Logic-based Benders decomposition

Benders decomposition uses a strategy of ``learning from one's mistakes.'' The aim of this paper is to extend this strategy to a much larger class of problems. The key is to generalize the linear programming dual used in the classical method to an ``inference dual.'' Solutio...

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Bibliographic Details
Published in:Mathematical programming Vol. 96; no. 1; pp. 33 - 60
Main Authors: Hooker, J.N., Ottosson, G.
Format: Journal Article
Language:English
Published: Heidelberg Springer 01.04.2003
Springer Nature B.V
Subjects:
Applied sciences
Decomposition
Digital Object Identifier
Exact sciences and technology
Integer programming
Linear programming
Logic
Mathematical programming
Operational research and scientific management
Operational research. Management science
Optimization
Propositional logic
Constraint satisfaction
Linear programming
Zero one programming
Constrained optimization
Mathematical programming
ISSN:0025-5610, 1436-4646
Online Access:Get full text
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Summary:Benders decomposition uses a strategy of ``learning from one's mistakes.'' The aim of this paper is to extend this strategy to a much larger class of problems. The key is to generalize the linear programming dual used in the classical method to an ``inference dual.'' Solution of the inference dual takes the form of a logical deduction that yields Benders cuts. The dual is therefore very different from other generalized duals that have been proposed. The approach is illustrated by working out the details for propositional satisfiability and 0-1 programming problems. Computational tests are carried out for the latter, but the most promising contribution of logic-based Benders may be to provide a framework for combining optimization and constraint programming methods.
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ISSN:0025-5610
1436-4646
DOI:10.1007/s10107-003-0375-9