## 4 Applied Methods
### Group Method of Data Handling  
GMDH, which was introduced by [PERSON] in the 1960s [114], refers to a machine learning technique that works on the basis of the heuristic self-organizing principle [115]. This evolutionary computation technique is able to perform a series of operations like crossbreeding, rearing, seeding, and selection and rejection of seeds corresponding. These operations are related to the determination of the input variables, structure, and parameters of model, and the selection of model by the termination principle [116]. GMDH enjoys a high degree of flexibility and users are able to hybridize it by means of evolutionary and iterative algorithms, e.g., PSO [117], and GA [118]. GMDH helps to represent a model as set of neurons (nodes) wherein various pairs of existing neurons within each layer are linked to each other by quadratic polynomial, thereby generating new neurons in the succeeding layer. This type of representation is applicable to modelling processes for the purpose of mapping inputs to outputs and it can solve almost all non-linear and complex problems. Formally, the system identification problem is described as exploring a function \(\hat{\mathsf{f}}\) that can be approximately utilized instead of actual function \(\mathsf{f}\) in a way to estimate the output \(\hat{\mathsf{y}}\) for a certain input vector \(\mathsf{X}=(\mathsf{x}_{1},\,\mathsf{x}_{2},\,\mathsf{x}_{3},\,\ldots,\, \mathsf{x}_{n})\) in a way to be with the minimum distant to its actual output \(\mathsf{y}\). Aiming at finding an effective solution, GMDH constructs a general link between the output and input variables which can be in the shape of a mathematical description. In designing GMDH, all polynomials of the neurons existing within each of the network layers are identical and also the network has been designed on the basis of the same processes. The second-order polynomial is actually the fundamental structure of the GMDH network originally introduced by [PERSON] [114]. In general, various types of polynomial, including tri-quadratic, quadratic, bilinear, and third order have been applied to the process of designing the self-organized systems. Compared to the quadratic type of polynomial, with employing the third order and tri-quadratic polynomial, networks of a higher complexity will be constructed. Bilinear polynomial produced lower complicated structure. The quadratic polynomial involves six weighting coefficients that have been found effective in solving engineering problems [119]. Literature shows that selecting one among different types of polynomials depends upon two factors: (1) The minimum error of objective function, and (2) complexity of the polynomial type. In order to get more details about the GMDH model and its implementation, some other studies are suggested [21; 114; 115]. Figure 9: Scatter plot of the predicted vs. actual iron ore price developing artificial neural network (ANN) model. In order to design a GMDH model, its effective parameters i.e., the number of neurons, the number of GMDH layers, and selection pressure should be taken into consideration. Selection pressure factor is actually a criterion that allows the system to select the best fit in each step and moves them to the next layer. This process is repeated till receiving to the defined criteria which is normally system error. Hence, a parametric study has been conducted to see the effects of this parameter through the trial-and-error procedure. The results showed that selection pressure of 50% can be considered as the one among all values. Therefore, it has been used in the rest of modelling process. The design of another effective parameter (neuron number) on the GMDH model needs another parametric study.