## 6 Results and Discussion  
The parametric model generates meshes at the instance of the optimisation algorithm over the PEMADE surface and simulates the initial bending stress by applying the process described in the previous sections, considering \(E=18\),108 MPa [7]. Figure 18 shows the six-step algorithm process for an individual with gene values of 0.072 origin position, 0.4 radians grid angle, 40 mm depth, and 70 mm width. For each individual, the parametric model sends the results (mesh and initial stresses) and its gene values to the optimisation algorithm for evaluation. In Step 1, the optimisation algorithm produces a solution space of 1091 individuals (100 individuals in 10 generations plus 91 non-dominated solutions) whose maximum initial bending stresses in the surface study area range from 19.96 MPa to 88.78 MPa depending on the cross-section size. Table 2 shows the main results for all the cross-sections generated according to the defined range of size genes. For each of the cross-sections, the minimum and maximum values (\(\sigma_{\text{m,min}}\) and \(\sigma_{\text{m,max}}\)) of the maximum initial bending stress in the study area, the absolute improvement (AI = \(\sigma_{\text{m,max}}\) - \(\sigma_{\text{m,min}}\)) and the relative improvement As expected, the minimum value (19.96 MPa) is obtained for the smallest cross-section (50 \(\times\) 25 mm\({}^{2}\)), where the algorithm focuses its search generating a total of 364 individuals. The absolute improvement achieved in this cross-section is 9.81 MPa and the relative improvement is 33%. Figure 19 shows the value of the maximum initial bending stress in the study area for the 364 solution individuals with 50 \(\times\) 25 mm\({}^{2}\) cross-section. The evolutionary optimisation process considerably increases the number of individuals with maximum stress values close to the minimum (around 20 MPa) which offers a wide space of possible solutions for the DM. In the rest of cross-sections, the optimisation algorithm generates a much smaller number of individuals--generally smaller the larger the cross-section--even a single individual in some of the larger cross-sections. This is due to the internal functioning of the optimisation algorithm. Those solutions far from the fittest at the time of processing a generation, are more likely prevented from passing their genes to the next generation; thus, this area of the solution vector escape is skipped by the algorithm, and no further search is performed in this area throughout the rest of the optimisation. Although the algorithm  
Figure 19: Evolution of initial bending stress for 50 \(\times\) 25 mm\({}^{2}\) cross-section in Step 1. Figure 18: Parametric model and simulation applied on the PEMADE surface: (**a**) Extended surface and geodesic master curves; (**b**) Surface subdivision based on curvature and adaptative subdivision of geodesic curves; (**c**) Grid points by Adaptative Compass Method; (**d**) Untrimmed mesh; (**e**) Trimmed mesh; (**f**) Initial stresses. does not perform an exhaustive search in these cross-sections, the results obtained give an idea of the maximum stress and improvement values that can be achieved. The results show absolute improvements between 5.28 MPa and 45.01 MPa and relative improvements between 14% and 61%, highlighting the great importance of the optimisation process. Furthermore, it should not be forgotten that in an optimisation process focused on a single cross-section, the minimum stress values presented in Table 2 should foreseeably be reduced, and consequently, the improvements should increase. The results obtained in Step 1 allow the DM to have an overview of the cross-sections that can be used for a given maximum value of initial bending stress. For example, for a value of 15 MPa, no cross-section is available, so it would be necessary to change the material or the shape of the surface.