{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,28]],"date-time":"2026-02-28T04:28:27Z","timestamp":1772252907933,"version":"3.50.1"},"reference-count":40,"publisher":"MDPI AG","issue":"9","license":[{"start":{"date-parts":[[2018,8,29]],"date-time":"2018-08-29T00:00:00Z","timestamp":1535500800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100001871","name":"Funda\u00e7\u00e3o para a Ci\u00eancia e a Tecnologia","doi-asserted-by":"publisher","award":["PEst-OE\/EEI\/UI0066\/2014, (IF\/00325\/2015)"],"award-info":[{"award-number":["PEst-OE\/EEI\/UI0066\/2014, (IF\/00325\/2015)"]}],"id":[{"id":"10.13039\/501100001871","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Sensors"],"abstract":"<jats:p>This work addresses the energy-based source localization problem in wireless sensors networks. Instead of circumventing the maximum likelihood (ML) problem by applying convex relaxations and approximations, we approach it directly by the use of metaheuristics. To the best of our knowledge, this is the first time that metaheuristics are applied to this type of problem. More specifically, an elephant herding optimization (EHO) algorithm is applied. Through extensive simulations, the key parameters of the EHO algorithm are optimized such that they match the energy decay model between two sensor nodes. A detailed analysis of the computational complexity is presented, as well as a performance comparison between the proposed algorithm and existing non-metaheuristic ones. Simulation results show that the new approach significantly outperforms existing solutions in noisy environments, encouraging further improvement and testing of metaheuristic methods.<\/jats:p>","DOI":"10.3390\/s18092849","type":"journal-article","created":{"date-parts":[[2022,5,19]],"date-time":"2022-05-19T21:56:59Z","timestamp":1652997419000},"page":"2849","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":36,"title":["Elephant Herding Optimization for Energy-Based Localization"],"prefix":"10.3390","volume":"18","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-1111-3513","authenticated-orcid":false,"given":"S\u00e9rgio D.","family":"Correia","sequence":"first","affiliation":[{"name":"Instituto de Telecomunica\u00e7\u00f5es, P\u00f3lo II da Univ. de Coimbra, 3030-290 Coimbra, Portugal"},{"name":"Instituto Polit\u00e9cnico de Portalegre, Departamento de Tecnologia, 7300-555 Portalegre, Portugal"}]},{"given":"Marko","family":"Beko","sequence":"additional","affiliation":[{"name":"COPELABS, Universidade Lus\u00f3fona de Humanidades e Tecnologias, Campo Grande 376, 1749-024 Lisboa, Portugal"},{"name":"CTS\/UNINOVA, Campus da FCT\/UNL, Monte de Caparica, 2829-516 Caparica, Portugal"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-1141-4404","authenticated-orcid":false,"given":"Luis A.","family":"Da Silva Cruz","sequence":"additional","affiliation":[{"name":"Instituto de Telecomunica\u00e7\u00f5es, P\u00f3lo II da Univ. de Coimbra, 3030-290 Coimbra, Portugal"},{"name":"Dep. de Eng. Elect. e de Computadores, Universidade de Coimbra, P\u00f3lo II, 3030-290 Coimbra, Portugal"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-5537-6716","authenticated-orcid":false,"given":"Slavisa","family":"Tomic","sequence":"additional","affiliation":[{"name":"COPELABS, Universidade Lus\u00f3fona de Humanidades e Tecnologias, Campo Grande 376, 1749-024 Lisboa, Portugal"},{"name":"ISR\/IST, LARSyS, Universidade de Lisboa, Av. Rovisco Pais 1, 1049-001 Lisbon, Portugal"}]}],"member":"1968","published-online":{"date-parts":[[2018,8,29]]},"reference":[{"key":"ref_1","unstructured":"Hightower, J., Brumitt, B., and Borriello, G. (2002, January 20\u201321). The location stack: A layered model for location in ubiquitous computing. Proceedings of the Fourth IEEE Workshop on Mobile Computing Systems and Applications, Callicoon, NY, USA."