On the separability of subproblems in Benders decompositions

Marco Cadoli () and Fabio Patrizi ()

Annals of Operations Research, 2009, vol. 171, issue 1, 27-43

Abstract: Benders decomposition is a well-known procedure for solving a combinatorial optimization problem by defining it in terms of a master problem and a slave problem. Its effectiveness relies, among other factors, on the possibility of synthesizing Benders cuts that rule out not only one, but a large class of trial values for the master problem. In turn, for the class of problems we consider (i.e., optimization plus constraint satisfaction) the possibility of separating the slave problem into several subproblems—i.e., problems exhibiting strong intra-relationships and weak inter-relationships—can be exploited for improving searching procedures efficiency. The notion of separation is typically given informally, or relying on syntactical aspects. This paper formally addresses the notion of slave problem separability by giving a semantic definition and exploring it from the computational point of view. Several examples of separable problems are provided, including some proving that a semantic notion of separability is much more helpful than a syntactic one. We show that separability can be formally characterized as equivalence of logical formulae, and prove the undecidability of the separability check problem. Finally, we show how there are cases where automated tools can still be used for checking subproblem separability. Copyright Springer Science+Business Media, LLC 2009

Keywords: Benders decomposition; Constraint programming; Problem separation (search for similar items in EconPapers)
Date: 2009
References: View references in EconPapers View complete reference list from CitEc
Citations:

Downloads: (external link)
http://hdl.handle.net/10.1007/s10479-008-0383-5 (text/html)
Access to full text is restricted to subscribers.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:spr:annopr:v:171:y:2009:i:1:p:27-43:10.1007/s10479-008-0383-5

Ordering information: This journal article can be ordered from
http://www.springer.com/journal/10479

DOI: 10.1007/s10479-008-0383-5

Access Statistics for this article

Annals of Operations Research is currently edited by Endre Boros

More articles in Annals of Operations Research from Springer
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().