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Finding the set of alternatives in discrete multicriterion problems

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Literature Cited

  1. V. S. Mikhalevich and V. L. Volkovich, Computational Methods of Analysis and Design of Complex Systems [in Russian], Nauka, Moscow (1982).

    Google Scholar 

  2. N. N. Moiseev, Mathematical Problems of System Analysis [in Russian], Nauka, Moscow (1981).

    Google Scholar 

  3. G. S. Pospelov, V. A. Irikov, and A. E. Kurilov, Procedures and Algorithms for the Construction of Complex Programs [in Russian], Nauka, Moscow (1985).

    Google Scholar 

  4. M. R. Garey and D. S. Johnson, Computers and Intractability, W. H. Freeman (1979).

  5. H. Papadimitriu and K. Staiglitz, Combinatorial Optimization. Algorithms and Complexity [Russian translation], Mir, Moscow (1985).

    Google Scholar 

  6. V. S. Mikhalevich, V. A. Trubin, and N. Z. Shor, Optimization Problems for Industrial and Transportation Planning: Models, Methods, Algorithms [in Russian], Nauka, Moscow (1986).

    Google Scholar 

  7. I. V. Sergienko, Mathematical Models and Methods of Solution of Discrete Optimization Problems [in Russian], Naukova Dumka, Kiev (1985).

    Google Scholar 

  8. V. A. Emelichev and V. A. Perepelitsa, “Complexity bounds of multicriterion transportation problems,” Dokl. AN BSSR,30, No. 7, 593–596 (1986).

    Google Scholar 

  9. Yu. A. Dubov, S. I. Travkin, and V. N. Yakimets, Multicriterion Models of Generating and Choosing Alternative Systems [in Russian], Nauka, Moscow (1986).

    Google Scholar 

  10. Yu. K. Mashunin, Methods and Models of Vector Optimization [in Russian], Nauka, Moscow (1986).

    Google Scholar 

  11. V. V. Podinovskii and V. M. Gavrilov, Optimization by Sequential Criteria [in Russian], Sovetskoe Radio, Moscow (1975).

    Google Scholar 

  12. A. V. Karzanov, “On maximum matchings of given weight in complete and complete bipartite graphs,” Kibernetika, No. 1, 7–11 (1987).

    Google Scholar 

  13. O. B. Lupanov, “On methods of obtaining complexity bounds and computation of individual functions,” Diskretnyi Analiz., No. 25, 3–18 (1974).

    Google Scholar 

  14. G. Hartmanis and J. E. Hopcroft, “A survey of the theory of computational complexity,” Kibernet. Sb., New Ser., No. 11, 131–176 (1974).

    Google Scholar 

  15. R. E. Tar'yan, “Complexity of combinatorial algorithms,” Kibern. Sb., New Ser., No. 17, 61–113 (1980).

    Google Scholar 

  16. A. Aho and J. Hopcroft, The Design and Analysis of Computer Algorithms, Addison-Wesley (1974).

  17. E. Mainika, Optimization Algorithms on Networks and Graphs [Russian translation], Mir, Moscow (1981).

    Google Scholar 

  18. V. A. Emelichev and V. A. Perepelitsa, “On algorithmic problems of vector optimization on graphs,” in: Software Systems for the Solution of Optimal Planning Problems [in Russian], Abstracts of 9th All-Union Symp. (Minsk, 23 Feb-3 March, 1986), TsEMI AN SSSR, Moscow (1986) p. 79–80.

    Google Scholar 

  19. A. M. Kochkarov and V. A. Perepelitsa, “The multicriterion problem of covering a graph by long and short chains,” Vestn. AN BSSR, Ser. Fiz-mat., Nauk, No. 5, 39–44 (1985).

    Google Scholar 

  20. B. V. Cherkasskii, “A new algorithm for generating spanning trees,” Kibernetika, No. 1, 85–89 (1987).

    Google Scholar 

  21. A. A. Kakhichko, “On the construction of perfect matchings of a graph,” in: Methods of Solution of Nonlinear Problems and Data Processing [in Russian], Dnepr. Gos. Univ., Dnepropetrovsk (1986), pp. 41–44.

    Google Scholar 

  22. N. Christofides, Graph Theory. An Algorithmic Approach [Russian translation], Mir, Moscow (1978).

    Google Scholar 

  23. V. V. Podinovskii and V. D. Nogin, Pareto-Optimal Solutions of Multicriterion Problems [in Russian], Nauka, Moscow (1982).

