Applying triple-block patterns in solving the two-dimensional bin packing problem
针对二维切割装箱问题，提出一种结合模式生成、方案生成和方案改进三步的启发式算法，能显著缩小与下界的差距，对物流和制造业有参考价值。
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.