Surrogate modeling is a family of engineering techniques that attracts great interest today and can be applied in many challenging fields. A big advantage of it is that surrogate models (models based on these techniques) offer reliable results by being computationally cheaper than other candidate models. The savings in computational time is usually paramount for problems that involve a lot of variables and parameters and many iterative processes.

In the wind energy industry in particular, the design of the best layout of the wind farm is a problem that has been presented in the literature as an optimization problem; that is, a problem to optimize the wind farm layout in respect to some objective the modeler deems appropriate. More often than not, maximizing the expected power of the layout is mainly considered as this objective. The layout's expected power is -- among other things -- heavily dependent on the layout and the wake interactions between the turbines. The iterative search among many layouts to find the best one can be done with the help of a well-known optimization tool, the binary genetic algorithm. However, this tool cannot work alone, it solely facilitates the search over an adequate number of candidate solutions. To make it work, the modeler should provide it with some model that assesses how good in terms of the objective that has been set.

In this thesis therefore, the theory, the development and the use of two models of interest are investigated: Gaussian Process Regression (a surrogate model) and the Monte Carlo Method (a method based on random sampling). Great care was given to compile the theoretical basis of these models in order to be a good reference point for the non-experienced reader. The nature of these two models differs quite a bit, but they both can be used by the modeler to yield interesting results. These results will be compared to each other and against a third model's results, a specific wake model. This third model is the Original Model which the Gaussian Process Regression model and the Monte Carlo Method model utilize and compare against. The reliability of the results and computational speed will be the measure of success and ranking for these three models.

Finally, the comparison of the three models continues in how potent they are to propose an optimized layout for a wind farm. Each of the three models is coupled with the binary genetic algorithm that is developed specifically to connect with them. Afterwards, the proposed best layouts are discussed. The results show that the Gaussian Process Regression model performs reliably and very fast in comparison to the Original model. On the other hand, the Monte Carlo model, although also fast when it is used to find an optimized layout, could not be verified that it performs reliably and therefore, its results cannot be trusted without going into further investigation. After the comparison, further discussion follows with some recommendations for future research.