Компонування м’яких багатогранників у опуклому контейнері мінімального об’єму
State-of-the-art applications require considering non-standard placement constraints for geometric figures that can change their shapes under pressure of external forces while preserving their area / volume (soft objects). In particular, such problems arise in geology, materials science, medicine, b...
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| Datum: | 2025 |
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| Hauptverfasser: | , |
| Format: | Artikel |
| Sprache: | Ukrainian |
| Veröffentlicht: |
V.M. Glushkov Institute of Cybernetics of NAS of Ukraine
2025
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| Schlagworte: | |
| Online Zugang: | https://jais.net.ua/index.php/files/article/view/436 |
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| Назва журналу: | Problems of Control and Informatics |
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Problems of Control and Informatics| Zusammenfassung: | State-of-the-art applications require considering non-standard placement constraints for geometric figures that can change their shapes under pressure of external forces while preserving their area / volume (soft objects). In particular, such problems arise in geology, materials science, medicine, biology, logistics, and additive manufacturing. The paper considers a problem of arranging a given set of soft polyhedra into a convex container of minimal volume. Polyhedra have a variable shape within the given limits of elasticity parameters while preserving their convexity and volume under shape transformations. Two scenarios of the problem are considered: layout of polyhedra with variable vertices and given elasticity parameters; layout of polyhedra with variable motion vectors and variable elasticity parameters. Appropriate tools of mathematical modeling of the placement conditions (non-overlapping and containment constraints) for soft polyhedra are proposed using the phi-function technique. The corresponding mathematical models are constructed as nonlinear programming problems. A solution method is developed using an algorithm for generating feasible starting points and a decomposition algorithm, which allows reducing a large-scale problem to a sequence of the smaller nonlinear programming problems, linear to the number of polyhedra. The results of computational experiments for the arrangement of soft pyramids and cuboids in rectangular, spherical and cylindrical containers are provided and illustrated with pictures. |
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