DOI: 10.1287/ijoc.2022.0257 ISSN:

A Numerically Exact Algorithm for the Bin-Packing Problem

Roberto Baldacci, Stefano Coniglio, Jean-François Cordeau, Fabio Furini
  • Management Science and Operations Research
  • Computer Science Applications
  • Information Systems
  • Software

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.

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