{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,9,18]],"date-time":"2025-09-18T18:48:24Z","timestamp":1758221304212,"version":"3.44.0"},"reference-count":35,"publisher":"Elsevier BV","license":[{"start":{"date-parts":[[2025,11,1]],"date-time":"2025-11-01T00:00:00Z","timestamp":1761955200000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.elsevier.com\/tdm\/userlicense\/1.0\/"},{"start":{"date-parts":[[2025,11,1]],"date-time":"2025-11-01T00:00:00Z","timestamp":1761955200000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.elsevier.com\/legal\/tdmrep-license"},{"start":{"date-parts":[[2025,11,1]],"date-time":"2025-11-01T00:00:00Z","timestamp":1761955200000},"content-version":"stm-asf","delay-in-days":0,"URL":"https:\/\/doi.org\/10.15223\/policy-017"},{"start":{"date-parts":[[2025,11,1]],"date-time":"2025-11-01T00:00:00Z","timestamp":1761955200000},"content-version":"stm-asf","delay-in-days":0,"URL":"https:\/\/doi.org\/10.15223\/policy-037"},{"start":{"date-parts":[[2025,11,1]],"date-time":"2025-11-01T00:00:00Z","timestamp":1761955200000},"content-version":"stm-asf","delay-in-days":0,"URL":"https:\/\/doi.org\/10.15223\/policy-012"},{"start":{"date-parts":[[2025,11,1]],"date-time":"2025-11-01T00:00:00Z","timestamp":1761955200000},"content-version":"stm-asf","delay-in-days":0,"URL":"https:\/\/doi.org\/10.15223\/policy-029"},{"start":{"date-parts":[[2025,11,1]],"date-time":"2025-11-01T00:00:00Z","timestamp":1761955200000},"content-version":"stm-asf","delay-in-days":0,"URL":"https:\/\/doi.org\/10.15223\/policy-004"}],"content-domain":{"domain":["elsevier.com","sciencedirect.com"],"crossmark-restriction":true},"short-container-title":["Applied Soft Computing"],"published-print":{"date-parts":[[2025,11]]},"DOI":"10.1016\/j.asoc.2025.113635","type":"journal-article","created":{"date-parts":[[2025,7,28]],"date-time":"2025-07-28T17:45:07Z","timestamp":1753724707000},"page":"113635","update-policy":"https:\/\/doi.org\/10.1016\/elsevier_cm_policy","source":"Crossref","is-referenced-by-count":0,"special_numbering":"C","title":["Adaptive evolutionary algorithms with linear average convergence rate for optimization problems with Lipschitz continuous functions"],"prefix":"10.1016","volume":"183","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-2217-8518","authenticated-orcid":false,"given":"Fabiano Borges da","family":"Silva","sequence":"first","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0003-4254-1385","authenticated-orcid":false,"given":"L\u00edvia Teresa Minami","family":"Borges","sequence":"additional","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0002-6258-7068","authenticated-orcid":false,"given":"Leonardo","family":"Nepomuceno","sequence":"additional","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0002-7615-5768","authenticated-orcid":false,"given":"Edilaine Martins","family":"Soler","sequence":"additional","affiliation":[]}],"member":"78","reference":[{"key":"10.1016\/j.asoc.2025.113635_b1","doi-asserted-by":"crossref","DOI":"10.1016\/j.rcim.2022.102509","article-title":"A hybrid genetic algorithm with multiple decoding methods for energy-aware remanufacturing system scheduling problem","volume":"81","author":"Wang","year":"2023","journal-title":"Robot. Comput.-Integr. Manuf."},{"key":"10.1016\/j.asoc.2025.113635_b2","doi-asserted-by":"crossref","first-page":"157","DOI":"10.1016\/j.cie.2016.05.006","article-title":"Hybrid genetic algorithm and tabu search for finite capacity material requirement planning system in flexible flow shop with assembly operations","volume":"97","author":"Sukkerd","year":"2016","journal-title":"Comput. Ind. Eng."