A squeaky wheel optimisation methodology for two-dimensional strip packing

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 art Reactive GRASP and SVC(SubKP) iterative procedures. The contribution of this paper is to present a much simpler but equally competitive iterative packing methodology based on squeaky wheel optimisation. After each complete packing (iteration), a penalty is applied to pieces that directly decreased the solution quality. These penalties inform the packing in the next iteration, so that the offending pieces are packed earlier. This methodology is deterministic and very easy to implement, and can obtain some best results on benchmark instances from the literature.