## 5 Results  
A series of experiments have been conducted to validate the following proposals:  
* The LAPD aggregation method results in a solution similar to that obtained with the LAVD aggregation method, but 200 times faster. This validates the hypothesis that this method can be used during the optimization process. * The linear nature of this method mainly improves the performance of gradient-based methods, achieving better performance of the proposed optimization algorithm compared to a genetic algorithm used as a reference. * The AEP of the layout obtained with the proposed algorithm will be compared with the AEP obtained from the actual layout of the Anholt park, using two types of wake aggregation, LAVD and LAPD. The farms Horns Rev 1 and Anholt serve as test beds for the experiments. The first testbed is the rhomboid delimited by the Horns Rev 1 wind farm, with dimensions (\(max_{x}=5.5\) km, \(max_{y}=3.9\) km) in which 80 turbines must be placed. The second test bed is the CA of the Anholt wind farm, which is an irregular polygon (\(max_{x}=10.8\) km, \(max_{y}=22\) km) in which 111 turbines must be placed. The wind conditions and the model used are shown in Tables 1 and 2. To compare the proposed algorithm with a traditional one, an EA has been programmed and launched whose fitness is \(\overline{\delta P}\). For this algorithm, chromosomes do not contain binary string-type solutions as in most genetic algorithms for OWFLOP; instead, the \(nt\) chromosomes of an individual contain the turbine position, that is, its x and y components, coded as real values. Its configuration parameters are offspring size obtained from the crossover, 25%; offspring size obtained from mutation, 25%; individuals disregarded when obtaining the offspring, 20%; population size, 200 individuals; maximum number of generations, 3000; maximum number of stagnant generations, 300. Figure 7 shows the evolution of the objective function (\(\overline{\delta P}\)) for both methods: LAPD (green) and LAVD (magenta). Both aggregation methods (LAPD and LAVD) show parallel evolutions in the EA, regardless of which method is used. The figure also shows that after a certain number of iterations, the EA does not improve its optimum solution, and it yields a higher power deficit than that obtained with the proposed **GD + GR** algorithm. The power deficit estimation for the actual layouts appears as dashed lines, calculated with both aggregation methods and using the same input data. Observing the LAVD curves in green, a traditional EA algorithm does not improve the actual layout. However, the proposed **GD + GR** one reduces the power deficit, especially in the case of HR1. Exact values will be presented in Table 3.  
A set of experiments (ten per situation) have been repeated to compare the performance of both algorithms, both for the test beds of Anholt and HR1. In order to speed up the searches, the LAPD method has been used to estimate \(\overline{P}\), and also for the potential maps and gradients. A third set of experiments has been launched using EA implementing the LAVD estimation as fitness. It will be named EA-LAVD and corresponds to a traditional procedure. The original single-thread (ST) code has been modified to allow for multiprocessing (MT) in an Intel(r) Core(tm) i7-10750H CPU @ 2.60 GHz (6 cores, 12 threads). Figures 8 and 9, together with Table 3 show the result of comparing the proposed method with an improved EA. The first of the figures represents the computation time, visualizing the superiority of the proposed method in terms of speed. An EA can also benefit from the speed improvement by using LAPD, showing significantly lower times than an EA using LAVD. As seen, the proposed GD + GR algorithm and the improved EA require a few seconds to complete the OWFLOP, in farms with 111 and 80 turbines. Figure 8: Computation time required to solve the OWFLOP with data from Anholt (**left**) and Horns Rev 1 (**right**). MT and ST refer, respectively, to parallel CPU processing and a single thread.