{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,11,28]],"date-time":"2025-11-28T11:55:12Z","timestamp":1764330912305,"version":"build-2065373602"},"reference-count":19,"publisher":"MDPI AG","issue":"9","license":[{"start":{"date-parts":[[2016,8,25]],"date-time":"2016-08-25T00:00:00Z","timestamp":1472083200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>This article is devoted to the application of the cellular automata mathematical apparatus to the problem of continuous optimization. The cellular automaton with an objective function is introduced as a new modification of the classic cellular automaton. The algorithm of continuous optimization, which is based on dynamics of the cellular automaton having the property of geometric symmetry, is obtained. The results of the simulation experiments with the obtained algorithm on standard test functions are provided, and a comparison between the analogs is shown.<\/jats:p>","DOI":"10.3390\/sym8090084","type":"journal-article","created":{"date-parts":[[2016,8,25]],"date-time":"2016-08-25T10:11:44Z","timestamp":1472119904000},"page":"84","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":6,"title":["The Algorithm of Continuous Optimization Based on the Modified Cellular Automaton"],"prefix":"10.3390","volume":"8","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-8257-2082","authenticated-orcid":false,"given":"Oleg","family":"Evsutin","sequence":"first","affiliation":[{"name":"Tomsk State University of Control Systems and Radioelectronics, 40 Lenina Prospect, Tomsk 634050, Russia"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Alexander","family":"Shelupanov","sequence":"additional","affiliation":[{"name":"Tomsk State University of Control Systems and Radioelectronics, 40 Lenina Prospect, Tomsk 634050, Russia"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Roman","family":"Meshcheryakov","sequence":"additional","affiliation":[{"name":"Tomsk State University of Control Systems and Radioelectronics, 40 Lenina Prospect, Tomsk 634050, Russia"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Dmitry","family":"Bondarenko","sequence":"additional","affiliation":[{"name":"Tomsk State University of Control Systems and Radioelectronics, 40 Lenina Prospect, Tomsk 634050, Russia"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Angelika","family":"Rashchupkina","sequence":"additional","affiliation":[{"name":"Tomsk State University of Control Systems and Radioelectronics, 40 Lenina Prospect, Tomsk 634050, Russia"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2016,8,25]]},"reference":[{"key":"ref_1","unstructured":"Kennedy, J., and Ebenhart, R. (December, January 27). Particle Swarm Optimization. Proceedings of the 1995 IEEE International Conference on Neural Networks, University of Western Australia, Perth, Australia."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"341","DOI":"10.1023\/A:1008202821328","article-title":"Differential evolution\u2014A simple and efficient heuristic for global optimization over continuous spaces","volume":"11","author":"Storn","year":"1997","journal-title":"J. Glob. Optim."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"61","DOI":"10.1007\/s10462-009-9127-4","article-title":"A survey: Algorithms simulating bee swarm intelligence","volume":"31","author":"Karaboga","year":"2009","journal-title":"Artif. Intell. Rev."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"54","DOI":"10.3103\/S8756699012010086","article-title":"Identification of fuzzy systems using a continuous ant colony algorithm","volume":"48","author":"Khodashinskii","year":"2012","journal-title":"Optoelectron. Instrum. Data Process."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"201","DOI":"10.1007\/s00158-008-0351-3","article-title":"Cellular genetic algorithm technique for the multicriterion design optimization","volume":"40","author":"Canyurt","year":"2010","journal-title":"Struct. Multidiscip. Optim."},{"key":"ref_6","first-page":"351","article-title":"Cell-based genetic algorithm and simulated annealing for spatial groundwater allocation","volume":"5","author":"Sidiropoulos","year":"2009","journal-title":"WSEAS Trans. Environ. Dev."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"1532","DOI":"10.4236\/am.2012.330213","article-title":"Harmony Search and Cellular Automata in Spatial Optimization","volume":"3","author":"Sidiropoulos","year":"2012","journal-title":"Appl. Math."},{"key":"ref_8","doi-asserted-by":"crossref","unstructured":"Du, T.S., Fei, P.S., and Shen, Y.J. (2008, January 18\u201320). A new cellular automata-based mixed cellular ant algorithm for solving continuous system optimization programs. Proceedings of the 4th International Conference on Natural Computation, Jinan, China.","DOI":"10.1109\/ICNC.2008.393"},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"86","DOI":"10.1016\/j.compstruc.2013.04.024","article-title":"Layout optimization of truss structures by hybridizing cellular automata and particle swarm optimization","volume":"125","author":"Gholizadeh","year":"2013","journal-title":"Comput. Struct."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"1205","DOI":"10.1115\/1.2336251","article-title":"Topology optimization using a hybrid cellular automation method with local control rules","volume":"128","author":"Tovar","year":"2006","journal-title":"J. Mech. Des."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"201","DOI":"10.1007\/s00158-009-0360-x","article-title":"Convergence analysis of hybrid cellular automata for topology optimization","volume":"40","author":"Penninger","year":"2010","journal-title":"Struct. Multidiscip. Optim."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"23","DOI":"10.1080\/0305215X.2011.561843","article-title":"Novel local rules of cellular automata applied to topology and size optimization","volume":"44","author":"Bochenek","year":"2012","journal-title":"Eng. Optim."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"219","DOI":"10.1016\/j.ins.2014.02.057","article-title":"An evolutionary membrane algorithm for global numerical optimization problems","volume":"276","author":"Han","year":"2014","journal-title":"Inf. Sci."},{"key":"ref_14","doi-asserted-by":"crossref","unstructured":"Toffoli, T., and Margolus, M. (1987). Cellular Automata Machines, MIT Press.","DOI":"10.7551\/mitpress\/1763.001.0001"},{"key":"ref_15","doi-asserted-by":"crossref","unstructured":"Yazdani, D., Golyari, S., and Meybodi, M.R. (2010, January 4\u20136). A New Hybrid Algorithm for Optimization Based on Artificial Fish Swarm Algorithm and Cellular Learning Automata. Proceedings of the 5th International Symposium on Telecommunications, Sharif University of Technology, Tehran, Iran.","DOI":"10.1109\/ISTEL.2010.5734156"},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"735","DOI":"10.1007\/s10489-011-0292-1","article-title":"CLA-DE: A hybrid model based on cellular learning automata for numerical optimization","volume":"36","author":"Vafashoar","year":"2012","journal-title":"Appl. Intell."},{"key":"ref_17","doi-asserted-by":"crossref","unstructured":"Bandman, O.L. (2010, January 16\u201319). Discrete Models of Physicochemical Processes and Their Parallel Implementation. Proceedings of the Second Russia-Taiwan Symposium on Methods and Tools of Parallel Programming Multicomputers, Vladivostok, Russia.","DOI":"10.1007\/978-3-642-14822-4_3"},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"1768","DOI":"10.3390\/sym7041768","article-title":"Effects of Initial Symmetry on the Global Symmetry of One-Dimensional Legal Cellular Automata","volume":"7","author":"Tanaka","year":"2015","journal-title":"Symmetry"},{"key":"ref_19","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. 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