{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,7,4]],"date-time":"2026-07-04T01:39:12Z","timestamp":1783129152370,"version":"3.54.6"},"reference-count":22,"publisher":"MDPI AG","issue":"3","license":[{"start":{"date-parts":[[2024,2,26]],"date-time":"2024-02-26T00:00:00Z","timestamp":1708905600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Ministry of Science and Higher Education of the Republic of Kazakhstan","award":["AP19579370"],"award-info":[{"award-number":["AP19579370"]}]},{"name":"Ministry of Science and Higher Education of the Republic of Kazakhstan","award":["BR18574144"],"award-info":[{"award-number":["BR18574144"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Algorithms"],"abstract":"<jats:p>Unpredictable strings are sequences of data with complex and erratic behavior, which makes them an object of interest in various scientific fields. Unpredictable strings related to chaos theory was investigated using a genetic algorithm. This paper presents a new genetic algorithm for converting large binary sequences into their periodic form. The MakePeriod method is also presented, which is aimed at optimizing the search for such periodic sequences, which significantly reduces the number of generations to achieve the result of the problem under consideration. The analysis of the deviation of a nonperiodic sequence from its considered periodic transformation was carried out, and methods of crossover and mutation were investigated. The proposed algorithm and its associated conclusions can be applied to processing large sequences and different values of the period, and also emphasize the importance of choosing the right methods of crossover and mutation when applying genetic algorithms to this task.<\/jats:p>","DOI":"10.3390\/a17030101","type":"journal-article","created":{"date-parts":[[2024,2,26]],"date-time":"2024-02-26T06:50:23Z","timestamp":1708930223000},"page":"101","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":6,"title":["Application of Genetic Algorithms for Periodicity Recognition and Finite Sequences Sorting"],"prefix":"10.3390","volume":"17","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-8164-8199","authenticated-orcid":false,"given":"Mukhtar","family":"Zhassuzak","sequence":"first","affiliation":[{"name":"Department of Computer Science, Al-Farabi Kazakh National University, 71 al-Farabi Ave., Almaty 050040, Kazakhstan"},{"name":"LTD DigitAlem, 71 al-Farabi Ave., Almaty 050040, Kazakhstan"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-2985-286X","authenticated-orcid":false,"given":"Marat","family":"Akhmet","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Middle East Technical University, Dumlup\u0131nar Bulvar\u0131 No:1, Ankara 06800, Turkey"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-6528-0619","authenticated-orcid":false,"given":"Yedilkhan","family":"Amirgaliyev","sequence":"additional","affiliation":[{"name":"Department of Computer Science, Al-Farabi Kazakh National University, 71 al-Farabi Ave., Almaty 050040, Kazakhstan"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-3486-227X","authenticated-orcid":false,"given":"Zholdas","family":"Buribayev","sequence":"additional","affiliation":[{"name":"Department of Computer Science, Al-Farabi Kazakh National University, 71 al-Farabi Ave., Almaty 050040, Kazakhstan"},{"name":"LTD DigitAlem, 71 al-Farabi Ave., Almaty 050040, Kazakhstan"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"1968","published-online":{"date-parts":[[2024,2,26]]},"reference":[{"key":"ref_1","unstructured":"Gleick, J. (2008). Chaos: Making a New Science, Penguin."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"18292","DOI":"10.1364\/OE.18.018292","article-title":"Synchronization of random bit generators based on coupled chaotic lasers and application to cryptography","volume":"18","author":"Kanter","year":"2010","journal-title":"Opt. Express"},{"key":"ref_3","unstructured":"Akhmet, M., and Tola, A. (2020). Unpredictable strings. arXiv."},{"key":"ref_4","doi-asserted-by":"crossref","unstructured":"Casta\u00f1eda, L.B., Arunachalam, V., and Dharmaraja, S. (2012). Introduction to Probability and Stochastic Processes with Applications, John Wiley & Sons.","DOI":"10.1002\/9781118344972"},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"168","DOI":"10.1016\/j.mee.2011.04.005","article-title":"Chaotic block cryptosystem using high precision approaches to tent map","volume":"90","year":"2012","journal-title":"Microelectron. Eng."