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An exact separation algorithm for unsplittable flow capacitated network design arc-set polyhedron

Author

Listed:
  • Liang Chen

    (Academy of Mathematics and Systems Science, Chinese Academy of Sciences
    University of Chinese Academy of Sciences)

  • Wei-Kun Chen

    (Beijing Institute of Technology)

  • Mu-Ming Yang

    (Academy of Mathematics and Systems Science, Chinese Academy of Sciences
    University of Chinese Academy of Sciences)

  • Yu-Hong Dai

    (Academy of Mathematics and Systems Science, Chinese Academy of Sciences
    University of Chinese Academy of Sciences)

Abstract

In this paper, we concentrate on generating cutting planes for the unsplittable capacitated network design problem. We use the unsplittable flow arc-set polyhedron of the considered problem as a substructure and generate cutting planes by solving the separation problem over it. To relieve the computational burden, we show that, in some special cases, a closed form of the separation problem can be derived. For the general case, a brute-force algorithm, called exact separation algorithm, is employed in solving the separation problem of the considered polyhedron such that the constructed inequality guarantees to be facet-defining. Furthermore, a new technique is presented to accelerate the exact separation algorithm, which significantly decreases the number of iterations in the algorithm. Finally, a comprehensive computational study on the unsplittable capacitated network design problem is presented to demonstrate the effectiveness of the proposed algorithm.

Suggested Citation

  • Liang Chen & Wei-Kun Chen & Mu-Ming Yang & Yu-Hong Dai, 2021. "An exact separation algorithm for unsplittable flow capacitated network design arc-set polyhedron," Journal of Global Optimization, Springer, vol. 81(3), pages 659-689, November.
    • Handle: RePEc:spr:jglopt:v:81:y:2021:i:3:d:10.1007_s10898-020-00967-z
    DOI: 10.1007/s10898-020-00967-z
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    References listed on IDEAS

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