{"about":{"site":"https://codewithpapers.app","non_affiliation":"Code with Papers and Syntology are not affiliated with, endorsed by, or sponsored by Papers with Code, Meta, or the pwc-archive mirror.","licence":"CC BY-SA 4.0","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","attribution":"https://codewithpapers.app/attribution","modified":"archive material modified by Syntology; see the attribution page"},"url":"/paper/merge-non-dominated-sorting-algorithm-for","title":"Merge Non-Dominated Sorting Algorithm for Many-Objective Optimization","arxiv_id":"1809.06106","date":"2018-09-17","proceeding":null,"authors":["Javier Moreno","Daniel Rodriguez","Antonio Nebro","Jose A. Lozano"],"abstract":"Many Pareto-based multi-objective evolutionary algorithms require to rank the\nsolutions of the population in each iteration according to the dominance\nprinciple, what can become a costly operation particularly in the case of\ndealing with many-objective optimization problems. In this paper, we present a\nnew efficient algorithm for computing the non-dominated sorting procedure,\ncalled Merge Non-Dominated Sorting (MNDS), which has a best computational\ncomplexity of $\\Theta(NlogN)$ and a worst computational complexity of\n$\\Theta(MN^2)$. Our approach is based on the computation of the dominance set\nof each solution by taking advantage of the characteristics of the merge sort\nalgorithm. We compare the MNDS against four well-known techniques that can be\nconsidered as the state-of-the-art. The results indicate that the MNDS\nalgorithm outperforms the other techniques in terms of number of comparisons as\nwell as the total running time.","url_abs":"http://arxiv.org/abs/1809.06106v1","url_pdf":"http://arxiv.org/pdf/1809.06106v1.pdf","source":{"archive":"pwc-archive (Hugging Face), CC BY-SA 4.0","snapshot":"2025-07-28","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","row_kind":"abstracts"},"code_links":[{"paper_slug":"merge-non-dominated-sorting-algorithm-for","repo_url":"https://github.com/jMetal/jMetal","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"none","reach":null}],"tasks":[{"task_slug":"evolutionary-algorithms","task_name":"Evolutionary Algorithms"}],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":null,"mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}