{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,6,9]],"date-time":"2025-06-09T11:10:08Z","timestamp":1749467408089,"version":"3.41.0"},"reference-count":30,"publisher":"Springer Science and Business Media LLC","issue":"3","license":[{"start":{"date-parts":[[2025,6,1]],"date-time":"2025-06-01T00:00:00Z","timestamp":1748736000000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"},{"start":{"date-parts":[[2025,6,1]],"date-time":"2025-06-01T00:00:00Z","timestamp":1748736000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["J Syst Sci Complex"],"published-print":{"date-parts":[[2025,6]]},"DOI":"10.1007\/s11424-025-4261-x","type":"journal-article","created":{"date-parts":[[2025,6,9]],"date-time":"2025-06-09T10:45:35Z","timestamp":1749465935000},"page":"1092-1108","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Runtime Analysis in Non-Elitist Evolutionary Algorithms via Population Distribution"],"prefix":"10.1007","volume":"38","author":[{"given":"Xuanming","family":"Ni","sequence":"first","affiliation":[]},{"given":"Qiaochu","family":"Zhao","sequence":"additional","affiliation":[]},{"given":"Song","family":"Huang","sequence":"additional","affiliation":[]},{"given":"Lian","family":"Yu","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2025,6,9]]},"reference":[{"key":"4261_CR1","doi-asserted-by":"publisher","first-page":"47","DOI":"10.1007\/s00453-002-0940-2","volume":"34","author":"T Jansen","year":"2002","unstructured":"Jansen T and Wegener I, The analysis of evolutionary algorithms \u2014 A proof that crossover really can help, Algorithmica, 2002, 34: 47\u201366.","journal-title":"Algorithmica"},{"key":"4261_CR2","volume-title":"Genetic Algorithms in Search, Optimization and Machine Learning","author":"D E Goldberg","year":"1989","unstructured":"Goldberg D E, Genetic Algorithms in Search, Optimization and Machine Learning, Addison-Wesley Longman Publishing Co., Inc., USA, 1989."},{"issue":"2","key":"4261_CR3","doi-asserted-by":"publisher","first-page":"185","DOI":"10.1162\/evco.1998.6.2.185","volume":"6","author":"S Droste","year":"1998","unstructured":"Droste S, Jansen T, and Wegener I, A rigorous complexity analysis of the (1 + 1) evolutionary algorithm for separable functions with boolean inputs, Evolutionary Computation, 1998, 6(2): 185\u2013196.","journal-title":"Evolutionary Computation"},{"issue":"1\u20132","key":"4261_CR4","doi-asserted-by":"publisher","first-page":"51","DOI":"10.1016\/S0304-3975(01)00182-7","volume":"276","author":"S Droste","year":"2002","unstructured":"Droste S, Jansen T, and Wegener I, On the analysis of the (1 + 1) evolutionary algorithm, Theoretical Computer Science, 2002, 276(1\u20132): 51\u201381.","journal-title":"Theoretical Computer Science"},{"issue":"2","key":"4261_CR5","doi-asserted-by":"publisher","first-page":"173","DOI":"10.1162\/evco.1999.7.2.173","volume":"7","author":"J Garnier","year":"1999","unstructured":"Garnier J, Kallel L, and Schoenauer M, Rigorous hitting times for binary mutations, Evolutionary Computation, 1999, 7(2): 173\u2013203.","journal-title":"Evolutionary Computation"},{"issue":"5","key":"4261_CR6","doi-asserted-by":"publisher","first-page":"495","DOI":"10.1109\/TEVC.2002.800886","volume":"6","author":"J He","year":"2002","unstructured":"He J and Yao X, From an individual to a population: An analysis of the first hitting time of population-based evolutionary algorithms, IEEE Transactions on Evolutionary Computation, 2002, 6(5): 495\u2013511.","journal-title":"IEEE Transactions on Evolutionary Computation"},{"issue":"1","key":"4261_CR7","first-page":"65","volume":"14","author":"C Witt","year":"2006","unstructured":"Witt C, Runtime analysis of the (\u03bc + 1) EA on simple pseudo-boolean functions, Evolutionary Computation, 2006, 14(1): 65\u201386.","journal-title":"Evolutionary Computation"},{"issue":"1","key":"4261_CR8","doi-asserted-by":"publisher","first-page":"57","DOI":"10.1016\/S0004-3702(01)00058-3","volume":"127","author":"J He","year":"2001","unstructured":"He J and Yao X, Drift analysis and average time complexity of evolutionary algorithms, Artificial Intelligence, 2001, 127(1): 57\u201385.","journal-title":"Artificial Intelligence"},{"key":"4261_CR9","doi-asserted-by":"publisher","first-page":"21","DOI":"10.1023\/B:NACO.0000023417.31393.c7","volume":"3","author":"J He","year":"2004","unstructured":"He J and Yao X, A study of drift analysis for estimating computation time of evolutionary algorithms, Natural Computing, 2004, 3: 21\u201335.","journal-title":"Natural Computing"},{"key":"4261_CR10","volume-title":"International Conference on Parallel Problem Solving from Nature","author":"P K Lehre","year":"2010","unstructured":"Lehre P K, Negative drift in populations, International Conference on Parallel Problem Solving from Nature, Eds. by Schaefer R, Cotta C, Ko\u0142odziej J, et al., Berlin, Heidelberg, 2010."