期刊
EUROPEAN JOURNAL OF OPERATIONAL RESEARCH
卷 287, 期 2, 页码 410-437出版社
ELSEVIER
DOI: 10.1016/j.ejor.2020.04.001
关键词
Combinatorial optimization; Maximum flow; Conflict; branch-and-bound; Benders decomposition; Russian doll search
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. (C) 2020 Elsevier B.V. All rights reserved.
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