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A framework of distributionally robust possibilistic optimization

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Abstract

In this paper, an optimization problem with uncertain constraint coefficients is considered. Possibility theory is used to model the uncertainty. Namely, a joint possibility distribution in constraint coefficient realizations, called scenarios, is specified. This possibility distribution induces a necessity measure in a scenario set, which in turn describes an ambiguity set of probability distributions in a scenario set. The distributionally robust approach is then used to convert the imprecise constraints into deterministic equivalents. Namely, the left-hand side of an imprecise constraint is evaluated by using a risk measure with respect to the worst probability distribution that can occur. In this paper, the Conditional Value at Risk is used as the risk measure, which generalizes the strict robust, and expected value approaches commonly used in literature. A general framework for solving such a class of problems is described. Some cases which can be solved in polynomial time are identified.

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The data that support the findings of this study are available from the corresponding authors upon request.

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Acknowledgements

Romain Guillaume has benefitted from the AI Interdisciplinary Institute ANITI funding. ANITI is funded by the French Investing for the Future - PIA3 program under the Grant agreement ANR-19-PI3A-0004. Adam Kasperski and Paweł Zieliński were supported by the National Science Centre, Poland, grant 2022/45/B/HS4/00355.

Funding

Romain Guillaume has benefitted from the AI Interdisciplinary Institute ANITI funding. ANITI is funded by the French Investing for the Future - PIA3 program under the Grant agreement ANR-19-PI3A-0004. Adam Kasperski and Paweł Zieliński were supported by the National Science Centre, Poland, grant 2022/45/B/HS4/00355.

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Authors and Affiliations

  1. Université de Toulouse-IRIT Toulouse, 118 Route de Narbonne, 31062, Toulouse, France

    Romain Guillaume

  2. Wrocław University of Science and Technology, Wybrzeże Wyspiańskiego 27, 50-370, Wrocław, Poland

    Adam Kasperski & Paweł Zieliński

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  1. Romain Guillaume
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  2. Adam Kasperski
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  3. Paweł Zieliński
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Correspondence to Adam Kasperski.

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Guillaume, R., Kasperski, A. & Zieliński, P. A framework of distributionally robust possibilistic optimization. Fuzzy Optim Decis Making 23, 253–278 (2024). https://doi.org/10.1007/s10700-024-09420-2

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