Mixed integer quadratically-constrained programming model to solve the irregular strip packing problem with continuous rotations
- 80 Downloads
The irregular strip packing problem consists of cutting a set of convex and non-convex two-dimensional polygonal pieces from a board with a fixed height and infinite length. Owing to the importance of this problem, a large number of mathematical models and solution methods have been proposed. However, only few papers consider that the pieces can be rotated at any angle in order to reduce the board length used. Furthermore, the solution methods proposed in the literature are mostly heuristic. This paper proposes a novel mixed integer quadratically-constrained programming model for the irregular strip packing problem considering continuous rotations for the pieces. In the model, the pieces are allocated on the board using a reference point and its allocation is given by the translation and rotation of the pieces. To reduce the number of symmetric solutions for the model, sets of symmetry-breaking constraints are proposed. Computational experiments were performed on the model with and without symmetry-breaking constraints, showing that symmetry elimination improves the quality of solutions found by the solution methods. Tests were performed with instances from the literature. For two instances, it was possible to compare the solutions with a previous model from the literature and show that the proposed model is able to obtain numerically accurate solutions in competitive computational times.
KeywordsMixed integer non-linear programming Nesting problems Irregular pieces Continuous rotations
This research was sponsored and funded by FAPESP (2015/24987-4, 2015/03066-8 and 2013/07375-0) and CNPq (477481/2013-2).
- 11.Fujita, K., Akagi, S., Hirokawa, N.: Hybrid approach for optimal nesting using a genetic algorithm and a local minimization algorithm. In: Proceedings of the 19th Annual ASME Design Automation Conference, Part 1, pp. 477–484 (1993)Google Scholar
- 13.Gottschalk, S.: Collision queries using oriented bounding boxes. PhD thesis, The University of North Carolina at Chapel Hill (2000)Google Scholar
- 14.Greene, D.H.: The decomposition of polygons into convex parts. Comput. Geom. 1, 235–259 (1983)Google Scholar
- 16.Leão, A.A.S., Toledo, F.M.B., Oliveira, J.F., Carravilla, M.A.: A semi-continuous MIP model for the irregular strip packing problem. Int. J. Prod. Res. 54, 1–10 (2015)Google Scholar