{"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/self-adjusting-population-sizes-for-the-1-l","title":"Self-adjusting Population Sizes for the $(1, λ)$-EA on Monotone Functions","arxiv_id":"2204.00531","date":"2022-04-01","proceeding":null,"authors":["Marc Kaufmann","Maxime Larcher","Johannes Lengler","Xun Zou"],"abstract":"We study the $(1,\\lambda)$-EA with mutation rate $c/n$ for $c\\le 1$, where the population size is adaptively controlled with the $(1:s+1)$-success rule. Recently, Hevia Fajardo and Sudholt have shown that this setup with $c=1$ is efficient on \\onemax for $s<1$, but inefficient if $s \\ge 18$. Surprisingly, the hardest part is not close to the optimum, but rather at linear distance. We show that this behavior is not specific to \\onemax. If $s$ is small, then the algorithm is efficient on all monotone functions, and if $s$ is large, then it needs superpolynomial time on all monotone functions. In the former case, for $c<1$ we show a $O(n)$ upper bound for the number of generations and $O(n\\log n)$ for the number of function evaluations, and for $c=1$ we show $O(n\\log n)$ generations and $O(n^2\\log\\log n)$ evaluations. We also show formally that optimization is always fast, regardless of $s$, if the algorithm starts in proximity of the optimum. All results also hold in a dynamic environment where the fitness function changes in each generation.","url_abs":"https://arxiv.org/abs/2204.00531v2","url_pdf":"https://arxiv.org/pdf/2204.00531v2.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":"self-adjusting-population-sizes-for-the-1-l","repo_url":"https://github.com/zuxu/onelambdaea","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":0,"framework":"none","reach":null}],"tasks":[],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":null,"mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}