{"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/speeding-up-the-nsga-ii-with-a-simple-tie","title":"Speeding Up the NSGA-II With a Simple Tie-Breaking Rule","arxiv_id":"2412.11931","date":"2024-12-16","proceeding":null,"authors":["Benjamin Doerr","Tudor Ivan","Martin S. Krejca"],"abstract":"The non-dominated sorting genetic algorithm~II (NSGA-II) is the most popular multi-objective optimization heuristic. Recent mathematical runtime analyses have detected two shortcomings in discrete search spaces, namely, that the NSGA-II has difficulties with more than two objectives and that it is very sensitive to the choice of the population size. To overcome these difficulties, we analyze a simple tie-breaking rule in the selection of the next population. Similar rules have been proposed before, but have found only little acceptance. We prove the effectiveness of our tie-breaking rule via mathematical runtime analyses on the classic OneMinMax, LeadingOnesTrailingZeros, and OneJumpZeroJump benchmarks. We prove that this modified NSGA-II can optimize the three benchmarks efficiently also for many objectives, in contrast to the exponential lower runtime bound previously shown for OneMinMax with three or more objectives. For the bi-objective problems, we show runtime guarantees that do not increase when moderately increasing the population size over the minimum admissible size. For example, for the OneJumpZeroJump problem with representation length $n$ and gap parameter $k$, we show a runtime guarantee of $O(\\max\\{n^{k+1},Nn\\})$ function evaluations when the population size is at least four times the size of the Pareto front. For population sizes larger than the minimal choice $N = \\Theta(n)$, this result improves considerably over the $\\Theta(Nn^k)$ runtime of the classic NSGA-II.","url_abs":"https://arxiv.org/abs/2412.11931v2","url_pdf":"https://arxiv.org/pdf/2412.11931v2.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":"speeding-up-the-nsga-ii-with-a-simple-tie","repo_url":"https://zenodo.org/record/14501034","is_official":1,"mentioned_in_paper":0,"mentioned_in_github":0,"framework":"none","reach":null}],"tasks":[],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"syntology_url":null,"atlas_url":"https://app.syntology.ai/?focus=2412.11931","mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}