We consider the irregular strip packing problem of rasterized shapes, where a given set pieces shapes represented in pixels should be placed into rectangular container without overlap. The provide simple procedures intersection test any exceptional handling due to geometric issues, while they often require much memory and computational effort high-resolution. To reduce complexity we propose pai...

The strip packing problem is to pack a set of rectangles into a strip of fixed width and minimum length. We present asymptotic polynomial time approximation schemes for this problem without and with 90o rotations. The additive constant in the approximation ratios of both algorithms is 1, improving on the additive term in the approximation ratios of the algorithm by Kenyon and Rémila (for the pr...

We present algorithms for the following three-dimensional (3D) guillotine cutting problems: Unbounded Knapsack, Cutting Stock and Strip Packing. We consider the case where the items have fixed orientation and the case where orthogonal rotations around all axes are allowed. For the Unbounded 3D Knapsack problem, we extend the recurrence formula proposed by Beasley for the Rectangular Knapsack Pr...

In this paper, we present a parallel hyper-heuristic approach for two-dimensional rectangular strip-packing problems (2DSP). This is an island model with a special master-slave structure, and in all the islands we run a memetic algorithm-based hyper-heuristic (HH). The basic technique of this HH is a memory-based evolutionary technique, the “extended virtual loser” (EVL). The memory-based techn...

This paper mainly investigates the circular open dimension problem (CODP), which consists of packing a set of circles of known radii into a strip of fixed width and unlimited length without overlapping. The objective is to minimize the length of the strip. An iterated tabu search approach, named ITS, is proposed. ITS starts from a randomly generated solution and attempts to gain improvements by...

The irregular strip packing problem is a combinatorial optimization problem that asks to place a given set of 2-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 ob...