{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,6,10]],"date-time":"2026-06-10T16:35:23Z","timestamp":1781109323827,"version":"3.54.1"},"reference-count":32,"publisher":"MDPI AG","issue":"7","license":[{"start":{"date-parts":[[2021,4,4]],"date-time":"2021-04-04T00:00:00Z","timestamp":1617494400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"National Science Foundation Council of China","award":["61771006, 61976080, U1804149, 61701170"],"award-info":[{"award-number":["61771006, 61976080, U1804149, 61701170"]}]},{"name":"Key research projects of university in Henan province of China","award":["21A413002, 19A413006, 20B510001"],"award-info":[{"award-number":["21A413002, 19A413006, 20B510001"]}]},{"name":"Programs for Science and Technology Development of Henan Province","award":["192102210254"],"award-info":[{"award-number":["192102210254"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Sensors"],"abstract":"<jats:p>Aiming at high network energy consumption and data delay induced by mobile sink in wireless sensor networks (WSNs), this paper proposes a cluster-based energy optimization algorithm called Cluster-Based Energy Optimization with Mobile Sink (CEOMS). CEOMS algorithm constructs the energy density function of network nodes firstly and then assigns sensor nodes with higher remaining energy as cluster heads according to energy density function. Meanwhile, the directivity motion performance function of mobile sink is constructed to enhance the probability of remote sensor nodes being assigned as cluster heads. Secondly, based on Low Energy Adaptive Clustering Hierarchy Protocol (LEACH) architecture, the energy density function and the motion performance function are introduced into the cluster head selection process to avoid random assignment of cluster head. Finally, an adaptive adjustment function is designed to improve the adaptability of cluster head selection by percentage of network nodes death and the density of all surviving nodes of the entire network. The simulation results show that the proposed CEOMS algorithm improves the cluster head selection self-adaptability, extends the network life, reduces the data delay, and balances the network load.<\/jats:p>","DOI":"10.3390\/s21072523","type":"journal-article","created":{"date-parts":[[2021,4,5]],"date-time":"2021-04-05T11:48:29Z","timestamp":1617623309000},"page":"2523","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":47,"title":["A Cluster-Based Energy Optimization Algorithm in Wireless Sensor Networks with Mobile Sink"],"prefix":"10.3390","volume":"21","author":[{"given":"Qian","family":"Wei","sequence":"first","affiliation":[{"name":"School of Artificial Intelligence, Henan University, Kaifeng 475004, China"},{"name":"School of Computer and Information Engineering, Henan University, Kaifeng 475004, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-3523-9009","authenticated-orcid":false,"given":"Ke","family":"Bai","sequence":"additional","affiliation":[{"name":"School of Artificial Intelligence, Henan University, Kaifeng 475004, China"},{"name":"School of Computer and Information Engineering, Henan University, Kaifeng 475004, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-2700-834X","authenticated-orcid":false,"given":"Lin","family":"Zhou","sequence":"additional","affiliation":[{"name":"School of Artificial Intelligence, Henan University, Kaifeng 475004, China"},{"name":"School of Computer and Information Engineering, Henan University, Kaifeng 475004, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Zhentao","family":"Hu","sequence":"additional","affiliation":[{"name":"School of Artificial Intelligence, Henan University, Kaifeng 475004, China"},{"name":"School of Computer and Information Engineering, Henan University, Kaifeng 475004, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-9325-5966","authenticated-orcid":false,"given":"Yong","family":"Jin","sequence":"additional","affiliation":[{"name":"School of Artificial Intelligence, Henan University, Kaifeng 475004, China"},{"name":"School of Computer and Information Engineering, Henan University, Kaifeng 475004, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Junwei","family":"Li","sequence":"additional","affiliation":[{"name":"School of Artificial Intelligence, Henan University, Kaifeng 475004, China"},{"name":"School of Computer and Information Engineering, Henan University, Kaifeng 475004, China"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"1968","published-online":{"date-parts":[[2021,4,4]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"41","DOI":"10.1016\/j.aeue.2019.02.006","article-title":"Energy aware cluster based multi-hop energy efficient routing protocol using multiple mobile nodes (MEACBM) in wireless sensor networks","volume":"102","author":"Toor","year":"2019","journal-title":"AEU Int. J. Electron. Commun."