{"paper":{"title":"The Runtime of the Compact Genetic Algorithm on Jump Functions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.DS"],"primary_cat":"cs.NE","authors_text":"Benjamin Doerr","submitted_at":"2019-08-18T22:45:18Z","abstract_excerpt":"In the first and so far only mathematical runtime analysis of an estimation-of-distribution algorithm (EDA) on a multimodal problem, Hasen\\\"ohrl and Sutton (GECCO 2018) showed for any $k = o(n)$ that the compact genetic algorithm (cGA) with any hypothetical population size $\\mu = \\Omega(ne^{4k} + n^{3.5+\\varepsilon})$ with high probability finds the optimum of the $n$-dimensional jump function with jump size $k$ in time $O(\\mu n^{1.5} \\log n)$.\n  We significantly improve this result for small jump sizes $k \\le \\frac 1 {20} \\ln n -1$. In this case, already for $\\mu = \\Omega(\\sqrt n \\log n) \\cap"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1908.06527","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/1908.06527/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}