## 4 Discussion  
The capability of the micro-scale spherical and cylindrical surface modeling is established based on the model fitting accuracy [55,56]. Therefore, the contribution of the proposed technique is determined based on the model fitting to the surface. This statement includes the model fitting to the surface, and the algorithm efficiency. The model fitting to the surface and the algorithm efficiency are achieved in a good manner. The model fitting is determined via quality gap, which is computed via Equation (29). Thus, the proposed technique fits the spherical and cylindrical surface model to the surface data with a relative error smaller than 3.8%. The algorithm efficiency is determined via algorithm structure and solution quality, which is determined via running time. The algorithm structure provides an efficient procedure to optimize the surface model parameters. It is because the metaheuristic algorithm determines the initial population by the best candidates, which are sampled by solving the spherical and cylindrical surface models. This procedure leads to providing the initial population near the optimal parameters. Thus, the algorithm provides a low error since the first generation. This leads to reduced iterations to obtain the optimal parameters. Therefore, the running time is achieved in less than 140 iterations. Thus, the proposed micro-scale surface modeling improves the model fitting of the traditional optical microscope imaging systems. It is because the traditional optical microscope imaging systems perform micro-scale spherical and cylindrical surface modeling with a relative error over 5.0% [57,58], where, the spherical and cylindrical surface modeling is performed via polynomial regression by means of the least squared method [59,60]. In this way, a spherical model via least squared is generated for the plastic surface shown in Figure 6a and for the metallic shown in Figure 9a. However, the fitting accuracy is a relative error over 8%. This means that surface modeling via the metaheuristic algorithm improves the model fitting of the optical microscope imaging systems. Additionally, the surface data accuracy has an influence on the surface model fitting. In this matter, the optical microscope imaging systems perform the spherical and cylindrical surface modeling by means of surface, which is determined via gray-level [61,62]. However, the gray-level profile does not reproduce the surface profile under the test. Therefore, the gray-level does not help to improve the model fitting. Instead, the micro-scale contouring via micro laser line reproduces the surface profile with high accuracy. It is because the micro laser line reflection depicts the object surface profile. Additionally, the artificial intelligence algorithms have been employed by the contact methods to perform the spherical and cylindrical surface modeling [63,64]. These algorithms optimize the mathematical parameters of the spherical and cylindrical models by employing the traditional search structure [65,66]. In this matter, the proposed metaheuristic algorithm performs an analytic process to determine the search space, which provides initial values near to the optimal model parameters. This procedure is carried out via Equations (3)-(5) for the spherical surface modeling and Equations (15)-(18) for the cylindrical surface modeling. Thus, the metaheuristic algorithm determines the initial parameters by solving the surface model via surface geometry data. These initial parameters are the best candidates for the first solution of the surface model parameters. In this way, the search procedure begins on a path, which provides the optimal parameters. It is because the search procedure begins near to the optimal parameters. This leads to improving the metaheuristic algorithm efficiency by reducing iterations to find the best model parameters. It is elucidated by the low error in the first generation. Thus, the metaheuristic algorithm determines the optimal parameters from the surface data.