{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,18]],"date-time":"2025-10-18T20:58:37Z","timestamp":1760821117851,"version":"build-2065373602"},"reference-count":20,"publisher":"MDPI AG","issue":"23","license":[{"start":{"date-parts":[[2019,11,22]],"date-time":"2019-11-22T00:00:00Z","timestamp":1574380800000},"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":["41974195, 41674144"],"award-info":[{"award-number":["41974195, 41674144"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Sensors"],"abstract":"<jats:p>With the rapid development of unmanned aerial vehicle in space exploration and national defense, large-scale wireless sensor network (WSN) became an important and effective technology. It may require highly accurate locating for the nodes in some real applications. The dynamic node topology control of a large-scale WSN in an unmanned region becomes a hot research topic recently, which helps improve the system connectivity and coverage. In this paper, a hybrid optimization based on two different virtual force algorithms inspired by the interactions among physical sensor nodes is proposed to address the self-consistent node deployment in a large-scale WSN. At the early stage, the deployment algorithm was to deploy the sensor nodes by leveraging the particle motions in dusty plasma to achieve the hexagonal topology of the so-called \u201cYukawa crystal\u201d. After that, another virtual exchange force model was combined to present a hybrid optimization, which could yield perfect hexagonal topology, better network uniformity, higher coverage rate, and faster convergence speed. The influence of node position, velocity, and acceleration during the node deployment stage on the final network topology are carefully discussed for this scheme. It can aid engineers to control the network topology for a large number of wireless sensors with affordable system cost by choosing suitable parameters based on physical environments or application scenarios in the near future.<\/jats:p>","DOI":"10.3390\/s19235108","type":"journal-article","created":{"date-parts":[[2019,11,22]],"date-time":"2019-11-22T09:02:52Z","timestamp":1574413372000},"page":"5108","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":9,"title":["A Hybrid Optimization from Two Virtual Physical Force Algorithms for Dynamic Node Deployment in WSN Applications"],"prefix":"10.3390","volume":"19","author":[{"given":"Qiang","family":"Li","sequence":"first","affiliation":[{"name":"Department of Physics, School of Science, Nanchang University, Nanchang 330031, China"},{"name":"Institute of Space Science and Technology, Nanchang University, Nanchang 330031, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Qiang","family":"Yi","sequence":"additional","affiliation":[{"name":"Institute of Space Science and Technology, Nanchang University, Nanchang 330031, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-0154-3456","authenticated-orcid":false,"given":"Rongxin","family":"Tang","sequence":"additional","affiliation":[{"name":"Department of Physics, School of Science, Nanchang University, Nanchang 330031, China"},{"name":"Institute of Space Science and Technology, Nanchang University, Nanchang 330031, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Xin","family":"Qian","sequence":"additional","affiliation":[{"name":"One Microsoft Way, Redmond, WA 98052-6399, USA"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Kai","family":"Yuan","sequence":"additional","affiliation":[{"name":"Institute of Space Science and Technology, Nanchang University, Nanchang 330031, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Shiyun","family":"Liu","sequence":"additional","affiliation":[{"name":"Usun Microelectronics, Nanchang 330072, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2019,11,22]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"1017","DOI":"10.1109\/TCAD.2009.2018865","article-title":"A framework for energy-consumption-based design space exploration for wireless sensor nodes","volume":"28","author":"Chouhan","year":"2009","journal-title":"IEEE Trans. Comput. Des. Integr. Circuits Syst."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"923","DOI":"10.1016\/j.sysarc.2013.08.002","article-title":"Design and implementation of a P2P communication infrastructure for WSN-based vehicular traffic control applications","volume":"59","year":"2013","journal-title":"J. Syst. Archit."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"1088","DOI":"10.1109\/TITS.2014.2366512","article-title":"Wireless sensor networks for condition monitoring in the railway industry: A survey","volume":"16","author":"Hodge","year":"2015","journal-title":"IEEE Trans. Intell. Transp. Syst."