{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,27]],"date-time":"2026-03-27T02:27:51Z","timestamp":1774578471335,"version":"3.50.1"},"reference-count":25,"publisher":"MDPI AG","issue":"7","license":[{"start":{"date-parts":[[2017,7,19]],"date-time":"2017-07-19T00:00:00Z","timestamp":1500422400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Sensors"],"abstract":"<jats:p>Routing protocols based on topology control are significantly important for improving network longevity in wireless sensor networks (WSNs). Traditionally, some WSN routing protocols distribute uneven network traffic load to sensor nodes, which is not optimal for improving network longevity. Differently to conventional WSN routing protocols, we propose a dynamic hierarchical protocol based on combinatorial optimization (DHCO) to balance energy consumption of sensor nodes and to improve WSN longevity. For each sensor node, the DHCO algorithm obtains the optimal route by establishing a feasible routing set instead of selecting the cluster head or the next hop node. The process of obtaining the optimal route can be formulated as a combinatorial optimization problem. Specifically, the DHCO algorithm is carried out by the following procedures. It employs a hierarchy-based connection mechanism to construct a hierarchical network structure in which each sensor node is assigned to a special hierarchical subset; it utilizes the combinatorial optimization theory to establish the feasible routing set for each sensor node, and takes advantage of the maximum\u2013minimum criterion to obtain their optimal routes to the base station. Various results of simulation experiments show effectiveness and superiority of the DHCO algorithm in comparison with state-of-the-art WSN routing algorithms, including low-energy adaptive clustering hierarchy (LEACH), hybrid energy-efficient distributed clustering (HEED), genetic protocol-based self-organizing network clustering (GASONeC), and double cost function-based routing (DCFR) algorithms.<\/jats:p>","DOI":"10.3390\/s17071665","type":"journal-article","created":{"date-parts":[[2017,7,20]],"date-time":"2017-07-20T04:28:26Z","timestamp":1500524906000},"page":"1665","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":31,"title":["Dynamic Hierarchical Energy-Efficient Method Based on Combinatorial Optimization for Wireless Sensor Networks"],"prefix":"10.3390","volume":"17","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-2643-8054","authenticated-orcid":false,"given":"Yuchao","family":"Chang","sequence":"first","affiliation":[{"name":"Science and Technology on Microsystem Laboratory, Shanghai Institute of Microsystem and Information Technology, Chinese Academy of Sciences, Shanghai 201800, China"},{"name":"University of Chinese Academy of Sciences, Beijing 100049, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Hongying","family":"Tang","sequence":"additional","affiliation":[{"name":"Science and Technology on Microsystem Laboratory, Shanghai Institute of Microsystem and Information Technology, Chinese Academy of Sciences, Shanghai 201800, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Yongbo","family":"Cheng","sequence":"additional","affiliation":[{"name":"Science and Technology on Microsystem Laboratory, Shanghai Institute of Microsystem and Information Technology, Chinese Academy of Sciences, Shanghai 201800, China"},{"name":"University of Chinese Academy of Sciences, Beijing 100049, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Qin","family":"Zhao","sequence":"additional","affiliation":[{"name":"Science and Technology on Microsystem Laboratory, Shanghai Institute of Microsystem and Information Technology, Chinese Academy of Sciences, Shanghai 201800, China"},{"name":"University of Chinese Academy of Sciences, Beijing 100049, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Baoqing","family":"Yuan","sequence":"additional","affiliation":[{"name":"Science and Technology on Microsystem Laboratory, Shanghai Institute of Microsystem and Information Technology, Chinese Academy of Sciences, Shanghai 201800, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2017,7,19]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","unstructured":"Goyal, D., and Tripathy, M.R. (2012, January 7\u20138). Routing Protocols in Wireless Sensor Networks: A Survey. Proceedings of 2012 Second International Conference on Advanced Computing & Communication Technologies (ACCT), Rohtak, Haryana, India.","DOI":"10.1109\/ACCT.2012.98"},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"24125","DOI":"10.3390\/s150924125","article-title":"Self-Adaptive Strategy Based on Fuzzy Control Systems for Improving Performance in Wireless Sensors Networks","volume":"15","author":"Diaz","year":"2015","journal-title":"Sensors"},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"3981","DOI":"10.1109\/JSEN.2016.2539360","article-title":"Fair Routing for Overlapped Cooperative Heterogeneous Wireless Sensor Networks","volume":"16","author":"Kinoshita","year":"2016","journal-title":"IEEE Sens. J."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"11","DOI":"10.1109\/TII.2011.2166778","article-title":"A Distributed Topology Control Technique for Low Interference and Energy Efficiency in Wireless Sensor Networks","volume":"8","author":"Chiwewe","year":"2012","journal-title":"IEEE Trans. Ind. Inf."},{"key":"ref_5","doi-asserted-by":"crossref","unstructured":"Sayyed, R., Kundu, S., Warty, C., and Nema, S. (2014, January 18\u201321). Resource Optimization using Software Defined Networking for Smart Grid Wireless Sensor Network. Proceedings of 2014 3rd International Conference on Eco-Friendly Computing and Communication Systems (ICECCS), Mangalore, India.","DOI":"10.1109\/Eco-friendly.2014.48"},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"551","DOI":"10.1109\/SURV.2012.062612.00084","article-title":"Energy-Efficient Routing Protocols in Wireless Sensor Networks: A Survey","volume":"15","author":"Pantazis","year":"2013","journal-title":"IEEE Commun. Surv. Tutor."