Comparação de malhas para problemas de corte e empacotamento

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Universidade Federal de Goiás


This work brings the use of grid of points in the resolution of cutting and packing problems that consider rectangular shaped items. The grids can be considered for mathematical programming models and heuristics, and they are independent of the problem. The following grids that are defined by the literature are considered for this work: canonical dissections (also known as normal patterns), reduced raster points, useful numbers, corner points, regular normal patterns, extreme points, and meet-in-the-middle patterns. The objective is to assess the influence of each grid on the resolution of cutting and packing problems, before and after applying reduction procedures, as the one related to update the items size. Theoretical results are obtained from relations of set and size between the grids, showing that the grid of normal patterns and useful numbers are equivalent and, thus, proving formally that the grid of reduced raster points ensures an optimal solution (this result has been formally opened in the literature). In addition, we propose a new procedure to reduce the size of grids. In order to validate the proposed procedure and evaluate the grids, we perform experiments over instances from the literature, where it is possible to observe that the grids of reduced raster points and meet-in-the-middle patterns are the smallest. Experiments were also conducted in a two-dimensional packing problem that uses an integer linear programming model to pack the items in points of a grid. The results indicate that using the reduction procedures it is possible to obtain optimal solutions quicker.



Problemas de corte e empacotamento, Malha de pontos, Procedimentos de redução, Normal patterns, Reduced raster points, Cutting and packing problems, Grid of points, Reduction procedures, Normal patterns, Reduced raster points


CUNHA, J. G. A. Comparação de malhas para problemas de corte e empacotamento. 2018. 139 f. Dissertação (Mestrado em Modelagem e Otimização) - Universidade Federal de Goiás, Catalão, 2018.