},{"key":"10.1016\/j.asoc.2025.113635_b3","doi-asserted-by":"crossref","first-page":"93","DOI":"10.1016\/j.ijpe.2016.01.016","article-title":"An effective hybrid genetic algorithm and tabu search for flexible job shop scheduling problem","volume":"174","author":"Li","year":"2016","journal-title":"Int. J. Prod. Econ."},{"key":"10.1016\/j.asoc.2025.113635_b4","doi-asserted-by":"crossref","first-page":"650","DOI":"10.1016\/j.jmsy.2022.01.014","article-title":"An improved genetic algorithm for flexible job shop scheduling problem considering reconfigurable machine tools with limited auxiliary modules","volume":"62","author":"Fan","year":"2022","journal-title":"J. Manuf. Syst."},{"key":"10.1016\/j.asoc.2025.113635_b5","doi-asserted-by":"crossref","first-page":"35","DOI":"10.1016\/j.tcs.2004.11.017","article-title":"Convergence results for the (1,\u03bb)-SA-ES using the theory of \u03c6-irreducible Markov chains","volume":"334","author":"Auger","year":"2005","journal-title":"Theoret. Comput. Sci."},{"year":"2013","series-title":"The Theory of Evolution Strategies","author":"Beyer","key":"10.1016\/j.asoc.2025.113635_b6"},{"key":"10.1016\/j.asoc.2025.113635_b7","doi-asserted-by":"crossref","DOI":"10.1016\/j.swevo.2024.101481","article-title":"Differential evolution with evolutionary scale adaptation","volume":"85","author":"Zhang","year":"2024","journal-title":"Swarm Evol. Comput."},{"key":"10.1016\/j.asoc.2025.113635_b8","doi-asserted-by":"crossref","DOI":"10.1016\/j.swevo.2023.101427","article-title":"A differential evolution algorithm for solving mixed-integer nonlinear programming problems","volume":"84","author":"Molina-P\u00e9rez","year":"2024","journal-title":"Swarm Evol. Comput."},{"key":"10.1016\/j.asoc.2025.113635_b9","doi-asserted-by":"crossref","DOI":"10.1016\/j.swevo.2023.101450","article-title":"Triple competitive differential evolution for global numerical optimization","volume":"84","author":"Yang","year":"2024","journal-title":"Swarm Evol. Comput."},{"key":"10.1016\/j.asoc.2025.113635_b10","doi-asserted-by":"crossref","DOI":"10.1016\/j.swevo.2020.100807","article-title":"A genetic programming hyper-heuristic for the distributed assembly permutation flow-shop scheduling problem with sequence dependent setup times","volume":"60","author":"Song","year":"2021","journal-title":"Swarm Evol. Comput."},{"key":"10.1016\/j.asoc.2025.113635_b11","article-title":"Solving energy-efficient distributed job shop scheduling via multi-objective evolutionary algorithm with decomposition","volume":"58","author":"Wang","year":"2020","journal-title":"Swarm Evol. Comput."},{"key":"10.1016\/j.asoc.2025.113635_b12","first-page":"375","article-title":"Convergence rates of evolutionary algorithms for a class of convex objective functions","volume":"26","author":"Rudolph","year":"1997","journal-title":"Control Cybernet."},{"key":"10.1016\/j.asoc.2025.113635_b13","doi-asserted-by":"crossref","first-page":"601","DOI":"10.1016\/S1383-7621(01)00018-2","article-title":"Conditions for the convergence of evolutionary algorithms","volume":"47","author":"He","year":"2001","journal-title":"J. Syst. Arch."},{"key":"10.1016\/j.asoc.2025.113635_b14","doi-asserted-by":"crossref","first-page":"363","DOI":"10.1162\/106365603322519279","article-title":"Analysis of convergence of an evolutionary algorithm with self-adaptation using a stochastic Lyapunov function","volume":"11","author":"Semenov","year":"2003","journal-title":"Evol. Comput."},{"issue":"4","key":"10.1016\/j.asoc.2025.113635_b15","doi-asserted-by":"crossref","first-page":"249","DOI":"10.1109\/4235.687885","article-title":"Local convergence rates of simple evolutionary algorithms with Cauchy mutations","volume":"1","author":"Rudolph","year":"1997","journal-title":"IEEE Trans. Evol. Comput."