Ranking with Multiple Reference Points: Efficient SAT-based learning procedures. (February 2023) - Belahcène, Khaled; Mousseau, Vincent; Ouerdane, Wassila; Pirlot, Marc; Sobrie, Olivier
Abstract: We consider the multicriteria ranking problem, and specifically a ranking procedure based on reference points recently proposed in the literature, named Ranking with Multiple reference Points (RMP). Implementing RMP in a real world decision problem requires to elicit the model preference parameters. This can be done indirectly by inferring the parameters from stated preferences. Learning an RMP model from stated preferences proves however to be computationally costly, and can hardly be put in practice using currently available algorithms. In this paper, we propose a Boolean satisfiability formulation for inferring an RMP model from a set of pairwise comparisons which is much faster than the existing algorithms. Highlights: We consider RMP a multiple ranking model based on reference points. We learn the RMP parameter from comparisons provided by the decision maker. The learning algorithm is based on a Boolean satisfiability formulation and solved using a SAT solver. Numerical tests show the performance of the approach. An real world example illustrates how the approach can be put in practice.