IDEAS home Printed from https://ideas.repec.org/a/eee/ejores/v224y2013i3p449-457.html
   My bibliography  Save this article

On accuracy, robustness and tolerances in vector Boolean optimization

Author

Listed:
  • Nikulin, Y.
  • Karelkina, O.
  • Mäkelä, M.M.

Abstract

A Boolean programming problem with a finite number of alternatives where initial coefficients (costs) of linear payoff functions are subject to perturbations is considered. We define robust solution as a feasible solution which for a given set of realizations of uncertain parameters guarantees the minimum value of the worst-case relative regret among all feasible solutions. For the Pareto optimality principle, an appropriate definition of the worst-case relative regret is specified. It is shown that this definition is closely related to the concept of accuracy function being recently intensively studied in the literature. We also present the concept of robustness tolerances of a single cost vector. The tolerance is defined as the maximum level of perturbation of the cost vector which does not destroy the solution robustness. We present formulae allowing the calculation of the robustness tolerance obtained for some initial costs. The results are illustrated with several numerical examples.

Suggested Citation

  • Nikulin, Y. & Karelkina, O. & Mäkelä, M.M., 2013. "On accuracy, robustness and tolerances in vector Boolean optimization," European Journal of Operational Research, Elsevier, vol. 224(3), pages 449-457.
  • Handle: RePEc:eee:ejores:v:224:y:2013:i:3:p:449-457
    DOI: 10.1016/j.ejor.2012.09.018
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0377221712006820
    Download Restriction: Full text for ScienceDirect subscribers only

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Nikulin, Yury & Mäkelä, Marko M., 2010. "Stability and accuracy functions for a multicriteria Boolean linear programming problem with parameterized principle of optimality "from Condorcet to Pareto"," European Journal of Operational Research, Elsevier, vol. 207(3), pages 1497-1505, December.
    2. Montemanni, R. & Gambardella, L. M., 2005. "A branch and bound algorithm for the robust spanning tree problem with interval data," European Journal of Operational Research, Elsevier, vol. 161(3), pages 771-779, March.
    3. Zielinski, Pawel, 2004. "The computational complexity of the relative robust shortest path problem with interval data," European Journal of Operational Research, Elsevier, vol. 158(3), pages 570-576, November.
    4. Kasperski, Adam & Zielinski, Pawel, 2010. "Minmax regret approach and optimality evaluation in combinatorial optimization problems with interval and fuzzy weights," European Journal of Operational Research, Elsevier, vol. 200(3), pages 680-687, February.
    Full references (including those not matched with items on IDEAS)

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:ejores:v:224:y:2013:i:3:p:449-457. See general information about how to correct material in RePEc.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Dana Niculescu). General contact details of provider: http://www.elsevier.com/locate/eor .

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service hosted by the Research Division of the Federal Reserve Bank of St. Louis . RePEc uses bibliographic data supplied by the respective publishers.