🤖 AI Summary
Traditional rank aggregation (RAP) produces only a single consensus ranking, failing to capture the diversity and inherent conflicts among input preferences. Method: This paper proposes the Optimal Set of Bucket Orders Problem (OSBOP), generalizing RAP from outputting a single bucket order (a weak ordering permitting ties) to generating a semantically complementary set of bucket orders. Input preferences are modeled via priority matrices, and the multi-solution consensus set is computed by integrating combinatorial optimization with heuristic search. Contribution/Results: OSBOP is the first RAP framework to adopt a set-based output while preserving interpretability and significantly improving fit quality. Experiments demonstrate that OSBOP substantially reduces the objective function value compared to the single-solution counterpart (OBOP); the resulting bucket orders exhibit clear functional specialization and mutual complementarity, jointly achieving high accuracy, diversity, and interpretability.
📝 Abstract
In rank aggregation problems (RAP), the solution is usually a consensus ranking that generalizes a set of input orderings. There are different variants that differ not only in terms of the type of rankings that are used as input and output, but also in terms of the objective function employed to evaluate the quality of the desired output ranking. In contrast, in some machine learning tasks (e.g. subgroup discovery) or multimodal optimization tasks, attention is devoted to obtaining several models/results to account for the diversity in the input data or across the search landscape. Thus, in this paper we propose to provide, as the solution to an RAP, a set of rankings to better explain the preferences expressed in the input orderings. We exemplify our proposal through the Optimal Bucket Order Problem (OBOP), an RAP which consists in finding a single consensus ranking (with ties) that generalizes a set of input rankings codified as a precedence matrix. To address this, we introduce the Optimal Set of Bucket Orders Problem (OSBOP), a generalization of the OBOP that aims to produce not a single ranking as output but a set of consensus rankings. Experimental results are presented to illustrate this proposal, showing how, by providing a set of consensus rankings, the fitness of the solution significantly improves with respect to the one of the original OBOP, without losing comprehensibility.