SPATIAL MODELS OF THE THEORY OF OPTIMAL DIVISION OF SETS’ CONTINUOUS PROBLEMS
Abstract
The paper investigates the problems of optimal partitioning of a section of a spatial curve, which are special cases of a continuous Optimal Partitioning Sets (OPS) problem with the determination of location of the centers of subsets. New formulations of OPS problems for special cases are proposed. Each problem is a generalization of the previous one. The cost function is interpreted as the geometric characteristic of the curve. The effect of curvature and torsion on the cost of movement is considered. In fact, a new metric is introduced for this class of problems. It is shown that in such formulations it is possible to integrate the objective function and obtain a problem of the classical form. The overall result of the studies carried out in this work can be formulated as taking into account during the motion not only the length of the trajectory, but also the cost of maneuvering along this trajectory in the framework of the OPS problem with obtaining the placement of centers. Taking into account the geometric characteristics transfers the described OPS problem to the applied field. Modern requirements for the goods transfer require taking into account the maximum number of factors affecting the process, which means that data and dependencies are required within the process itself. In this case, it is the geometry of the trajectories; the next step is the physics of the process, interaction with the road or airspace.
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