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Learning Non-Compensatory Sorting models using efficient SAT/MaxSAT formulations

Abstract : The Non-Compensatory Sorting model aims at assigning alternatives evaluated on multiple criteria to one of the predefined ordered categories. Computing parameters of the Non-Compensatory Sorting model compatible to a set of reference assignments is computationally demanding. To overcome this problem, two formulations based on Boolean satisfiability have recently been proposed to learn the parameters of the Non-Compensatory Sorting model from perfect preference information, i.e. when the set of reference assignments can be completely represented in the model. In this paper, two popular variants of the Non-Compensatory Sorting model are considered, the Non-Compensatory Sorting model with a unique profile and the Non-Compensatory Sorting model with a unique set of sufficient coalitions. For each variant, we start by extending the formulation based on a separation principle to the multiple category case. Moreover, we extend the two formulations to handle inconsistency in the preference information using the Maximum satisfiability problem language. A computational study is proposed to compare the efficiency of both formulations to learn the two Non-Compensatory Sorting models (with a unique profile and with a unique set of sufficient coalitions) from noiseless and noisy preference information.
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https://hal.archives-ouvertes.fr/hal-03347526
Contributor : Wassila Ouerdane Connect in order to contact the contributor
Submitted on : Friday, September 17, 2021 - 11:57:29 AM
Last modification on : Sunday, June 26, 2022 - 3:13:40 AM

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Ali Tlili, Khaled Belahcene, Oumaima Khaled, Vincent Mousseau, Wassila Ouerdane. Learning Non-Compensatory Sorting models using efficient SAT/MaxSAT formulations. European Journal of Operational Research, Elsevier, 2021, 298 (3), pp.979-1006. ⟨10.1016/j.ejor.2021.08.017⟩. ⟨hal-03347526⟩

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