Abstract
The paper considers a combinatorial object (a fragmentary structure) and investigates the properties of this object. It is shown that a number of discrete optimization problems can be considered as optimization problems on a fragmentary structure. Optimization problem reduces to an unconditional combinatorial optimization problem on a set of permutations. Variants of algorithms to find approximate solutions for optimization problems of fragmentary structure are proposed.
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References
H. Whitney, “On the abstract properties of linear dependence,” Amer. J. of Mathematics, Vol. 57, No. 3, 509–533 (1935).
Â. Korte, L. Lovasz, and R. Schrader, Greedoids, Springer-Verlag, Berlin (1991).
V. P. Il’ev, “Problems on independence systems solvable by greedy algorithm,” Diskr. Matem., Vol. 21, No. 4, 85–94 (2009).
V. A. Perepelitsa, Multicriteria Models and Methods for Optimization Problems on Graphs, LAP Lambert Academic Publ. GmbH&Co. KG, Saarbrucken (2013).
G. P. Donets, Graseful Tree Numbering [in Ukrainian], Kyiv (2017).
J. F. Goncalves, “A hybrid genetic algorithm-heuristic for a two-dimensional orthogonal packing problem,” Europ. J. of Operational Research, Vol. 183(3), 1212–1229 (2007).
I. V. Kozin, “Evolutionary–fragmentary model of the pentomino packing problem,” Diskr. Analiz i Issled. Operatsii, Vol. 21, No. 6, 35– 50 (2014).
B. K. Lebedev and E. I. Voronin, “Genetic algorithm of the distribution of junctions over layers in multilayered global tracing VLSIC,” Izvestiya YuFU, Tekhnicheskie Nauki, Special Issue: Intellectual CAD Systems, No. 7 (132), 14–21 (2012).
I. V. Kozin and E. V. Krivtsun, “Modeling of one-layer and two-layer tracings,” Upravl. Sistemy i Mashiny, No. 2, 58–64 (2016).
N. K. Maksyshko and T. V. Zakhovalko, Models and Methods to Solve Applied Covering Problems on Graphs and Hypergraphs [in Ukrainian], Poligraph, Zaporozhye (2009).
P. Brucker, “On the complexity of clustering problems,” in: M. Beckmenn and H. P. Kunzi (eds.), Optimization and Operations Research, Lecture Notes in Economics and Mathematical Systems, Vol. 157, 45–54 (1978).
R. Ruiz and C. Maroto, “A comprehensive review and evaluation of permutation flowshop heuristics,” Europ. J. of Operational Research, Vol. 165, 479–494 (2005).
I. V. Sergienko and V. P. Shilo, Discrete Optimization Problems: Challenges, Solution Methods, Analysis [in Russian], Naukova Dumka, Kyiv (2003).
J. H. Holland, Adaptation in Natural and Artificial Systems, MIT Press, Boston, MA (1992).
V. M. Kureichik, Genetic Algorithms. State of the Art. Problems. Prospects. Izvestiya RAN, TiSU, No. 1, 144–160 (1999).
Ì. Dorigo, Optimization, Learning, and Natural Algorithms, PhD Thesis, Dipartimento di Elettronica, Politechnico Di Milano, Italy (1992).
S. D. Shtovba, “Ant algorithms: Theory and application,” Programmirovanie, No. 4, 1–16 (2005).
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Translated from Kibernetika i Sistemnyi Analiz, No. 6, November–December, 2017, pp. 125–131.
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Kozin, I.V., Maksyshko, N.K. & Perepelitsa, V.A. Fragmentary Structures in Discrete Optimization Problems. Cybern Syst Anal 53, 931–936 (2017). https://doi.org/10.1007/s10559-017-9995-6
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DOI: https://doi.org/10.1007/s10559-017-9995-6