Hybrid search method for Zermelo’s navigation problem
In this paper, we present a novel algorithm called the Hybrid Search algorithm to tackle the Zermelo’s navigation problem. This method can be regarded as an extension of the recent Ferraro–Martín de Diego-Sato algorithm to allow for further exploration in search for the global optimum, in situations...
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| Vydáno v: | Computational & applied mathematics Ročník 43; číslo 4 |
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Springer International Publishing
01.06.2024
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| ISSN: | 2238-3603, 1807-0302 |
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| Abstract | In this paper, we present a novel algorithm called the Hybrid Search algorithm to tackle the Zermelo’s navigation problem. This method can be regarded as an extension of the recent Ferraro–Martín de Diego-Sato algorithm to allow for further exploration in search for the global optimum, in situations of complex vector fields where many locally optimal trajectories exist. Our algorithm is designed to work in both Euclidean and spherical spaces and utilizes a heuristic that allows the vessel to move forward while remaining within a predetermined search cone centered around the destination. This approach not only improves efficiency but also includes obstacle avoidance, making it well-suited for real-world applications. We evaluate the performance of the Hybrid Search algorithm on synthetic vector fields and real ocean currents, demonstrating its effectiveness and performance. |
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| AbstractList | In this paper, we present a novel algorithm called the Hybrid Search algorithm to tackle the Zermelo’s navigation problem. This method can be regarded as an extension of the recent Ferraro–Martín de Diego-Sato algorithm to allow for further exploration in search for the global optimum, in situations of complex vector fields where many locally optimal trajectories exist. Our algorithm is designed to work in both Euclidean and spherical spaces and utilizes a heuristic that allows the vessel to move forward while remaining within a predetermined search cone centered around the destination. This approach not only improves efficiency but also includes obstacle avoidance, making it well-suited for real-world applications. We evaluate the performance of the Hybrid Search algorithm on synthetic vector fields and real ocean currents, demonstrating its effectiveness and performance. |
| ArticleNumber | 250 |
| Author | Gómez-Ullate, David Precioso, Daniel Milson, Robert Bu, Louis Menchions, Yvonne |
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| Cites_doi | 10.1016/j.apor.2013.07.010 10.2514/1.G001389 10.1016/j.ress.2022.109015 10.1016/j.joes.2016.02.001 10.1002/zamm.19310110205 10.1007/s10732-020-09449-7 10.1016/j.oceaneng.2020.107697 10.1007/s11802-022-4709-8 10.1016/j.oceaneng.2022.111427 10.1093/occmed/kqu017 10.1016/j.oceaneng.2016.09.007 10.1016/j.ifacol.2021.11.097 |
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| Keywords | 49M15 Newton-type methods Weather routing 70-08 Computational methods for problems pertaining to mechanics of particles and systems 70-10 Mathematical modeling or simulation for problems pertaining to mechanics of particles and systems Time optimal trajectories 70Q05 Control of mechanical systems 49Mxx Numerical methods in optimal control Optimization 65K10 Numerical optimization and variational techniques Zermelo navigation problem 65L10 Numerical solution of boundary value problems involving ordinary differential equations |
