Sorting Permutations by Reversals through a Hybrid Genetic Algorithm based on Breakpoint Elimination and Exact Solutions for Signed Permutations

Abstract

Abstract—Sorting permutations by reversals is one of the most challenging problems related with the analysis of the evolutionary distance between organisms. Genome rearrangement can be done through several operations with biological significance, such as block interchange, transposition and reversal, among others; but sorting by reversals, that consists in finding the shortest sequence of reversals to transform one genome into another, came arise as one of the most challenging problems from the combinatorial and algebraic points of view. In fact, sorting by reversal unsigned permutations is a N P-hard problem, for which the question of N P-completeness remains open for more than two decades and for which several interesting combinatorial questions, such as the average number of reversals needed to sort permutations of the same size, remain without solution. In contrast to the unsigned case, sorting by reversals signe