凸多边形二维不规则装箱问题的组合Benders分解框架

中文摘要 AI 辅助

二维不规则装箱问题将组合性的箱子分配决策与困难的几何可行性约束相结合，使得精确优化极具挑战性。本文针对凸多边形二维不规则装箱问题，提出了一种精确的组合Benders分解框架，将基于模式的master问题与精确的单箱几何可行性oracle相结合。动态加强的Benders master问题通过定制的精确分支定价过程求解，该过程融入了目标分层搜索和自适应精确定价。从oracle获得的几何信息通过动态生成的Benders可行性割进一步反馈到master和定价过程中，这些割逐步限制后续的定价问题。计算实验在来自18个类别的540个基准实例上进行。所提出的方法在3600秒的时间限制内，为12个类别的318个实例获得了最优解。在这些类别上，所提出的方法比直接的混合整数规划公式和基线组合Benders分解方法解决了更多的实例。

英文摘要

Two-dimensional irregular bin packing combines combinatorial bin-assignment decisions with difficult geometric feasibility constraints, making exact optimization challenging. This paper develops an exact combinatorial Benders decomposition framework for the two-dimensional irregular bin packing problem with convex polygons, coupling a pattern-based master problem with an exact single-bin geometric feasibility oracle. The dynamically strengthened Benders master is solved by a tailored exact branch-and-price procedure that incorporates objective-layered search and adaptive exact pricing. Geometric information obtained from the oracle is further fed back to the master and pricing processes through dynamically generated Benders feasibility cuts, which progressively restrict the subsequent pricing problems. Computational experiments are conducted on 540 benchmark instances from 18 classes. The proposed method obtains the optimal solution for 318 instances across 12 classes within a 3600-second time limit. On these classes, the proposed method solves more instances than a direct mixed-integer programming formulation and a baseline combinatorial Benders decomposition approach.

发表机构

• University of Science and Technology of China（中国科学技术大学）

机构由 AI 辅助整理，请以论文原文为准。