},{"key":"10.1016\/j.asoc.2025.113635_b16","doi-asserted-by":"crossref","first-page":"23","DOI":"10.1016\/S0304-3975(99)00091-2","article-title":"On the convergence rate of genetic algorithms","volume":"229","author":"He","year":"1999","journal-title":"Theoret. Comput. Sci."},{"issue":"1","key":"10.1016\/j.asoc.2025.113635_b17","doi-asserted-by":"crossref","first-page":"38","DOI":"10.1016\/j.tcs.2006.04.004","article-title":"How the (1+ 1) ES using isotropic mutations minimizes positive definite quadratic forms","volume":"361","author":"J\u00e4gersk\u00fcpper","year":"2006","journal-title":"Theoret. Comput. Sci."},{"issue":"3","key":"10.1016\/j.asoc.2025.113635_b18","doi-asserted-by":"crossref","first-page":"329","DOI":"10.1016\/j.tcs.2007.02.042","article-title":"Algorithmic analysis of a basic evolutionary algorithm for continuous optimization","volume":"379","author":"J\u00e4gersk\u00fcpper","year":"2007","journal-title":"Theoret. Comput. Sci."},{"key":"10.1016\/j.asoc.2025.113635_b19","doi-asserted-by":"crossref","first-page":"1589","DOI":"10.1137\/140984038","article-title":"Linear convergence of comparison-based step-size adaptive randomized search via stability of markov chains","volume":"26","author":"Auger","year":"2016","journal-title":"SIAM J. Optim."},{"key":"10.1016\/j.asoc.2025.113635_b20","doi-asserted-by":"crossref","first-page":"531","DOI":"10.1016\/S0252-9602(17)30442-3","article-title":"Convergence rates for a class of evolutionary algorithms with elitist strategy","volume":"21","author":"Ding","year":"2001","journal-title":"Acta Math. Sci."},{"issue":"1\u20132","key":"10.1016\/j.asoc.2025.113635_b21","doi-asserted-by":"crossref","first-page":"23","DOI":"10.1016\/S0304-3975(99)00091-2","article-title":"On the convergence rates of genetic algorithms","volume":"229","author":"He","year":"1999","journal-title":"Theoret. Comput. Sci."},{"key":"10.1016\/j.asoc.2025.113635_b22","doi-asserted-by":"crossref","first-page":"42","DOI":"10.1016\/j.tcs.2018.05.015","article-title":"Quality gain analysis of the weighted recombination evolution strategy on general convex quadratic functions","volume":"832","author":"Akimoto","year":"2020","journal-title":"Theoret. Comput. Sci."},{"key":"10.1016\/j.asoc.2025.113635_b23","first-page":"1","article-title":"On asymptotic convergence rate of random search","author":"Tarlowski","year":"2023","journal-title":"J. Global Optim."},{"issue":"2","key":"10.1016\/j.asoc.2025.113635_b24","doi-asserted-by":"crossref","first-page":"501","DOI":"10.1109\/TEVC.2023.3266955","article-title":"Convergence rate of the (1+1)-ES on locally strongly convex and Lipschitz smooth functions","volume":"28","author":"Morinaga","year":"2024","journal-title":"IEEE Trans. Evol. Comput."},{"issue":"2","key":"10.1016\/j.asoc.2025.113635_b25","doi-asserted-by":"crossref","first-page":"316","DOI":"10.1109\/TEVC.2015.2444793","article-title":"Average convergence rate of evolutionary algorithms","volume":"20","author":"He","year":"2015","journal-title":"IEEE Trans. Evol. Comput."},{"key":"10.1016\/j.asoc.2025.113635_b26","doi-asserted-by":"crossref","first-page":"200","DOI":"10.1016\/j.ins.2020.12.076","article-title":"Average convergence rate of evolutionary algorithms in continuous optimization","volume":"562","author":"Chen","year":"2021","journal-title":"Inform. Sci."},{"key":"10.1016\/j.asoc.2025.113635_b27","doi-asserted-by":"crossref","first-page":"33","DOI":"10.1016\/j.asoc.2017.12.048","article-title":"A novel hybrid genetic algorithm with granular information for feature selection and optimization","volume":"65","author":"Dong","year":"2018","journal-title":"Appl. Soft Comput."},{"key":"10.1016\/j.asoc.2025.113635_b28","doi-asserted-by":"crossref","first-page":"815","DOI":"10.1631\/FITEE.1601553","article-title":"Synergistic fibroblast optimization: a novel nature-inspired computing algorithm","volume":"19","author":"Dhivyaprabha","year":"2018","journal-title":"Front. Inf. Technol. Electron. Eng."