In this paper we introduce an evolutionary hyperheuristic approach to solve difficult strip packing problems. We have designed a genetic based hyperheuristic using the most recently proposed low-level heuristics in the literature. Two versions for tuning parameters have also been evaluated. The results obtained are very encouraging showing that our approach outperforms the single heuristics and...

In the three dimensional strip packing problem, we are given a set of three dimensional rectangular items and a three dimensional box B. The goal is to pack all the items in B such that the height of the packing is minimized. We consider the most basic version of the problem, where the items must be packed with their edges parallel to the edges of B and cannot be rotated. Building upon Caprara’...

The oriented strip packing problem is very important to manufacturing industries: given a strip of xed width and a set of many (> 100) nonconvex polygons with 1, 2, 4, or 8 orientations permitted for each polygon, nd a set of translations and orientations for the polygons that places them without overlapping into the strip of minimum length. Heuristics are given for two versions of strip packin...

Given a set of irregular shapes, the strip nesting problem is the problem of packing the shapes within a rectangular strip of material such that the strip length is minimized, or equivalently the utilization of material is maximized. If the packing found is to be repeated, e.g., on a roll of fabric or a coil of metal, then the separation between repeats is going to be a straight line. This cons...

In this paper we consider a two dimensional strip packing problem. The problem consists of packing a set of rectangular items in one strip of width W and infinite height. They must be packed without overlapping, parallel to the edge of the strip and we assume that the items are oriented, i.e. they cannot be rotated. To solve this problem, we use three exact methods: a branch and bound method, a...

Bansal and Sviridenko [4] proved that there is no asymptotic PTAS for 2-dimensional Orthogonal Bin Packing (without rotations), unless P = NP. We show that similar approximation hardness results hold for several 2and 3-dimensional rectangle packing and covering problems even if rotations by ninety degrees are allowed. Moreover, for some of these problems we provide explicit lower bounds on asym...

When handling 2D packing problems, numerous incomplete and complete algorithms maintain a so-called bottomleft (BL) property: every rectangle placed in a container is propped up bottom and left. While it is easy to make a rectangle BL when it is is added in a container, it is more expensive to maintain all the placed pieces BL when a rectangle is removed. This prevents researchers from designin...

The rectangular Strip Packing Problem (SPP) consists of packing a given set of rectangles in a rectangular strip with fixed width w and variable height minimizing the height of the packing. In this work we propose a ”Greedy Randomized and Adaptive Constructive” heuristic, a GRASP metaheuristic without the post-processing phase, for the SPP in the version where the rectangles can be freely rotat...

We consider the relaxed online strip packing problem, where rectangular items arrive online and have to be packed into a strip of fixed width such that the packing height is minimized. Thereby, repacking of previously packed items is allowed. The amount of repacking is measured by the migration factor, defined as the total size of repacked items divided by the size of the arriving item. First, ...

Here, we focus on a generalized version of the strip packing problem; namely have several open-end strips with different widths, and wish to pack rectangular items into these without overlapping such that minimize either makespan (i.e. top topmost item), or total area used. We investigate online variant problem, where are arriving one-by-one, make irrevocable decisions their packing. A similar ...