},{"key":"ref_2","first-page":"41","article-title":"Efficient path planning for a mobile sink to reliably gather data from sensors with diverse sensing rates and limited buffers","volume":"18","author":"Wang","year":"2018","journal-title":"IEEE Trans. Mob. Comput."},{"key":"ref_3","doi-asserted-by":"crossref","unstructured":"Yuan, X.X., and Zhang, R.H. (2011, January 23\u201325). An energy-efficient mobile sink routing algorithm for wireless sensor networks. Proceedings of the 2011 7th International Conference on Wireless Communications, Networking and Mobile Computing, Wuhan, China.","DOI":"10.1109\/wicom.2011.6040374"},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"142","DOI":"10.1016\/j.eswa.2017.09.008","article-title":"Optimizing K-coverage of mobile WSNs","volume":"92","author":"Elhoseny","year":"2018","journal-title":"Expert Syst. Appl."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"770","DOI":"10.1109\/TMC.2014.2338315","article-title":"Mobile data gathering with load balanced clustering and dual data uploading in wireless sensor networks","volume":"14","author":"Zhao","year":"2014","journal-title":"IEEE Trans. Mob. Comput."},{"key":"ref_6","first-page":"41","article-title":"Key management for static wireless sensor networks with node adding","volume":"10","author":"Gandino","year":"2013","journal-title":"IEEE Trans. Ind. Inform."},{"key":"ref_7","doi-asserted-by":"crossref","unstructured":"Ye, G., Zhang, B., and Chai, S. (2014, January 13\u201314). Energy balanced virtual force-based approach for mobile WSNs. Proceedings of the 2014 7th International Symposium on Computational Intelligence and Design, Hangzhou, China.","DOI":"10.1109\/ISCID.2014.167"},{"key":"ref_8","unstructured":"Khandnor, P., and Aseri, T.C. (2014, January 6\u20138). Comparison of routing protocols in wireless sensor network using mobile sink\u2014A survey. Proceedings of the Recent Advances in Engineering and Computational Sciences (RAECS), Chandigarh, India."},{"key":"ref_9","doi-asserted-by":"crossref","unstructured":"He, X., Fu, X., Yang, Y., and Zhang, J. (2018, January 6\u20137). Mobile Sink path selection and routing optimization algorithm for network energy balance. Proceedings of the International Symposium in Sensing and Instrumentation in IoT Era (ISSI), Shanghai, China.","DOI":"10.1109\/ISSI.2018.8538112"},{"key":"ref_10","doi-asserted-by":"crossref","unstructured":"Wang, J., Gao, Y., Liu, W., Sangaiah, A.K., and Kim, H.J. (2019). Energy efficient routing algorithm with mobile sink support for wireless sensor networks. Sensors, 19.","DOI":"10.3390\/s19071494"},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"14301","DOI":"10.3390\/s131114301","article-title":"An energy efficient stable election-based routing algorithm for wireless sensor networks","volume":"13","author":"Wang","year":"2013","journal-title":"Sensors"},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"92813","DOI":"10.1109\/ACCESS.2019.2927627","article-title":"A Fast and Efficient Broadcast Protocol With a Mobile Sink Node in Asynchronous Wireless Sensor Networks","volume":"7","author":"Cheng","year":"2019","journal-title":"IEEE Access"},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"4576","DOI":"10.1109\/JSEN.2015.2424296","article-title":"Mobile sink-based adaptive immune energy-efficient clustering protocol for improving the lifetime and stability period of wireless sensor networks","volume":"15","author":"Ahmed","year":"2015","journal-title":"IEEE Sens. J."},{"key":"ref_14","unstructured":"Heinzelman, W.R., Chandrakasan, A., and Balakrishnan, H. (2000, January 4\u20137). Energy-efficient communication protocol for wireless microsensor networks. Proceedings of the 33rd Annual Hawaii International Conference on System Sciences, Maui, HI, USA."},{"key":"ref_15","unstructured":"Jia, X., Ning, J., Lou, X., Peng, T., Zhou, Q., and Chen, Y. (2012, January 29\u201331). Improvement of LEACH protocol for WSN. Proceedings of the 2012 9th International Conference on Fuzzy Systems and Knowledge Discovery, Chongqing, China."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"366","DOI":"10.1109\/TMC.2004.41","article-title":"HEED: A hybrid, energy-efficient, distributed clustering approach for ad hoc sensor networks","volume":"3","author":"Younis","year":"2004","journal-title":"IEEE Trans. Mob. Comput."},{"key":"ref_17","unstructured":"Smaragdakis, G., Matta, I., and Bestavros, A. (2004). SEP: A Stable Election Protocol for Clustered Heterogeneous Wireless Sensor Networks, Boston University Computer Science Department."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"660","DOI":"10.1109\/TWC.2002.804190","article-title":"An application-specific protocol architecture for wireless microsensor networks","volume":"1","author":"Heinzelman","year":"2002","journal-title":"IEEE Trans. Wirel. Commun."