-runoff modeling process is complex and non-linear due to the large uncertainties in the field of water resources. None of the statistical and conceptual methods are able to provide a better and capable model for that. But today using nonlinear networks as intelligent system for forecasting such complicated events can be efficient and effective in many problems of ecology.
 
Materials and Methods
Gene expression programming, a branch of evolutionary algorithms, is able to optimize the model structure and its components. Therefore, for modeling river flow we also used artificial neural network and as well as Genetic programming as an explicit method of evolutionary algorithms in Amame watershed in the Northern Slope of the Alborz Range in Mazandaran province, Iran. This is for a period of fifty five years from 1970-1971 to 2011-2012 periods (42 years). For this purpose, the meteorological and hydrometric data were used in the form of 62 proposed models. Every ANN is interconnected network of many processing units called neuron. Neurons are the smallest unit in artificial neural network. These neurons are very similar to biological neuron and the cell of human brain. Whereas the speed of these neurons is more than biological neurons, their ability and capacity are less than them. Neuron in every layer is connected through weights to next layer of neurons. The associated parameters with each of these connections are called weights. These weights represent the information being used by the net to solve a problem. During the training network, these weights, constant amount of that assemble with them, and biases are changed consecutively until the target function reached the favorite amount. We used activation functions (sometimes called a transfer function or threshold function) for transfer of output from every layer to next layer. These activation functions may be logistic sigmoid, linear, threshold, Gaussian or hyperbolic tangent functions, depending on the type of network and employed training algorithm. On the other hand, the method which used for achieving weights and biases are learning rule for favorite and terminal amount. In fact, this rule is a complex mathematical algorithm. Every network needs two groups of data for creation: training series and testing series. About 80 percent out of the data is belonging to training and the rest is used for testing. Duration of learning time, learning of network is evaluated continually by target function. In all cases, a multi-layer perceptron (MLP) ANN was employed for rainfall–runoff modeling, with the weights determined by error back-propagation. Sigmoid activation functions were used at all nodes in the hidden and output layers. For ANN method, we used Muti Layer Perceptron with Back Propagation algorithm and from one to three hidden layers and from one to thirty neurons. In spite of statistical methods such as ANN, decision tree etc., GP is self-parameterizing that build models without any user tuning. A GP method is a member of the Evolutionary Algorithm family, which are based upon concept of natural section and genetic. In fact, the basic search strategy behind GP is a genetic algorithm (GA) that was created by Holland (1975), although GP was developed and introduced much later by Koza (1992). This method has many similarities with genetic algorithm such as GP works with a number of solution sets as a population rather than a single solution at any time. Therefore, the possibility of getting trapped in a local optimum is avoided. As you know it is one the most important problems in ANN. But GP is different from traditional genetic algorithm in that it typically operates on parse tree instead of bit string. A parse tree is built up from a terminal set (the input variables in the problem and randomly generated constants, i.e. empirical model coefficients) and a function set, basic operators used to form the GP model.
 
Results and Discussion
The results showed that a MLP method with two hidden layer has the best function. Furthermore, increase in the number of neurons in the hidden layer can somewhat reduce errors, but then increase in the number of neurons not only increases efficiency but also cause increased errors in the models. The results indicated Amameh is used as hidden layer neurons between 1 and 16, while the hidden layer neurons are used between 1 and 12. In addition, out of many models, genetic programming has fewer errors and when mathematical function and power used it has also less errors.
Conclusion
Given the evaluation criteria used in this study including MSE, RMSE and MAE, the proposed structure of input (model number 54) meteorological variables such as temperature, rain and rain delays up to two days, relative humidity and evapotranspiration and delays during the two days was obtained as the best the model. Therefore, the errors of this model for MSE, RMSE and MSE were 0.001, 0.031 0.009 and 0.001, 0.032, 0.009 in modeling and testing phase, respectively.