IDEAS home Printed from https://ideas.repec.org/a/spr/joptap/v168y2016i3d10.1007_s10957-015-0841-6.html
   My bibliography  Save this article

Strongly Proper Efficient Solutions: Efficient Solutions with Bounded Trade-Offs

Author

Listed:
  • Kazhal Khaledian

    (Amirkabir University of Technology)

  • Esmaile Khorram

    (Amirkabir University of Technology)

  • Majid Soleimani-damaneh

    (University of Tehran
    Institute for Research in Fundamental Sciences (IPM))

Abstract

In multiple-objective optimization literature, a properly efficient solution has been interpreted as a point in which the trade-offs between all objectives are bounded. In this paper, it is shown that this boundedness does not necessarily hold for problems with three or more objective functions. It is possible that in a properly efficient solution the trade-offs between some objectives are unbounded. To overcome this, in this paper strongly proper efficient solutions are introduced, in which the trade-offs between all objectives are bounded. This notion is defined in different senses, and the relationships between them are investigated. In addition to theoretical discussions, some clarifying examples are given.

Suggested Citation

  • Kazhal Khaledian & Esmaile Khorram & Majid Soleimani-damaneh, 2016. "Strongly Proper Efficient Solutions: Efficient Solutions with Bounded Trade-Offs," Journal of Optimization Theory and Applications, Springer, vol. 168(3), pages 864-883, March.
    • Handle: RePEc:spr:joptap:v:168:y:2016:i:3:d:10.1007_s10957-015-0841-6
    DOI: 10.1007/s10957-015-0841-6
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s10957-015-0841-6
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.
    File URL: https://libkey.io/10.1007/s10957-015-0841-6?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    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. Lizhen Shao & Matthias Ehrgott, 2008. "Approximately solving multiobjective linear programmes in objective space and an application in radiotherapy treatment planning," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 68(2), pages 257-276, October.
    2. I. Kaliszewski & W. Michalowski, 1997. "Efficient Solutions and Bounds on Tradeoffs," Journal of Optimization Theory and Applications, Springer, vol. 94(2), pages 381-394, August.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Shokouh Shahbeyk & Majid Soleimani-damaneh & Refail Kasimbeyli, 2018. "Hartley properly and super nondominated solutions in vector optimization with a variable ordering structure," Journal of Global Optimization, Springer, vol. 71(2), pages 383-405, June.
    2. Fereshteh Akbari & Mehrdad Ghaznavi & Esmaile Khorram, 2018. "A Revised Pascoletti–Serafini Scalarization Method for Multiobjective Optimization Problems," Journal of Optimization Theory and Applications, Springer, vol. 178(2), pages 560-590, August.
    3. Morteza Rahimi & Majid Soleimani-damaneh, 2018. "Robustness in Deterministic Vector Optimization," Journal of Optimization Theory and Applications, Springer, vol. 179(1), pages 137-162, October.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Fereshteh Akbari & Mehrdad Ghaznavi & Esmaile Khorram, 2018. "A Revised Pascoletti–Serafini Scalarization Method for Multiobjective Optimization Problems," Journal of Optimization Theory and Applications, Springer, vol. 178(2), pages 560-590, August.
    2. Rennen, G. & van Dam, E.R. & den Hertog, D., 2009. "Enhancement of Sandwich Algorithms for Approximating Higher Dimensional Convex Pareto Sets," Other publications TiSEM e2255959-6691-4ef1-88a4-5, Tilburg University, School of Economics and Management.
    3. Timothy C. Y. Chan & Tim Craig & Taewoo Lee & Michael B. Sharpe, 2014. "Generalized Inverse Multiobjective Optimization with Application to Cancer Therapy," Operations Research, INFORMS, vol. 62(3), pages 680-695, June.
    4. Andreas Löhne & Birgit Rudloff & Firdevs Ulus, 2014. "Primal and dual approximation algorithms for convex vector optimization problems," Journal of Global Optimization, Springer, vol. 60(4), pages 713-736, December.
