Memetic algorithm for sorting unsigned permutations by reversals

Sorting by reversals unsigned permutations is a problem exhaustively studied in the fields of combinatorics of permutations and bioinformatics with crucial applications in the analysis of evolutionary distance between organisms. This problem was shown to be NP-hard, which gave rise to the development of a series of approximation and heuristic algorithms. Among these approaches, evolutionary algorithms were also proposed, from which to the best of our knowledge a parallel version of the first proposed genetic algorithm computes the highest quality results. These solutions were not optimized for the case when the population reaches a degenerate state, that is when individuals of the population remain very similar, and the procedure still continues consuming computational resources, but without improving the individuals. In this paper, a memetic algorithm is proposed for sorting unsigned permutations by reversals, using the local search as a way to improve the fitness function image of the individuals. Also, the entropy of the population is controlled, such that, when a degenerate state is reached the population is restarted. Several experiments were performed using permutations generated from biological data as well as hundreds of randomly generated permutations of different size, from which some ones were chosen and used as benchmark permutations. Experiments have shown that the proposed memetic algorithm uses more adequately the computational resources and gives competitive results in comparison with the parallel genetic algorithm and outperforms the results of the standard genetic algorithm.