},{"key":"10.1016\/j.asoc.2025.113635_b29","doi-asserted-by":"crossref","first-page":"37","DOI":"10.1016\/j.petrol.2018.10.005","article-title":"Self-adapt reservoir clusterization method to enhance robustness of well placement optimization","volume":"173","author":"Janiga","year":"2019","journal-title":"J. Pet. Sci. Eng."},{"key":"10.1016\/j.asoc.2025.113635_b30","doi-asserted-by":"crossref","first-page":"24109","DOI":"10.1109\/ACCESS.2019.2900078","article-title":"Binary differential evolution based on individual entropy for feature subset optimization","volume":"7","author":"Li","year":"2019","journal-title":"IEEE Access"},{"year":"2012","series-title":"Introduction To Stochastic Calculus with Applications","author":"Klebaner","key":"10.1016\/j.asoc.2025.113635_b31"},{"year":"2007","series-title":"Computational Intelligence: An Introduction","author":"Engelbrecht","key":"10.1016\/j.asoc.2025.113635_b32"},{"issue":"1","key":"10.1016\/j.asoc.2025.113635_b33","doi-asserted-by":"crossref","first-page":"3","DOI":"10.1016\/j.swevo.2011.02.002","article-title":"A practical tutorial on the use of nonparametric statistical tests as a methodology for comparing evolutionary and swarm intelligence algorithms","volume":"1","author":"Derrac","year":"2011","journal-title":"Swarm Evol. Comput."},{"issue":"6","key":"10.1016\/j.asoc.2025.113635_b34","article-title":"Non-convex economic dispatch with prohibited operating zones through gravitational search algorithm","volume":"5","author":"Hota","year":"2015","journal-title":"Int. J. Electr. Comput. Eng."},{"key":"10.1016\/j.asoc.2025.113635_b35","doi-asserted-by":"crossref","first-page":"121","DOI":"10.1016\/j.ijepes.2014.07.031","article-title":"A novel modified hybrid PSOGSA based on fuzzy logic for non-convex economic dispatch problem with valve-point effect","volume":"64","author":"Duman","year":"2015","journal-title":"Int. J. Electr. Power Energy Syst."}],"container-title":["Applied Soft Computing"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/api.elsevier.com\/content\/article\/PII:S1568494625009469?httpAccept=text\/xml","content-type":"text\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/api.elsevier.com\/content\/article\/PII:S1568494625009469?httpAccept=text\/plain","content-type":"text\/plain","content-version":"vor","intended-application":"text-mining"}],"deposited":{"date-parts":[[2025,9,18]],"date-time":"2025-09-18T09:56:14Z","timestamp":1758189374000},"score":1,"resource":{"primary":{"URL":"https:\/\/linkinghub.elsevier.com\/retrieve\/pii\/S1568494625009469"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2025,11]]},"references-count":35,"alternative-id":["S1568494625009469"],"URL":"https:\/\/doi.org\/10.1016\/j.asoc.2025.113635","relation":{},"ISSN":["1568-4946"],"issn-type":[{"type":"print","value":"1568-4946"}],"subject":[],"published":{"date-parts":[[2025,11]]},"assertion":[{"value":"Elsevier","name":"publisher","label":"This article is maintained by"},{"value":"Adaptive evolutionary algorithms with linear average convergence rate for optimization problems with Lipschitz continuous functions","name":"articletitle","label":"Article Title"},{"value":"Applied Soft Computing","name":"journaltitle","label":"Journal Title"},{"value":"https:\/\/doi.org\/10.1016\/j.asoc.2025.113635","name":"articlelink","label":"CrossRef DOI link to publisher maintained version"},{"value":"article","name":"content_type","label":"Content Type"},{"value":"\u00a9 2025 Elsevier B.V. All rights are reserved, including those for text and data mining, AI training, and similar technologies.","name":"copyright","label":"Copyright"}],"article-number":"113635"}}