Optimal solutions for the balanced minimum evolution problem

In this paper, we investigate one of the most significant versions of the PEP, called the balanced minimum evolution problem. We propose an exact algorithm based on the enumeration of non-isomorphic trees and the subsequent solution of quadratic assignment problems. Furthermore, by exploiting the underlying parallelism of the algorithm, we present a parallel version of the algorithm which shows a linear speed-up with respect to the sequential version. Extensive computational results prove the effectiveness of the proposed algorithms.