## 3 Results of Micro-Scale Spherical and Cylindrical Surface Modeling
To carry it out, the genetic algorithm determines the origin and direction coordinates (\(k_{0}\), \(l_{0}\), \(k_{n}\), \(l_{n}\)) as described in Section 2.2. In this way, the genetic algorithm performs the first step to determine the initial population by employing the surface coordinates (\(x_{i,j}\), \(y_{i,j}\), \(z_{i,j}\)). Thus, a sampling of the model is carried out to obtain the best candidates. To do so, Equations (15)-(20) are computed by employing \(m=160\) and \(n=180\). Thus, the parent \(P_{1,1}\) is computed via surface whose sub-indices are (\(i=0,j=0\), \(\delta=45\), \(\Delta=80\), \(\kappa=160\)), the parent \(P_{2,1}\) is determined via sub-indices (\(i=45,j=0\), \(\delta=45\), \(\Delta=80\), \(\kappa=160\)), the parent \(P_{3,1}\) is computed via sub-indices (\(i=90\), \(j=0\), \(\delta=45\), \(\Delta=80\), \(\kappa=160\)), and \(P_{4,1}\) is determined via sub-indices (\(i=135\), \(j=0\), \(\delta=45\), \(\Delta=80\), \(\kappa=160\)). In this way, four coordinates (\(k_{0}\), \(l_{0}\), \(k_{n}\), \(l_{n}\)) are obtained and they are defined as the first parents (\(P_{1,t}\), \(P_{2,t}\), \(P_{3,t}\), \(P_{4,t}\)). Additionally, the ratio \(\bar{r}\) is defined as the average distance between the coordinates (\(k_{i}\), \(l_{i}\)) and the surface coordinates (\(x_{i,j}\), \(y_{i,j}\), \(z_{i,j}\)). From this procedure, the parent \(P_{1,1}\) is represented by the parameters (\(k_{0}=1188.2\)\(\upmu\)m, \(l_{0}=-4496.4\)\(\upmu\)m, \(k_{n}=1236.5\)\(\upmu\)m, \(l_{n}=-4328.2\)\(\upmu\)m), the parent \(P_{2,1}\) is defined by the parameters (\(k_{0}=1291.5\)\(\upmu\)m, \(l_{0}=-4122.6\)\(\upmu\)m, \(k_{n}=1315.4\)\(\upmu\)m, \(l_{n}=-4110.5\)\(\upmu\)m), the parent \(P_{3,1}\) is represented by the parameters (\(k_{0}=1346.2\)\(\upmu\)m, \(l_{0}=-4259.3\)\(\upmu\)m, \(k_{n}=1352.4\)\(\upmu\)m, \(l_{n}=-4235.1\)\(\upmu\)m), and the parent \(P_{4,1}\) is determined by the parameters (\(k_{0}=1401.2\)\(\upmu\)m, \(l_{0}=-4432.8\)\(\upmu\)m, \(k_{n}=1408.3\)\(\upmu\)m, \(l_{n}=-4425.7\)\(\upmu\)m). Furthermore, the ratio \(\bar{r}\) is computed via Equation (19) by employing the coordinates (\(k_{i}\), \(l_{i}\)) and the surface coordinates (\(x_{i,j}\), \(y_{i,j}\), \(z_{i,j}\)). Additionally, the minimum and maximum of the coordinate \(k_{0}\) are defined as \(y_{0,0}\) and \(y_{0,m}\), respectively. The minimum and maximum of the coordinate \(k_{n}\), are defined as \(y_{n,0}\) and \(y_{0,m}\), respectively. The minimum and maximum of the coordinate \(l_{0}\) are defined as (\(l_{0}+\bar{r}/2\)) and (\(l_{0}-\bar{r}\)), respectively, where, \(l_{0}\) is computed via Equation (16). The minimum and maximum of the coordinate \(l_{n}\) are defined as (\(l_{n}+\bar{r}/2\)) and (\(l_{n}-\bar{r}\)), respectively, where, \(l_{n}\) is computed via Equation (18). Then, the genetic algorithm performs the second step to compute the children by substituting \(q=0\) and \(q=1\) in Equations (7)-(10). The probability of crossover is determined via fitness. When the average fitness of the parents is improved, the crossover is carried out. Thus, the probability of crossover is in the interval from 0.0 to 0.48. This result is obtained by computing the same experiment several times. Then, the algorithm performs the third step to evaluate the fitness. In this procedure, Equation (21) is computed by means of the coordinates (\(k_{0}\), \(l_{0}\), \(k_{n}\), \(l_{n}\)) and the coordinates (\(k_{i}\), \(l_{i}\)), which are determined via Equation (13) and Equation (14). Then, the algorithm performs the fourth step to select the parents of the next generation. In this way, the parents \(P_{1,t+1}\) and \(P_{3,t+1}\) are selected from the pairs (\(P_{1,t}\), \(P_{2,t}\)) and (\(P_{3,t}\), \(P_{4,t}\)), respectively.