},{"key":"4261_CR11","doi-asserted-by":"publisher","first-page":"224","DOI":"10.1007\/s00453-011-9585-3","volume":"65","author":"B Doerr","year":"2013","unstructured":"Doerr B and Goldberg L A, Adaptive drift analysis, Algorithmica, 2013, 65: 224\u2013250.","journal-title":"Algorithmica"},{"issue":"3","key":"4261_CR12","doi-asserted-by":"publisher","first-page":"502","DOI":"10.2307\/1426671","volume":"14","author":"B Hajek","year":"1982","unstructured":"Hajek B, Hitting-time and occupation-time bounds implied by drift analysis with applications, Advances in Applied probability, 1982, 14(3): 502\u2013525.","journal-title":"Advances in Applied probability"},{"issue":"5","key":"4261_CR13","doi-asserted-by":"publisher","first-page":"1092","DOI":"10.1109\/TSMCB.2008.2012167","volume":"39","author":"T Chen","year":"2009","unstructured":"Chen T, He J, Sun G, et al., A new approach for analyzing average time complexity of population-based evolutionary algorithms on unimodal problems, IEEE Transactions on Systems, Man, and Cybernetics, Part B (Cybernetics), 2009, 39(5): 1092\u20131106.","journal-title":"IEEE Transactions on Systems, Man, and Cybernetics, Part B (Cybernetics)"},{"issue":"5","key":"4261_CR14","doi-asserted-by":"publisher","first-page":"707","DOI":"10.1109\/TEVC.2017.2753538","volume":"22","author":"D Corus","year":"2017","unstructured":"Corus D, Dang D C, Eremeev A V, et al., Level-based analysis of genetic algorithms and other search processes, IEEE Transactions on Evolutionary Computation, 2017, 22(5): 707\u2013719.","journal-title":"IEEE Transactions on Evolutionary Computation"},{"issue":"3","key":"4261_CR15","doi-asserted-by":"publisher","first-page":"418","DOI":"10.1109\/TEVC.2012.2202241","volume":"17","author":"D Sudholt","year":"2012","unstructured":"Sudholt D, A new method for lower bounds on the running time of evolutionary algorithms, IEEE Transactions on Evolutionary Computation, 2012, 17(3): 418\u2013435.","journal-title":"IEEE Transactions on Evolutionary Computation"},{"issue":"6","key":"4261_CR16","doi-asserted-by":"publisher","first-page":"777","DOI":"10.1109\/TEVC.2014.2378891","volume":"19","author":"Y Yu","year":"2014","unstructured":"Yu Y, Qian C, and Zhou Z H, Switch analysis for running time analysis of evolutionary algorithms, IEEE Transactions on Evolutionary Computation, 2014, 19(6): 777\u2013792.","journal-title":"IEEE Transactions on Evolutionary Computation"},{"key":"4261_CR17","doi-asserted-by":"publisher","first-page":"673","DOI":"10.1007\/s00453-012-9622-x","volume":"64","author":"B Doerr","year":"2012","unstructured":"Doerr B, Johannsen D, and Winzen C, Multiplicative drift analysis, Algorithmica, 2012, 64: 673\u2013697.","journal-title":"Algorithmica"},{"key":"4261_CR18","volume-title":"Methods for the Analysis of Evolutionary Algorithms on Pseudo-Boolean Functions","author":"R Sarker","year":"2002","unstructured":"Sarker R, Mohammadian M, Yao X, et al., Methods for the Analysis of Evolutionary Algorithms on Pseudo-Boolean Functions, Springer, Boston, MA, 2002."},{"key":"4261_CR19","doi-asserted-by":"publisher","first-page":"587","DOI":"10.1007\/s00453-016-0214-z","volume":"78","author":"C Gie\u00dfen","year":"2017","unstructured":"Gie\u00dfen C and Witt C, The interplay of population size and mutation probability in the (1 + \u03bb) EA on onemax, Algorithmica, 2017, 78: 587\u2013609.","journal-title":"Algorithmica"},{"issue":"6","key":"4261_CR20","doi-asserted-by":"publisher","first-page":"1659","DOI":"10.1007\/s00453-021-00896-7","volume":"84","author":"B Doerr","year":"2022","unstructured":"Doerr B, Does comma selection help to cope with local optima?, Algorithmica, 2022, 84(6): 1659\u20131693.","journal-title":"Algorithmica"},{"issue":"5","key":"4261_CR21","doi-asserted-by":"publisher","first-page":"720","DOI":"10.1109\/TEVC.2017.2745715","volume":"22","author":"D Corus","year":"2017","unstructured":"Corus D and Oliveto P S, Standard steady state genetic algorithms can hillclimb faster than mutation-only evolutionary algorithms, IEEE Transactions on Evolutionary Computation, 2017, 22(5): 720\u2013732.","journal-title":"IEEE Transactions on Evolutionary Computation"},{"issue":"3","key":"4261_CR22","doi-asserted-by":"publisher","first-page":"484","DOI":"10.1109\/TEVC.2017.2724201","volume":"22","author":"D C Dang","year":"2017","unstructured":"Dang D C, Friedrich T, Kotzing T, et al., Escaping local optima using crossover with emergent diversity, IEEE Transactions on Evolutionary Computation, 2017, 22(3): 484\u2013497.","journal-title":"IEEE Transactions on Evolutionary Computation"},{"key":"4261_CR23","volume-title":"Proceedings of the 13th Annual Conference on Genetic and Evolutionary Computation","author":"T Kotzing","year":"2011","unstructured":"Kotzing T, Sudholt D, and Theile M, How crossover helps in pseudo-boolean optimization?, Proceedings of the 13th Annual Conference on Genetic and Evolutionary Computation, Dublin, Ireland, 2011."