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Learning non-compensatory sorting models using efficient SAT/MaxSAT formulations
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DOI：10.1016/j.ejor.2021.08.017.png)
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Abstract
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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 NonCompensatory 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. (c) 2021 Elsevier B.V. All rights reserved.
Keywords:
Multiple criteria analysis
Non-compensatory sorting
Preference learning
SAT
MaxSAT
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