Using metaheuristic algorithms for parameter estimation in generalized Mallows models

This paper deals with the problem of parameter estimation in the generalized Mallows model (GMM) by using both local and global search metaheuristic (MH) algorithms. The task we undertake is to learn parameters for defining the GMM from a dataset of complete rankings/permutations. Several approaches can be found in the literature, some of which are based on greedy search and branch and bound search. The greedy approach has the disadvantage of usually becoming trapped in local optima, while the branch and bound approach, basically A^* search, usually comes down to approximate search because of memory requirements, losing in this way its guaranteed optimality. Here, we carry out a comparative study of several MH algorithms (iterated local search (ILS) methods, variable neighborhood search (VNS) methods, genetic algorithms (GAs) and estimation of distribution algorithms (EDAs)) and a tailored algorithm A^* to address parameter estimation in GMMs. We use 22 real datasets of different complexity, all but one of which were created by the authors by preprocessing real raw data. We provide a complete analysis of the experiments in terms of accuracy, number of iterations and CPU time requirements.