  Many Pareto-based multi-objective evolutionary algorithms require to rank the
solutions of the population in each iteration according to the dominance
principle, what can become a costly operation particularly in the case of
dealing with many-objective optimization problems. In this paper, we present a
new efficient algorithm for computing the non-dominated sorting procedure,
called Merge Non-Dominated Sorting (MNDS), which has a best computational
complexity of $\Theta(NlogN)$ and a worst computational complexity of
$\Theta(MN^2)$. Our approach is based on the computation of the dominance set
of each solution by taking advantage of the characteristics of the merge sort
algorithm. We compare the MNDS against four well-known techniques that can be
considered as the state-of-the-art. The results indicate that the MNDS
algorithm outperforms the other techniques in terms of number of comparisons as
well as the total running time.
