A Linear time algorithm for computing the Voronoi diagram of a convex polygon
STOC '87 Proceedings of the nineteenth annual ACM symposium on Theory of computing
On the limited memory BFGS method for large scale optimization
Mathematical Programming: Series A and B
An algorithm to compute the Minkowski sum outer-face of two simple polygons
Proceedings of the twelfth annual symposium on Computational geometry
The irregular cutting-stock problem mdash; a new procedure for deriving the no-fit polygon
Computers and Operations Research
A Review of the Application ofMeta-Heuristic Algorithms to 2D Strip Packing Problems
Artificial Intelligence Review
Penetration depth of two convex polytopes in 3D
Nordic Journal of Computing
Incremental Penetration Depth Estimation between Convex Polytopes Using Dual-Space Expansion
IEEE Transactions on Visualization and Computer Graphics
Computational Geometry: Algorithms and Applications
Computational Geometry: Algorithms and Applications
A heuristic approach for packing identical rectangles in convex regions
Computers and Operations Research
Computers and Operations Research
Collision free region determination by modified polygonal Boolean operations
Computer-Aided Design
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The irregular strip packing problem is a combinatorial optimization problem that requires to place a given set of two-dimensional polygons within a rectangular container so that no polygon overlaps with other polygons or protrudes from the container, where each polygon is not necessarily convex. The container has a fixed width, while its length can change so that all polygons are placed in it. The objective is to find a layout of the set of polygons that minimizes the length of the container. We propose an algorithm that separates overlapping polygons based on nonlinear programming, and an algorithm that swaps two polygons in a layout so as to find their new positions in the layout with the least overlap. We incorporate these algorithms as components into an iterated local search algorithm for the overlap minimization problem and then develop an algorithm for the irregular strip packing problem using the iterated local search algorithm. Computational comparisons on representative instances disclose that our algorithm is competitive with other existing algorithms. Moreover, our algorithm updates several best known results.