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Exact solution algorithms for the maximum flow problem with additional conflict constraints

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  • Şuvak, Zeynep
  • Altınel, İ. Kuban
  • Aras, Necati

Abstract

We consider a variant of the maximum flow problem on a given directed graph where some arc pairs are incompatible or conflicting; in other words, they are not allowed to carry positive flow simultaneously. This problem, called the maximum flow problem with conflicts, is known to be strongly NP-hard. In this paper, we present mixed-integer linear programming formulations for the problem and develop exact solution methods based on Benders decomposition, branch-and-bound, and Russian Doll Search over the conflict graph which represents the conflict relations. The effectiveness of the proposed algorithms is tested on a large number of randomly generated instances. The results reveal that their performances are superior to solving the mixed-integer linear programming formulations with a commercial software.

Suggested Citation

  • Şuvak, Zeynep & Altınel, İ. Kuban & Aras, Necati, 2020. "Exact solution algorithms for the maximum flow problem with additional conflict constraints," European Journal of Operational Research, Elsevier, vol. 287(2), pages 410-437.
    • Handle: RePEc:eee:ejores:v:287:y:2020:i:2:p:410-437
    DOI: 10.1016/j.ejor.2020.04.001
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    References listed on IDEAS

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