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
Hlavní autoři:	Precioso, Daniel, Milson, Robert, Bu, Louis, Menchions, Yvonne, Gómez-Ullate, David
Médium:	Journal Article
Jazyk:	angličtina
Vydáno:	Cham Springer International Publishing 01.06.2024
Témata:	Applications of Mathematics Computational Mathematics and Numerical Analysis Mathematical Applications in Computer Science Mathematical Applications in the Physical Sciences Mathematics Mathematics and Statistics 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
ISSN:	2238-3603, 1807-0302
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Popis
Shrnutí:	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.
ISSN:	2238-3603 1807-0302
DOI:	10.1007/s40314-024-02756-w