{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,30]],"date-time":"2026-04-30T14:41:36Z","timestamp":1777560096093,"version":"3.51.4"},"reference-count":46,"publisher":"MDPI AG","issue":"7","license":[{"start":{"date-parts":[[2023,4,3]],"date-time":"2023-04-03T00:00:00Z","timestamp":1680480000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"S&amp;T Program of Hebei","award":["22282203Z"],"award-info":[{"award-number":["22282203Z"]}]},{"name":"S&amp;T Program of Hebei","award":["E2022209086"],"award-info":[{"award-number":["E2022209086"]}]},{"DOI":"10.13039\/501100003787","name":"Natural Science Foundation of Hebei Province","doi-asserted-by":"publisher","award":["22282203Z"],"award-info":[{"award-number":["22282203Z"]}],"id":[{"id":"10.13039\/501100003787","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100003787","name":"Natural Science Foundation of Hebei Province","doi-asserted-by":"publisher","award":["E2022209086"],"award-info":[{"award-number":["E2022209086"]}],"id":[{"id":"10.13039\/501100003787","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Sensors"],"abstract":"<jats:p>The localization of sensor nodes is an important problem in wireless sensor networks. The DV-Hop algorithm is a typical range-free algorithm, but the localization accuracy is not high. To further improve the localization accuracy, this paper designs a DV-Hop algorithm based on multi-objective salp swarm optimization. Firstly, hop counts in the DV-Hop algorithm are subdivided, and the average hop distance is corrected based on the minimum mean-square error criterion and weighting. Secondly, the traditional single-objective optimization model is transformed into a multi-objective optimization model. Then, in the third stage of DV-Hop, the improved multi-objective salp swarm algorithm is used to estimate the node coordinates. Finally, the proposed algorithm is compared with three improved DV-Hop algorithms in two topologies. Compared with DV-Hop, The localization errors of the proposed algorithm are reduced by 50.79% and 56.79% in the two topology environments with different communication radii. The localization errors of different node numbers are decreased by 38.27% and 56.79%. The maximum reductions in localization errors are 38.44% and 56.79% for different anchor node numbers. Based on different regions, the maximum reductions in localization errors are 56.75% and 56.79%. The simulation results show that the accuracy of the proposed algorithm is better than that of DV-Hop, GWO-DV-Hop, SSA-DV-Hop, and ISSA-DV-Hop algorithms.<\/jats:p>","DOI":"10.3390\/s23073698","type":"journal-article","created":{"date-parts":[[2023,4,3]],"date-time":"2023-04-03T04:45:33Z","timestamp":1680497133000},"page":"3698","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":27,"title":["DV-Hop Algorithm Based on Multi-Objective Salp Swarm Algorithm Optimization"],"prefix":"10.3390","volume":"23","author":[{"given":"Weimin","family":"Liu","sequence":"first","affiliation":[{"name":"College of Mechanical Engineering, North China University of Science and Technology, Tangshan 063210, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Jinhang","family":"Li","sequence":"additional","affiliation":[{"name":"College of Mechanical Engineering, North China University of Science and Technology, Tangshan 063210, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Aiyun","family":"Zheng","sequence":"additional","affiliation":[{"name":"HUIDA Sanitary Ware Co., Ltd., Tangshan 063000, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-1454-7042","authenticated-orcid":false,"given":"Zhi","family":"Zheng","sequence":"additional","affiliation":[{"name":"College of Mechanical Engineering, North China University of Science and Technology, Tangshan 063210, China"},{"name":"HUIDA Sanitary Ware Co., Ltd., Tangshan 063000, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Xinyu","family":"Jiang","sequence":"additional","affiliation":[{"name":"College of Mechanical Engineering, North China University of Science and Technology, Tangshan 063210, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Shaoning","family":"Zhang","sequence":"additional","affiliation":[{"name":"College of Mechanical Engineering, North China University of Science and Technology, Tangshan 063210, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2023,4,3]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"3044","DOI":"10.1007\/s11227-020-03385-w","article-title":"DV-Hop-based range-free localization algorithm for wireless sensor network using runner-root optimization","volume":"77","author":"Kanwar","year":"2020","journal-title":"J. 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