{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,7,11]],"date-time":"2026-07-11T01:51:15Z","timestamp":1783734675312,"version":"3.55.0"},"reference-count":30,"publisher":"MDPI AG","issue":"3","license":[{"start":{"date-parts":[[2026,3,15]],"date-time":"2026-03-15T00:00:00Z","timestamp":1773532800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100003819","name":"Hubei Provincial Natural Science Foundation","doi-asserted-by":"publisher","award":["2025AFB921"],"award-info":[{"award-number":["2025AFB921"]}],"id":[{"id":"10.13039\/501100003819","id-type":"DOI","asserted-by":"publisher"}]},{"name":"Youth Fund of the National Natural Science Foundation of China","award":["42404009"],"award-info":[{"award-number":["42404009"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Algorithms"],"abstract":"<jats:p>Aiming at solving the problem that existing automatic route-planning algorithms fail to consider the navigation rules in traffic separation scheme (TSS) zones, this paper proposes a ship automatic route-planning algorithm that fully considers TSS-zone navigation constraints. First, a formalized TSS-zone automatic planning module with a quadrilateral decomposition mechanism is designed, which realizes standardized processing of regular TSS zones and completes TSS-compliant route replanning through three core steps: invalid waypoint deletion, TSS-zone-traversal-order determination, and constrained route replanning. Second, a particle swarm optimization (PSO) algorithm is selected as the base global route-planning algorithm via a multi-algorithm comparative framework, considering the requirements of optimality, stability and real-time performance for ship-navigation. The TSS module is deeply integrated with the PSO algorithm, forming a unified global route-planning algorithm that balances TSS compliance and route optimality. Comparative experiments with four mainstream swarm intelligence algorithms (PSO\/SSA\/IVY\/GOA) show that the PSO algorithm outperforms the others in terms of route length, stability and comprehensive efficiency, with an optimal route length of 57.71 and a low standard deviation of 3.42. Furthermore, the proposed algorithm is validated by real nautical chart data of Bohai Bay under single- and double-TSS-zone scenarios. The results indicate that the algorithm can stably generate TSS-compliant routes, with only a small increase in route length (0.6% and 4.4% for a single TSS zone, 1.1% and 1.8% for two TSS zones) and computational time and can automatically adjust the traversal strategy according to the start\u2013end point settings. The designed TSS module has good scalability and can be integrated with other optimization algorithms, providing a feasible technical solution for an intelligent ship navigation system to realize automatic and compliant route planning in TSS zones with dense traffic.<\/jats:p>","DOI":"10.3390\/a19030220","type":"journal-article","created":{"date-parts":[[2026,3,16]],"date-time":"2026-03-16T08:41:26Z","timestamp":1773650486000},"page":"220","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["A TSS-Compliant Ship Automatic Route-Planning Algorithm"],"prefix":"10.3390","volume":"19","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-5949-6624","authenticated-orcid":false,"given":"Ning","family":"Zhang","sequence":"first","affiliation":[{"name":"Naval University of Engineering, Wuhan 430000, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0009-0003-3826-7544","authenticated-orcid":false,"given":"Fang","family":"He","sequence":"additional","affiliation":[{"name":"Naval University of Engineering, Wuhan 430000, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-6705-3401","authenticated-orcid":false,"given":"Lubin","family":"Chang","sequence":"additional","affiliation":[{"name":"Naval University of Engineering, Wuhan 430000, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Jingwen","family":"Zong","sequence":"additional","affiliation":[{"name":"Naval Submarine Academy, Qingdao 266000, China"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"1968","published-online":{"date-parts":[[2026,3,15]]},"reference":[{"key":"ref_1","first-page":"43","article-title":"Research on the Application of Particle Swarm Optimization Algorithm in NP-hard Problems","volume":"39","author":"Tingwei","year":"2023","journal-title":"J. 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