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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.

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File URL: http://mpra.ub.uni-muenchen.de/35579/
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Bibliographic Info

Paper provided by University Library of Munich, Germany in its series MPRA Paper with number 35579.

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Date of creation: 10 Feb 2011
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Publication status: Published in Applied Mathematical Sciences no. 50.Vol. 5(2011): pp. 2451-2466
Handle: RePEc:pra:mprapa:35579

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Keywords: Integer programming; Optimization over the efficient set; Multiple objective linear fractional programming; Global optimization;

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  1. Jonathan S. H. Kornbluth & Ralph E. Steuer, 1981. "Multiple Objective Linear Fractional Programming," Management Science, INFORMS, vol. 27(9), pages 1024-1039, September.
  2. 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.
  3. 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.
  4. 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.
  5. Costa, Joao Paulo, 2007. "Computing non-dominated solutions in MOLFP," European Journal of Operational Research, Elsevier, vol. 181(3), pages 1464-1475, September.
  6. 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.
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