## 3 Optimization Results
The black dashed arrows indicate that control points are expected to be shifted downwards with respect to the original geometry. Fixed control points are shown with green color. The additional control points ex1 and ex2, on the upper side of the LE, are depicted with squares. The y-coordinates of the 14 variable control points (7 for the TE and 7 for the LE regions) vary within specific ranges, which constitute an input parameter of the design process. A proper selection of the above ranges ensures that acceptable LE and TE shapes are generated during the optimization loop and that no redundant computational cost is added to the computations. Proper selection consists in choosing the smallest possible intervals through which overlapping of the allowable y-coordinate range of neighboring control points is avoided. In this way the number of non-physical solutions, such as \"wavy\" geometries is reduced. Even though non-physical solutions may be finally excluded through the geometrical constraints, unnecessary design computations are added when large intervals are considered. An initial estimation of the intervals level is obtained using a reference deformation shape of the original airfoil geometry for given LE and TE deployment angles: The mean airfoil line is deformed through a polynomial relationship with respect to the distance from the LE (or TE) (see Appendix A), whilst the initial thickness at each x-position is retained. In the present work, the LE and TE deployment angles are chosen as \(12^{\circ}\) and \(14^{\circ}\) respectively. In the TE region, the shape of the reference deformation is used to define the mean value of each control point's interval. For CPs 8, 9, 13, and 14 (numbering of points is shown in Figure 2b), the difference between the y-coordinates of the baseline (undeformed) and the deformed airfoil is used as the interval width. For the TE point 11, the interval width is kept small and corresponds to a \(\pm 3\%\) deviation with respect to the TE deployment angle of \(14^{\circ}\). For points 10 and 12, the interval width is set 1.5 times larger than that of the TE point 11. The selected ranges for the TE control points are depicted in Figure 3b. In the LE region, higher overall deformations are required in order to substantially affect the overall loading of the airfoil. On the upper side the shape of the reference deformation is used to define the lower bound of each control point's interval, whilst on the lower side the reference deformation is used to define the upper bound of each control point's interval. For CPs 1, 2, 3, 6, and 7 (numbering of points is shown in Figure 2a), the difference between the y-coordinates of the baseline (undeformed) and the deformed airfoil is used as the interval width. For LE points 4 and 5, the interval width corresponds to a \(25\%\) deviation with respect to the LE deployment angle of \(12^{\circ}\). The selected ranges for the LE control points are depicted in Figure 3a. In the following, the three optimization algorithms described in Section 2 are tested for the case of combined LE and TE morphing. In Table 1, the \(\text{C}_{\text{L,max}}\) values obtained by the three algorithms are provided as a function of the number of generations of the optimization process. The optimization setup is the same for all three algorithms, meaning  
Figure 3: Range of variation of design variables at (**a**) the LE region and (**b**) the TE region (indicated by the blue bar). The initial NACA 64A010 is depicted in red and the airfoil geometry after the reference deformation is depicted in green. that the same number of initial airfoils are created and the same number of offspring are produced at each generation. In the present work, the default number of offspring is used, defined as 8 times the number of the design variables (8 \(\times\) 14 = 112). Therefore, the number of total fitness evaluations equals the product of the total generations multiplied by the number of offspring at each generation, plus the initial population.