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GEOMETRIC MODELS OF LOCAL OPTIMIZATION OF TRACING TRANSPORT AND LOGISTICS NETWORKS OF HIGHWAYS

Authors

Name Affiliation
Kaiyrbek Kuspekov

K.I.Satpayev Kazakh National Research Technical University

Issue:

Volume 1, No. 1, 2026

Pages:

42-51

Views:

17

Keywords:

geometric model, configuration, optimization, Steiner polar network, distances, polar coordinate system, polar metric, curved quadrilateral

Abstract

Tracing and building an optimal network configuration is one of the main tasks of logistics. The article is devoted to improving the methods of discrete local optimization of tracing transport and logistics networks of highways. The main goal is to determine the shortest distance of cargo delivery from the place of loading to the place of unloading that meets the specified requirements in advance. To solve the problem, various variants of geometric network models with a polar metric are systematized and generalized. Based on the method of least elongation, an algorithm for tracing  a  local  network for four points is formulated and developed. Network tracing belongs to the extreme and class of NP-hard discrete optimization problems. The required network configuration is achieved by adding a Steiner point. The algorithm allows you to take into account the obstacle avoidance and build the shortest route of the road. The constructed network configuration consists of radial segments and arcs of circles. The total length of the arcs and circles should be minimal.

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References

  1. Geraerts R., Overmars M.H. A comparative study of probabilistic roadmap planners // Proceedings of the Workshop on the Algorithmic Foundations of Robotics (WAFR) (15–17 December 2002). Nice, France, 2002, pp. 43–57.
  2. Kavraki L.E., Latombe J.-C. Randomized preprocessing of configuration space for fast path planning // Proceedings of the IEEE International Conference on Robotics and Automation (8–13 May 1994). San Diego, CA, USA: IEEE Press, 1994, pp. 2138–2145.
  3. Халтурин Р.А. Состояние и опыт строительства дорожной сети в России и за рубежом. Экономические науки, 2011, № 74, С. 223–226. // Khalturin R.A. Sostoyanie i opyt stroitel’stva dorozhnoi seti v Rossii i za rubezhom [A condition and the experience of construction of road networks in Russia and abroad]. Ekonomicheskie nauki, 2011, No. 74, pp. 223–226. (In Russ.)
  4. Kuspekov K.A., Rotkov S.I. (2016). Geometrical methods of tracing of transport-logistic networks. Proceedings of the 26th International Conference on Computer Graphics and Vision (GraphiCon), pp. 531–534.
  5. Kuspekov K.A. Optimization of geometric models of transport network tracing used in city planning. International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences, 2023, Vol. 48(5/W2-2023), pp. 63–69.
  6. Неруш М.Ю., Неруш А.Ю. Логистика: учебник и практикум для СПО. 5-е изд., перераб. и доп. М.: Юрайт, 2019. 559 с. (Серия: Профессиональное образование). // Nerush M.Iu., Nerush A.Iu. Logistika: uchebnik i praktikum dlia SPO [Logistics: textbook and workshop for secondary vocational education]. 5th ed., revised and expanded. Moscow: Yurait Publishing House, 2019. 559 p. (In Russ.)
  7. Topcon. Official website. URL: http://www.topconpositioning.eu/0/30/products.html (accessed: 07.07.2013).
