Extraction of spatial relationships between georeferenced layers is one of the important objectives in spatial modeling in Geographic Information Systems (GIS). In last decades, a lot of techniques have been proposed for spatial modeling. Among them, Computational Intelligence techniques have been successfully employed in a wide range of spatial modeling.
Most Computational Intelligence techniques automatically solve problems with requiring the user to know or specify the form or structure of the solution in advance. However, in most cases determining the structure of the solution in advance is difficult and may lead to inaccurate results.
In order to overcome this challenge Genetic Programming (GP) which is a systematic, domain-independent method inspired by evolution is applied. In GP, user is not required to specify the structural complexity of the solution in advance but the algorithm tries to find an explicit relationship between the input and output. GP uses a tree-structure which captures the executional ordering of the functional components within a program: such that a program output appears at the root node; functions are internal tree nodes; a function's arguments are given by its child nodes; and terminal arguments are found at leaf nodes. However, GP can have a tendency to find solutions that are biased towards the training set (Overfitting). In this research we proposed a new method for limiting the effect of overfitting in GP. Also, for achieving more accurate results we use multigene GP in which individual consists of one or more trees.
At the final stage, Sensitivity Analysis (SA) which is the study of how uncertainty in the output of a model can be apportioned to different sources of uncertainty in the model input is used to determine what inputs, parameters or decision variables contribute more to the variance in the output of a model. There are three types of SA: 1-Screening SA, 2-Local SA and 3-Global SA. Screening SA methods are approximate but with low computational cost. When dealing with models containing large amounts of uncertain input factors, screening methods could be useful because they are able to isolate the set of factors with strongest effect on the output variability by very few model evaluations. A drawback of this feature is that the sensitivity measure is only qualitative which means the input factors are ranked in order of importance. Local SA looks at the local impact of each factor on the model output. The input variables are basically changed one at a time and the impact of this individual parameter perturbation on the model output is calculated using local sensitivity indices. A drawback of this feature is that the method does not work when the model is either nonlinear or several input factors are affected by different uncertainties. In global SA, both relative contributions of each individual parameter and the interactions between parameters to the model output variance are simultaneously evaluated by varying all input parameters simultaneously over the entire input parameters space. Several types of global SA, such as partial rank correlation coefficient, multiparametric sensitivity analysis, Fourier amplitude sensitivity analysis (FAST) and Sobol’s method have been used successfully in different models. Among different methods of sensitivity analysis, Sobol’s and EFAST as the methods of variance-based are employed.
The proposed method has several applications in spatial modeling issues. As a case study, the proposed procedures were applied to produce mineral potential map of Aliabad copper deposit. Results indicate that total field intensity criterion has the most effect and lithology has the minimal impact on the mineral potential mapping.