On the determination of the optimum path in space (original) (raw)

DETERMINATION OF THE OPTIMUM PATH ON THE EARTH'S SURFACE (extended abstract)

Citeseer

Various algorithms have been proposed for the determination of the optimum paths in linear networks. Moving on a surface is a far more complex problem, where research has been scarce. An example would be the determination of the shortest sea course between two given ports. This paper presents a solution to the problem, which can be easily applied to a variety of surfaces, while considering different travel cost models. The applicability of the solution to representative surfaces is examined.

Determination of the Optimum Path on the Earth's Surface

A shortest path method on a surface in space

International Journal of Advanced Trends in Computer Science and Engineering, 2019

The objective of this work is to determine the shortest path passing through two points of a surface in the space z = f (x, y). The presented work firstly highlights the limitations of employing the conventional method which relies on solving the system of second-order differential equations (Euler-Lagrange) in finding effective solutions, then introduce a random numerical method to approach this problem [2]. The method of Euler Lagrange requires the search for initial velocity for differential equations of the second order. This leads to a solution connecting two fixed points of the plan. Here, I modify the initial velocity at one point to find the solutions passing through the other point. Such a solution is called the geodesic path, which passes through these two points and is considered the shortest path between the two points. However, this is not always true (i.e. the case of a sphere) [1, 2]. At the beginning of this work, I present a method for the search of the initial velocity of the Euler-Lagrang system. I apply it on real examples in order to illustrate the limits of the efficiency of this method, then I introduce a numerical method based on random changes to determine the shortest path.

An Effective Algorithm for Finding Shortest Paths in Tubular Spaces

Algorithms, 2022

We propose a novel algorithm to determine the Euclidean shortest path (ESP) from a given point (source) to another point (destination) inside a tubular space. The method is based on the observation data of a virtual particle (VP) assumed to move along this path. In the first step, the geometric properties of the shortest path inside the considered space are presented and proven. Utilizing these properties, the desired ESP can be segmented into three partitions depending on the visibility of the VP. Our algorithm will check which partition the VP belongs to and calculate the correct direction of its movement, and thus the shortest path will be traced. The proposed method is then compared to Dijkstra’s algorithm, considering different types of tubular spaces. In all cases, the solution provided by the proposed algorithm is smoother, shorter, and has a higher accuracy with a faster calculation speed than that obtained by Dijkstra’s method.

Modification of ship routing algorithms for the case of navigation in ice

2019

Navigation in ice-covered waters has a number of specific features that distinguish it from the open water operation; they are the non-stationary ice conditions, ice channels on the fairways, and the additional opportunities such as the possibility to involve an icebreaker and change the mode of movement (sternor bow forward). All these features should be considered when solving the problem of ship route optimization in ice. In this paper, we propose the modifications of the well-known graph-based and cell-free (wave-based) mathematical methods of path finding to adapt them to the problem of route optimization in dynamic ice conditions considering all above-mentioned features. We formulated the versatile cost function that involves such factors as the total voyage time, fuel consumption, freight rates of ships and risks of ice operation. The optimization task is set in such a way to allow finding the route segments where the icebreaker assistance is economically proven and optimize ...

Minimum Time Sailing Boat Path Algorithm

IEEE Journal of Oceanic Engineering

An iterative procedure to solve the nonlinear problem of fastest-path sailing vessel routing in an environment with variable winds and currents is proposed. In the routing of a sailing vessel, the primary control variable is the pointing (heading) of the vessel (assuming that the sails are chosen and trimmed optimally). Sailing vessel routing is highly nonlinear when considering environmental factors, such as winds and currents, and the behavior of the boat, given the weather conditions (i.e., polar diagrams that predict how fast one can sail, given the vessel's pointing relative to the true wind and the wind speed). The key algorithmic contribution of this article is a fastest-path algorithm for graphs with nonconvex edge costs that depend on weather, current, and boat polars. An illustrative scenario, with idealized weather attributes, and a real-world scenario, with parameters generated by numerical weather and current prediction models, are simulated and tested to compare the proposed algorithm against open-source routing software validated by active sailors. Preliminary results from the simulation setups tested are as follows: 1) the proposed sailing boat path algorithm is comparable to the open-source software available; and 2) exploiting the often unused but significant impactor of surface currents and incorporating leeway into sailing boat path planning enables higher fidelity guidance and faster (i.e., shorter time) routes, in comparing against the freely available baseline.

Rectilinear shortest paths among obstacles in the plane

1995

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On the determination of the optimum path in space (original) (raw)

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