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An equivalent transformation of multi-objective optimization problems

Author

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  • Masoud Zarepisheh

    (University of Florida)

  • Panos M. Pardalos

    (University of Florida)

Abstract

A new equivalent definition of proper efficiency is presented. With the aid of the new definition of properness, a transformation technique is proved to transform a multi-objective problem to a more convenient one. Some conditions are determined under which the original and the transformed problems have the same Pareto and properly efficient solutions. This transformation could be employed for the sake of convexification and simplification in order to improve the computational efficiency for solving the given problem. Moreover, some existing results about the weighted sum method in the multi-objective optimization literature are generalized using the special case of the proposed transformation scheme.

Suggested Citation

  • Masoud Zarepisheh & Panos M. Pardalos, 2017. "An equivalent transformation of multi-objective optimization problems," Annals of Operations Research, Springer, vol. 249(1), pages 5-15, February.
    • Handle: RePEc:spr:annopr:v:249:y:2017:i:1:d:10.1007_s10479-014-1782-4
    DOI: 10.1007/s10479-014-1782-4
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    References listed on IDEAS

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    1. C. J. Goh & X. Q. Yang, 1998. "Convexification of a Noninferior Frontier," Journal of Optimization Theory and Applications, Springer, vol. 97(3), pages 759-768, June.
    2. D. Li & M. P. Biswal, 1998. "Exponential Transformation in Convexifying a Noninferior Frontier and Exponential Generating Method," Journal of Optimization Theory and Applications, Springer, vol. 99(1), pages 183-199, October.
    3. Jyrki Wallenius & James S. Dyer & Peter C. Fishburn & Ralph E. Steuer & Stanley Zionts & Kalyanmoy Deb, 2008. "Multiple Criteria Decision Making, Multiattribute Utility Theory: Recent Accomplishments and What Lies Ahead," Management Science, INFORMS, vol. 54(7), pages 1336-1349, July.
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    Cited by:

    1. Ambrose Lo & Zhaofeng Tang, 2019. "Pareto-optimal reinsurance policies in the presence of individual risk constraints," Annals of Operations Research, Springer, vol. 274(1), pages 395-423, March.
    2. Chernonog, Tatyana & Avinadav, Tal & Ben-Zvi, Tal, 2019. "How to set price and quality in a supply chain of virtual products under bi-criteria and risk consideration," International Journal of Production Economics, Elsevier, vol. 209(C), pages 156-163.
    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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