发表机构
University of Siegen; eleQtron GmbH; University of Trento; INFN-TIFPA, Trento Institute for Fundamental Physics and Applications（锡根大学; eleQtron有限公司; 特伦托大学; 意大利国家核物理研究所-特伦托基础物理与应用研究所）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文提出多阶段二维切割下料问题的线性规划表述，并推导其QUBO非精确重构，通过模拟退火和迭代增广拉格朗日方法求解受限问题，并探讨量子退火的应用前景。
AI 中文摘要
切割下料问题与众多工业领域密切相关。本文针对带Guillotine切割的多阶段二维切割下料问题的一个受限版本，提出了一种线性规划表述，并在已发表的基准实例上进行了测试。随后，我们通过非平衡惩罚推导出该问题在二次无约束二元优化（QUBO）形式下的非精确重构，并展示了这种重构在建模可用余料方面可能具有的优势。本文主要考虑受限表述，其中每次切割的尺寸由单个所需工件的尺寸决定。我们进一步讨论了如何将该方法扩展到非受限问题，该问题允许涉及多个所需工件尺寸的切割模式，这自然会在问题表述的不等式中产生二次项。我们通过模拟退火求解器展示了受限问题类别的解，并主要研究了迭代增广拉格朗日方法的性能。我们还讨论了量子退火在此场景中的可能应用，作为研究QUBO表述的强烈动机。
英文摘要
Cutting stock problems are of large relevance to a variety of industry branches. Here, we present a linear programming formulation for a restricted version of the multistage 2D cutting stock problem with Guillotine cuts and test it on published benchmark instances. After this, we derive a non-exact reformulation in quadratic unconstrained binary optimization (QUBO) form via unbalanced penalization, which we show to have possible benefits in modeling the problem with usable leftovers. This work mainly considers the restricted formulation, in which the dimensions of each cut are determined by those of a single required piece. We further discuss how the approach can be extended to the unrestricted problem, which allows more general cutting patterns involving cuts with dimensions of multiple required pieces and naturally gives rise to quadratic terms in the inequalities of the problem formulation. We showcase solutions via a Simulated Annealing solver for the restricted problem class, where we mainly study the performance of the iterative augmented Lagrangian method. We also discuss possible applications of Quantum Annealing in this setting, as a strong motivation to research QUBO formulations.
Comments21 pages, 10 figures
