Abstract
A novel approach to pure 0-1 integer programming problems called Resolution Search has been proposed by Chvatal (Discrete Applied Mathematics, vol. 73, pp. 81–99, 1997) as an alternative to implicit enumeration, with a demonstration that the method can yield more effective branching strategies. We show that an earlier method called Dynamic Branch-and-Bound (B&B) yields the same branching strategies as Resolution Search, and other strategic alternatives in addition. Moreover, Dynamic B&B is not restricted to pure 0-1 problems, but applies to general mixed integer programs containing both general integer and continuous variables.
We provide examples comparing Resolution Search to enhanced variants. We also show the relation of these approaches to Dynamic B&B, suggesting the value of further study of this neglected approach.
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References
V. Chvatal, “Resolution search,” Discrete Applied Mathematics, vol. 73, pp. 81–99, 1997.
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Hanafi, S., Glover, F. Resolution Search and Dynamic Branch-and-Bound. Journal of Combinatorial Optimization 6, 401–423 (2002). https://doi.org/10.1023/A:1019573820792
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DOI: https://doi.org/10.1023/A:1019573820792