## 1 Introduction  
The problem of the distribution of turbines in an Offshore wind farm (OWF), also known as Offshore wind farm layout optimization problem (OWFLOP), is the most important factor determining the wind speed deficit, and consequently, it strongly influences the generation of income from the sale of electrical energy. The five most important groups of optimization algorithms used for the OWFLOP are heuristic, pattern search, simulated annealing, evolutionary algorithms, and gradient search [1]. Table 1, taken from [2, 3], presents a summary of previous works related to the aforementioned issue of layout optimization, indicating the type of search engine. A more complete review was provided by [4], where most of the cases under study spin around random search algorithms, especially those using a Genetic algorithm (GA). For most  
of them, the objective function to optimize is the Annual Energy Production (AEP), or correspondingly, the average farm power (\(\mathbb{E}[P]\)). The review of the literature reveals that most of the research on the OWFLOP starts from a small and uniform rectangular space divided into columns and rows, forming a mesh of cells. Then, the algorithm decides whether to locate a turbine in the center of a cell or not. Obviously, a coarse lattice considerably limits the solution space for the turbine locations, while a sufficiently fine lattice increases the computational cost of the algorithm execution process given that the number of possible solutions is  
\[Nsol=\frac{Nc!}{nt!(Nc-nt)!} \tag{1}\]  
where \(Nc\) is the number of cells and \(nt\) is the number of turbines. Due to the high computational cost of these traditional techniques, most articles are reduced to 10 \(\times\) 10 or 20 \(\times\) 20 meshes. In [5], a collection of 46 articles with these characteristics is presented, many of them using algorithms based on animal behavior (genetic algorithm, particle swarm, Harris hawk, elephant herding, cuckoo, or algae), and mostly showing a contrived solution to the layout problem. All in all, the general trend is the use of meta-heuristic algorithms where the achievement of the optimum (in relation to the mathematical formulation of the problem) is not guaranteed, especially when the solution space is increased. Gradient descent (GD) methods are often disregarded because of their poorer performance in terms of accuracy since they are prone to fall in local maxima. Although they perform quite well due to their guaranteed convergence [6], some authors have pointed out that depending on the gradient calculation method, their computational time can be prohibitive for large OWFs [7]. The calculation of the objective function in any type of optimization algorithm requires many operations, and in the case of using its gradient, it requires even more. A finite-difference approximation of gradients (FDAG) with respect to the variables to be optimized (typically the x,y components of each turbine) entails tripling the number of operations necessary to estimate the AEP. Obtaining the gradient using analytical formulas, as in [8], takes an amount of time that would slow down any search method given the high number of trigonometric, quadratic and inverse operations required.