On accuracy, robustness and tolerances in vector Boolean optimization
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.
If you experience problems downloading a file, check if you have the proper application to view it first. In case of further problems read the IDEAS help page. Note that these files are not on the IDEAS site. Please be patient as the files may be large.
As the access to this document is restricted, you may want to look for a different version under "Related research" (further below) or search for a different version of it.
Volume (Year): 224 (2013)
Issue (Month): 3 ()
|Contact details of provider:|| Web page: http://www.elsevier.com/locate/eor|
References listed on IDEAS
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
- 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.
- 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.
- 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.
- 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.
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)
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 references are entirely missing, you can add them using this form.
If the full references list an item that is present in RePEc, but the system did not link 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 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.