A MIP-based approach to learn MR-Sort models with single-peaked preferences

Pegdwendé Minoungou (), Vincent Mousseau (), Wassila Ouerdane () and Paolo Scotton ()
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Pegdwendé Minoungou: Université Paris-Saclay
Vincent Mousseau: Université Paris-Saclay
Wassila Ouerdane: Université Paris-Saclay
Paolo Scotton: IBM Research – Zurich

Annals of Operations Research, 2023, vol. 325, issue 2, No 3, 795-817

Abstract: Abstract The Majority Rule Sorting (MR-Sort) method assigns alternatives evaluated on multiple criteria to one of the predefined ordered categories. The Inverse MR-Sort problem (Inv-MR-Sort) consists in computing MR-Sort parameters that match a dataset. Existing learning algorithms for Inv-MR-Sort consider monotone preference on criteria. We extend this problem to the case where the preference on criteria are not necessarily monotone, but possibly single-peaked (or single-valley). We propose a mixed-integer programming based algorithm that learns from the training data the preference on criteria together with the other MR-Sort parameters. Numerical experiments investigate the performance of the algorithm, and we illustrate its use on a real-world case study.

Keywords: Multicriteria sorting; MR-Sort; Single-peaked preferences; Preference learning (search for similar items in EconPapers)
Date: 2023
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DOI: 10.1007/s10479-022-05007-5

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