Geodesic
Mathematical modeling and computer design for water distribution system
News of the Kabardin-Balkar scientific center of RAS, Tome 26 (2024) no. 6, pp. 98-114.

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. 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–Steiner 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–Steiner 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.
Keywords: branched pipeline water supply network, Kirchhoff-Steiner network, mathematical modeling and computer design, rank 2 optimization, objective function, pipeline costs, energy costs, pumping station
Mots-clés : transformation 
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M. A. Bagov. Mathematical modeling and computer design for water distribution system. News of the Kabardin-Balkar scientific center of RAS, Tome 26 (2024) no. 6, pp. 98-114. http://geodesic.mathdoc.fr/item/IZKAB_2024_26_6_a7/

[1] E. N. Gilbert, G. O. Pollack, “Steiner minimal trees”, Cybernetic Collection. New Series, 1971, no. 8, 19–49 (In Russian)

[2] E. N. Gordeev, O. G. Tarastsov, “Steiner Problem. Review”, Discrete Mathematics, 5:2 (1993), 3–28 (In Russian) | Zbl

[3] E. N. Gilbert, “Minimal Cost Communication Networks”, Bell System technological Journal, 1967, no. 9, 48–50

[4] W. M. Boyce, “An improved program for the full Steiner tree problem”, ACM Trans. J Math. Software, 3 (1977), 359–385 | DOI | MR | Zbl

[5] W. M. Boyce, J. B. Seery, “STEINER 72: An improved version of the minimal network problem”, Rech. Rep. No. 35. Comp. Sci. Res., CTR. Bell. Lab.,, Murray Hill, N. Y

[6] M. A. Bagov, “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, 2023, no. 6 (116), 55–64 (In Russian) | DOI

[7] N. N. Abramov, M. M. Pospelova, M. A. Somov et al., Calculation of water supply networks, Stroyizdat, Moscow, 1983, 278 pp. (In Russian)

[8] “H. Tui”, Concave programming under linear constraints, 159:1 (1964), 32–35 (In Russian) | Zbl

[9] V. A. Trubin, Properties and methods for solving problems of optimal network synthesis, Znanie, Kyiv, 1982, 23 pp. (In Russian)

[10] V. S. Mikhalevich, V. A. Trubin, N. Z. Shor, Optimization problems of production and transport planning, Nauka, Moscow, 1986, 260 pp. (In Russian)

[11] A. P. Merenkov, E. V. Sennova, S. V. Sumarokov et al., Mathematical modeling and optimization of heat, water, oil and gas supply systems, Nauka, Novosibirsk, 1992, 407 pp. (In Russian)

[12] V. P. Bulatov, L. I. Kassinskaya, “Some methods for minimizing a concave function on a convex polyhedron”, Optimization methods and their applications, 1987, 151–172, SEI SB RAS USSR, Irkutsk (In Russian) | MR

[13] M. B. Abazokov, M. A. Bagov, V. Ch. Kudaev, “Computer design of large pipeline networks of high optimality rank”, Adyghe International Scientific Journal, 22:4 (2022), 39–56 (In Russian) | DOI

[14] E. R. Stavrovsky, R. A. Trunov, “New problems and computer programs for optimizing the configuration and parameters of regional gas distribution networks during their design”, Collection of scientific papers «Pipeline systems of energy. Methods of mathematical modeling and optimization», Nauka, Novosibirsk, 2007, 258 pp. (In Russian)