Merge Non-Dominated Sorting Algorithm for Many-Objective Optimization
This work addresses efficiency bottlenecks for researchers and practitioners using Pareto-based evolutionary algorithms in many-objective optimization problems.
The paper tackles the computational cost of non-dominated sorting in many-objective optimization by introducing the Merge Non-Dominated Sorting (MNDS) algorithm, which achieves best-case complexity of Θ(NlogN) and outperforms state-of-the-art techniques in comparisons and running time.
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 $Θ(NlogN)$ and a worst computational complexity of $Θ(MN^2)$. 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.