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Information × Registration Number 0224U032114, 0122U200468 , R & D reports Title Technologies, means of mathematical modeling, optimization and system analysis of coverage problems in space monitoring systems popup.stage_title Head Yakovlev Serhii V., д.ф.-м.н. Registration Date 24-07-2024 Organization National Aerospace University "Kharkiv Aviation Institute" popup.description2  The problem of location of service points (space monitoring sensors) with maximum service area coverage (MCLP) in a continuous setting was considered. It was assumed that the given area of ​​coverage and the family of covering geometric objects have arbitrary shapes. The task was to find such an arrangement of geometric objects to cover as much of the area as possible. A mathematical model of MCLP was proposed in the form of an unconstrained nonlinear optimization problem. To formalize the coverage conditions, the concept of building the configuration space of geometric objects and a special class of functions are used to establish the dependence of the measure (area, volume) of the coverage configuration on the placement parameters of the covering objects. Since it is extremely difficult to obtain an analytical view of the specified functions, an algorithmic approach for their calculation is proposed. Python computational geometry packages were used to solve the problem, in particular, to calculate the area of ​​the partial coverage area. Many experiments were conducted, which made it possible to describe the statistical dependence of the time of calculation of the area of ​​the coverage area on the number of coverage objects. The BFGS method with first-order differences was used to obtain the local solution. An approach to the numerical evaluation of the gradient of the objective function is proposed, which significantly reduces the computational costs, which was confirmed experimentally. The proposed approach for solving the problem of maximal coverage of a rectangular area by a family of ellipses is shown. Product Description popup.authors Belei Maksym S. Kartashov Oleksii V. Korobchynskyi Kyryl P. Yakovlev Serhii V. Yarova Olha V. popup.nrat_date 2024-07-24 Close