Log in

Solving optimization problems with linear-fractional objective functions and additional constraints on arrangements

  • Published:
Cybernetics and Systems Analysis Aims and scope

Abstract

The paper proposes an exact method to solve an optimization problem on arrangements with a linear-fractional objective function and additional linear constraints. The efficiency of the solution algorithm is analyzed by means of numerical experiments.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Subscribe and save

Springer+ Basic
EUR 32.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or Ebook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

Price includes VAT (Spain)

Instant access to the full article PDF.

Similar content being viewed by others

References

  1. Yu. G. Stoyan and O. O. Yemets’, Theory and Methods of Euclidean Combinatory Optimization [in Ukrainain], ISDO, Kyiv (1993).

    Google Scholar 

  2. O. O. Yemets’ and L. M. Kolechkina, “Optimization problem on permutations with a fractional-linear objective function: properties of the set of feasible solutions,” Ukr. Mat. Zh., 52, No. 12, 1630–1640 (2000).

    Google Scholar 

  3. O. O. Yemets’, O. V. Roskladka, and S. I. Nedobachii, “A nonreducible system of constraints for a general polyhedron of arrangements,” Ukr. Mat. Zh., 55, No. 1, 3–11 (2003).

    Google Scholar 

  4. O. A. Yemets and O. A. Chernenko, “A nonreducible system of constraints of a combinatorial polyhedron in a linear-fractional optimization problem on arrangements,” Cybern. Syst. Analysis, Vol. 41, No. 2, 246–254 (2005).

    Article  Google Scholar 

  5. O. O. Chernenko, “Analysis of the set of feasible solutions for an optimization problem for a fractional-linear function on a Euclidean combinatorial set of arrangements,” in: Proc. 10th Acad. M. Kravchuk Intern. Sci. Conf. (May 13–15, 2004, Kyiv) [in Ukrainian], Kyiv (2004), p. 548.

  6. 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, Vol. 40, No. 5, 726–734 (2004).

    Article  Google Scholar 

  7. O. A. Yemets and L. N. Kolechkina, “Solution of optimization problem with fractional-linear objective functions and additional linear constraints on permutations,” Cybern. Syst. Analysis, Vol. 40, No. 3, 329–339 (2004).

    Article  Google Scholar 

  8. O. A. Emets and T. N. Barbolina, “Solving linear optimization problems on arrangements by the truncation method,” Cybern. Syst. Analysis, Vol. 39, No. 6, 726–734 (2003).

    MathSciNet  Google Scholar 

  9. A. A. Korbut and Yu. Yu. Finkel’shtein, Discrete Programming [in Russian], Nauka, Moscow (1969).

    Google Scholar 

  10. Yu. Yu. Chervak, “Method of lexicographic search of solutions for discrete problems of convex programming,” Ukr. Mat. Zh., 26, No. 2, 269–272 (1974).

    Google Scholar 

  11. A. A. Kolokolov and T. V. Levanova, “Algorithms of decomposition and enumeration of L-classes for the solution of some problems of arrangement,” Vestn. Omsk. Univ., Issue 1, 21–23 (1996).

    Google Scholar 

  12. G. V. Reklaitis, A. Ravindran, and K. M. Ragsdell, Optimization: Methods and Applications, John Wiley and Sons, NY (1983).

    Google Scholar 

  13. B. N. Pshenichnyi, E. I. Nenakhov, and V. N. Kuz’menko, “Mixed method for solving the general convex programming problem,” Cybern. Syst. Analysis, Vol. 34, No. 4, 577–587 (1998).

    MathSciNet  Google Scholar 

  14. http://www2.msstate.edu/∼dgh2/cvxpt.htm.

Download references

Author information

Authors and Affiliations

Authors

Additional information

__________

Translated from Kibernetika i Sistemnyi Analiz, No. 5, pp. 79–85, September–October 2006.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Yemets, O.A., Barbolina, T.N. & Chernenko, O.A. Solving optimization problems with linear-fractional objective functions and additional constraints on arrangements. Cybern Syst Anal 42, 680–685 (2006). https://doi.org/10.1007/s10559-006-0106-3

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10559-006-0106-3

Keywords

Navigation