},{"key":"ref_2","doi-asserted-by":"crossref","unstructured":"Jiang, J., Guo, Y., Liao, W., Li, S., Xie, X., Yuan, L., and Nian, L. (2014, January 1\u20133). Research on RTLS-based coordinate guided vehicle (CGV) for material distribution in discrete manufacturing workshop. Proceedings of the 2014 IEEE International Conference on Internet of Things (iThings), and IEEE Green Computing and Communications (GreenCom), and IEEE Cyber-Physical-Social Computing (CPS), Taipei, Taiwan.","DOI":"10.1109\/iThings.2014.10"},{"key":"ref_3","doi-asserted-by":"crossref","unstructured":"Micio, R., Fontanili, F., Marqu\u00e8s, G., Bomert, P., and Lauras, M. (2015, January 24\u201328). RTLS-based Process Mining: Towards an automatic process diagnosis in healthcare. Proceedings of the IEEE International Conference on Automation Science and Engineering, Gothenburg, Sweden.","DOI":"10.1109\/CoASE.2015.7294294"},{"key":"ref_4","doi-asserted-by":"crossref","unstructured":"Moreira, A., Nicolau, M.J., Meneses, F., and Costa, A. (2015, January 13\u201316). Wi-Fi fingerprinting in the real world - RTLS@UM at the EvAAL competition. Proceedings of the 2015 International Conference on Indoor Positioning and Indoor Navigation (IPIN 2015), Banff, AB, Canada.","DOI":"10.1109\/IPIN.2015.7346967"},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"12","DOI":"10.1109\/MSP.2005.1458273","article-title":"Signal processing techniques in network-aided positioning: A survey of state-of-the-art positioning designs","volume":"22","author":"Sun","year":"2005","journal-title":"IEEE Signal Process. Mag."},{"key":"ref_6","doi-asserted-by":"crossref","unstructured":"Fross, D., Langer, J., Fross, A., Roossler, M., and Heinkel, U. (2010, January 15\u201317). Hardware implementation of a Particle Filter for location estimation. Proceedings of the International Conference on Indoor Positioning and Indoor Navigation (IPIN), Zurich, Switzerland.","DOI":"10.1109\/IPIN.2010.5648092"},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"42","DOI":"10.1109\/CC.2013.6488829","article-title":"Situation and development tendency of indoor positioning","volume":"10","author":"Deng","year":"2013","journal-title":"China Commun."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"1263","DOI":"10.1109\/TVT.2015.2403868","article-title":"Indoor Tracking: Theory, Methods, and Technologies","volume":"64","author":"Dardari","year":"2015","journal-title":"IEEE Trans. Veh. Technol."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"877","DOI":"10.1145\/1113830.1113837","article-title":"Range-free localization and its impact on large scale sensor networks","volume":"4","author":"He","year":"2005","journal-title":"ACM Trans. Embed. Comput. Syst."},{"key":"ref_10","doi-asserted-by":"crossref","unstructured":"Gui, L., Wei, A., and Val, T. (2012, January 28\u201331). A Range-Free Localization Protocol for Wireless Sensor Networks. Proceedings of the International Symposium on Wireless Communication Systems (ISWCS), Paris, France.","DOI":"10.1109\/ISWCS.2012.6328417"},{"key":"ref_11","doi-asserted-by":"crossref","unstructured":"Zhang, S., Wang, J., Liu, X., and Cao, J. (2012, January 18\u201321). Range-free selective multilateration for anisotropic wireless sensor networks. Proceedings of the Annual IEEE Communications Society Conference on Sensor, Mesh and Ad Hoc Communications and Networks, Seoul, Korea.","DOI":"10.1109\/SECON.2012.6275791"},{"key":"ref_12","unstructured":"Liu, C., and Wu, K. (2005, January 7\u20139). Performance evaluation of range-free localization methods for wireless sensor networks. Proceedings of the 24th IEEE International Performance, Computing, and Communications Conference (PCCC2005), Phoenix, AZ, USA."},{"key":"ref_13","unstructured":"Lee, S., and Kim, K. (August, January 31). Determination of communication range for range-free multi-hop localization in wireless sensor networks. Proceedings of the International Conference on Computer Communications and Networks (ICCCN), Maui, HI, USA."},{"key":"ref_14","first-page":"1","article-title":"RSS-based Localization in Wireless Sensor Networks Using Convex Relaxation: Noncooperative and Cooperative Schemes","volume":"9545","author":"Tomic","year":"2014","journal-title":"IEEE Trans. Veh. Technol."