{"paper":{"title":"A General Dichotomy of Evolutionary Algorithms on Monotone Functions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.NE","authors_text":"Johannes Lengler","submitted_at":"2018-03-25T10:33:25Z","abstract_excerpt":"It is known that the evolutionary algorithm $(1+1)$-EA with mutation rate $c/n$ optimises every monotone function efficiently if $c<1$, and needs exponential time on some monotone functions (HotTopic functions) if $c\\geq 2.2$. We study the same question for a large variety of algorithms, particularly for $(1+\\lambda)$-EA, $(\\mu+1)$-EA, $(\\mu+1)$-GA, their fast counterparts like fast $(1+1)$-EA, and for $(1+(\\lambda,\\lambda))$-GA. We find that all considered mutation-based algorithms show a similar dichotomy for HotTopic functions, or even for all monotone functions. For the $(1+(\\lambda,\\lambd"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1803.09227","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}