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

Zeynep Şuvak, İ. Kuban Altınel and Necati Aras

European Journal of Operational Research, 2020, vol. 287, issue 2, 410-437

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.

Keywords: Combinatorial optimization; Maximum flow; Conflict; branch-and-bound; Benders decomposition; Russian doll search (search for similar items in EconPapers)
Date: 2020
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Citations: View citations in EconPapers (2)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:ejores:v:287:y:2020:i:2:p:410-437

DOI: 10.1016/j.ejor.2020.04.001

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