A Numerically Exact Algorithm for the Bin-Packing Problem
提出一种基于分支-定价-切割框架和模式枚举的数值精确算法，通过高精度对偶界计算和整数标签定价算法，解决了传统浮点求解器在大型装箱问题实例中的数值不精确问题，性能优于现有非精确算法。
We propose a numerically exact algorithm for solving the Bin-Packing Problem (BPP) based on a branch-price-and-cut framework combined with a pattern-enumeration method. Key to the algorithm is a novel technique for the computation of numerically safe dual bounds for the widely adopted set covering reformulation of the BPP (tightened with additional valid inequalities) with a precision that is higher than the one of general-purpose floating-point solvers. Our branch-price-and-cut algorithm also relies on an exact integer (fixed-point) label setting algorithm for solving the pricing problem associated with the tightened set-covering formulation. To the best of our knowledge, ours is the first algorithm for the BPP that is numerically exact and practical for solving large-scale instances. Extensive computational results on instances affected by notorious numerical difficulties (those of the Augmented Non-IRUP class) show that our exact algorithm outperforms all of the not numerically exact state-of-the-art algorithms based on branch-and-cut-and-price techniques that rely on a set-covering formulation of the BPP. History: Accepted by Andrea Lodi, Area Editor for Design & Analysis of Algorithms − Discrete.