Applying triple-block patterns in solving the two-dimensional bin packing problem

Abstract

This paper presents a heuristic for the guillotine two-dimensional bin packing problem, where a set of rectangular items are packed using guillotine patterns into bins of the same size, such that the number of bins used is minimized. Both oriented and non-oriented items are considered. The algorithm considers a novel combination of three procedures. The first is a pattern-generation procedure that generates a set of triple-block patterns on each call. The second is a plan-generation procedure that uses some of these patterns to compose the solution. The third is a plan-improvement procedure that solves an integer linear programming model over a given set of patterns generated previously to improve the solution. According to the computational results, the heuristic can obtain very good solution quality. For some classes of instances, the gap to lower bound is reduced by more than 30% compared to algorithms recently published.

Keywords:

• Two-dimensional bin packing
• triple-block patterns
• cutting stock

Acknowledgements

This research is part of Projects 61363026 and 71371058 supported by National Natural Science Foundation of China.

Notes

Please note this paper has been re-typeset by Taylor & Francis from the manuscript originally provided to the previous publisher.