Computing the trajectories for the development of optimal routes

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 $$U\subset \mathbb {R}^{3}$$ U ⊂ R 3 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.

OPTE special issue on technical operations research (TOR)

“…Its solvability for standard mixed-integer solvers is demonstrated on several test-instances. Zazai and Fügenschuh (2021) demonstrates a further branch of variety for Technical Operations Research. Planning the construction of new transport routes or power lines on terrain is usually carried out manually by engineers, with no guarantee of optimality.…”

Modeling of cargo flow processes in the logistics of the transport system

“…Therefore, the movement of material flows, that is, finished products, raw materials, fuel resources, construction materials, agricultural products, industrial waste, etc. By space, it is necessary to navigate through the shortest distance, at the lowest cost [1].…”

“…1) ∑ 𝑎 𝑖 > ∑ 𝑎 𝑗 𝑗 𝑖 or, conversely, 2) ∑ 𝑎 𝑖 < ∑ 𝑏 𝑗 𝑗 𝑖In such cases, the initial data of the question is artificially output to ∑ 𝑎 𝑖 = ∑ 𝑏 𝑗 𝑗 𝑖 . For case 1, in which the above condition is met ∑ 𝑎 𝑖 = ∑ 𝑏1…”