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| References | Zermelo (CR18) 1930; 39 CR4 CR3 Marchidan, Bakolas (CR13) 2016; 39 Roberts, Nielsen, Kotłowski, Jaremin (CR15) 2014; 64 CR6 Zhao (CR20) 2022; 21 Kuhlemann, Tierney (CR11) 2020; 26 Zyczkowski, Szlapczynski (CR22) 2023; 232 Zis, Psaraftis, Ding (CR21) 2020; 213 CR9 CR16 Grandcolas (CR7) 2022; 3 CR10 Lin, Fang, Yeung (CR12) 2013; 43 Perera, Soares (CR14) 2017; 130 Bao, Robles, Shen (CR1) 2004; 66 Walther, Rizvanolli, Wendebourg, Jahn (CR17) 2016; 4 Zermelo (CR19) 1931; 11 Grifoll, Borén, Castells-Sanabra (CR8) 2022; 255 Ferraro, Martín de Diego, Martín, de Almagro (CR5) 2021; 54 Bialystocki, Konovessis (CR2) 2016; 1 TP Zis (2756_CR21) 2020; 213 2756_CR16 E Zermelo (2756_CR18) 1930; 39 A Marchidan (2756_CR13) 2016; 39 W Zhao (2756_CR20) 2022; 21 2756_CR6 M Grifoll (2756_CR8) 2022; 255 S Kuhlemann (2756_CR11) 2020; 26 N Bialystocki (2756_CR2) 2016; 1 2756_CR4 2756_CR3 2756_CR10 YH Lin (2756_CR12) 2013; 43 E Zermelo (2756_CR19) 1931; 11 S Grandcolas (2756_CR7) 2022; 3 LP Perera (2756_CR14) 2017; 130 M Zyczkowski (2756_CR22) 2023; 232 2756_CR9 SE Roberts (2756_CR15) 2014; 64 D Bao (2756_CR1) 2004; 66 SJ Ferraro (2756_CR5) 2021; 54 L Walther (2756_CR17) 2016; 4 |
| References_xml | – volume: 43 start-page: 184 year: 2013 end-page: 194 ident: CR12 article-title: The optimization of ship weather-routing algorithm based on the composite influence of multi-dynamic elements publication-title: Appl Ocean Res doi: 10.1016/j.apor.2013.07.010 – volume: 39 start-page: 188 year: 2016 end-page: 193 ident: CR13 article-title: Numerical techniques for minimum-time routing on sphere with realistic winds publication-title: J Guid Control Dyn doi: 10.2514/1.G001389 – volume: 232 start-page: 109015 year: 2023 ident: CR22 article-title: Collision risk-informed weather routing for sailboats publication-title: Reliab Eng Syst Saf doi: 10.1016/j.ress.2022.109015 – volume: 1 start-page: 157 year: 2016 end-page: 166 ident: CR2 article-title: On the estimation of ship’s fuel consumption and speed curve: a statistical approach publication-title: J Ocean Eng Sci doi: 10.1016/j.joes.2016.02.001 – volume: 11 start-page: 114 year: 1931 end-page: 124 ident: CR19 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start-page: 44 year: 1930 end-page: 48 ident: CR18 article-title: Über die navigation in der luft als problem der variationsrechnung publication-title: Jahresbericht der deutschen Mathematiker-Vereinigung, Angelegenheiten – volume: 130 start-page: 684 year: 2017 end-page: 695 ident: CR14 article-title: Weather routing and safe ship handling in the future of shipping publication-title: Ocean Eng doi: 10.1016/j.oceaneng.2016.09.007 – volume: 130 start-page: 684 year: 2017 ident: 2756_CR14 publication-title: Ocean Eng doi: 10.1016/j.oceaneng.2016.09.007 – volume: 232 start-page: 109015 year: 2023 ident: 2756_CR22 publication-title: Reliab Eng Syst Saf doi: 10.1016/j.ress.2022.109015 – ident: 2756_CR4 doi: 10.1016/j.ifacol.2021.11.097 – ident: 2756_CR3 – volume: 255 start-page: 111427 year: 2022 ident: 2756_CR8 publication-title: Ocean Eng doi: 10.1016/j.oceaneng.2022.111427 – volume: 54 start-page: 321 year: 2021 ident: 2756_CR5 publication-title: IFAC-Pap – volume: 26 start-page: 801 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10.2514/1.G001389 – volume: 66 start-page: 377 year: 2004 ident: 2756_CR1 publication-title: J Differ Geometry – ident: 2756_CR6 – volume: 21 start-page: 28 year: 2022 ident: 2756_CR20 publication-title: J Ocean Univ China doi: 10.1007/s11802-022-4709-8 – volume: 3 start-page: 35 year: 2022 ident: 2756_CR7 publication-title: Oper Res – volume: 64 start-page: 259 year: 2014 ident: 2756_CR15 publication-title: Occup Med doi: 10.1093/occmed/kqu017 |
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| Title | Hybrid search method for Zermelo’s navigation problem |
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