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Optimization over an integer efficient set of a Multiple Objective Linear Fractional Problem

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  • Zerdani, Ouiza
  • Moulai, Mustapha

Abstract

The problem of optimizing a real valued function over an efficient set of the Multiple Objective Linear Fractional Programming problem (MOLFP) is an important field of research and has not received as much attention as did the problem of optimizing a linear function over an efficient set of the Multiple Objective Linear Programming problem (MOLP).In this work an algorithm is developed that optimizes an arbitrary linear function over an integer efficient set of problem (MOLFP) without explicitly having to enumerate all the efficient solutions. The proposed method is based on a simple selection technique that improves the linear objective value at each iteration.A numerical illustration is included to explain the proposed method.

Suggested Citation

  • 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.
    • Handle: RePEc:pra:mprapa:35579
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    File URL: https://mpra.ub.uni-muenchen.de/35579/1/MPRA_paper_35579.pdf
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    References listed on IDEAS

    as
    1. Chergui, M. E-A & Moulai, M., 2007. "An exact method for a discrete multiobjective linear fractional optimization," MPRA Paper 12097, University Library of Munich, Germany, revised 09 Jan 2008.
    2. Yamada, Syuuji & Tanino, Tetsuzo & Inuiguchi, Masahiro, 2001. "An inner approximation method incorporating a branch and bound procedure for optimization over the weakly efficient set," European Journal of Operational Research, Elsevier, vol. 133(2), pages 267-286, January.
    3. Jonathan S. H. Kornbluth & Ralph E. Steuer, 1981. "Multiple Objective Linear Fractional Programming," Management Science, INFORMS, vol. 27(9), pages 1024-1039, September.
    4. 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.
    5. 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.
    6. Le Thi, Hoai An & Pham, Dinh Tao & Thoai, Nguyen V., 2002. "Combination between global and local methods for solving an optimization problem over the efficient set," European Journal of Operational Research, Elsevier, vol. 142(2), pages 258-270, October.
    7. Costa, Joao Paulo, 2007. "Computing non-dominated solutions in MOLFP," European Journal of Operational Research, Elsevier, vol. 181(3), pages 1464-1475, September.
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    Cited by:

    1. 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.

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    More about this item

    Keywords

    Integer programming; Optimization over the efficient set; Multiple objective linear fractional programming; Global optimization;
    All these keywords.

    JEL classification:

    • I23 - Health, Education, and Welfare - - Education - - - Higher Education; Research Institutions
    • C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis

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