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Optim."],"published-print":{"date-parts":[[2022,12,31]]},"abstract":"<jats:p>\n            The self-adjusting (1\u00a0+\u00a0(\u03bb, \u03bb)) GA is the best known genetic algorithm for problems with a good fitness-distance correlation as in\n            <jats:sc>OneMax<\/jats:sc>\n            . It uses a parameter control mechanism for the parameter\u00a0\u03bb that governs the mutation strength and the number of offspring. However, on multimodal problems, the parameter control mechanism tends to increase \u03bb uncontrollably.\n          <\/jats:p>\n          <jats:p>\n            We study this problem for the standard\n            <jats:sc>Jump<\/jats:sc>\n            <jats:sub>\n              <jats:italic>k<\/jats:italic>\n            <\/jats:sub>\n            benchmark problem class using runtime analysis. The self-adjusting (1\u00a0+\u00a0(\u03bb, \u03bb)) GA behaves like a (1\u00a0+\u00a0\n            <jats:italic>n<\/jats:italic>\n            ) \u00a0EA whenever the maximum value for \u03bb is reached. This is ineffective for problems where large jumps are required. Capping \u03bb at smaller values is beneficial for such problems. Finally, resetting \u03bb to 1 allows the parameter to cycle through the parameter space. We show that resets are effective for all\n            <jats:sc>Jump<\/jats:sc>\n            <jats:sub>\n              <jats:italic>k<\/jats:italic>\n            <\/jats:sub>\n            problems: the self-adjusting (1\u00a0+\u00a0(\u03bb, \u03bb)) GA performs as well as the (1\u00a0+\u00a01)\u00a0EA with the optimal mutation rate and evolutionary algorithms with heavy-tailed mutation, apart from a small polynomial overhead.\n          <\/jats:p>\n          <jats:p>\n            Along the way, we present new general methods for translating existing runtime bounds from the (1\u00a0+\u00a01)\u00a0EA to the self-adjusting (1\u00a0+\u00a0(\u03bb, \u03bb)) GA. We also show that the algorithm presents a bimodal parameter landscape with respect to \u03bb on\n            <jats:sc>Jump<\/jats:sc>\n            <jats:sub>\n              <jats:italic>k<\/jats:italic>\n            <\/jats:sub>\n            . For appropriate\n            <jats:italic>n<\/jats:italic>\n            and\n            <jats:italic>k<\/jats:italic>\n            , the landscape features a local optimum in a wide basin of attraction and a global optimum in a narrow basin of attraction. To our knowledge this is the first proof of a bimodal parameter landscape for the runtime of an evolutionary algorithm on a multimodal problem.\n          <\/jats:p>","DOI":"10.1145\/3564755","type":"journal-article","created":{"date-parts":[[2022,9,28]],"date-time":"2022-09-28T11:47:29Z","timestamp":1664365649000},"page":"1-39","update-policy":"https:\/\/doi.org\/10.1145\/crossmark-policy","source":"Crossref","is-referenced-by-count":4,"title":["Theoretical and Empirical Analysis of Parameter Control Mechanisms in the (1\u00a0+\u00a0(\u03bb,\u00a0\u03bb))\u00a0Genetic\u00a0Algorithm"],"prefix":"10.1145","volume":"2","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-3529-0434","authenticated-orcid":false,"given":"Mario Alejandro","family":"Hevia Fajardo","sequence":"first","affiliation":[{"name":"Department of Computer Science, University of Sheffield, Sheffield, United Kingdom"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-6020-1646","authenticated-orcid":false,"given":"Dirk","family":"Sudholt","sequence":"additional","affiliation":[{"name":"Department of Computer Science, University of Sheffield, Sheffield, United Kingdom and Chair of Algorithms for Intelligent Systems, University of Passau, Passau, Germany"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"320","published-online":{"date-parts":[[2023,1,14]]},"reference":[{"key":"e_1_3_2_2_1","doi-asserted-by":"publisher","DOI":"10.1145\/3377930.3390172"},{"key":"e_1_3_2_3_1","doi-asserted-by":"crossref","first-page":"1115","DOI":"10.1145\/3449639.3459377","volume-title":"Proceedings of the Genetic and Evolutionary Computation Conference (GECCO\u201921)","author":"Antipov Denis","year":"2021","unstructured":"Denis Antipov, Maxim Buzdalov, and Benjamin Doerr. 2021. 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