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.

本研究解决了传统排名聚合问题（RAP）中只有单一共识排名的局限，通过提出最优桶顺序问题的扩展——最优桶顺序集问题，提供多个共识排名，以更好地反映输入排序中的偏好。实验结果表明，通过提供一组共识排名，解决方案的适应性显著提高，同时保持了结果的可理解性。

部分排名聚合的共识集：桶顺序问题的最优集