{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,6,16]],"date-time":"2026-06-16T17:03:49Z","timestamp":1781629429071,"version":"3.54.5"},"reference-count":38,"publisher":"MDPI AG","issue":"2","license":[{"start":{"date-parts":[[2021,2,7]],"date-time":"2021-02-07T00:00:00Z","timestamp":1612656000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Algorithms"],"abstract":"<jats:p>K-Means Clustering is a popular technique in data analysis and data mining. To remedy the defects of relying on the initialization and converging towards the local minimum in the K-Means Clustering (KMC) algorithm, a chaotic adaptive artificial bee colony algorithm (CAABC) clustering algorithm is presented to optimally partition objects into K clusters in this study. This algorithm adopts the max\u2013min distance product method for initialization. In addition, a new fitness function is adapted to the KMC algorithm. This paper also reports that the iteration abides by the adaptive search strategy, and Fuch chaotic disturbance is added to avoid converging on local optimum. The step length decreases linearly during the iteration. In order to overcome the shortcomings of the classic ABC algorithm, the simulated annealing criterion is introduced to the CAABC. Finally, the confluent algorithm is compared with other stochastic heuristic algorithms on the 20 standard test functions and 11 datasets. The results demonstrate that improvements in CAABA-K-means have an advantage on speed and accuracy of convergence over some conventional algorithms for solving clustering problems.<\/jats:p>","DOI":"10.3390\/a14020053","type":"journal-article","created":{"date-parts":[[2021,2,8]],"date-time":"2021-02-08T20:51:51Z","timestamp":1612817511000},"page":"53","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":19,"title":["K-Means Clustering Algorithm Based on Chaotic Adaptive Artificial Bee Colony"],"prefix":"10.3390","volume":"14","author":[{"given":"Qibing","family":"Jin","sequence":"first","affiliation":[{"name":"School of Information, Science and Technology, Beijing University of Chemical Technology, Beijing 100029, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Nan","family":"Lin","sequence":"additional","affiliation":[{"name":"School of Information, Science and Technology, Beijing University of Chemical Technology, Beijing 100029, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Yuming","family":"Zhang","sequence":"additional","affiliation":[{"name":"School of Information, Science and Technology, Beijing University of Chemical Technology, Beijing 100029, China"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"1968","published-online":{"date-parts":[[2021,2,7]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"100","DOI":"10.2307\/2346830","article-title":"A K-Means Clustering Algorithm","volume":"28","author":"Hartigan","year":"1979","journal-title":"Appl. Stat."},{"key":"ref_2","first-page":"641","article-title":"A rapid hybrid clustering algorithm for large volumes of high dimensional data","volume":"31","author":"Punit","year":"2018","journal-title":"IEEE Trans. Knowl. Data Eng."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"012090","DOI":"10.1088\/1757-899X\/725\/1\/012090","article-title":"Improve birch algorithm for big data clustering","volume":"725","author":"Ramadhani","year":"2020","journal-title":"IOP Conf. Ser. Mater. Sci. Eng."},{"key":"ref_4","doi-asserted-by":"crossref","unstructured":"Cerreto, F., Nielsen, B.F., Nielsen, O.A., and Harrod, S.S. (2018). Application of data clustering to railway delay pattern recognition. J. Adv. Transp., 377\u2013394.","DOI":"10.1155\/2018\/6164534"},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"1107","DOI":"10.1039\/C9CP05616E","article-title":"Bayesian analysis of data from segmented super-resolution images for quantifying protein clustering","volume":"22","author":"Kouta","year":"2020","journal-title":"Phys. Chem. Chem. Phys."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"501","DOI":"10.1016\/j.ins.2018.09.053","article-title":"Evolutionary mining of skyline clusters of attributed graph data","volume":"509","author":"Dhifli","year":"2020","journal-title":"Inf. Sci."},{"key":"ref_7","unstructured":"Eberhart, S.Y. (2001, January 27\u201330). Particle swarm optimization: Developments, applications and resources. Proceedings of the Congress on Evolutionary Computation, Seoul, Korea."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"54","DOI":"10.1016\/j.cie.2017.10.022","article-title":"A novel artificial bee colony algorithm based on the cosine similarity","volume":"115","author":"Xiang","year":"2018","journal-title":"Comput. Ind. Eng."