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"3381","DOI":"10.1109\/JSEN.2015.2388857","article-title":"Measuring and Modeling the Energy Cost of Reconfiguration in Sensor Networks","volume":"15","author":"Ramachandran","year":"2015","journal-title":"IEEE Sens. J."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"1027","DOI":"10.1049\/iet-com.2015.0884","article-title":"Reliable routing in wireless sensor networks based on coalitional game theory","volume":"10","author":"Feng","year":"2016","journal-title":"IET Commun."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"927","DOI":"10.1109\/TMC.2010.238","article-title":"Energy-Balanced Transmission Policies for Wireless Sensor Networks","volume":"10","author":"Azad","year":"2011","journal-title":"IEEE Trans. Mob. Comput."},{"key":"ref_10","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_11","unstructured":"Heinzelman, W.R., Chandrakasan, A.P., and Balakrishnan, H. (2000, January 7). Energy-Efficient Communication Protocol for Wireless Microsensor Networks. Proceedings of the 33rd Annual Hawaii International Conference on System Sciences, Maui, HI, USA."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"2194","DOI":"10.1109\/LCOMM.2014.2381226","article-title":"Balancing Energy Consumption in Heterogeneous Wireless Sensor Networks Using Genetic Algorithm","volume":"19","author":"Elhoseny","year":"2015","journal-title":"IEEE Commun. Lett."},{"key":"ref_13","unstructured":"Smaragdakis, G., Matta, I., and Matta, A. (2017, July 17). SEP: A Stable Election Protocol for Clustered Heterogeneous Wireless Sensor Networks. Available online: http:\/\/open.bu.edu\/handle\/2144\/1548."},{"key":"ref_14","unstructured":"Elbhiri, B., Saadane, R., Fldhi, E.S., and Aboutajdine, D. (October, January 30). Developed Distributed Energy-Efficient Clustering (DDEEC) for Heterogeneous Wireless Sensor Networks. Proceedings of the 5th International Symposium on I\/V Communications and Mobile Network (ISVC), Rabat, Morocco."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"788","DOI":"10.1109\/TII.2015.2411231","article-title":"Lifetime and Energy Hole Evolution Analysis in Data-Gathering Wireless Sensor Networks","volume":"12","author":"Ren","year":"2016","journal-title":"IEEE Trans. Ind. Inform."},{"key":"ref_16","unstructured":"Lindsey, S., and Raghavendra, C.S. (2002, January 9\u201316). PEGASIS: Power-Efficient Gathering in Sensor Information Systems. Proceedings of the IEEE on Aerospace Conference Proceedings, Big Sky, MT, USA."},{"key":"ref_17","unstructured":"Li, C.F., Ye, M., Chen, G.H., and Wu, J. (2005, January 7). An Energy-Efficient Unequal Clustering Mechanism for Wireless Sensor Networks. Proceedings of the 2nd IEEE International Conference on Mobile Ad-Hoc and Sensor Systems, Washington, DC, USA."},{"key":"ref_18","doi-asserted-by":"crossref","unstructured":"Nadeem, Q., Rasheed, M.B., Javaid, N., Khan, Z.A., Maqsood, Y., and Din, A. (2013, January 28\u201330). M-GEAR: Gateway-Based Energy-Aware Multi-Hop Routing Protocol for WSNs. Proceedings of the 2013 Eighth International Conference on Broadband and Wireless Computing, Communication and Applications (BWCCA), Compiegne, France.","DOI":"10.1109\/BWCCA.2013.35"},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"1471","DOI":"10.1109\/TMC.2006.141","article-title":"A Comment on \u201cHEED: A Hybrid, Energy-Efficient, Distributed Clustering Approach for Ad Hoc Sensor Networks\u201d","volume":"5","author":"Lin","year":"2006","journal-title":"IEEE Trans. Mob. Comput."},{"key":"ref_20","doi-asserted-by":"crossref","unstructured":"Shirmohammadi, M.M., Faez, K., and Chhardoli, M. (2009, January 6\u20138). LELE: Leader Election with Load Balancing Energy in Wireless Sensor Network. Proceedings of the CMC \u201909. WRI International Conference on Communications and Mobile Computing, Yunnan, China.","DOI":"10.1109\/CMC.2009.227"},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"21","DOI":"10.1007\/s10922-016-9379-7","article-title":"A Genetic Algorithm-Based, Dynamic Clustering Method Towards Improved WSN Longevity","volume":"25","author":"Yuan","year":"2017","journal-title":"J Netw. Syst. Manag."},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"310","DOI":"10.1016\/j.jnca.2013.07.010","article-title":"Ant colony optimization with greedy migration mechanism for node deployment in wireless sensor networks","volume":"39","author":"Liu","year":"2014","journal-title":"J. Netw. Comput. Appl."},{"key":"ref_23","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_24","doi-asserted-by":"crossref","unstructured":"Tang, J.Q., Yang, W., Zhu, L.Y., Wang, D., and Feng, X. (2017). An Adaptive Clustering Approach Based on Minimum Travel Route Planning for Wireless Sensor Networks with a Mobile Sink. Sensors, 17.","DOI":"10.3390\/s17050964"},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"1469","DOI":"10.1016\/j.adhoc.2012.04.004","article-title":"An Energy-aware Distributed Clustering Protocol in Wireless Sensor Networks using Fuzzy Logic","volume":"10","author":"Taheri","year":"2012","journal-title":"Ad Hoc Netw."}],"container-title":["Sensors"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1424-8220\/17\/7\/1665\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T18:43:17Z","timestamp":1760208197000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1424-8220\/17\/7\/1665"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2017,7,19]]},"references-count":25,"journal-issue":{"issue":"7","published-online":{"date-parts":[[2017,7]]}},"alternative-id":["s17071665"],"URL":"https:\/\/doi.org\/10.3390\/s17071665","relation":{},"ISSN":["1424-8220"],"issn-type":[{"value":"1424-8220","type":"electronic"}],"subject":[],"published":{"date-parts":[[2017,7,19]]}}}