Approaching rank aggregation problems by using evolution strategies: The case of the optimal bucket order problem

Abstract

The optimal bucket order problem consists in obtaining a complete consensus ranking (ties are allowed) from a matrix of preferences (possibly obtained from a database of rankings). In this paper, we tackle this problem by using (1 + λ) evolution strategies. We designed specific mutation operators which are able to modify the inner structure of the buckets, which introduces more diversity into the search process. We also study different initialization methods and strategies for the generation of the population of descendants. The proposed evolution strategies are tested using a benchmark of 52 databases and compared with the current state-of-the-art algorithm LIA M P 2 G . We carry out a standard machine learning statistical analysis procedure to identify a subset of outstanding configurations of the proposed evolution strategies. The study shows that the best evolution strategy improves upon the accuracy obtained by the standard greedy method (BPA) by 35%, and that of LIA M P 2 G by 12.5%.

Learning decision trees for the partial label ranking problem

“…The seminal method used to solve the OBOP. Bucket Pivot Algorithm with least indecision assumption () 5 . The concepts of utopian matrix and Distance to Achieve the Nearest Idealization indexes ( DANI indexes ) are introduced to select the pivot in an informed way (instead of randomly). Evolutionary strategy algorithm 6 . The search engine to tackle the OBOP is improved (although more CPU time is needed).…”

“…Evolutionary strategy algorithm 6 . The search engine to tackle the OBOP is improved (although more CPU time is needed).…”

“…bucket orders ), that is, complete rankings with possibly tied items, indicating no preference among them. Nonetheless, in contrast to other ranking‐based problems (like rank aggregation), where the aggregation of bucket orders has received great attention, 5‐8 this is not the case of the prediction problem. In fact, Vembu and Gärtner 4 recognize that, in general, the algorithms available in the literature are constrained to output a permutation of the class labels 9‐13 .…”

The acclamation consensus state and an associated ranking rule

“…We highlight the introduction of effective pruning techniques reducing the number of rankings for which we need to compute the cost associated with a closest profile of rankings for which is the acclaimed ranking. Another reasonable possibility would be to adopt a heuristic approach that would speed up the computation time of our proposed ranking rule, although some voters could feel deceived if a (slighlty) different outcome than the optimal one would be obtained.…”

Extensión del concepto de utopía para el problema de la agregación de rankings sin empates

“…Estos algoritmos son rápidos, pero las soluciones así obtenidas están lejos de ser óptimas. Las metaheurísticas han mostrado un buen equilibrio entre la eficiencia y la precisión en problemas de este tipo [15], [16].…”