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Generating the efficient set of MultiObjective Integer Linear plus Linear Fractional Programming Problems

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  • Yasmine Cherfaoui

    (USTHB)

  • Mustapha Moulaï

    (USTHB)

Abstract

The problem of optimizing a linear plus linear fractional function is an important field of search, it is a difficult problem since the linear plus linear fractional function doesn’t possess any convexity propriety. In this paper, we propose a method that generates the set of the efficient solutions of multiobjective integer linear plus linear fractional programming problem. Our method consists in Branch-and-Bound exploration combined with cutting plane technique that allows to remove from search inefficient solutions. The cutting plane technique takes into account the inefficiency of a solution in another problem that implies the inefficiency of that solution in our problem and uses this link to reduce the exploration’s domain.

Suggested Citation

  • Yasmine Cherfaoui & Mustapha Moulaï, 2021. "Generating the efficient set of MultiObjective Integer Linear plus Linear Fractional Programming Problems," Annals of Operations Research, Springer, vol. 296(1), pages 735-753, January.
    • Handle: RePEc:spr:annopr:v:296:y:2021:i:1:d:10.1007_s10479-020-03581-0
    DOI: 10.1007/s10479-020-03581-0
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    References listed on IDEAS

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    1. A. Charnes & W. W. Cooper, 1962. "Programming with linear fractional functionals," Naval Research Logistics Quarterly, John Wiley & Sons, vol. 9(3‐4), pages 181-186, September.
    2. Bela Martos & Andrew & Veronika Whinston, 1964. "Hyperbolic programming," Naval Research Logistics Quarterly, John Wiley & Sons, vol. 11(2), pages 135-155, June.
    3. Chadha, S. S., 1993. "Dual of the sum of a linear and linear fractional program," European Journal of Operational Research, Elsevier, vol. 67(1), pages 136-139, May.
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    Cited by:

    1. Nacéra Maachou & Mustapha Moulaï, 2022. "Branch and cut method for solving integer indefinite quadratic bilevel programs," Annals of Operations Research, Springer, vol. 316(1), pages 197-227, September.

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