The median problem is significantly applied to derive
the most reasonable rearrangement phylogenetic tree for many
species. More specifically, the problem is concerned with finding
a permutation that minimizes the sum of distances between itself
and a set of three signed permutations. Genomes with equal number
of genes but different order can be represented as permutations.
In this paper, an algorithm, namely BeamGA median, is proposed
that combines a heuristic search approach (local beam) as an
initialization step to generate a number of solutions, and then a
Genetic Algorithm (GA) is applied in order to refine the solutions,
aiming to achieve a better median with the smallest possible reversal
distance from the three original permutations. In this approach,
any genome rearrangement distance can be applied. In this paper,
we use the reversal distance. To the best of our knowledge, the
proposed approach was not applied before for solving the median
problem. Our approach considers true biological evolution scenario
by applying the concept of common intervals during the GA
optimization process. This allows us to imitate a true biological
behavior and enhance genetic approach time convergence. We were
able to handle permutations with a large number of genes, within
an acceptable time performance and with same or better accuracy as
compared to existing algorithms.
Median problem, phylogenetic tree, permutation,
genetic algorithm, beam search, genome rearrangement distance.