Computing the trajectories for the development of optimal routes
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Computing the trajectories for the development of optimal routes M. Fawad Zazai1 · Armin R. Fügenschuh2 Received: 10 December 2019 / Revised: 19 September 2020 / Accepted: 23 September 2020 © The Author(s) 2020
Abstract Planning the construction of new transport routes or power lines on terrain is usually carried out manually by engineers, with no guarantee of optimality. We introduce a new approach for the computation of an optimal trajectory for the construction of new transit routes and power lines between two locations on a submanifold U ⊂ ℝ3 representing the topography of a terrain. U is approximatively modeled by a special weighted grid. On this grid, the shortest paths for the construction of new routes are determined, whereby we consider three optimization criteria: routes with minimum distance, routes with lowest construction costs and routes with minimum absolute altitude variations or minimum absolute gradients. Subsequently, a combination of these criteria is used to expand this problem into a multi-criteria optimization problem. A shortest path algorithm, such as the Dijkstra algorithm, is used to compute optimal compromises for the construction of new routes. Keywords Shortest path · Graph construction · GIS · topography · Multi-criteria optimization (Pareto frontier) · Trajectory planning
1 Introduction Worldwide, many developing countries have an undeveloped technical and logistical infrastructure. This not only causes numerous problems for the inhabitants in their daily life, but also has negative economic consequences (more on this can be found in Fay and Yepes (2003), Gaal (2017), Gurara et al. (2017), Oyedele (2016)). * Armin R. Fügenschuh fuegenschuh@b‑tu.de M. Fawad Zazai zazaif@hsu‑hh.de 1
Helmut Schmidt University/University of the Federal Armed Forces Hamburg, Holstenhofweg 85, 22043 Hamburg, Germany
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Brandenburgische Technische Universität Cottbus-Senftenberg, Platz der Deutschen Einheit 1, 03034 Cottbus, Germany
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M. F. Zazai, A. R. Fügenschuh
Classical examples of a logistical infrastructure are transport networks such as roads, tracks, and waterways. On the technical side, these are supply networks such as power lines, freshwater and wastewater lines, and communication networks. An immature technical infrastructure can severely curb the energy and transport sector. These containments can not only increase the manufacturing and transport costs of a product but can also impact entire construction projects, transport networks, and economic networks. The resulting consequences can reduce the development and progress of these countries. Besides, investors lose interest in investing in underdeveloped countries with a high amount of natural resources since the risk of a misinvestment is too high. Infrastructure projects are usually very costly. Planning firms or consulting companies often plan the development of new routes (alignment) based on empirical values or using estimation methods. However, these methods do not guarantee optimality. Such planning proj
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