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It is well known that the performance of EAs may depend drastically on these parameters. Recent theoretical studies have shown that self-adjusting parameter control mechanisms that tune parameters during the algorithm run can provably outperform the best static parameters in EAs on discrete problems. However, the majority of these studies concerned elitist EAs and we do not have a clear answer on whether the same mechanisms can be applied for non-elitist EAs. We study one of the best-known parameter control mechanisms, the one-fifth success rule, to control the offspring population size\u00a0<jats:inline-formula><jats:alternatives><jats:tex-math>$$\\lambda $$<\/jats:tex-math><mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n                  <mml:mi>\u03bb<\/mml:mi>\n                <\/mml:math><\/jats:alternatives><\/jats:inline-formula> in the non-elitist <jats:inline-formula><jats:alternatives><jats:tex-math>$${(1,\\lambda )}$$<\/jats:tex-math><mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n                  <mml:mrow>\n                    <mml:mo>(<\/mml:mo>\n                    <mml:mn>1<\/mml:mn>\n                    <mml:mo>,<\/mml:mo>\n                    <mml:mi>\u03bb<\/mml:mi>\n                    <mml:mo>)<\/mml:mo>\n                  <\/mml:mrow>\n                <\/mml:math><\/jats:alternatives><\/jats:inline-formula>\u00a0EA. It is known that the <jats:inline-formula><jats:alternatives><jats:tex-math>$${(1,\\lambda )}$$<\/jats:tex-math><mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n                  <mml:mrow>\n                    <mml:mo>(<\/mml:mo>\n                    <mml:mn>1<\/mml:mn>\n                    <mml:mo>,<\/mml:mo>\n                    <mml:mi>\u03bb<\/mml:mi>\n                    <mml:mo>)<\/mml:mo>\n                  <\/mml:mrow>\n                <\/mml:math><\/jats:alternatives><\/jats:inline-formula>\u00a0EA has a sharp threshold with respect to the choice of\u00a0<jats:inline-formula><jats:alternatives><jats:tex-math>$$\\lambda $$<\/jats:tex-math><mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n                  <mml:mi>\u03bb<\/mml:mi>\n                <\/mml:math><\/jats:alternatives><\/jats:inline-formula> where the expected runtime on the benchmark function <jats:sc>OneMax<\/jats:sc> changes from polynomial to exponential time. Hence, it is not clear whether parameter control mechanisms are able to find and maintain suitable values of\u00a0<jats:inline-formula><jats:alternatives><jats:tex-math>$$\\lambda $$<\/jats:tex-math><mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n                  <mml:mi>\u03bb<\/mml:mi>\n                <\/mml:math><\/jats:alternatives><\/jats:inline-formula>. For <jats:sc>OneMax<\/jats:sc> we show that the answer crucially depends on the success rate\u00a0<jats:italic>s<\/jats:italic> (i.\u00a0e. a one-<jats:inline-formula><jats:alternatives><jats:tex-math>$$(s+1)$$<\/jats:tex-math><mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n                  <mml:mrow>\n                    <mml:mo>(<\/mml:mo>\n                    <mml:mi>s<\/mml:mi>\n                    <mml:mo>+<\/mml:mo>\n                    <mml:mn>1<\/mml:mn>\n                    <mml:mo>)<\/mml:mo>\n                  <\/mml:mrow>\n                <\/mml:math><\/jats:alternatives><\/jats:inline-formula>-th success rule). We prove that, if the success rate is appropriately small, the self-adjusting <jats:inline-formula><jats:alternatives><jats:tex-math>$${(1,\\lambda )}$$<\/jats:tex-math><mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n                  <mml:mrow>\n                    <mml:mo>(<\/mml:mo>\n                    <mml:mn>1<\/mml:mn>\n                    <mml:mo>,<\/mml:mo>\n                    <mml:mi>\u03bb<\/mml:mi>\n                    <mml:mo>)<\/mml:mo>\n                  <\/mml:mrow>\n                <\/mml:math><\/jats:alternatives><\/jats:inline-formula>\u00a0EA optimises <jats:sc>OneMax<\/jats:sc> in <jats:italic>O<\/jats:italic>(<jats:italic>n<\/jats:italic>) expected generations and <jats:inline-formula><jats:alternatives><jats:tex-math>$$O(n \\log n)$$<\/jats:tex-math><mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n                  <mml:mrow>\n                    <mml:mi>O<\/mml:mi>\n                    <mml:mo>(<\/mml:mo>\n                    <mml:mi>n<\/mml:mi>\n                    <mml:mo>log<\/mml:mo>\n                    <mml:mi>n<\/mml:mi>\n                    <mml:mo>)<\/mml:mo>\n                  <\/mml:mrow>\n                <\/mml:math><\/jats:alternatives><\/jats:inline-formula> expected evaluations, the best possible runtime for any unary unbiased black-box algorithm. A small success rate is crucial: we also show that if the success rate is too large, the algorithm has an exponential runtime on <jats:sc>OneMax<\/jats:sc> and other functions with similar characteristics.\n<\/jats:p>","DOI":"10.1007\/s00453-023-01153-9","type":"journal-article","created":{"date-parts":[[2023,7,24]],"date-time":"2023-07-24T12:02:31Z","timestamp":1690200151000},"page":"526-565","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":5,"title":["Self-adjusting Population Sizes for Non-elitist Evolutionary Algorithms: Why Success Rates Matter"],"prefix":"10.1007","volume":"86","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-3529-0434","authenticated-orcid":false,"given":"Mario Alejandro","family":"Hevia Fajardo","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-6020-1646","authenticated-orcid":false,"given":"Dirk","family":"Sudholt","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"297","published-online":{"date-parts":[[2023,7,24]]},"reference":[{"key":"1153_CR1","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-662-44874-8","volume-title":"Introduction to Evolutionary Computing","author":"AE Eiben","year":"2015","unstructured":"Eiben, A.E., Smith, J.E.: Introduction to Evolutionary Computing, 2nd edn. 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