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Volume-based branch-and-cut algorithm for large-scale fixed-charge multicommodity network design

Author

Listed:
  • Rui S. Shibasaki

    (UPJV
    UCA
    UFMG)

  • Mourad Baïou

    (UCA)

  • Francisco Barahona

    (IBM)

  • Philippe Mahey

    (UCA)

  • Maurício C. de Souza

    (UFMG)

Abstract

The fixed-charge multicommodity capacitated network design (FCMC) problem remains challenging, particularly in large-scale contexts. In this particular case, the ability to produce good-quality solutions in a reasonable amount of time depends on the availability of efficient algorithms. Therefore, this paper proposes a Volume-based branch-and-cut algorithm, which applies a relax-and-cut procedure to solve linear programs in each node of the enumeration tree. Moreover, a Lagrangian feasibility pump heuristic using the Volume Algorithm as a solver for linear programs was implemented to accelerate the search for good feasible solutions in large-scale cases. The obtained results showed that the proposed branch-and-cut scheme is competitive with other state-of-the-art algorithms, and presents better performance when solving large-scale instances.

Suggested Citation

  • Rui S. Shibasaki & Mourad Baïou & Francisco Barahona & Philippe Mahey & Maurício C. de Souza, 2025. "Volume-based branch-and-cut algorithm for large-scale fixed-charge multicommodity network design," Annals of Operations Research, Springer, vol. 351(1), pages 133-166, August.
    • Handle: RePEc:spr:annopr:v:351:y:2025:i:1:d:10.1007_s10479-024-06303-y
    DOI: 10.1007/s10479-024-06303-y
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