},{"key":"ref_9","unstructured":"Karaboga, D. (2005). An Idea Based on Honey bee Swarm for Numerical Optimization, Erciyes University. Technical Report-tr06."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"737","DOI":"10.1109\/TMAG.2013.2281818","article-title":"A modification of artificial bee colony algorithm applied to loudspeaker design problem","volume":"50","author":"Zhang","year":"2014","journal-title":"IEEE Trans. Magn."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"3166","DOI":"10.1016\/j.amc.2010.08.049","article-title":"Gbest-guided artificial bee colony algorithm for numerical function optimization","volume":"217","author":"Zhu","year":"2010","journal-title":"Appl. Math. Comput."},{"key":"ref_12","first-page":"1672","article-title":"Research on global artificial bee colony algorithm based on crossover","volume":"11","author":"Zhang","year":"2017","journal-title":"J. Shandong Univ. Technol."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"1012","DOI":"10.1016\/j.ins.2016.07.022","article-title":"A novel artificial bee colony algorithm with depth-first search framework and elite-guided search equation","volume":"367\u2013368","author":"Cui","year":"2016","journal-title":"Inf. Sci."},{"key":"ref_14","doi-asserted-by":"crossref","unstructured":"Sharma, T.K., and Pant, M. (2011, January 20\u201322). Enhancing Scout Bee Movements in Artificial Bee Colony Algorithm. Proceedings of the International Conference on Soft Computing for Problem Solving, Roorkee, India.","DOI":"10.1007\/978-81-322-0487-9_58"},{"key":"ref_15","doi-asserted-by":"crossref","unstructured":"Yang, Z., Gao, H., and Hu, H. (2018, January 29\u201331). Artificial bee colony algorithm based on self-adaptive greedy strategy. Proceedings of the IEEE International Conference on Advanced Computational Intelligence, Xiamen, China.","DOI":"10.1109\/ICACI.2018.8377489"},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"2741","DOI":"10.1016\/j.cam.2012.01.013","article-title":"A global best artificial bee colony algorithm for global optimization","volume":"236","author":"Gao","year":"2012","journal-title":"J. Comput. Appl. Math."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"3763","DOI":"10.1016\/j.asoc.2013.05.012","article-title":"A novel artificial bee colony algorithm with Powell\u2019s method","volume":"13","author":"Gao","year":"2013","journal-title":"Appl. Soft Comput."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"2621","DOI":"10.1016\/j.camwa.2012.06.026","article-title":"Hybrid harmony search and artificial bee colony algorithm for global optimization problems","volume":"64","author":"Wu","year":"2012","journal-title":"Comput. Math. Appl."},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"1781","DOI":"10.1016\/j.asoc.2012.12.025","article-title":"Artificial bee colony algorithm and pattern search hybridized for global optimization","volume":"13","author":"Kang","year":"2013","journal-title":"Appl. Soft Comput."},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"3459","DOI":"10.1016\/j.ins.2011.04.018","article-title":"A discrete artificial bee colony algorithm for the total flowtime minimization in permutation flow shops","volume":"181","author":"Tasgetiren","year":"2011","journal-title":"Inf. Sci."},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"1067","DOI":"10.1016\/S1004-9541(12)60588-6","article-title":"A Discrete Artificial Bee Colony Algorithm for Minimizing the Total Flow Time in the Blocking Flow Shop Scheduling","volume":"20","author":"Guanlong","year":"2012","journal-title":"Chin. J. Chem. Eng."},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"167","DOI":"10.1016\/j.ijpe.2012.03.035","article-title":"A hybrid artificial bee colony algorithm for the job shop scheduling problem","volume":"141","author":"Zhang","year":"2013","journal-title":"Int. J. Prod. Econ."},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"42","DOI":"10.1016\/j.omega.2013.12.004","article-title":"A novel discrete artificial bee colony algorithm for the hybrid flowshop scheduling problem with makespan minimisation","volume":"45","author":"Pan","year":"2014","journal-title":"Omega"},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1016\/j.knosys.2016.06.014","article-title":"Artificial bee colony algorithm for scheduling and rescheduling fuzzy flexible job shop problem with new job insertion","volume":"109","author":"Gao","year":"2016","journal-title":"Knowl. Based Syst."