MATHEMATICAL MODELING OF OPTIMAL HEIGHTS OF EXTERNAL GEODESIC SIGNS

  • O. Voronkov O.M. Beketov National University of Urban Economy in Kharkiv
  • O. Baistryk O.M. Beketov National University of Urban Economy in Kharkiv
  • A. Danylyuk O.M. Beketov National University of Urban Economy in Kharkiv
Keywords: geodetic sign, optimization, modeling.

Abstract

Due to the great importance of geodetic networks for the formation of a unified coordinate system on the territory of Ukraine, external geodetic signs have been established, which need to be restored and further developed. At the design stage, the calculation of the heights of geodetic signs is performed on topographic maps. The cost of erection of geodetic signs on average is 50 - 60% of the total cost of creating a geodetic network, so there is a need to pay close attention to the choice of places to build signs that provide their optimal height. The article presents a methodical approach  to  determining  the  heights  of  external  geodetic  signs,  based  on  the  mathematical apparatus used for modeling and solving optimization problems. The principle of construction of the optimization model of the problem during the design of external geodetic signs in the conditions when their direct visibility should be provided is considered. The article considers in detail the types and structures of external geodetic signs, identifies the features of their location and construction. The resulting optimization model includes objective function, which is a quadratic form, and line restriction. This model is a model of quadratic programming, that belongs to a class of nonlinear programming models, but have their particular case and the simplest of nonlinear. This is because property quadratic model, which consists in the fact that since the problem of quadratic programming set of feasible solutions is convex, then, if the objective function is concave, any local maximum is global, and if the objective function is convex, then any local minimum is also global. The necessity of solving the problem of optimizing the heights of geodetic signs is substantiated, which is still connected with the financial costs for their construction and reconstruction. It is concluded that the approach to determining the heights of external geodetic signs presented in the article, which uses a mathematical apparatus for solving optimization problems, is an effective and efficient approach, and allows to numerically justify the minimum required and sufficient height of external geodetic signs. Using the present approach to the determination of geodetic heights external signs to optimize the financial costs of their construction, which is essential.

Author Biographies

O. Voronkov, O.M. Beketov National University of Urban Economy in Kharkiv

PhD, Associate Professor, Associate Professor of the Department

O. Baistryk, O.M. Beketov National University of Urban Economy in Kharkiv

Student

A. Danylyuk, O.M. Beketov National University of Urban Economy in Kharkiv

Student

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Published
2021-03-26
How to Cite
VoronkovO., BaistrykO., & DanylyukA. (2021). MATHEMATICAL MODELING OF OPTIMAL HEIGHTS OF EXTERNAL GEODESIC SIGNS. Municipal Economy of Cities, 1(161), 109-115. Retrieved from https://khg.kname.edu.ua/index.php/khg/article/view/5722