Simulated annealing applied to the irregular rotational placement of shapes over containers with fixed dimensions

Authors:
T. C. Martins;M. S. G. Tsuzuki
Affiliations:
Escola Politécnica da Universidade de São Paulo, Department of Mechatronics and Mechanical Systems Engineering, Computational Geometry Laboratory, Av. Prof. Mello Moraes 2231, São P ...;Escola Politécnica da Universidade de São Paulo, Department of Mechatronics and Mechanical Systems Engineering, Computational Geometry Laboratory, Av. Prof. Mello Moraes 2231, São P ...
Venue:
Expert Systems with Applications: An International Journal
Year:
2010

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Abstract

This work deals with the problem of minimizing the waste of space that occurs on a rotational placement of a set of irregular two dimensional polygons inside a two dimensional container. This problem is approached with an heuristic based on simulated annealing. Traditional ''external penalization'' techniques are avoided through the application of the no-fit polygon, that determinates the collision free area for each polygon before its placement. The simulated annealing controls: the rotation applied, the placement and the sequence of placement of the polygons. For each non placed polygon, a limited depth binary search is performed to find a scale factor that when applied to the polygon, would allow it to be fitted in the container. It is proposed a crystallization heuristic, in order to increase the number of accepted solutions. The bottom left and larger first deterministic heuristics were also studied. The proposed process is suited for non convex polygons and containers, the containers can have holes inside.