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A coverage-based Box-Algorithm to compute a representation for optimization problems with three objective functions

Author

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  • Tobias Kuhn

    (Technische Universität Kaiserslautern)

  • Stefan Ruzika

    (Universität Koblenz-Landau)

Abstract

In this paper, a method for computing a substitute of the nondominated set, a so-called representation system, is proposed for tricriteria optimization problems. Our algorithm is easy to implement, it is flexibly applicable to a wide range of problems, and it takes several quality measures which have been proposed in the literature into account. The resulting representation system satisfies provably certain quality levels and, thus, it may be utilized to make proper and confident decisions.

Suggested Citation

  • Tobias Kuhn & Stefan Ruzika, 2017. "A coverage-based Box-Algorithm to compute a representation for optimization problems with three objective functions," Journal of Global Optimization, Springer, vol. 67(3), pages 581-600, March.
    • Handle: RePEc:spr:jglopt:v:67:y:2017:i:3:d:10.1007_s10898-016-0425-5
    DOI: 10.1007/s10898-016-0425-5
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    References listed on IDEAS

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    2. Kerstin Dächert & Kathrin Klamroth, 2015. "A linear bound on the number of scalarizations needed to solve discrete tricriteria optimization problems," Journal of Global Optimization, Springer, vol. 61(4), pages 643-676, April.
    3. Dhaenens, C. & Lemesre, J. & Talbi, E.G., 2010. "K-PPM: A new exact method to solve multi-objective combinatorial optimization problems," European Journal of Operational Research, Elsevier, vol. 200(1), pages 45-53, January.
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    5. Ehrgott, Matthias & Tenfelde-Podehl, Dagmar, 2003. "Computation of ideal and Nadir values and implications for their use in MCDM methods," European Journal of Operational Research, Elsevier, vol. 151(1), pages 119-139, November.
    6. Kirlik, Gokhan & Sayın, Serpil, 2014. "A new algorithm for generating all nondominated solutions of multiobjective discrete optimization problems," European Journal of Operational Research, Elsevier, vol. 232(3), pages 479-488.
    7. S. Ruzika & M. M. Wiecek, 2005. "Approximation Methods in Multiobjective Programming," Journal of Optimization Theory and Applications, Springer, vol. 126(3), pages 473-501, September.
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    Cited by:

    1. Doğan, Ilgın & Lokman, Banu & Köksalan, Murat, 2022. "Representing the nondominated set in multi-objective mixed-integer programs," European Journal of Operational Research, Elsevier, vol. 296(3), pages 804-818.

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