{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,4,26]],"date-time":"2025-04-26T01:19:08Z","timestamp":1745630348387,"version":"3.37.3"},"reference-count":51,"publisher":"MDPI AG","issue":"7","license":[{"start":{"date-parts":[[2022,7,15]],"date-time":"2022-07-15T00:00:00Z","timestamp":1657843200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["61872085"],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100003392","name":"Natural Science Foundation of Fujian Province","doi-asserted-by":"publisher","award":["2018J01638"],"id":[{"id":"10.13039\/501100003392","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"In wireless sensor networks (WSN), most sensor nodes are powered by batteries with limited power, meaning the quality of the network may deteriorate at any time. Therefore, to reduce the energy consumption of sensor nodes and extend the lifetime of the network, this study proposes a novel energy-efficient clustering mechanism of a routing protocol. First, a novel metaheuristic algorithm is proposed, based on differential equations of bamboo growth and the Gaussian mixture model, called the bamboo growth optimizer (BFGO). Second, based on the BFGO algorithm, a clustering mechanism of a routing protocol (BFGO-C) is proposed, in which the encoding method and fitness function are redesigned. It can maximize the energy efficiency and minimize the transmission distance. In addition, heterogeneous nodes are added to the WSN to distinguish tasks among nodes and extend the lifetime of the network. Finally, this paper compares the proposed BFGO-C with three classic clustering protocols. The results show that the protocol based on the BFGO-C can be successfully applied to the clustering routing protocol and can effectively reduce energy consumption and enhance network performance.<\/jats:p>","DOI":"10.3390\/e24070980","type":"journal-article","created":{"date-parts":[[2022,7,18]],"date-time":"2022-07-18T01:00:28Z","timestamp":1658106028000},"page":"980","source":"Crossref","is-referenced-by-count":17,"title":["Energy-Efficient Clustering Mechanism of Routing Protocol for Heterogeneous Wireless Sensor Network Based on Bamboo Forest Growth Optimizer"],"prefix":"10.3390","volume":"24","author":[{"given":"Qing","family":"Feng","sequence":"first","affiliation":[{"name":"College of Computer Science and Engineering, Shandong University of Science and Technology, Qingdao 266590, China"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-2117-0618","authenticated-orcid":false,"given":"Shu-Chuan","family":"Chu","sequence":"additional","affiliation":[{"name":"College of Computer Science and Engineering, Shandong University of Science and Technology, Qingdao 266590, China"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-3128-9025","authenticated-orcid":false,"given":"Jeng-Shyang","family":"Pan","sequence":"additional","affiliation":[{"name":"College of Computer Science and Engineering, Shandong University of Science and Technology, Qingdao 266590, China"},{"name":"Department of Information Management, Chaoyang University of Technology, Taichung 41349, Taiwan"}]},{"given":"Jie","family":"Wu","sequence":"additional","affiliation":[{"name":"School of Electrical and Information Engineering, Zhengzhou University of Light Industry, Zhengzhou 450002, China"}]},{"given":"Tien-Szu","family":"Pan","sequence":"additional","affiliation":[{"name":"Department of Electronic Engineering, National Kaohsiung University of Science and Technology, Kaohsiung 82445, Taiwan"}]}],"member":"1968","published-online":{"date-parts":[[2022,7,15]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","unstructured":"Gallart, V., Felici-Castell, S., Delamo, M., Foster, A., and Perez, J.J. (2011, January 17\u201322). Evaluation of a real, low cost, urban wsn deployment for accurate environmental monitoring. Proceedings of the 2011 IEEE Eighth International Conference on Mobile Ad-Hoc and Sensor Systems, Valencia, Spain.","DOI":"10.1109\/MASS.2011.66"},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"454","DOI":"10.1016\/j.comcom.2009.10.013","article-title":"The room shortage problem of tree-based ZigBee\/IEEE 802.15. 4 wireless networks","volume":"33","author":"Yen","year":"2010","journal-title":"Comput. Commun."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"209","DOI":"10.1504\/IJAHUC.2013.055465","article-title":"Gatherer: An environmental monitoring application based on IPv6 using wireless sensor networks","volume":"13","author":"Ramos","year":"2013","journal-title":"Int. J. Hoc Ubiquitous Comput."