Heuristics for the Sorting by Length-Weighted Inversions Problem on Signed Permutations

Genome Rearrangement is a field that addresses the problem of finding the minimum number of global operations that transform a given genome into another. In this work, we deal with inversion events, which occur when a segment of DNA sequence in the genome is reversed. In our model, each inversion costs the number of elements in the reversed segment. We present a new heuristic for this problem and we show that our method outperforms a previous approach. Our method uses the metaheuristic called Greedy Randomized Adaptive Search Procedure (GRASP) that has been routinely used to find solutions for combinatorial optimization problems. In essence, we implemented an iterative process in which each iteration receives a feasible solution whose neighborhood is investigated for a better solution. We use as initial solution a sequence of inversions of minimum length when each inversion costs one unit, which is a problem that already has several polynomial time algorithms. In almost every case, we were able to improve that initial solution by providing a less-costly sequence of inversions.