},{"key":"ref_19","doi-asserted-by":"crossref","unstructured":"Kumar, S., Verma, A., Gautam, P.R., Dayal, A., and Kumar, A. (2018, January 2\u20134). The load balancing of optimizing leach clustering algorithm with mobile sink and rendezvous nodes. Proceedings of the 2018 5th IEEE Uttar Pradesh Section International Conference on Electrical, Electronics and Computer Engineering (UPCON), Gorakhpur, India.","DOI":"10.1109\/UPCON.2018.8596989"},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"153504","DOI":"10.1016\/j.aeue.2020.153504","article-title":"Energy-balanced data collection with path-constrained mobile sink in wireless sensor networks","volume":"127","author":"Fu","year":"2020","journal-title":"AEU Int. J. Electron. Commun."},{"key":"ref_21","unstructured":"Zhang, R., Pan, J., Liu, J., and Xie, D. (2015, January 9\u201312). A hybrid approach using mobile element and hierarchical clustering for data collection in WSNs. Proceedings of the IEEE Wireless Communications and Networking Conference (WCNC), New Orleans, LA, USA."},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"381","DOI":"10.1109\/ACCESS.2015.2424452","article-title":"A tree-cluster-based data-gathering algorithm for industrial WSNs with a mobile sink","volume":"3","author":"Zhu","year":"2015","journal-title":"IEEE Access"},{"key":"ref_23","doi-asserted-by":"crossref","unstructured":"Jing, Y., Zetao, L., and Yi, L. (2013, January 25\u201327). An improved routing algorithm based on LEACH for wireless sensor networks. Proceedings of the 2013 25th Chinese Control and Decision Conference (CCDC), Guiyang, China.","DOI":"10.1109\/CCDC.2013.6561594"},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"807","DOI":"10.1016\/j.procs.2015.07.481","article-title":"A proposed energy efficient distance based cluster head (DBCH) Algorithm: An Improvement over LEACH","volume":"57","author":"Sharma","year":"2015","journal-title":"Procedia Comput. Sci."},{"key":"ref_25","doi-asserted-by":"crossref","unstructured":"Darabkh, K.A., and Zomot, J.N. (2018, January 25\u201329). An improved cluster head selection algorithm for wireless sensor networks. Proceedings of the 2018 14th International Wireless Communications & Mobile Computing Conference (IWCMC), Limassol, Cyprus.","DOI":"10.1109\/IWCMC.2018.8450446"},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"28","DOI":"10.1109\/TII.2015.2489160","article-title":"An energy-balanced heuristic for mobile sink scheduling in hybrid WSNs","volume":"12","author":"Zhou","year":"2015","journal-title":"IEEE Trans. Ind. Inform."},{"key":"ref_27","doi-asserted-by":"crossref","unstructured":"Kushal, B.Y., and Chitra, M. (2016, January 21\u201322). Cluster based routing protocol to prolong network lifetime through mobile sink in WSN. Proceedings of the IEEE International Conference on Recent Trends in Electronics, Information & Communication Technology (RTEICT), Bangalore, India.","DOI":"10.1109\/RTEICT.2016.7808039"},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"473","DOI":"10.1109\/JIOT.2017.2748987","article-title":"Sensor Fusion for Public Space Utilization Monitoring in a Smart City","volume":"5","author":"Lau","year":"2018","journal-title":"IEEE Internet Things J."},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"223","DOI":"10.1109\/TSMC.2020.3042898","article-title":"Internet of Things as System of Systems: A Review of Methodologies, Frameworks, Platforms, and Tools","volume":"51","author":"Fortino","year":"2021","journal-title":"IEEE Trans. Syst. Man Cybern. Syst."},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"3944","DOI":"10.1109\/JSEN.2014.2358567","article-title":"SEECH: Scalable energy efficient clustering hierarchy protocol in wireless sensor networks","volume":"14","author":"Tarhani","year":"2014","journal-title":"IEEE Sens. J."},{"key":"ref_31","first-page":"1073","article-title":"A hardware-efficient sigmoid function with adjustable precision for a neural network system","volume":"62","author":"Tsai","year":"2015","journal-title":"IEEE Trans. Circuits Syst. II Express Briefs"},{"key":"ref_32","doi-asserted-by":"crossref","unstructured":"Das, D., Rehena, Z., Roy, S., and Mukherjee, N. (2013, January 7\u201310). Multiple-sink placement strategies in wireless sensor networks. Proceedings of the 2013 Fifth International Conference on Communication Systems and Networks (COMSNETS), Bangalore, India.","DOI":"10.1109\/COMSNETS.2013.6465578"}],"container-title":["Sensors"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1424-8220\/21\/7\/2523\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,13]],"date-time":"2025-10-13T13:58:20Z","timestamp":1760363900000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1424-8220\/21\/7\/2523"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2021,4,4]]},"references-count":32,"journal-issue":{"issue":"7","published-online":{"date-parts":[[2021,4]]}},"alternative-id":["s21072523"],"URL":"https:\/\/doi.org\/10.3390\/s21072523","relation":{},"ISSN":["1424-8220"],"issn-type":[{"value":"1424-8220","type":"electronic"}],"subject":[],"published":{"date-parts":[[2021,4,4]]}}}