},{"key":"ref_15","unstructured":"Wang, Y., Susheng, S., Yang, X., and Ma, A. (2013, January 11\u201314). Bluetooth Indoor Positioning using RSSI and Least Square Estimation. Proceedings of the IEEE Consumer Communications and Networking Conference (CCNC2013), Las Vegas, NV, USA."},{"key":"ref_16","doi-asserted-by":"crossref","unstructured":"Waadt, A.E., Kocks, C., Wang, S.W.S., Bruck, G.H., and Jung, P. (2010, January 7\u201310). Maximum likelihood localization estimation based on received signal strength. Proceedings of the 3rd International Symposium on Applied Sciences in Biomedical and Communication Technologies, Rome, Italy.","DOI":"10.1109\/ISABEL.2010.5702817"},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"8569","DOI":"10.3390\/s110908569","article-title":"Weighted least squares techniques for improved received signal strength based localization","volume":"11","author":"Bernardos","year":"2011","journal-title":"Sensors"},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"531","DOI":"10.1109\/LSP.2018.2810829","article-title":"Exact Robust Solution to TW-ToA-Based Target Localization Problem with Clock Imperfections","volume":"25","author":"Tomic","year":"2018","journal-title":"IEEE Signal Process. Lett."},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"680","DOI":"10.1109\/LWC.2016.2615614","article-title":"A Closed-Form Solution for RSS\/AoA Target Localization by Spherical Coordinates Conversion","volume":"5","author":"Tomic","year":"2016","journal-title":"IEEE Wirel. Commun. Lett."},{"key":"ref_20","doi-asserted-by":"crossref","unstructured":"Tomic, S., Marikj, M., Beko, M., Dinis, R., and Orfao, N. (2015, January 24\u201328). Hybrid RSS-AoA technique for 3-D node localization in wireless sensor networks. Proceedings of the 2015 International Wireless Communications and Mobile Computing Conference (IWCMC), Dubrovnik, Croatia.","DOI":"10.1109\/IWCMC.2015.7289266"},{"key":"ref_21","doi-asserted-by":"crossref","unstructured":"Tomic, S., Beko, M., Dinis, R., and Gomes, J.P. (2017). Target tracking with sensor navigation using coupled RSS and AOA measurements. Sensors, 17.","DOI":"10.3390\/s17112690"},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"158","DOI":"10.1016\/j.phycom.2017.10.005","article-title":"Bayesian methodology for target tracking using combined RSS and AoA measurements","volume":"25","author":"Tomic","year":"2017","journal-title":"Phys. Commun."},{"key":"ref_23","doi-asserted-by":"crossref","unstructured":"Beko, M. (2011, January 28\u201331). Energy-based localization in wireless sensor networks using semidefinite relaxation. Proceedings of the 2011 IEEE Wireless Communications and Networking Conference, Cancun, Mexico.","DOI":"10.1109\/WCNC.2011.5779361"},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"1847","DOI":"10.1007\/s11277-014-1612-7","article-title":"Energy-Based Localization in Wireless Sensor Networks Using Second-Order Cone Programming Relaxation","volume":"77","author":"Beko","year":"2014","journal-title":"Wirel. Pers. Commun."},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"2542","DOI":"10.1109\/TASL.2007.903312","article-title":"An accurate algebraic closed-form solution for energy-based source localization","volume":"15","author":"Ho","year":"2007","journal-title":"IEEE Trans. Audio Speech Lang. Process."},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"365","DOI":"10.1109\/TSP.2007.900757","article-title":"On energy-based acoustic source localization for sensor networks","volume":"56","author":"Meesookho","year":"2008","journal-title":"IEEE Trans. Signal Process."