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"729680","DOI":"10.1155\/2015\/729680","article-title":"A balanced power consumption algorithm based on enhanced parallel cat swarm optimization for wireless sensor network","volume":"11","author":"Kong","year":"2015","journal-title":"Int. J. Distrib. Sens. Netw."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"1091","DOI":"10.1007\/s11276-009-0190-1","article-title":"Integration of wireless sensor networks in environmental monitoring cyber infrastructure","volume":"16","author":"Yang","year":"2010","journal-title":"Wirel. Netw."},{"key":"ref_6","doi-asserted-by":"crossref","unstructured":"Rodr\u00edguez, A., Del-Valle-Soto, C., and Vel\u00e1zquez, R. (2020). Energy-efficient clustering routing protocol for wireless sensor networks based on yellow saddle goatfish algorithm. Mathematics, 8.","DOI":"10.3390\/math8091515"},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"304","DOI":"10.1016\/j.ins.2020.11.056","article-title":"An efficient surrogate-assisted hybrid optimization algorithm for expensive optimization problems","volume":"561","author":"Pan","year":"2021","journal-title":"Inf. Sci."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"104049","DOI":"10.1016\/j.engappai.2020.104049","article-title":"Digital watermarking with improved SMS applied for QR code","volume":"97","author":"Pan","year":"2021","journal-title":"Eng. Appl. Artif. Intell."},{"key":"ref_9","unstructured":"Kennedy, J., and Eberhart, R. (December, January 27). Particle swarm optimization. Proceedings of the ICNN\u201995-International Conference on Neural Networks, Perth, WA, Australia."},{"key":"ref_10","first-page":"138","article-title":"Classification of Multiple Power Quality Disturbances Based on PSO-SVM of Hybrid Kernel Function","volume":"10","author":"Zhao","year":"2019","journal-title":"J. Inf. Hiding Multim. Signal Process."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"65","DOI":"10.1007\/BF00175354","article-title":"A genetic algorithm tutorial","volume":"4","author":"Whitley","year":"1994","journal-title":"Stat. Comput."},{"key":"ref_12","unstructured":"Wang, F.H., Jain, L.C., and Pan, J.S. (2003). A novel VQ-based watermarking scheme with genetic codebook partition. Design and Application of Hybrid Intelligent Systems, IOS Press."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"464","DOI":"10.1108\/02644401211235834","article-title":"Bat algorithm: A novel approach for global engineering optimization","volume":"29","author":"Yang","year":"2012","journal-title":"Eng. Comput."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"169","DOI":"10.1016\/j.knosys.2018.11.024","article-title":"Seagull optimization algorithm: Theory and its applications for large-scale industrial engineering problems","volume":"165","author":"Dhiman","year":"2019","journal-title":"Knowl.-Based Syst."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"46","DOI":"10.1016\/j.advengsoft.2013.12.007","article-title":"Grey Wolf Optimizer","volume":"69","author":"Mirjalili","year":"2014","journal-title":"Adv. Eng. Softw."},{"key":"ref_16","doi-asserted-by":"crossref","unstructured":"Helali, S., Masmoudi, A., and Slaoui, Y. (2022). Semi-Parametric Estimation Using Bernstein Polynomial and a Finite Gaussian Mixture Model. Entropy, 24.","DOI":"10.3390\/e24030315"},{"key":"ref_17","doi-asserted-by":"crossref","unstructured":"Bai, D., Yao, W., Wang, S., and Wang, J. (2022). Multiscale Weighted Permutation Entropy Analysis of Schizophrenia Magnetoencephalograms. Entropy, 24.","DOI":"10.3390\/e24030314"},{"key":"ref_18","unstructured":"Handy, M., Haase, M., and Timmermann, D. (2002, January 9\u201311). Low energy adaptive clustering hierarchy with deterministic cluster-head selection. Proceedings of the 4th International Workshop on Mobile and Wireless Communications Network, Stockholm, Sweden."},{"key":"ref_19","doi-asserted-by":"crossref","unstructured":"Mhatre, V., and Rosenberg, C. (2004, January 20\u201324). Homogeneous vs heterogeneous clustered sensor networks: A comparative study. Proceedings of the 2004 IEEE International Conference on Communications (IEEE Cat. No. 04CH37577), Paris, France.","DOI":"10.1109\/ICC.2004.1313223"},{"key":"ref_20","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_21","unstructured":"Smaragdakis, G., Matta, I., and Bestavros, A. (2004, January 22\u201324). SEP: A stable election protocol for clustered heterogeneous wireless sensor networks. Proceedings of the 2nd International Workshop on Sensor and Actor Network Protocols and Applications (SANPA 2004), Boston, MA, USA."