One-dimensional heuristics adapted for two-dimensional rectangular strip packing

Abstract

We consider two-dimensional rectangular strip packing without rotation of items and without the guillotine cutting constraint. We propose two iterative heuristics. The first one, SVC(SubKP), is based on a single-pass heuristic SubKP which fills every most bottom-left free space in a one-dimensional knapsack fashion, that is, considering only item widths. It appears especially important to assign suitable ‘pseudo-profits’ in this knapsack problem. The second heuristic BS(BLR) is based on the known randomized framework Bubble-Search. It generates different item sequences and runs a new sequence-based heuristic Bottom-Left-Right (BLR), a simple modification of the Bottom-Left heuristic. We investigate the solution sets of SubKP and BLR and their relation to each other. In the tests, SVC(SubKP) improves the results for larger instances of the waste-free classes of Hopper and Turton and, on average, for the tested non-waste-free classes, compared to the latest literature. BS(BLR) gives the best results in some classes with smaller number of items (20,40).

Keywords:

• strip packing
• heuristics
• greedy
• stochastic search
• knapsack

Acknowledgements

We are grateful to the two anonymous referees for valuable suggestions concerning presentation quality. We also thank François Clautiaux and Antoine Jouglet for running the two-step method on the waste-free instances of Hopper and Turton.