{"paper":{"title":"The quasispecies regime for the simple genetic algorithm with ranking selection","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.NE"],"primary_cat":"math.PR","authors_text":"Rapha\\\"el Cerf","submitted_at":"2014-03-21T11:45:05Z","abstract_excerpt":"We study the simple genetic algorithm with a ranking selection mechanism (linear ranking or tournament). We denote by $\\ell$ the length of the chromosomes, by $m$ the population size, by $p_C$ the crossover probability and by $p_M$ the mutation probability. We introduce a parameter $\\sigma$, called the selection drift, which measures the selection intensity of the fittest chromosome. We show that the dynamics of the genetic algorithm depend in a critical way on the parameter $$\\pi \\,=\\,\\sigma(1-p_C)(1-p_M)^\\ell\\,.$$ If $\\pi<1$, then the genetic algorithm operates in a disordered regime: an adv"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1403.5427","kind":"arxiv","version":1},"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"}