Mixtures of Generalized Mallows models for solving the quadratic assignment problem

Recently, distance-based exponential probability models have demonstrated their validity in the context of estimation of distribution algorithms when solving permutation-based combinatorial optimisation problems. However, despite their successful performance, some of these models are unimodal, and, therefore, they might not be flexible enough to model the different modalities that may be represented in heterogeneous populations. In this paper, we address the particular case of the Generalized Mallows models under the Cayley distance, and propose mixtures of these models in the context of estimation of distribution algorithms. In order to evaluate their competitiveness, we considered the quadratic assignment problem as a case of study, and conducted experiments over a set of 90 instances for four different configurations of mixtures. Results reveal that the EDA with mixtures is able to outperform the Generalized Mallows EDA, especially in large instances.