Understanding the relationship between decision and objective space in the multi-objective phylogenetic inference problem

Phylogenetic inference allows us to make a hypothesis about the evolutionary relationships among a group of organisms. Several methods based on different criteria have been proposed to infer phylogeny. However, the obtained evolutionary hypothesis varies depending on the applied method. During the last decade, different multi-objective optimisation strategies have been designed to reduce this dependency. All of them improve the solutions using dominance levels and different metrics over the objective space. However, in the multi-objective phylogenetic inference context, the relationship between the topological features of the representation (decision space) and the objective space has not been studied. In this work, we use clustering techniques to compare both spaces by considering: (1) different topological metrics designed to contrast phylogenetic trees, and (2) four different criteria used to infer phylogeny. The results show that the decision space is surjective but not injective, and it is not related to the objective space. That means that the convergence process of the current approaches could discard solutions which allow us to explore different regions of the decision space, biasing the resultant topologies. This work is a contribution for the design of new multi-objective strategies that consider a smart exploration of the decision space.