Zerdani, Ouiza and Moulai, Mustapha
(2011):
*Optimization over an integer efficient set of a Multiple Objective Linear Fractional Problem.*
Published in: Applied Mathematical Sciences
, Vol. Vol. 5, No. no. 50
(10 May 2011): pp. 2451-2466.

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## 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.

Item Type: | MPRA Paper |
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Original Title: | Optimization over an integer efficient set of a Multiple Objective Linear Fractional Problem |

Language: | English |

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

Subjects: | I - Health, Education, and Welfare > I2 - Education and Research Institutions > I23 - Higher Education ; Research Institutions C - Mathematical and Quantitative Methods > C6 - Mathematical Methods ; Programming Models ; Mathematical and Simulation Modeling > C61 - Optimization Techniques ; Programming Models ; Dynamic Analysis |

Item ID: | 35579 |

Depositing User: | Mustapha MOULAI |

Date Deposited: | 26 Dec 2011 21:03 |

Last Modified: | 26 Sep 2019 22:48 |

References: | [1] M. Abbas and M. Moulai, Integer linear fractional programming with multiple objective, Journal of the Italian Operations Research Society, 32 (2002), N◦103 − 104, 15 − 38. [2] M. Abbas and D. Chaabane, Optimizing a linear function over an integer efficient set, European Journal of Operational Research, 174 (2006), 1140-1161. [3] D.J. Ashton and D.R. Atkins, Multicriteria programming for financial planning, Journal of the Operational Research Society, 30 (1989), N◦3, 259-270. [4] H.P. Benson, An All-Linear Programming Relaxation Algorithm for Optimizing over the Efficient Set, Journal of Global Optimization, 1 (1991), 83-104. [5] H.P. Benson, A finite Nonadjacent Extreme Point Search Algorithm over the Efficient Set, Journal of Optimization Theory and Applications, 73 (1992), N◦1, 47-64. [6] H.P. Benson and S. Sayin, Optimizing over the Efficient Set: Four Special Cases, Journal of Optimization Theory and Applications, 80 (1994), N◦1, 3-17. [7] A. Cambini and L. Martein, A modified version of Martos’algorithm for the linear fractional problem, Mathematics of Operations Research, 53 (1986), 33-44. [8] A. Cambini, L. Martein and I.M. Stancu-Minasian, A survey of bicriteria fractional problems, Advanced Modeling and Optimization, 1 (1999), N◦1, 9-46. [9] D. Chaabane and M. Pirlot, A method for optimizing over the integer efficient set, Journal of industrial and management optimization, 6 (2010), N◦4, 811-823. [10] M.E.A. Chergui and M. Moulai, An exact method for a discrete multiobjective linear fractional optimization, Journal of Applied Mathematics and Decision sciences, 2008 (2008), Article ID 760191,12 pages. [11] J.P. Costa, Computing non-dominated solutions in MOLFP, European Journal of Operational Research, 181 (2007), N◦3, 1464-1475. [12] N. Datta and D. Bhatia, Algorithm to determine an initial efficient basic solution for a linear fractional multiple objective transportation problem, Cahiers Centre Etudes Rech.Oper., 26 (1984), N◦1 − 2, 127-136. [13] J.G. Ecker and J.H. Song, Optimizing a Linear Function over an Efficient Set, Journal of Optimization Theory and Applications, 83 (1994), N◦3, 541-563. [14] M. Ehrgott, H.W. Hamacher, K. Klamroth, S. Nickel, A. Schobel and M.M. Wiecek, A note on the equivalence of balance points and Pareto solutions in multiple-objective programming, Journal of Optimization Theory and Applications, 92 (1997), N◦1, 209-212. [15]D. Granot and F. Granot, On integer and mixed integer fractional programming problems, Annals of Discrete Mathematics, 1 (1977), 221-231. [16] H. Isermann and R.E. Steuer, Computational Experience Concerning Payoff Tables and Minimum Criterion Values over the Efficient Set, European Journal of Operational Research, 33 (1987), 91-97. [17] J.M. Jorge, An algorithm for optimizing a linear function over an integer efficient set, European Journal of Operational Research, 195 (2009), 98-103. [18] J.S.H. Kornbluth and R.E. Steuer, Multiple objective linear fractional programming, Management Science, 27 (1981), N◦9, 1024-1039. [19] J.S.H. Kornbluth, Ratio goals in manpower planning models, INFORcanad. J.Oper.Res.Inform.Process., 21 (1983), N◦2, 151-154. [20] B. Martos, Hyperbolic Programming, Naval Res. Logist. Quart., 11 (1964), 135-155. [21] N.C. Nguyen, An Algorithm for Optimizing a Linear Function over the Integer Efficient Set, Konrad-Zuse-zentrum fur Informationstechnik Berlin, (1992). [22] J. Philip, Algorithms for the vector maximization problem, Mathematical programming, 2 (1972), 207-229. [23] O.M. Saad and J.B. Hughes, Bicriterion integer linear fractional programs with parameters in the objective functions, Journal of Information and optimization Sciences, 19 (1998), N◦1, 97-108. [24] R.E. Steuer, Multiple criteria optimization: Theory, computation and application, Wiley Series in probability and Mathematical Statistics: Applied Probability and Statistics, John Wiley and Sons, Inc.XXII, New York, 1986. [25] J. Teghem and P. Kunsch, A survey of techniques to determine the efficient solutions to multi-objective integer linear programming, Asia Pacific Journal of Operations Research, 3 (1986), 95-108. [26] H.A.L. Thi, D.T. Pham and N.V. Thoai, Combination between Global and Local Methods for Solving an Optimization Problem over the Efficient Set, European Journal of Operational Research, 142 (2002), N◦2, 258-272. [27] S. Yamada, T. Tanino and M. Inuiguchi, An Inner approximation method Incorporating a Branch and Bound procedure for Optimization over the Weakly Efficient Set, European Journal of Operational Research, 133 (2001), N◦2, 267-286. [28] Y. Yamamoto, Optimization over the Efficient Set: overview, Journal of Global Optimization, 22 (2002), N◦1 − 4, 285-317. |

URI: | https://mpra.ub.uni-muenchen.de/id/eprint/35579 |