## 1 Introduction
The metaheuristic algorithms include algorithms such as genetic algorithms, particle swarm optimization, ant colony optimization, and simulated annealing [31]. Metaheuristic algorithms such as particle swarm optimization, ant colony optimization, and simulated annealing have been implemented to construct mathematical models to represent the free-form surface [32; 33]. For instance, the particle swarm makes the optimization via the position and velocity of particles [34]. Where, the objective function is provided by an inertia equation and the population is determined by a particle velocity equation. The ant colony optimization chooses paths marked by a strong pheromone concentration to determine the surface model parameters [35]. The simulated annealing makes a random search, which decreases and increases the objective function to determine the surface model [36], where the tentative solution is generated by a small perturbation. Moreover, the metaheuristic algorithms construct models via multi-objective optimization in domains such as online learning, scheduling, transportation, medicine, data classification, and so on. For instance, the online learning optimizes many objective functions to determine the mathematical models [37]. In addition, the multi-objective optimization via evolutionary algorithms is implemented to determine the parameters of mathematical models [38]. On the other hand, the scheduling domain employs structures of different metaheuristic algorithms to determine the parameters of mathematical models [39]. Additionally, the transportation domain employs several metaheuristic algorithms to determine routing of mathematical models [40]. Additionally, the evacuation domain employs several metaheuristic algorithms to optimize the multi-objective functions to determine routing of mathematical models [41]. Furthermore, the metaheuristic algorithms employ data classification to determine diagnoses in medicine [42]. The above-mentioned algorithms optimize parameters for mathematical models, which are not defined by a specific equation. For instance, the particle swarm, ant colony, and simulated annealing construct free-form surface models, which are not defined by a specific equation. Furthermore, the metaheuristic algorithms based on multi-objective optimization determine mathematical models, which are not defined by a specific equation. This leads to implementing complex algorithms due to the missing of a reference equation to optimize the model parameters. Moreover, these algorithms begin the optimization with a random solution, which leads to computing a huge iterations number. Furthermore, the objective function is deduced by an equation, which includes additional parameters to the surface model. Furthermore, the spherical and cylindrical surfaces can be represented by having a specific equation. In this way, a genetic algorithm provides a suitable structure to optimize the spherical and cylindrical surface models. For instance, the genetic algorithm is allowed to define an objective function by means of the equations that represent the spherical and cylindrical surface. Therefore, additional parameters are not required. In addition, it is possible to begin the optimization by employing the best candidates, which provides a solution near the optimal solution. The best candidates are deduced from the search space via spherical and cylindrical equations and known surface data. Moreover, exploration and exploitation are carried out to find the optimal solution inside or outside of the best candidates. Thus, all research space can be analyzed. Based on these statements, the metaheuristic genetic algorithm is chosen to construct the spherical and cylindrical surface models. The genetic algorithm viability to construct micro-scale spherical and cylindrical surface models is elucidated via quality gap, solution quality, suitable structure, and experimental results.