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Efficient Solutions and Bounds on Tradeoffs

Author

Listed:
  • I. Kaliszewski

    (Polish Academy of Sciences)

  • W. Michalowski

    (Carleton University)

Abstract

The modified Tchebycheff method, widely used to generate efficient solutions to a vector optimization problem, provides means to identify properly efficient solutions with a preimposed common bound on all tradeoffs. In this paper, we show how to generate weakly efficient solutions when different bounds are preimposed on the subsets of tradeoffs.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:joptap:v:94:y:1997:i:2:d:10.1023_a:1022687729559
    DOI: 10.1023/A:1022687729559
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    References listed on IDEAS

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    1. Kaliszewski, Ignacy, 1995. "A theorem on nonconvex functions and its application to vector optimization," European Journal of Operational Research, Elsevier, vol. 80(2), pages 439-445, January.
    2. E. U. Choo & D. R. Atkins, 1983. "Proper Efficiency in Nonconvex Multicriteria Programming," Mathematics of Operations Research, INFORMS, vol. 8(3), pages 467-470, August.
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    Cited by:

    1. 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.
    2. 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.
    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.
    4. 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.

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