A Novel Algorithm for Optimizing the Covering of a Bounded Planar Domain with Simple Geometric Figures

In this paper, we address the problem of covering a given bounded domain in the plane using simple geometric figures. The proposed approach is based on a discretization of the domain, which leads to a corresponding discrete optimization problem. To solve this problem, we introduce a novel iterative algorithm that minimizes a given objective function by generating successive neighboring nodal points. As the covering elements, circular sectors with centers located outside the domain are considered. The objective is to determine the locations of the sector centers and their radii in such a way that the entire domain is completely covered, while the ratio of the total area of the covering sectors to the area of the domain is minimized. Finally, the algorithm is demonstrated on a representative example, and the resulting coverings are illustrated.

کلیدواژه ها:

Optimal coverage ، Discretization of the domain ، Discrete optimization