Particle swarm optimization for preference rankings

Abstract

Preference learning, or the analysis of preference rankings, is gaining more and more importance in various scientific disciplines. Preference learning methods allow predicting preferences on a set of alternatives. The ingredients are a pool of evaluators and a set of objects or items to be ranked in order of preference. The rank aggregation problem must be solved in order to aggregate preferences or rankings with the aim to find a consensus or collective decision. Branch-and-bound-like procedures are usable up to problems involving a relatively small number of objects, say less than 200. When the number of items becomes very large, the rank aggregation problem becomes increasingly difficult to approach so that it is universally recognized as an NP-hard problem. Several heuristic methods have been proposed to provide increasingly accurate solutions. These assume the Kemeny axiomatic approach that better deals with tied rankings. In this paper, we adopt a strategy based on Particle Swarm Optimization by adapting procedures born to solve optimization problems in continuous spaces to discrete combinatorial optimization problems. A simulation study shows the performance of the proposed algorithm in a controlled environment. A benchmarking complex data set and two real world data sets with large number of items are considered. As a result, the proposed algorithm provides significant savings in computational time and comparable accuracy with respect to other recent algorithms.