{"id":2265,"date":"2025-05-13T19:21:19","date_gmt":"2025-05-13T18:21:19","guid":{"rendered":"http:\/\/newskbncran.ru\/?page_id=2265"},"modified":"2026-04-10T14:15:43","modified_gmt":"2026-04-10T13:15:43","slug":"26-6-8-en","status":"publish","type":"page","link":"https:\/\/izvestiyakbncran.ru\/index.php\/en\/26-6-8-en\/","title":{"rendered":"26.6.8 en"},"content":{"rendered":"\n

Mathematical modeling and computer design for water distribution system based on Kirchhoff-Steiner large branched network<\/strong><\/h1>\n\n\n\n

M.A. Bagov<\/strong><\/strong><\/strong><\/p>\n\n\n\n

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Upload the full text<\/strong><\/p>\n\n\n\n

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Abstract.<\/em><\/strong> <\/em>A design of optimal hydraulic pipeline for regional and interregional water supply systems is highly relevant due to water scarcity in part of Russian regions. The article presents a method for transforming a network structure into a 2-optimal Kirchhoff\u2013Steiner network, i.e. such a network that cannot be improved by any change in the structure and coordinates of Steiner points of any subnet consisting of 2-reachable points from any vertex in the graph. Algorithms and a software system for computer-aided design of a Kirchhoff\u2013Steiner flow network for regional and interregional water supply and large irrigation systems have been developed. The computational experiments verified a high efficiency of the computer-aided approach proposed.<\/p>\n\n\n\n

Keywords:<\/em><\/strong> <\/strong>branched pipeline water supply network, transformation, Kirchhoff-Steiner network, mathematical modeling and computer design, rank 2 optimization, objective function, pipeline costs, energy costs, pumping station<\/p>\n\n\n\n

For citation<\/strong>. <\/strong>Bagov M.A. Mathematical modeling and computer design for water distribution system based on Kirchhoff-Steiner large branched network.  News of the Kabardino-Balkarian Scientific Center of RAS.<\/em> 2024. Vol. 26. No. 6. Pp. 98\u2013114. DOI: 10.35330\/1991-6639-2024-26-6-98-114<\/p>\n\n\n\n

