Approaching the rank aggregation problem by local search-based metaheuristics

Abstract

Encouraged by the success of applying metaheuristics algorithms to other ranking-based problems (Kemeny ranking problem and parameter estimation for Mallows distributions), in this paper we deal with the rank aggregation problem (RAP), which can be viewed as a generalization of the Kemeny problem to arbitrary rankings. While in the Kemeny problem the input is a set of permutations, the RAP consists in obtaining the consensus permutation for a sample of arbitrary rankings. This is an NP-hard problem which can be approached by using greedy heuristic algorithms (e.g. Borda). Such algorithms are fast but the solutions so obtained are far to be optimal. In this paper, we propose the use of more complex search processes to deal with the RAP. In particular, we perform a comparative study among some local-based search metaheuristics: hill climbing (HC), iterated local search (ILS), variable neighborhood search (VNS) and greedy randomized adaptive search procedure (GRASP). We provide a complete analysis of the experimental study regarding accuracy and number of iterations required to reach the best solution. From the results we can conclude that the selection of a suitable neighborhood plays a key role, and that depending on the available resources (cpu time) a different algorithm (VNS, ILS or GRASP) could be the proper choice.