},{"key":"ref_4","first-page":"197","article-title":"Improved mobicast routing protocol to minimize energy consumption for underwater sensor networks","volume":"3","author":"Patil","year":"2017","journal-title":"Int. J. Res. Sci. Eng."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"368","DOI":"10.1016\/j.actaastro.2018.06.041","article-title":"Guaranteeing prescribed performance for air-breathing hypersonic vehicles via an adaptive non-affine tracking controller","volume":"151","author":"Bu","year":"2018","journal-title":"Acta Astronaut."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"139","DOI":"10.1016\/S0166-218X(01)00359-6","article-title":"Packing equal circles in a square: a deterministic global optimization approach","volume":"122","author":"Locateli","year":"2002","journal-title":"Discret. Appl. Math."},{"key":"ref_7","doi-asserted-by":"crossref","unstructured":"Bai, X., Kumar, S., Xuan, D., Yun, Z., and Lai, T. (2006, January 22). Delpoying wireless sensors to achieve both coverage and connectivity. Proceedings of the 7th ACM international Symposium on Mobile ad Hoc Networking and Computing, Florence, Italy.","DOI":"10.1145\/1132905.1132921"},{"key":"ref_8","unstructured":"Asama, H., Arai, T., Fukuda, T., and Hasegawa, T. (2002). Mobile sensor network deployment using potential fields: A distributed, scalable solution to the area coverage problem. Distributed Autonomous Robotic Systems 5, Springer."},{"key":"ref_9","unstructured":"Heo, N., and Varshney, P.K. (2003, January 16\u201320). A distributed self spreading algorithm for mobile wireless sensor networks. Proceedings of the Wireless Communications and Networking, New Orleans, LA, USA."},{"key":"ref_10","doi-asserted-by":"crossref","unstructured":"Zou, Y., and Chakrabarty, K. (2003, January 1\u20133). Sensor deployment and target localization based on virtual forces. Proceedings of the Twenty-Second Annual Joint Conference of the IEEE Computer and Communications, San Francisco, CA, USA.","DOI":"10.1109\/INFCOM.2003.1208965"},{"key":"ref_11","doi-asserted-by":"crossref","unstructured":"Garetto, M., Gribaudo, M., Chiasserini, C.F., and Leonardi, E. (2007, January 8\u201311). A distributed sensor relocatlon scheme for environmental control. Proceedings of the Mobile Adhoc and Sensor Systems, Pisa, Italy.","DOI":"10.1109\/MOBHOC.2007.4428663"},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"152","DOI":"10.5772\/61443","article-title":"Optimized node deployment algorithm and parameter investigation in a mobile sensor network for robotic systems","volume":"12","author":"Tang","year":"2015","journal-title":"Int. J. Adv. Robot. Syst."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"79","DOI":"10.5772\/58427","article-title":"A deployment method based on spring force in wireless robot sensor networks","volume":"11","author":"Yu","year":"2014","journal-title":"Int. J. Adv. Robot. Syst."},{"key":"ref_14","first-page":"8","article-title":"A node deployment algorithm based on Van der Waals force in wireless sensor networks","volume":"9","author":"Yu","year":"2013","journal-title":"Int. J. Distrib. Sens. Netw."},{"key":"ref_15","unstructured":"Toumpis, S., and Tassiulas, L. (2005, January 13\u201317). Deployment of massively dense sensor networks as an electrostatics problem. Proceedings of the 24th Annual Joint Conference of the IEEE Computer and Communications Societies, Miami, FL, USA."},{"key":"ref_16","doi-asserted-by":"crossref","unstructured":"Pac, M.R., Erkmen, A.M., and Erkmen, I. (2006, January 9\u201315). Scalable self-deployment of mobile sensor networks: A fluid dynamics approach. Proceedings of the Intelligent Robots and Systems, Beijing, China.","DOI":"10.1109\/IROS.2006.281969"},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"1025","DOI":"10.1109\/TPS.2016.2556688","article-title":"Investigation of the Shielding Length on Yukawa System Crystallization in Mobile Sensor Network Applications","volume":"44","author":"Tang","year":"2016","journal-title":"IEEE Trans. Plasma Sci."},{"key":"ref_18","doi-asserted-by":"crossref","unstructured":"Deng, X., Yu, Z., Tang, R., Qian, X., Yuan, K., and Liu, S. (2019). An Optimized Node Deployment Solution Based on a 435 Virtual Spring Force Algorithm for Wireless Sensor Network Applications. Sensors, 19.","DOI":"10.3390\/s19081817"},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"3349","DOI":"10.1063\/1.1490346","article-title":"Molecular dynamics simulations of Mach cones in a two-dimensional Yukawa crystals","volume":"9","author":"Ma","year":"2002","journal-title":"Phys. Plasmas"},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"32","DOI":"10.1063\/1.1784300","article-title":"Dusty plasma in the laboratory, industry and space","volume":"57","author":"Merlino","year":"2004","journal-title":"Phys. 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