In this paper we present a hybrid metaheuristic approach called PVS (Progress and Verify Strategy) for the two-dimensional strip packing problem (2SPP). relies on two procedures: local search algorithm that delivers satisfying placements of items horizontal axis, an exact procedure searches positions vertical axis. This last one explores all possibilities, starting with most promising ones, can...

The two dimensional strip packing problem occurs in industries such as metal, wood, glass, paper, and textiles. The problem involves cutting shapes from a larger stock sheet or roll of material, while minimising waste. This is a well studied problem for which many heuristic methodologies are available in the literature, ranging from the basic ‘one-pass’ best-fit heuristic, to the state of the a...

We propose a satisfiability testing (SAT) based exact approach for solving the two-dimensional strip packing problem (2SPP). In this problem, we are given a set of rectangles and one large rectangle called a strip. The goal of the problem is to pack all rectangles without overlap, into the strip by minimizing the overall height of the packing. We show the method solves a 2SPP by translating it ...

Given a finite set of circles of different sizes we study the Strip Packing Problem (SPP) as well as the Knapsack Problem (KP). The SPP asks for a placement of all circles (without overlap) within a rectangular strip of fixed width so that the variable length of the strip is minimized. The KP requires packing of a subset of the circles in a rectangle of fixed dimensions so that the wasted area ...

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 this paper, we present a review of the recent approaches proposed in the literature for strip-packing problems. Many of them have been concurrently published, given some similar results for the same set of benchmarks. Due to the quantity of published papers, it is difficult to ascertain the level of current research in this area. & 2008 Published by Elsevier Ltd.