},{"key":"ref_27","doi-asserted-by":"crossref","unstructured":"Wang, G., and Yang, K. (2009, January 19\u201324). A Semidefinite Relaxation Method for Energy-based Source Localization in Sensor Networks. Proceedings of the IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP2009), Taipei, Taiwan.","DOI":"10.1109\/ICASSP.2009.4960069"},{"key":"ref_28","doi-asserted-by":"crossref","unstructured":"Rudafshani, M., and Datta, S. (2007, January 25\u201327). Localization in Wireless Sensor Networks. Proceedings of the 6th International Symposium on Information Processing in Sensor Networks (IPSN 2007), Cambridge, MA, USA.","DOI":"10.1109\/IPSN.2007.4379664"},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"2293","DOI":"10.1109\/TVT.2011.2142204","article-title":"A Semidefinite Relaxation Method for Energy-Based Source Localization in Sensor Networks","volume":"60","author":"Wang","year":"2011","journal-title":"IEEE Trans. Veh. Technol."},{"key":"ref_30","first-page":"321","article-title":"Energy Based Collaborative Source Localization Using Acoustic Micro-Sensor Array","volume":"2003","author":"Li","year":"2003","journal-title":"Appl. Signal Process."},{"key":"ref_31","doi-asserted-by":"crossref","first-page":"44","DOI":"10.1109\/TSP.2004.838930","article-title":"Maximum likelihood multiple-source localization using acoustic energy measurements with wireless sensor networks","volume":"53","author":"Sheng","year":"2005","journal-title":"IEEE Trans. Signal Process."},{"key":"ref_32","doi-asserted-by":"crossref","unstructured":"Wang, G.G., Deb, S., and Coelho, L.D.S. (2015, January 7\u20139). Elephant Herding Optimization. Proceedings of the 3rd International Symposium on Computational and Business Intelligence (ISCBI 2015), Bali, Indonesia.","DOI":"10.1109\/ISCBI.2015.8"},{"key":"ref_33","doi-asserted-by":"crossref","unstructured":"Deb, S. (2015, January 21\u201323). Elephant Search Algorithm for Optimization Problems. Proceedings of the 10th International Conference on Digital Information Management (ICDIM), Jeju, Korea.","DOI":"10.1109\/ICDIM.2015.7381893"},{"key":"ref_34","doi-asserted-by":"crossref","first-page":"2394","DOI":"10.19101\/IJATEE.2016.324005","article-title":"Elephant herding optimization based PID controller tuning","volume":"3","author":"Gupta","year":"2016","journal-title":"Int. J. Adv. Technol. Eng. Explor."},{"key":"ref_35","unstructured":"Chibani, S.S., and Tari, A. (2017). Elephant Herding Optimization for Service Selection in QoS-Aware Web. Int. J. Comput. Inf. Eng., 4."},{"key":"ref_36","unstructured":"Kinsler, L.E., Frey, A.R., Coppens, A.B., and Sanders, J.V. (1999). Fundamentals of Acoustics, Wiley. [4th ed.]."},{"key":"ref_37","doi-asserted-by":"crossref","first-page":"3614","DOI":"10.1109\/TSP.2006.879312","article-title":"Energy Based Sensor Network Source Localization via Projection onto Convex Sets (POCS )","volume":"54","author":"Blatt","year":"2006","journal-title":"IEEE Trans. Signal Process."},{"key":"ref_38","first-page":"221","article-title":"Natural Computing Algorithms\u2014A Survey","volume":"6","author":"Chawda","year":"2016","journal-title":"Int. J. Emerg. Technol. Adv. Eng."},{"key":"ref_39","first-page":"100","article-title":"Performance of Elephant Herding Optimization Algorithm on CEC 2013 real parameter single objective optimization","volume":"16","author":"Tuba","year":"2017","journal-title":"WSEAS Trans. Syst."},{"key":"ref_40","doi-asserted-by":"crossref","first-page":"1770","DOI":"10.1109\/TSP.2007.909342","article-title":"Exact and Approximate Solutions of Source Localization Problems","volume":"56","author":"Beck","year":"2008","journal-title":"IEEE Trans. Signal Process."}],"container-title":["Sensors"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1424-8220\/18\/9\/2849\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T15:21:48Z","timestamp":1760196108000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1424-8220\/18\/9\/2849"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2018,8,29]]},"references-count":40,"journal-issue":{"issue":"9","published-online":{"date-parts":[[2018,9]]}},"alternative-id":["s18092849"],"URL":"https:\/\/doi.org\/10.3390\/s18092849","relation":{"has-preprint":[{"id-type":"doi","id":"10.20944\/preprints201807.0051.v1","asserted-by":"object"}]},"ISSN":["1424-8220"],"issn-type":[{"value":"1424-8220","type":"electronic"}],"subject":[],"published":{"date-parts":[[2018,8,29]]}}}