    5. Gijs Rennen & Edwin R. van Dam & Dick den Hertog, 2011. "Enhancement of Sandwich Algorithms for Approximating Higher-Dimensional Convex Pareto Sets," INFORMS Journal on Computing, INFORMS, vol. 23(4), pages 493-517, November.
    6. Kaliszewski, Ignacy, 2003. "Dynamic parametric bounds on efficient outcomes in interactive multiple criteria decision making problems," European Journal of Operational Research, Elsevier, vol. 147(1), pages 94-107, May.
    7. Hunt, Brian J. & Wiecek, Margaret M. & Hughes, Colleen S., 2010. "Relative importance of criteria in multiobjective programming: A cone-based approach," European Journal of Operational Research, Elsevier, vol. 207(2), pages 936-945, December.
    8. Löhne, Andreas & Weißing, Benjamin, 2017. "The vector linear program solver Bensolve – notes on theoretical background," European Journal of Operational Research, Elsevier, vol. 260(3), pages 807-813.
    9. Raimundo, Marcos M. & Ferreira, Paulo A.V. & Von Zuben, Fernando J., 2020. "An extension of the non-inferior set estimation algorithm for many objectives," European Journal of Operational Research, Elsevier, vol. 284(1), pages 53-66.
    10. Matthias Ehrgott & Andreas Löhne & Lizhen Shao, 2012. "A dual variant of Benson’s “outer approximation algorithm” for multiple objective linear programming," Journal of Global Optimization, Springer, vol. 52(4), pages 757-778, April.
    11. Kuan-Min Lin & Matthias Ehrgott & Andrea Raith, 2017. "Integrating column generation in a method to compute a discrete representation of the non-dominated set of multi-objective linear programmes," 4OR, Springer, vol. 15(4), pages 331-357, December.
    12. Matthias Ehrgott & Çiğdem Güler & Horst Hamacher & Lizhen Shao, 2010. "Mathematical optimization in intensity modulated radiation therapy," Annals of Operations Research, Springer, vol. 175(1), pages 309-365, March.
    13. Shao, Lizhen & Ehrgott, Matthias, 2016. "Discrete representation of non-dominated sets in multi-objective linear programming," European Journal of Operational Research, Elsevier, vol. 255(3), pages 687-698.
    14. Matthias Ehrgott & Lizhen Shao & Anita Schöbel, 2011. "An approximation algorithm for convex multi-objective programming problems," Journal of Global Optimization, Springer, vol. 50(3), pages 397-416, July.
    15. Cacchiani, Valentina & D’Ambrosio, Claudia, 2017. "A branch-and-bound based heuristic algorithm for convex multi-objective MINLPs," European Journal of Operational Research, Elsevier, vol. 260(3), pages 920-933.
    16. Breedveld, Sebastiaan & Craft, David & van Haveren, Rens & Heijmen, Ben, 2019. "Multi-criteria optimization and decision-making in radiotherapy," European Journal of Operational Research, Elsevier, vol. 277(1), pages 1-19.
    17. Koenen, Melissa & Balvert, Marleen & Fleuren, H.A., 2023. "A Renewed Take on Weighted Sum in Sandwich Algorithms : Modification of the Criterion Space," Discussion Paper 2023-012, Tilburg University, Center for Economic Research.
    18. Piercy, Craig A. & Steuer, Ralph E., 2019. "Reducing wall-clock time for the computation of all efficient extreme points in multiple objective linear programming," European Journal of Operational Research, Elsevier, vol. 277(2), pages 653-666.
    19. Firdevs Ulus, 2018. "Tractability of convex vector optimization problems in the sense of polyhedral approximations," Journal of Global Optimization, Springer, vol. 72(4), pages 731-742, December.
    20. Koenen, Melissa & Balvert, Marleen & Fleuren, H.A., 2023. "A Renewed Take on Weighted Sum in Sandwich Algorithms : Modification of the Criterion Space," Other publications TiSEM 795b6c0c-c7bc-4ced-9d6b-a, Tilburg University, School of Economics and Management.

    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:spr:joptap:v:168:y:2016:i:3:d:10.1007_s10957-015-0841-6. See general information about how to correct material in RePEc.

    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 bibliographic 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.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

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

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.