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Solving multiobjective optimization problems with decision uncertainty: an interactive approach

Author

Listed:
  • Yue Zhou-Kangas

    (Faculty of Information Technology)

  • Kaisa Miettinen

    (Faculty of Information Technology)

  • Karthik Sindhya

    (Faculty of Information Technology)

Abstract

We propose an interactive approach to support a decision maker to find a most preferred robust solution to multiobjective optimization problems with decision uncertainty. A new robustness measure that is understandable for the decision maker is incorporated as an additional objective in the problem formulation. The proposed interactive approach utilizes elements of the synchronous NIMBUS method and is aimed at supporting the decision maker to consider the objective function values and the robustness of a solution simultaneously. In the interactive approach, we offer different alternatives for the decision maker to express her/his preferences related to the robustness of a solution. To consolidate the interactive approach, we tailor a visualization to illustrate both the objective function values and the robustness of a solution. We demonstrate the advantages of the interactive approach by solving example problems.

Suggested Citation

  • Yue Zhou-Kangas & Kaisa Miettinen & Karthik Sindhya, 2019. "Solving multiobjective optimization problems with decision uncertainty: an interactive approach," Journal of Business Economics, Springer, vol. 89(1), pages 25-51, February.
    • Handle: RePEc:spr:jbecon:v:89:y:2019:i:1:d:10.1007_s11573-018-0900-1
    DOI: 10.1007/s11573-018-0900-1
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    References listed on IDEAS

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    1. Dimitris Bertsimas & Melvyn Sim, 2004. "The Price of Robustness," Operations Research, INFORMS, vol. 52(1), pages 35-53, February.
    2. Azaron, A. & Brown, K.N. & Tarim, S.A. & Modarres, M., 2008. "A multi-objective stochastic programming approach for supply chain design considering risk," International Journal of Production Economics, Elsevier, vol. 116(1), pages 129-138, November.
    3. Margaret M. Wiecek & Vincent Y. Blouin & Georges M. Fadel & Alexander Engau & Brian J. Hunt & Vijay Singh, 2009. "Multi-scenario Multi-objective Optimization with Applications in Engineering Design," Lecture Notes in Economics and Mathematical Systems, in: Vincent Barichard & Matthias Ehrgott & Xavier Gandibleux & Vincent T'Kindt (ed.), Multiobjective Programming and Goal Programming, pages 283-298, Springer.
    4. Miettinen, Kaisa & Makela, Marko M., 2006. "Synchronous approach in interactive multiobjective optimization," European Journal of Operational Research, Elsevier, vol. 170(3), pages 909-922, May.
    5. Bokrantz, Rasmus & Fredriksson, Albin, 2017. "Necessary and sufficient conditions for Pareto efficiency in robust multiobjective optimization," European Journal of Operational Research, Elsevier, vol. 262(2), pages 682-692.
    6. Ehrgott, Matthias & Ide, Jonas & Schöbel, Anita, 2014. "Minmax robustness for multi-objective optimization problems," European Journal of Operational Research, Elsevier, vol. 239(1), pages 17-31.
    7. Vesa Ojalehto & Kaisa Miettinen & Timo Laukkanen, 2014. "Implementation aspects of interactive multiobjective optimization for modeling environments: the case of GAMS-NIMBUS," Computational Optimization and Applications, Springer, vol. 58(3), pages 757-779, July.
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    Cited by:

    1. Gabriele Eichfelder & Julia Niebling & Stefan Rocktäschel, 2020. "An algorithmic approach to multiobjective optimization with decision uncertainty," Journal of Global Optimization, Springer, vol. 77(1), pages 3-25, May.

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    More about this item

    Keywords

    Multiple criteria decision making; Robust solutions; Interactive methods; Handling uncertainties; NIMBUS; Robustness measure;
    All these keywords.

    JEL classification:

    • C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis

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