Merge Non-Dominated Sorting Algorithm for Many-Objective Optimization

TL;DR

This paper introduces Merge Non-Dominated Sorting (MNDS), an efficient algorithm for ranking solutions in many-objective optimization that outperforms existing methods in speed and comparison count.

Contribution

The paper presents MNDS, a novel non-dominated sorting algorithm with improved computational complexity leveraging merge sort characteristics for many-objective problems.

Findings

MNDS has a best-case complexity of Θ(NlogN).

MNDS outperforms four state-of-the-art techniques in comparisons and runtime.

MNDS is effective for large-scale many-objective optimization problems.

Abstract

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.