Optimization of coating of complex three-dimensional surfaces

The article discusses the problem of placing radio towers to cover an area of complex shape in three-dimensional space. Classical geometric methods (covering with spheres) do not take into account the uncertainties associated with relief, building, and signal attenuation. An approach is proposed in which the coverage area of each tower is described by a fuzzy membership function, and the choice of installation locations is carried out using a fuzzy inference system using expert rules. The simulation results are presented, demonstrating a reduction in the required number of towers and an increase in the robustness of the solution compared with classical greedy algorithms. The key advantage of the developed method is its high robustness to input data errors, which is especially important when working with real digital terrain models and cadastral information, which often contain noise and outdated information. Unlike deterministic algorithms, fuzzy metrics provide a smooth change in the degree of coverage with small fluctuations in environmental parameters, preventing the appearance of "blind spots". In addition, the fuzzy inference system allows for flexible integration of heterogeneous criteria such as building density and priority of territories, which makes the solution adaptive to various scenarios for the deployment of communication networks. The results of simulation modeling are presented, demonstrating a decrease in the required number of towers and an increase in the robustness of the solution compared with classical greedy algorithms.