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Robust optimization with scenarios using belief functions

Abstract : In this paper a robust optimization problem with uncertain objective function is considered. The uncertainty is modeled by specifying a scenario set, containing a finite number of objective function coefficients, called scenarios. Additional knowledge in scenario set can be represented by using a mass function defined on the power set of scenarios. This mass function defines a belief function, which in turn induces a family of probability distributions in scenario set. One can then use a generalized Hurwicz criterion, i.e. a convex combination of the upper and lower expectations, to solve the uncertain problem. Recently, possibility theory has been applied to extend the model of uncertainty based on belief functions. Namely, belief function can be induced by a random fuzzy set. In this paper we show how this generalized model can be applied to robust optimization.
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https://hal.archives-ouvertes.fr/hal-03324825
Contributor : Romain Guillaume Connect in order to contact the contributor
Submitted on : Thursday, August 26, 2021 - 1:52:42 PM
Last modification on : Friday, August 27, 2021 - 3:30:23 AM

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Romain Guillaume, Adam Kasperski, Pawel Zielinski. Robust optimization with scenarios using belief functions. International Conference on Fuzzy Systems (FUZZ-IEEE 2021), Jul 2021, Luxembourg, Luxembourg. ⟨10.1109/FUZZ45933.2021.9494494⟩. ⟨hal-03324825⟩

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