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

Liang Chen (), Wei-Kun Chen (), Mu-Ming Yang () and Yu-Hong Dai ()
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Liang Chen: Academy of Mathematics and Systems Science, Chinese Academy of Sciences
Wei-Kun Chen: Beijing Institute of Technology
Mu-Ming Yang: Academy of Mathematics and Systems Science, Chinese Academy of Sciences
Yu-Hong Dai: Academy of Mathematics and Systems Science, Chinese Academy of Sciences

Journal of Global Optimization, 2021, vol. 81, issue 3, No 5, 659-689

Abstract: 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.

Keywords: Cutting planes; Exact separation; Flow arc-set polyhedron; Unsplittable capacitated network design; 90C11; 90C27 (search for similar items in EconPapers)
Date: 2021
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DOI: 10.1007/s10898-020-00967-z

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