Integrating Benders Decomposition Within Constraint Programming

Cambazard, Hadrien; Jussien, Narendra

doi:10.1007/11564751_58

Cited by 9 publications

(6 citation statements)

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“…This is a concept interesting per se, and finds an immediate application in the context of Benders decompositions. In fact, it is well-known (Hooker and Ottosson 2003;Hooker 2000;Cambazard and Jussien 2005) that when the slave problem is formulated using several subproblems exhibiting strong intra-relationships and weak inter-relationships such decompositions are effective.…”

Section: Discussionmentioning

confidence: 98%

“…In Hooker and Ottosson (2003), Cambazard and Jussien (2005) generalizations of the above problem in which, e.g., variables from s may occur in the objective function, are studied. According to Hooker and Ottosson (2003), problems of the form (1) can be solved by applying a "logic-based" Benders decomposition schema that gives raise to the following problems:…”

Section: Preliminariesmentioning

confidence: 99%

“…In this paper, we focus on the second factor, and specifically on the notion of separability of the slave problem, which intuitively means that it can be formulated using several subproblems exhibiting strong intra-relationships and weak inter-relationships. As a matter of fact, it has been noted in Hooker and Ottosson (2003), Hooker (2000), Cambazard and Jussien (2005) that if the slave problem is separable then it is possible to design a Benders cut (or nogood) that excludes several instantiations of the primary variables or, in other words, a nogood which is a partial, and not a total, assignment to primary variables. Therefore, the ability to recognize slave problem separability is a very important factor for the efficiency of a Benders decomposition.…”

mentioning

confidence: 98%

“…Therefore, the ability to recognize slave problem separability is a very important factor for the efficiency of a Benders decomposition. In fact, previous work (Hooker and Ottosson 2003;Hooker 2000;Cambazard and Jussien 2005) assumes the slave problem is modeled by a set of easier (sub)problems.…”

mentioning

confidence: 99%

“…Usually (cf., e.g., Cambazard and Jussien 2005;Hooker 2000), when dealing with OPT + CS problems, slave problems are assumed separable and their subproblems are defined manually. The issue of stating when problems actually separate has not, to the best of our knowledge, been addressed, even though it might be helpful, as we show throughout the paper, for automatically detecting or, possibly, synthesizing effective Benders decompositions.…”

mentioning

confidence: 99%

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On the separability of subproblems in Benders decompositions

Cadoli

Patrizi

2008

Ann Oper Res

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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

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Section: Discussionmentioning

confidence: 98%