},{"key":"ref_22","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_23","first-page":"8","article-title":"Intelligent hierarchical cluster-based routing","volume":"7","author":"Matin","year":"2006","journal-title":"Life"},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"2230","DOI":"10.1016\/j.comcom.2006.02.017","article-title":"Design of a distributed energy-efficient clustering algorithm for heterogeneous wireless sensor networks","volume":"29","author":"Qing","year":"2006","journal-title":"Comput. Commun."},{"key":"ref_25","doi-asserted-by":"crossref","unstructured":"Latiff, N.A., Tsimenidis, C.C., and Sharif, B.S. (2007, January 3\u20137). Energy-aware clustering for wireless sensor networks using particle swarm optimization. Proceedings of the 2007 IEEE 18th International Symposium on Personal, Indoor and Mobile Radio Communications, Athens, Greece.","DOI":"10.1109\/PIMRC.2007.4394521"},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"79","DOI":"10.7763\/IJMLC.2011.V1.12","article-title":"LEACH-GA: Genetic algorithm-based energy-efficient adaptive clustering protocol for wireless sensor networks","volume":"1","author":"Liu","year":"2011","journal-title":"Int. J. Mach. Learn. Comput."},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"847","DOI":"10.1007\/s11276-012-0438-z","article-title":"Cluster based wireless sensor network routing using artificial bee colony algorithm","volume":"18","author":"Karaboga","year":"2012","journal-title":"Wirel. Netw."},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"1950","DOI":"10.1016\/j.asoc.2011.04.007","article-title":"A new evolutionary based routing protocol for clustered heterogeneous wireless sensor networks","volume":"12","author":"Khalil","year":"2012","journal-title":"Appl. Soft Comput."},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1016\/j.swevo.2016.03.003","article-title":"Hybrid HSA and PSO algorithm for energy efficient cluster head selection in wireless sensor networks","volume":"30","author":"Shankar","year":"2016","journal-title":"Swarm Evol. Comput."},{"key":"ref_30","doi-asserted-by":"crossref","unstructured":"Pal, R., Mittal, H., Pandey, A., and Saraswat, M. (2016, January 11\u201313). BEECP: Biogeography optimization-based energy efficient clustering protocol for HWSNs. Proceedings of the 2016 Ninth International Conference on Contemporary Computing (IC3), Noida, India.","DOI":"10.1109\/IC3.2016.7880201"},{"key":"ref_31","doi-asserted-by":"crossref","unstructured":"Bhushan, S., Pal, R., and Antoshchuk, S.G. (2018, January 21\u201325). Energy efficient clustering protocol for heterogeneous wireless sensor network: A hybrid approach using GA and K-means. Proceedings of the 2018 IEEE Second International Conference on Data Stream Mining Processing (DSMP), Lviv, Ukraine.","DOI":"10.1109\/DSMP.2018.8478538"},{"key":"ref_32","doi-asserted-by":"crossref","first-page":"108124","DOI":"10.1016\/j.knosys.2022.108124","article-title":"Parallel fish migration optimization with compact technology based on memory principle for wireless sensor networks","volume":"241","author":"Chu","year":"2022","journal-title":"Knowl.-Based Syst."},{"key":"ref_33","unstructured":"Lindsey, S., and Raghavendra, C.S. (2002, January 9\u201316). PEGASIS: Power-efficient gathering in sensor information systems. Proceedings of the Aerospace Conference, Big Sky, MT, USA."},{"key":"ref_34","doi-asserted-by":"crossref","first-page":"2826","DOI":"10.1016\/j.comcom.2007.05.024","article-title":"A survey on clustering algorithms for wireless sensor networks","volume":"30","author":"Abbasi","year":"2007","journal-title":"Comput. Commun."},{"key":"ref_35","first-page":"89","article-title":"Bamboo shoot growth model based on the stochastic process and its application","volume":"49","author":"Shi","year":"2013","journal-title":"Sci. Silvae Sin."},{"key":"ref_36","unstructured":"Sloboda, B. (1971). Zur Darstellung von Wachstumsprozessen mit Hilfe von Differentialgleichungen erster Ordnung, Mitteilungen der Baden-Wurttembergischen Forstlichen Versuchs- und Forschungsanstalt, Baden-Wurttembergische Forstliche Versuchs- und Forschungsanstalt."},{"key":"ref_37","first-page":"1","article-title":"Using population-based incremental learning algorithm for matching class diagrams","volume":"3","author":"Xue","year":"2019","journal-title":"Data Sci. Pattern Recognit."