  8. Герштейн А.М., Терехов А.Н. Маршрутизация транспорта при наличии опасных участков на дороге (на примере города Спрингфилда, Массачусетс). Компьютерные инструменты в образовании, 2022, № 2, С. 5–18. // Gerstein A.M., Terekhov A.N. Marshrutizatsiya transporta pri nalichii opasnykh uchastkov na doroge (na primere goroda Springfield, Massachusetts) [Transport routing in the presence of hazardous road sections]. Kompyuternye instrumenty v obrazovanii, 2022, No. 2, pp. 5–18. (In Russ.)
  9. Есмуханов Ж.М., Куспеков К.А. Особенности плоскости с полярной метрикой. Вестник КазНТУ, 2005, № 6(50), С. 226–230. // Esmukhanov Zh.M., Kuspekov K.A. Osobennosti ploskosti s polyarnoi metrikoi [Features of a plane with polar metric]. Vestnik KazNTU, 2005, No. 6(50), pp. 226–230. (In Russ.)
  10. Жигалов К.Ю., Клочкова Е.Н. Решение задачи построения оптимального маршрута движения транспорта по пересеченной местности с использованием ГИС. Московский экономический журнал, 2020, № 1. // Zhigalov K.Yu., Klochkova E.N. Reshenie zadachi postroeniya optimal’nogo marshruta dvizheniya transporta po peresechennoi mestnosti s ispol’zovaniem GIS [Solving the problem of optimal vehicle routing over rough terrain using GIS]. Moskovskii ekonomicheskii zhurnal, 2020, No. 1. (In Russ.)
  11. Куспеков К.А., Волков В.Я. Определение оптимальной топологии кратчайшего дерева для четырех точек плоскости с полярной метрикой. Вестник СибАДИ, 2011, Вып. 1(19), С. 66–68. // Kuspekov K.A., Volkov V.Ya. Opredelenie optimal’noi topologii kratchaishego dereva dlya chetyrekh tochek ploskosti s polyarnoi metrikoi [Determination of the optimal topology of the shortest tree for four points of a plane with polar metric]. Vestnik SibADI, 2011, Issue 1(19), pp. 66–68. (In Russ.)
  12. Немчинов Д.М., Кочетков А.В. Анализ планировочных схем сетей автомобильных дорог. Интернет-журнал «НАУКОВЕДЕНИЕ», 2016, Т. 8, № 5 (сентябрь–октябрь). URL: http://naukovedenie.ru // Nemchinov D.M., Kochetkov A.V. Analiz planirovochnykh skhem setei avtomobil’nykh dorog [Analysis of planning schemes of road networks]. Internet journal “NAUKOVEDENIE”, 2016, Vol. 8, No. 5. (In Russ.)
  13. Пегин П.А., Немчинов Д.М., Ильин А.А. Анализ эффективности развития сети автомобильных дорог. Бюллетень результатов научных исследований, 2023, Вып. 2, С. 71–80. https://doi.org/10.20295/2223-9987-2023-2-71-80 // Pegin P.A., Nemchinov D.M., Il’in A.A. Analiz effektivnosti razvitiya seti avtomobil’nykh dorog [Analysis of efficiency of road network development]. Byulleten’ rezul’tatov nauchnykh issledovanii, 2023, Issue 2, pp. 71–80. (In Russ.)
  14. Плехова А.А. Метод оптимального решения базовой задачи о кратчайшем скруглении. Информатика: сборник научных трудов. Киев: Наукова думка, 1998, Вып. 5, С. 124–126. // Plekhova A.A. Metod optimal’nogo resheniya bazovoi zadachi o kratchaishem skruglenii [Method of optimal solution of the basic problem of shortest rounding]. Informatika: sbornik nauchnykh trudov. Kyiv: Naukova Dumka, 1998, Issue 5, pp. 124–126. (In Russ.)
  15. Щербаков В.С., Корытов М.С. Оптимизация трассы автомобильной дороги на рельефе с препятствиями методом вероятностной дорожной карты. Вестник СибАДИ, 2012, № 6(28), С. 88–92. // Shcherbakov V.S., Korytov M.S. Optimizatsiya trassy avtomobil’noi dorogi na rel’efe s prepyatstviyami metodom veroyatnostnoi dorozhnoi karty [Optimization of road alignment on terrain with obstacles using the probabilistic roadmap method]. Vestnik SibADI, 2012, No. 6(28), pp. 88–92. (In Russ.)

Volume 1, No. 1, 2026

Kuspekov, К. (2026). GEOMETRIC MODELS OF LOCAL OPTIMIZATION OF TRACING TRANSPORT AND LOGISTICS NETWORKS OF HIGHWAYS. EKTU Journal of Engineering Sciences, 1(1), 42-51. https://doi.org/10.51885/3134-8009_JES_2026_1_4