},{"issue":"2","key":"4261_CR24","doi-asserted-by":"publisher","first-page":"237","DOI":"10.1162\/EVCO_a_00171","volume":"25","author":"D Sudholt","year":"2017","unstructured":"Sudholt D, How crossover speeds up building block assembly in genetic algorithms?, Evolutionary Computation, 2017, 25(2): 237\u2013274.","journal-title":"Evolutionary Computation"},{"key":"4261_CR25","volume-title":"International Conference on Parallel Problem Solving from Nature","author":"D C Dang","year":"2016","unstructured":"Dang D C, Friedrich T, K\u00f6tzing T, et al., Emergence of diversity and its benefits for crossover in genetic algorithms, International Conference on Parallel Problem Solving from Nature, Cham, 2016."},{"issue":"2","key":"4261_CR26","doi-asserted-by":"publisher","first-page":"111","DOI":"10.1007\/BF00203032","volume":"63","author":"D B Fogel","year":"1990","unstructured":"Fogel D B and Atmar J W, Comparing genetic operators with Gaussian mutations in simulated evolutionary processes using linear systems, Biological Cybernetics, 1990, 63(2): 111\u2013114.","journal-title":"Biological Cybernetics"},{"key":"4261_CR27","first-page":"221","volume-title":"Foundations of Genetic Algorithms","author":"W M Spears","year":"1993","unstructured":"Spears W M, Crossover or mutation?, Foundations of Genetic Algorithms, Elsevier, 1993, 2: 221\u2013237."},{"issue":"6","key":"4261_CR28","doi-asserted-by":"publisher","first-page":"1050","DOI":"10.1109\/TEVC.2019.2917275","volume":"24","author":"J Arabas","year":"2019","unstructured":"Arabas J and Opara K, Population diversity of nonelitist evolutionary algorithms in the exploration phase, IEEE Transactions on Evolutionary Computation, 2019, 24(6): 1050\u20131062.","journal-title":"IEEE Transactions on Evolutionary Computation"},{"issue":"5","key":"4261_CR29","doi-asserted-by":"publisher","first-page":"1165","DOI":"10.1109\/72.623217","volume":"8","author":"Y Leung","year":"1997","unstructured":"Leung Y, Gao Y, and Xu Z B, Degree of population diversity \u2014 A perspective on premature convergence in genetic algorithms and its Markov chain analysis, IEEE Transactions on Neural Networks, 1997, 8(5): 1165\u20131176.","journal-title":"IEEE Transactions on Neural Networks"},{"key":"4261_CR30","volume-title":"Theory of Evolutionary Computation: Recent Developments in Discrete Optimization","author":"D Sudholt","year":"2020","unstructured":"Sudholt D, The benefits of population diversity in evolutionary algorithms: A survey of rigorous runtime analyses, Theory of Evolutionary Computation: Recent Developments in Discrete Optimization, Cham, 2020."}],"container-title":["Journal of Systems Science and Complexity"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s11424-025-4261-x.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s11424-025-4261-x\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s11424-025-4261-x.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,6,9]],"date-time":"2025-06-09T10:45:38Z","timestamp":1749465938000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s11424-025-4261-x"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2025,6]]},"references-count":30,"journal-issue":{"issue":"3","published-print":{"date-parts":[[2025,6]]}},"alternative-id":["4261"],"URL":"https:\/\/doi.org\/10.1007\/s11424-025-4261-x","relation":{},"ISSN":["1009-6124","1559-7067"],"issn-type":[{"value":"1009-6124","type":"print"},{"value":"1559-7067","type":"electronic"}],"subject":[],"published":{"date-parts":[[2025,6]]},"assertion":[{"value":"12 June 2024","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"8 July 2024","order":2,"name":"revised","label":"Revised","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"9 June 2025","order":3,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"The authors declare no conflict of interest.","order":1,"name":"Ethics","group":{"name":"EthicsHeading","label":"Conflict of Interest"}}]}}