Abstract
A direct cut-off method to solve combinatorial optimization problems on polyarrangements with additional constraints is proposed and justified. The method allows obtaining a feasible solution at each stage without constructing the linear hull of the set of polyarrangements.
Similar content being viewed by others
References
I. V. Sergienko and M. F. Kaspshitskaya, Models and Methods for the Computer Solution of Combinatorial Optimization Problems [in Russian], Naukova Dumka, Kyiv (1981).
Yu. G. Stoyan and O. O. Iemets, Theory and Methods of Euclidean Combinatorial Optimization [in Ukrainian], ISDO, Kyiv (1993) (http://informatics.org.ua/uploads/books/stoyan_emets_eko.pdf).
Yu. G. Stoyan, O. O. Iemets, and Ye. M. Yemets, Optimization on Polyarrangements: Theory and Methods [in Ukrainian], RVTs PUSKU, Poltava (2005).
Yu. G. Stoyan, O. O. Iemets, and Ye. M. Yemets, “Sets of polyarrangements in combinatorial optimization,” Dop. NANU, No. 8, 37–41 (1999).
O. O. Iemets and T. N. Barbolina, Combinatorial Optimization on Arrangements: A Monograph [in Russian], Naukova Dumka, Kyiv (2008).
O. O. Iemets and L. M. Kolechkina, Combinatorial Optimization Problems with Linear Fractional Objective Functions [in Ukrainian], Naukova Dumka, Kyiv (2005).
O. O. Iemets and O. V. Roskladka, Optimization Problems on Polycombinatorial Sets: Properties and Solution [in Ukrainian], RVTs PUSKU, Poltava (2006).
O. O. Emets’ and T. N. Barbolina, “On the solution of problems of nonlinear conditional optimization on arrangements by the cutoff method,” Ukr. Math. J., 55, No. 5, 729–738 (2003).
G. A. Donets and L. N. Kolechkina, “Method of ordering the values of a linear function on a set of permutations,” Cybern. Syst. Analysis, 45, No. 2, 204–213 (2009).
O. A. Emets and A. A. Roskladka, “On estimates of minima of criterion functions in optimization on combinations,” Ukr. Math. J., 51, No. 8, 1262–1265 (1999).
O. A. Emets and T. N. Barbolina, “Solving linear optimization problems on arrangements by the truncation method,” Cybern. Syst. Analysis, 39, No. 6, 889–896 (2003).
O. A. Yemets and T. N. Barbolina, “Solution of Euclidean combinatorial optimization problems by the method of construction of a lexicographic equivalence,” Cybern. Syst. Analysis, 40, No. 5, 726–734 (2004).
T. C. Hu, Integer Programming and Network Flows, Addison Wesley Longman Publ. Co. (1970).
I. L. Akulich, Mathematical Programming in Examples and Problems: A Handbook for High-School Students in Economics [in Russian], Vyssh. Shk., Moscow (1986).
Author information
Authors and Affiliations
Corresponding author
Additional information
Translated from Kibernetika i Sistemnyi Analiz, No. 6, pp. 116–124, November–December 2011.
Rights and permissions
About this article
Cite this article
Iemets, O.O., Yemets, Y.M. & Oleksiichuk, Y.F. Direct cut-off method for combinatorial optimization problems with additional constraints. Cybern Syst Anal 47, 932–940 (2011). https://doi.org/10.1007/s10559-011-9372-9
Received:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10559-011-9372-9