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An exact method for optimizing a quadratic function over the efficient set of multiobjective integer linear fractional program

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Abstract

Optimizing a function over the efficient set of a multiojective problem plays an important role in many fields of application. This problem arises whenever the decision maker wants to select the efficient solution that optimizes his utility function. Several methods are proposed in literature to deal with the problem of optimizing a linear function over the efficient set of a multiobjective integer linear program MOILFP. However, in many real-world problems, the objective functions or the utility function are nonlinear. In this paper, we propose an exact method to optimize a quadratic function over the efficient set of a multiobjective integer linear fractional program MOILFP. The proposed method solves a sequence of quadratic integer problems. Where, at each iteration, the search domain is reduced s6uccessively, by introducing cuts, to eliminate dominated solutions. We conducted a computational experiment, by solving randomly generated instances, to analyze the performance of the proposed method.

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Notes

  1. We denote by \(\mathcal {U}(I_{min},~I_{max})\) a function that generates uniformly a random integer number between \(I_{min}\) and \( I_{max}\).

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Acknowledgements

The authors are grateful to Hadjer Moulai and anonymous referees for their substantive comments and suggestions that improved the quality and the presentation of the paper. Authors work was supported by the Direction Générale de la Recherche Scientifique et du Développement Technologique (DGRSDT) Grant ID: C0656104.

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  1. LaROMaD Laboratory, Department of Operations Research, Faculty of Mathematics, USTHB, P.B. 32 El-Alia, 16111, Bab Ezzouar, Algiers, Algeria

    Yacine Chaiblaine & Mustapha Moulaï

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  1. Yacine Chaiblaine
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  2. Mustapha Moulaï
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Correspondence to Yacine Chaiblaine.

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Chaiblaine, Y., Moulaï, M. An exact method for optimizing a quadratic function over the efficient set of multiobjective integer linear fractional program. Optim Lett 16, 1035–1049 (2022). https://doi.org/10.1007/s11590-021-01758-5

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