A logic-based method for integer programming
We propose a logic-based approach to integer programming that replaces traditional branch-and-cut techniques with logical analogs. Integer variables are regarded as atomic propositions. The constraints give rise to logical formulas that are analogous to separating cuts. No continuous relaxation is used. Rather, the cuts are selected so that they can be easily solved as a discrete relaxation. (In fact, defining a relaxation and generating cuts are best seen as the same problem.) We experiment with relaxations that have a k-tree structure and can be solved by nonserial dynamic programming. We also present logic-based analogs of facet-defining cuts, Chv{acute a}tal rank, etc. We conclude with some preliminary computational results.
- OSTI ID:
- 36139
- Report Number(s):
- CONF-9408161--
- Country of Publication:
- United States
- Language:
- English
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