},{"key":"ref_38","unstructured":"Xian, X., Shi, W., and Huang, H. (2008, January 3\u20135). Comparison of OMNET++ and other simulator for WSN simulation. Proceedings of the 2008 3rd IEEE Conference on Industrial Electronics and Applications, Singapore."},{"key":"ref_39","doi-asserted-by":"crossref","first-page":"50","DOI":"10.1186\/s13638-020-01663-y","article-title":"A parallel WOA with two communication strategies applied in DV-Hop localization method","volume":"2020","author":"Chai","year":"2020","journal-title":"EURASIP J. Wirel. Commun. Netw."},{"key":"ref_40","first-page":"50","article-title":"Energy Efficiency of Dynamically Distributed Clustering Routing for Naturally Scattering Wireless Sensor Networks","volume":"3","author":"Huang","year":"2018","journal-title":"J. Netw. Intell."},{"key":"ref_41","unstructured":"Jadhav, A.R., and Shankar, T. (2017). Whale optimization based energy-efficient cluster head selection algorithm for wireless sensor networks. arXiv."},{"key":"ref_42","doi-asserted-by":"crossref","first-page":"92","DOI":"10.1109\/MC.2008.441","article-title":"Wireless sensor networks","volume":"41","author":"Stankovic","year":"2008","journal-title":"Computer"},{"key":"ref_43","doi-asserted-by":"crossref","first-page":"45","DOI":"10.1016\/S1570-8705(03)00047-7","article-title":"Design guidelines for wireless sensor networks: Communication, clustering and aggregation","volume":"2","author":"Mhatre","year":"2004","journal-title":"Hoc Netw."},{"key":"ref_44","doi-asserted-by":"crossref","first-page":"105788","DOI":"10.1016\/j.asoc.2019.105788","article-title":"Genetic Algorithm-based Optimized Cluster Head selection for single and multiple data sinks in Heterogeneous Wireless Sensor Network","volume":"85","author":"Verma","year":"2019","journal-title":"Appl. Soft Comput."},{"key":"ref_45","unstructured":"Liang, J.J., Qu, B., Suganthan, P.N., and Hern\u00e1ndez-D\u00edaz, A.G. (2013). Problem Definitions and Evaluation Criteria for the CEC 2013 Special Session on Real-Parameter Optimization, Nanyang Technological University. Technical Report."},{"key":"ref_46","doi-asserted-by":"crossref","unstructured":"Awad, N.H., Ali, M.Z., and Suganthan, P.N. (2017, January 5\u20138). Ensemble sinusoidal differential covariance matrix adaptation with Euclidean neighborhood for solving CEC2017 benchmark problems. Proceedings of the 2017 IEEE Congress on Evolutionary Computation (CEC), San Sebasti\u00e1n, Spain.","DOI":"10.1109\/CEC.2017.7969336"},{"key":"ref_47","unstructured":"Song, P.C., Chu, S.C., Pan, J.S., and Yang, H. (2021). Simplified Phasmatodea population evolution algorithm for optimization. Complex Intell. Syst., 1\u201319."},{"key":"ref_48","doi-asserted-by":"crossref","first-page":"947","DOI":"10.1007\/s00158-009-0454-5","article-title":"An effective differential evolution with level comparison for constrained engineering design","volume":"41","author":"Wang","year":"2010","journal-title":"Struct. Multidiscip. Optim."},{"key":"ref_49","doi-asserted-by":"crossref","first-page":"51","DOI":"10.1016\/j.advengsoft.2016.01.008","article-title":"The whale optimization algorithm","volume":"95","author":"Mirjalili","year":"2016","journal-title":"Adv. Eng. Softw."},{"key":"ref_50","doi-asserted-by":"crossref","unstructured":"Darroudi, S.M., and Gomez, C. (2020). Experimental evaluation of 6blemesh: Ipv6-based ble mesh networks. Sensors, 20.","DOI":"10.3390\/s20164623"},{"key":"ref_51","doi-asserted-by":"crossref","unstructured":"Pal, R., and Sharma, A.K. (2013, January 8\u201310). FSEP-E: Enhanced stable election protocol based on fuzzy Logic for cluster head selection in WSNs. Proceedings of the 2013 Sixth International Conference on Contemporary Computing (IC3), Noida, India.","DOI":"10.1109\/IC3.2013.6612233"}],"container-title":["Entropy"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1099-4300\/24\/7\/980\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2024,8,2]],"date-time":"2024-08-02T05:13:31Z","timestamp":1722575611000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1099-4300\/24\/7\/980"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2022,7,15]]},"references-count":51,"journal-issue":{"issue":"7","published-online":{"date-parts":[[2022,7]]}},"alternative-id":["e24070980"],"URL":"https:\/\/doi.org\/10.3390\/e24070980","relation":{},"ISSN":["1099-4300"],"issn-type":[{"type":"electronic","value":"1099-4300"}],"subject":[],"published":{"date-parts":[[2022,7,15]]}}}