Learning a ranking based on multiple reference profiles preference model with a simulated annealing metaheuristic

Abstract Multiple criteria decision aiding helps decision‐makers (DMs) to reach better decisions in multi‐criteria problems using preference models, whose parameters are elicited to best correspond to the preferences of the DM using, among other things, holistic judgments. Regarding the elicitation of the Reference based on Multiple reference Profiles (RMP) model, the literature only contains an exact method based on a Boolean satisfiability formulation, while a mixed‐integer linear program and evolutionary metaheuristics focus on a more simpler version of the model (SRMP). Exact methods for preference elicitation usually struggle to solve cases with many criteria and a lot of preference information, while metaheuristics have a gap to optimal solutions. To address these two issues, we propose in this article a simulated annealing based metaheuristic to elicit an RMP model. In order to evaluate the performance of this method, we conducted numerical experiments on simulated instances. To this end, we developed a way to uniformly generate a weak‐order extension on the subsets of criteria, which allows us to create random DMs consistent with the RMP model. The results of these experiments show that the proposed method is able to solve at optimality big instances, as well as being closer to optimal solutions than other metaheuristics in SRMP elicitation.