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A preference elicitation approach for the ordered weighted averaging criterion using solution choice observations

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  • Baak, Werner
  • Goerigk, Marc
  • Hartisch, Michael

Abstract

Decisions under uncertainty or with multiple objectives usually require the decision maker to formulate a preference regarding risks or trade-offs. If this preference is known, the ordered weighted averaging (OWA) criterion can be applied to aggregate scenarios or objectives into a single function. Formulating this preference, however, can be challenging, as we need to make explicit what is usually only implicit knowledge. We explore an optimization-based method of preference elicitation to identify appropriate OWA weights. We follow a data-driven approach, assuming the existence of observations, where the decision maker has chosen the preferred solution, but otherwise remains passive during the elicitation process. We then use these observations to determine the underlying preference by finding the preference vector that is at minimum distance to the polyhedra of feasible vectors for each of the observations. Using our optimization-based model, weights are determined by solving an alternating sequence of linear programs and standard OWA problems. Numerical experiments on risk-averse preference vectors for selection, assignment and knapsack problems show that our passive elicitation method compares well against having to conduct pairwise comparisons and performs particularly well when there are inconsistencies in the decision maker’s choices.

Suggested Citation

  • Baak, Werner & Goerigk, Marc & Hartisch, Michael, 2024. "A preference elicitation approach for the ordered weighted averaging criterion using solution choice observations," European Journal of Operational Research, Elsevier, vol. 314(3), pages 1098-1110.
  • Handle: RePEc:eee:ejores:v:314:y:2024:i:3:p:1098-1110
    DOI: 10.1016/j.ejor.2023.11.020
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    References listed on IDEAS

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    1. Hasan Zabihi & Mohsen Alizadeh & Philip Kibet Langat & Mohammadreza Karami & Himan Shahabi & Anuar Ahmad & Mohamad Nor Said & Saro Lee, 2019. "GIS Multi-Criteria Analysis by Ordered Weighted Averaging (OWA): Toward an Integrated Citrus Management Strategy," Sustainability, MDPI, vol. 11(4), pages 1-17, February.
    2. Chassein, André & Goerigk, Marc & Kasperski, Adam & Zieliński, Paweł, 2020. "Approximating combinatorial optimization problems with the ordered weighted averaging criterion," European Journal of Operational Research, Elsevier, vol. 286(3), pages 828-838.
    3. Adam Kasperski & Paweł Zieliński, 2016. "Robust Discrete Optimization Under Discrete and Interval Uncertainty: A Survey," International Series in Operations Research & Management Science, in: Michael Doumpos & Constantin Zopounidis & Evangelos Grigoroudis (ed.), Robustness Analysis in Decision Aiding, Optimization, and Analytics, chapter 0, pages 113-143, Springer.
    4. Mingwei Lin & Wenshu Xu & Zhanpeng Lin & Riqing Chen, 2020. "Determine OWA operator weights using kernel density estimation," Economic Research-Ekonomska Istraživanja, Taylor & Francis Journals, vol. 33(1), pages 1441-1464, January.
    5. Dimitris Bertsimas & David B. Brown, 2009. "Constructing Uncertainty Sets for Robust Linear Optimization," Operations Research, INFORMS, vol. 57(6), pages 1483-1495, December.
    6. Chassein, André & Goerigk, Marc & Kasperski, Adam & Zieliński, Paweł, 2018. "On recoverable and two-stage robust selection problems with budgeted uncertainty," European Journal of Operational Research, Elsevier, vol. 265(2), pages 423-436.
    7. Reimann, Olivier & Schumacher, Christian & Vetschera, Rudolf, 2017. "How well does the OWA operator represent real preferences?," European Journal of Operational Research, Elsevier, vol. 258(3), pages 993-1003.
    8. Ogryczak, Wlodzimierz & Sliwinski, Tomasz, 2003. "On solving linear programs with the ordered weighted averaging objective," European Journal of Operational Research, Elsevier, vol. 148(1), pages 80-91, July.
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