{"paper":{"title":"Improved Runtime Bound for the $(\\mu + 1)$ EA on BinVal","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.NE","authors_text":"Johannes Lengler, Joris Belder, Raghu Raman Ravi","submitted_at":"2026-06-11T13:34:03Z","abstract_excerpt":"We study the $(\\mu+1)$ EA on the Binary Value function BinVal. We show that it needs at most $O(\\mu \\log \\mu \\cdot n \\log n)$ function evaluations to find the optimum when $\\mu = o(n/\\log n)$. This substantially improves upon the recent upper bound of $O(\\mu^5 n \\log(n/\\mu^4))$ by Krejca, Neumann and Witt. Our results hold for several mutation operators including standard bit mutation. In particular, our bound implies that the $(\\mu+1)$ EA is at most a factor $O(\\log \\mu \\cdot \\log n)$ slower on BinVal than on OneMax."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.13344","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2606.13344/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"}