R<\/strong>eferences<\/summary>\n
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  1. Gilbert E.N., Pollack G.O. Steiner minimal trees. Kiberneticheskiy sbornik. Novaya seriya. [Cybernetic Collection. New Series]. No. 8. 1971. Pp. 19\u201349. (In Russian)<\/li>\n\n\n\n
  2. Gordeev E.N., Tarastsov O.G. Steiner Problem. Review. Diskretnaya matematika [Discrete Mathematics]. Vol. 5. No. 2. 1993. Pp. 3\u201328. (In Russian)<\/li>\n\n\n\n
  3. Gilbert E.N. Minimal cost communication networks. Bell System technological Journal. No. 9. Pp. 48\u201350.<\/li>\n\n\n\n
  4. Boyce W.M. An improved program for the full Steiner tree problem. ACM Trans. J Math. Software. 1977. Vol. 3. Pp. 359\u2013385.<\/li>\n\n\n\n
  5. Boyce W.M., Seery J.B. STEINER 72: An improved version of the minimal network problem. Rech. Rep. Vol. 35. Comp. Sci. Res. CTR. Bell. Lab., Murray Hill, N.-Y., (undated) Bagov M.A. Method of computer design of branched hydraulic pipeline networks with an optimal number of Steiner points. News of the Kabardino-Balkarian Scientific Center of RAS. No. 6 (116). Pp. 55\u201364. DOI: 10.35330\/1991-6639-2023-6-116-55-64. (In Russian)<\/li>\n\n\n\n
  6. Abramov N.N., Pospelova M.M., Somov M.A. et al. Raschet vodoprovodnykh setey [Calculation of water supply networks]. Moscow: Stroyizdat, 1983. 278 p. (In Russian)<\/li>\n\n\n\n
  7. Tui H. Concave programming under linear constraints. Doklady AN SSSR [Reports of the USSR Academy of Sciences]. 1964. Vol. 159. No. 1. Pp. 32\u201335. (In Russian)<\/li>\n\n\n\n
  8. Trubin V.A. Svoystva i metody resheniya zadach optimal’nogo sinteza setey [Properties and methods for solving problems of optimal network synthesis]. Kyiv: Znanie, 1982. 23 p. (In Russian)<\/li>\n\n\n\n
  9. Mikhalevich V.S., Trubin V.A., Shor N.Z. Optimizatsionnyye zadachi proizvodstvenno- transportnogo planirovaniya [Optimization problems of production and transport planning]. Moscow: Nauka, 1986. 260 p. (In Russian)<\/li>\n\n\n\n
  10. Merenkov A.P., Sennova E.V., Sumarokov S.V. et al. Matematicheskoye modelirovaniye i optimizatsiya sistem teplo-, vodo-, nefte- i gazosnobzheniya [Mathematical modeling and optimization of heat, water, oil and gas supply systems]. Novosibirsk: Nauka, 1992. 407 p. (In Russian)<\/li>\n\n\n\n
  11. Bulatov V.P., Kassinskaya L.I. Some methods for minimizing a concave function on a convex polyhedron. Metody optimizatsii i ikh prilozheniya [Optimization methods and their applications]. Irkutsk: SEI SB RAS USSR. 1987. Pp. 151\u2013172. (In Russian)<\/li>\n\n\n\n
  12. Abazokov M.B., Bagov M.A., Kudayev V.Ch. Computer design of large pipeline networks of high optimality rank. Adyghe International Scientific Journal. 2022. Vol. 22. No. 4. Pp. 39\u201356. DOI: 10.47928\/1726-9946-2022-22-4-39-56. (In Russian)<\/li>\n\n\n\n
  13. Stavrovsky E.R., Trunov R.A. New problems and computer programs for optimizing the configuration and parameters of regional gas distribution networks during their design. Sbornik nauchnykh trudov \u201cTruboprovodnyye sistemy energetiki. Metody matematicheskogo modelirovaniya i optimizatsii\u201d. [Collection of scientific papers \u201cPipeline systems of energy. Methods of mathematical modeling and optimization\u201d]. Novosibirsk: Nauka, 2007. 258 p. (In Russian)<\/li>\n<\/ol>\n<\/details>\n\n\n\n
    Information about the author<\/strong><\/summary>\n
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    Marat A. Bagov<\/strong>, Researcher, Department of Computational Methods, Institute of Applied
    Mathematics and Automation of the Kabardino-Balkarian Scientific Center of the Russian Academy of
    Sciences;
    360000, Russia, Nalchik, 89 A Shortanov street;
    maratniipma@mail.ru, ORCID: https:\/\/orcid.org\/0000-0003-0899-898X, SPIN-code: 6145-5129<\/p>\n\n\n\n

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    <\/p>\n","protected":false},"excerpt":{"rendered":"

    Mathematical modeling and computer design for water distribution system based on Kirchhoff-Steiner large branched network M.A. Bagov Upload the full text Abstract. A design of optimal hydraulic pipeline for regional and interregional water supply systems is highly relevant due to water scarcity in part of Russian regions. The article presents a method for transforming a […]<\/p>\n","protected":false},"author":1,"featured_media":0,"parent":0,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"wp-custom-template-home","meta":{"footnotes":""},"class_list":["post-2265","page","type-page","status-publish","hentry"],"yoast_head":"\n26.6.8 en - \u0418\u0417\u0412\u0415\u0421\u0422\u0418\u042f \u041a\u0410\u0411\u0410\u0420\u0414\u0418\u041d\u041e-\u0411\u0410\u041b\u041a\u0410\u0420\u0421\u041a\u041e\u0413\u041e \u041d\u0410\u0423\u0427\u041d\u041e\u0413\u041e \u0426\u0415\u041d\u0422\u0420\u0410 \u0420\u0410\u041d\u00bb<\/title>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/izvestiyakbncran.ru\/index.php\/en\/26-6-8-en\/\" \/>\n<meta property=\"og:locale\" content=\"ru_RU\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"26.6.8 en - \u0418\u0417\u0412\u0415\u0421\u0422\u0418\u042f \u041a\u0410\u0411\u0410\u0420\u0414\u0418\u041d\u041e-\u0411\u0410\u041b\u041a\u0410\u0420\u0421\u041a\u041e\u0413\u041e \u041d\u0410\u0423\u0427\u041d\u041e\u0413\u041e \u0426\u0415\u041d\u0422\u0420\u0410 \u0420\u0410\u041d\u00bb\" \/>\n<meta property=\"og:description\" content=\"Mathematical modeling and computer design for water distribution system based on Kirchhoff-Steiner large branched network M.A. Bagov Upload the full text Abstract. 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