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Optimizing a linear fractional function over the integer efficient set

Author

Listed:
  • Wassila Drici

    (USTHB)

  • Fatma Zohra Ouail

    (USTHB)

  • Mustapha Moulaï

    (USTHB)

Abstract

In this article, a new exact method is proposed to solve a problem, say $$(ILFP)_E$$ ( I L F P ) E , of maximizing a linear fractional function over the integer efficient set of multi-objective integer linear programming problem (MOILP). The method is developed through the branch and cut technique and the continuous linear fractional programming, to come up with an integer optimal solution for problem $$(ILFP)_E$$ ( I L F P ) E without having to explicitly list all efficient solutions of problem (MOILP). The branching process is strengthened by an efficient cut as well as an efficiency test so that a large number of non-efficient feasible solutions can be avoided. Illustrative example and an experimental study are reported to show the merit of this new approach.

Suggested Citation

  • Wassila Drici & Fatma Zohra Ouail & Mustapha Moulaï, 2018. "Optimizing a linear fractional function over the integer efficient set," Annals of Operations Research, Springer, vol. 267(1), pages 135-151, August.
    • Handle: RePEc:spr:annopr:v:267:y:2018:i:1:d:10.1007_s10479-017-2691-0
    DOI: 10.1007/s10479-017-2691-0
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    References listed on IDEAS

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    1. M. Ehrgott & H. W. Hamacher & K. Klamroth & S. Nickel & A. Schöbel & M. M. Wiecek, 1997. "Equivalence of Balance Points and Pareto Solutions in Multiple-Objective Programming," Journal of Optimization Theory and Applications, Springer, vol. 92(1), pages 209-212, January.
    2. Jorge, Jesús M., 2009. "An algorithm for optimizing a linear function over an integer efficient set," European Journal of Operational Research, Elsevier, vol. 195(1), pages 98-103, May.
    3. Altannar Chinchuluun & Panos Pardalos, 2007. "A survey of recent developments in multiobjective optimization," Annals of Operations Research, Springer, vol. 154(1), pages 29-50, October.
    4. Manfred Padberg, 2005. "Classical Cuts for Mixed-Integer Programming and Branch-and-Cut," Annals of Operations Research, Springer, vol. 139(1), pages 321-352, October.
    5. Zerdani, Ouiza & Moulai, Mustapha, 2011. "Optimization over an integer efficient set of a Multiple Objective Linear Fractional Problem," MPRA Paper 35579, University Library of Munich, Germany.
    6. Banu Lokman & Murat Köksalan & Pekka J. Korhonen & Jyrki Wallenius, 2016. "An interactive algorithm to find the most preferred solution of multi-objective integer programs," Annals of Operations Research, Springer, vol. 245(1), pages 67-95, October.
    7. Schaible, Siegfried, 1981. "Fractional programming: Applications and algorithms," European Journal of Operational Research, Elsevier, vol. 7(2), pages 111-120, June.
    8. H. Isermann, 1974. "Technical Note—Proper Efficiency and the Linear Vector Maximum Problem," Operations Research, INFORMS, vol. 22(1), pages 189-191, February.
    9. Werner Dinkelbach, 1967. "On Nonlinear Fractional Programming," Management Science, INFORMS, vol. 13(7), pages 492-498, March.
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