    Google Scholar 

  24. E. I. Vilkas and E. Z. Maiminas, Decisions: Theory, Information, Modeling [in Russian], Radio i Svyaz', Moscow (1981).

    Google Scholar 

  25. V. A. Perepelitsa, “On the algorithmic problem for multicriterion problems of control system design,” in: Problems of Theoretical Cybernetics [in Russian], Abstracts of papers at 7th All-Union Conf. (Irkutsk, 18–20 Sept. 1985), part 1, Irkutsk. Gos. Univ., Irkutsk (1985), pp. 164–165.

    Google Scholar 

  26. A. M. Kochkarov and V. A. Perepelitsa, “Probabilistic analysis of one multicriterion problem in graph theory,” in: Problems of Theoretical Cybernetics [in Russian],Abstracts of papers at 7th All-Union Conf. (Irkutsk, 18–20 Sept. 1985), part 2, Irkutsk. Gos Univ., Irkutsk (1985), pp. 65–66.

    Google Scholar 

  27. V. A. Perepelitsa, “On the efficiency of discrete optimization methods for system analysis,” in: Theory, Methodology, and Practice of Systems Studies [in Russian], Abstracts of papers of All-Union Conf. (Moscow, 29–31 Jan. 1985), VNIISI GKNT i AN SSSR, Moscow (1984), pp. 198–200.

    Google Scholar 

  28. I. V. Sergienko and V. A. Perepelitsa, “On some algorithmic problems of decomposition, aggregation, hierarchy, and coordination in discrete multicriterion optimization problems,” in: Decomposition and Coordination in Complex Systems [in Russian], Abstracts of papers of All-Union Sci. Conf. (Chelyabinsk, March 1986), part I, Chelyab. Politekh. Inst. Chelyabinsk (1986), pp. 38–39.

    Google Scholar 

  29. V. A. Emelichev and V. A. Perepelitsa, “On complexity bounds and efficiency of decomposition algorithms for some multicriterion problems on graphs,” in: Decomposition and Coordination in Complex Systems [in Russian], Abstracts of papers of All-Union Sci. Conf. (Chelyabinsk, March 1986), part I, Chelyab. Politekh. Inst., Chelyabink (1986), pp. 73–74.

    Google Scholar 

  30. V. A. Perepelitsa and V. I. Smola, “On the problem of construction of Pareto-optimal algorithms for multicriterion problems of graph covering,” Methods and Programs of Solution of Optimization Problems on Graphs and Networks [in Russian], Abstracts of papers at 3rd All-Union Conf. (Tashkent, 28–30 Aug. 1984), part 2, VTs SO AN SSSR, Novosibirsk (1984), pp. 99–101.

    Google Scholar 

  31. V. A. Perepelitsa and N. K. Maksishko, “On the multicriterion problem of covering a directed graph by circuits,” Methods and Programs of Solution of Optimization Problems on Graphs and Networks [in Russian], Abstracts of papers at 3rd All-Union Conf. (Tashkent, 28–30 Aug. 1984), part 2, VTs SO AN SSSR, Novosibirsk (1984), pp. 97–98.

    Google Scholar 

  32. V. A. Emelichev, V. A. Perepelitsa, and Kh. D. Shungerov, “An asymptotic approach to the multicriterion problem of covering a graph by stars,” Dokl. AN BSSR,31, No. 5, 5–9 (1985).

    Google Scholar 

  33. J. Edmonds and D. R. Fulkerson, “Bottleneck extrema,” J. Combin. Theory,8, 299–306 (1970).

    Google Scholar 

  34. P. S. Klyaus, “Minimum total cost in one choice problem,” in: Mathematical Methods and Their Application [in Russian], Proc. of 3rd Conf. of Young Scientists of the Inst. of Math. of the Academy of Sciences of Belorussian SSR and the Inst. of Phys. and Math. of the Academy of Sciences of the Lithuanian SSR, Minsk (1977).

  35. A. D. Korshunov, “Main properties of stochastic graphs with many vertices and edges,” Usp. Mat. Nauk,40, No. 1, 107–173 (1985).

    Google Scholar 

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Authors
  1. I. V. Sergienko
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  2. V. A. Perepelitsa
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Translated from Kibernetika, No. 5, pp. 85–93, September–October, 1987.

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Sergienko, I.V., Perepelitsa, V.A. Finding the set of alternatives in discrete multicriterion problems. Cybern Syst Anal 23, 673–683 (1987). https://doi.org/10.1007/BF01074927

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  • DOI: https://doi.org/10.1007/BF01074927

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