Компонування м’яких багатокутників в опуклому полігональному контейнері
The problem of arranging irregular soft polygons into an optimized convex polygonal container given by a set of variable vertices is formulated. Polygons can change their shapes within the given limits of elasticity parameters, provided that their area is preserved. Free translations and continuous...
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| Datum: | 2024 |
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| Hauptverfasser: | , , |
| Format: | Artikel |
| Sprache: | Ukrainian |
| Veröffentlicht: |
V.M. Glushkov Institute of Cybernetics of NAS of Ukraine
2024
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| Schlagworte: | |
| Online Zugang: | https://jais.net.ua/index.php/files/article/view/424 |
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| Назва журналу: | Problems of Control and Informatics |
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Problems of Control and Informatics| Zusammenfassung: | The problem of arranging irregular soft polygons into an optimized convex polygonal container given by a set of variable vertices is formulated. Polygons can change their shapes within the given limits of elasticity parameters, provided that their area is preserved. Free translations and continuous rotations of polygons are allowed. The maximum number of container vertices m is fixed. However, the shape of the container is not fixed and is determined in such a way as to minimize its area/perimeter subject to a container convexity condition, pairwise non-overlapping of soft polygons and containment of each soft polygon into the container. Another interpretation of this problem is the problem of finding the minimum in perimeter/area convex hull with the number of vertices not exceeding m. Tools of mathematical modeling of soft object placement conditions have been constructed in the form of new classes of phi-functions and quasi phi-functions. The corresponding mathematical model of the optimized layout problem of soft irregular polygons is constructed as a nonlinear programming model. An algorithm of constructing feasible starting points for searching for local minima is proposed. A decomposition approach has been developed that allows reducing a large-scale problem to a sequence of nonlinear programming problems of considerably smaller dimension, linear to the number of convex components of irregular soft polygons. The computational results are provided. The optimal solutions for small problems is proven using the global solver BARON. For medium examples, the proposed heuristic and the local solver IPOPT are used. |
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