Divide-and-conquer based non-dominated sorting with Reduced Comparisons

Non-dominated sorting has attracted a lot of attention of the research community due to its use in solving multi- and many-objective optimization problems. In recent years, several approaches for non-dominated sorting have been proposed. In this paper, we have developed a non-dominated sorting framework, namely DCNSRC (Divide-and-Conquer based Non-dominated Sorting with Reduced Comparisons). Based on this framework, two approaches have been proposed by varying the search technique. These approaches perform a lower number of dominance comparisons than various other approaches. The duplicate solutions are also handled efficiently. These approaches save various comparisons while comparing the two solutions. The proposed approaches are validated using some theoretical analyses. The number of dominance comparisons performed by the proposed framework are theoretically analyzed in three different scenarios, both in the worst and the best cases. Experimental results on synthetic datasets and the benchmark problems show the superiority of the proposed approach over state-of-the-art algorithms.