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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
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    References listed on IDEAS

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    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.
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    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. 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.
    3. 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.

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