},{"key":"ref_25","doi-asserted-by":"crossref","unstructured":"Li, J.Q., and Pan, Q.K. (2015). Solving the Large-Scale Hybrid Flow Shop Scheduling Problem with Limited Buffers by a Hybrid Artificial Bee Colony Algorithm, Elsevier Science Inc.","DOI":"10.1016\/j.ins.2014.10.009"},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"32941","DOI":"10.1109\/ACCESS.2019.2903081","article-title":"Integrating Artificial Bee Colony Algorithm and BP Neural Network for Software Aging Prediction in IoT Environment","volume":"7","author":"Liu","year":"2019","journal-title":"IEEE Access"},{"key":"ref_27","doi-asserted-by":"crossref","unstructured":"Karaboga, D., and Gorkemli, B. (2012, January 2\u20134). A quick artificial bee colony -qABC- algorithm for optimization problems. Proceedings of the 2012 International Symposium on Innovations in Intelligent Systems and Applications, Trabzon, Turkey.","DOI":"10.1109\/INISTA.2012.6247010"},{"key":"ref_28","unstructured":"Zaragoza, J.C., Sucar, E., Morales, E., Bielza, C., and Larranaga, P. (2011, January 16\u201322). Bayesian Chain Classifiers for Multidimensional Classification. Proceedings of the International Joint Conference on Ijcai, Catalonia, Spain."},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"1879","DOI":"10.1016\/j.camwa.2013.05.030","article-title":"Application of artificial bee colony algorithm to topology optimization for dynamic stiffness problems","volume":"66","author":"Park","year":"2013","journal-title":"Comput. Math. Appl."},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"766","DOI":"10.1016\/j.asoc.2015.06.033","article-title":"A dynamic multi-colony artificial bee colony algorithm for multi-objective optimization","volume":"35","author":"Xiang","year":"2015","journal-title":"Appl. Soft Comput."},{"key":"ref_31","unstructured":"Borchani, H., Bielza, C., and Larranaga, P. (2010, January 13\u201315). Learning CB-decomposable multi-dimensional bayesian network classifiers. Proceedings of the 5th European Workshop on Probabilistic Graphical Models, Helsinki, Finland."},{"key":"ref_32","doi-asserted-by":"crossref","unstructured":"Lou, A. (2019, January 22\u201323). A Fusion Clustering Algorithm Based on Global Gravitation Search and Partitioning Around Medoid. Proceedings of the CSSE 2019: Proceedings of the 2nd International Conference on Computer Science and Software Engineering, Rome, Italy.","DOI":"10.1145\/3339363.3339368"},{"key":"ref_33","doi-asserted-by":"crossref","first-page":"3702","DOI":"10.1007\/s11227-018-2633-x","article-title":"Heuristic parallel selective ensemble algorithm based on clustering and improved simulated annealing","volume":"76","author":"Wu","year":"2018","journal-title":"J. Supercomput."},{"key":"ref_34","doi-asserted-by":"crossref","first-page":"405","DOI":"10.21629\/JSEE.2018.02.20","article-title":"Hybrid artificial bee colony algorithm with variable neighborhood search and memory mechanism","volume":"29","author":"Fan","year":"2018","journal-title":"J. Syst. Eng. Electron."},{"key":"ref_35","unstructured":"Tellaroli, P. (2018). CrossClustering: A Partial Clustering Algorithm. PLoS ONE, 11."},{"key":"ref_36","doi-asserted-by":"crossref","first-page":"1727","DOI":"10.1016\/j.cjche.2018.06.008","article-title":"An Improved Artificial Bee Colony Algorithm for Steelmaking-refining-Continuous Casting Scheduling Problem","volume":"26","author":"Peng","year":"2018","journal-title":"Chin. J. Chem. Eng."},{"key":"ref_37","first-page":"33","article-title":"An Adaptive Iterative Chaos Optimization Method","volume":"47","author":"Wenyuan","year":"2013","journal-title":"J. Xian Jiaotong Univ."},{"key":"ref_38","doi-asserted-by":"crossref","first-page":"747","DOI":"10.1016\/j.asoc.2017.08.032","article-title":"Two improved k-means algorithms","volume":"68","author":"Yu","year":"2018","journal-title":"Appl. Soft Comput."}],"container-title":["Algorithms"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1999-4893\/14\/2\/53\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T05:20:49Z","timestamp":1760160049000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1999-4893\/14\/2\/53"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2021,2,7]]},"references-count":38,"journal-issue":{"issue":"2","published-online":{"date-parts":[[2021,2]]}},"alternative-id":["a14020053"],"URL":"https:\/\/doi.org\/10.3390\/a14020053","relation":{},"ISSN":["1999-4893"],"issn-type":[{"value":"1999-4893","type":"electronic"}],"subject":[],"published":{"date-parts":[[2021,2,7]]}}}