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.

非支配排序因其用于解决多目标和多目标优化问题而引起了研究界的广泛关注。近年来，已经提出了几种用于非主导排序的方法。在本文中，我们开发了一个非主导的排序框架，即DCNSRC（基于分而治之的非主导排序，具有简化的比较）。在此框架的基础上，通过改变搜索技术提出了两种方法。与各种其他方法相比，这些方法执行的优势比较次数更少。重复的解决方案也得到有效处理。这些方法在比较两个解决方案时可以节省各种比较。通过一些理论分析验证了所提出的方法。理论上，在最坏的情况和最佳的情况下，在三种不同的情况下分析了所提出的框架执行的优势比较的次数。综合数据集和基准问题的实验结果表明，该方法优于最新算法。