Mathematical models to reconstruct phylogenetic trees under the minimum evolution criterion

A basic problem in molecular biology is to rebuild phylogenetic trees from a set of DNA or protein sequences. Among different criteria used for this purpose, the minimum evolution criterion is an optimality based criterion aiming to rebuild phylogenetic trees characterized by a minimal length. This problem is known to be NP-hard. We introduce in this paper some mixed integer programming models, and we also study possible cuts and lower bounds for the optimal value. So far, the number of sequences that can be involved in optimal phylogenetic reconstruction is still limited to 10.