},{"key":"ref_6","doi-asserted-by":"crossref","unstructured":"L\u00f3pez-Mancilla, D., L\u00f3pez-Cahuich, G., Posadas-Castillo, C., Casta\u00f1eda, C.E., Garc\u00eda-L\u00f3pez, J.H., V\u00e1zquez-Guti\u00e9rrez, J.L., and Tlelo-Cuautle, E. (2019). Synchronization of complex networks of identical and nonidentical chaotic systems via model-matching control. PLoS ONE, 14.","DOI":"10.1371\/journal.pone.0216349"},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"012024","DOI":"10.1088\/1742-6596\/274\/1\/012024","article-title":"Secure optoelectronic communication using laser diode driving by chaotic R\u00f6ssler oscillators","volume":"274","author":"Pisarchik","year":"2011","journal-title":"J. Phys. Conf. Ser."},{"key":"ref_8","doi-asserted-by":"crossref","unstructured":"Akhmet, M., Fen, M.O., and Alejaily, E.M. (2019). A randomly determined unpredictable function. arXiv.","DOI":"10.1007\/978-3-030-35854-9_7"},{"key":"ref_9","unstructured":"Robert, L.D. (2021). Introduction to Chaotic Dynamical Systems, CHAPMAN & HALL CRC."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"381","DOI":"10.1515\/sagmb-2015-0079","article-title":"Search of latent periodicity in amino acid sequences by means of genetic algorithm and dynamic programming","volume":"15","author":"Pugacheva","year":"2016","journal-title":"Stat. Appl. Genet. Mol. Biol."},{"key":"ref_11","doi-asserted-by":"crossref","unstructured":"Akhmet, M. (2010). Principles of Discontinuous Dynamical Systems, Springer Science & Business Media.","DOI":"10.1007\/978-1-4419-6581-3"},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"2557","DOI":"10.1016\/j.chaos.2007.10.049","article-title":"Logistic chaotic maps for binary numbers generations","volume":"40","author":"Kanso","year":"2009","journal-title":"Chaos Solitons Fractals"},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"657","DOI":"10.1016\/j.cnsns.2017.12.011","article-title":"Non-autonomous equations with unpredictable solutions","volume":"59","author":"Akhmet","year":"2018","journal-title":"Commun. Nonlinear Sci. Numer. Simul."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"104121","DOI":"10.1016\/j.engappai.2020.104121","article-title":"A hybrid of clustering and meta-heuristic algorithms to solve a p-mobile hub location\u2013allocation problem with the depreciation cost of hub facilities","volume":"98","author":"Mokhtarzadeh","year":"2021","journal-title":"Eng. Appl. Artif. Intell."},{"key":"ref_15","doi-asserted-by":"crossref","unstructured":"Lambora, A., Gupta, K., and Chopra, K. (2019, January 14\u201316). Genetic algorithm\u2014A literature review. Proceedings of the 2019 International Conference on Machine Learning, Big Data, Cloud and Parallel Computing (COMITCon), Faridabad, India.","DOI":"10.1109\/COMITCon.2019.8862255"},{"key":"ref_16","unstructured":"Wirsansky, E. (2020). Hands-On Genetic Algorithms with Python: Applying Genetic Algorithms to Solve Real-World Deep Learning and Artificial Intelligence Problems, Packt Publishing Ltd."},{"key":"ref_17","unstructured":"\u0160koda, P., and Adam, F. (2020). Knowledge Discovery in Big Data from Astronomy and Earth Observation, Elsevier."},{"key":"ref_18","unstructured":"Changat, M., Narasimha-Shenoi, P.G., Nezhad, F.H., Kov\u0161e, M., Mohandas, S., Ramachandran, A., and Stadler, P.F. (2017). Topological Representation of the Transit Sets of k-Point Crossover Operators. arXiv."},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"37","DOI":"10.1002\/(SICI)1099-0526(199609\/10)2:1<37::AID-CPLX9>3.0.CO;2-C","article-title":"Recombination Induced Hypergraphs: A New Approach to Mutation-Recombination Isomorphism","volume":"2","author":"Gitcho","year":"1996","journal-title":"Complexity"},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"245","DOI":"10.1016\/j.cor.2007.09.005","article-title":"An efficient genetic algorithm with uniform crossover for air traffic control","volume":"36","author":"Hu","year":"2009","journal-title":"Comput. Oper. Res."},{"key":"ref_21","unstructured":"Goldberg, D.E. (1989). Genetic Algorithms in Search, Optimization and Machine Learning, Addison Welssey Publishing Company."},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"66","DOI":"10.1038\/scientificamerican0792-66","article-title":"Genetic Algorithms","volume":"267","author":"Holland","year":"1992","journal-title":"Sci. Am."}],"container-title":["Algorithms"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1999-4893\/17\/3\/101\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,10]],"date-time":"2025-10-10T14:05:02Z","timestamp":1760105102000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1999-4893\/17\/3\/101"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2024,2,26]]},"references-count":22,"journal-issue":{"issue":"3","published-online":{"date-parts":[[2024,3]]}},"alternative-id":["a17030101"],"URL":"https:\/\/doi.org\/10.3390\/a17030101","relation":{},"ISSN":["1999-4893"],"issn-type":[{"value":"1999-4893","type":"electronic"}],"subject":[],"published":{"date-parts":[[2024,2,26]]}}}