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...evice. These are the simplest kind of no-goods that can be added to the master problem since they state that the current solution must not be computed again. Even if they can be improved, as shown in =-=[7]-=-, we will show in the next section that they are very effective. 5 Experimental results To validate the strength of our approach, we now compare the results obtained using this model (Hybrid in the fo...

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...-and-cut codes fall short. Currently there is active and promising research in the field of combining techniques from computational logic and constraint programming with integer programming, see e.g. =-=[5, 13]-=-. We contribute further to this development by using BDDs sucessfully and for the first time in a cutting plane engine. 1.1 Preliminaries from Polyhedral Theory Before we proceed we review some termin...

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...100s of software components, 1000s of software component communication interactions, and multiple interconnecting networks. Numerous optimization tricks can be applied, such as Bender’s Decomposition =-=[24, 22]-=-, but research has still only shown the ability to scale to 10’s of software components and communication interactions. As discussed in Section 3.3, ScatterD combines an evolutionary algorithm with he...

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... whereby a sat solver and a Mixed Integer Linear Program (mip) 2 J. Davies and F. Bacchus solver are used to cooperatively solve the maxsat problem using an approach similar to Bender’s Decomposition =-=[11]-=-. The mip solver is used to find optimal solutions which the sat solver then tests for feasibility. If the solution is not feasible the sat solver computes a new constraint to add to the mip model and...

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...the constraints can now contain negative b-variables. This means that the paradigm of maxhs changes from an implicit hitting set problem to something like a logic based Benders decomposition approach =-=[11]-=-. In particular, the optimization problem is being solved only over the b-variables while the sat solver is being used to add additional constraints to the optimization model until its solution also s...

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...position strategy for a multistage planing and scheduling problem. Maravelias and Grossmann [12] applied the decomposition to a scheduling of batch plants formulated as the State Task Network. Hooker =-=[13]-=- developed the logic Benders cuts for three different objectives (minimum cost, minimum makespan and minimum total tardiness) in general planning and scheduling problems. He modeled them as three diff...

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...th release times before segment i, and let J ′′ i = Ji \ J ′ i . Let ˆµi be the minimum makespan of the problem that remains after removing the jobs in S ⊂ J ′ i from segment i. It can be shown as in =-=[6]-=- that µ ∗ i − ˆµi ≤ pS + max j∈J ′ { ˜dj}−min i j∈J ′ { ˜dj} i (4) where pS = ∑ j∈S pj. Thus if jobs in J ′ i are removed from segment i, we have from (4) a lower bound on the resulting optimal makesp...

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... Beck [11] finds, however, that MIP software has improved to the point that it is competitive with or superior to LBBD on a class of planning and scheduling problems on which LBBD previously excelled =-=[19]-=-. MIP software has in fact improved significantly since the earlier results were published (2007). Yet the computation times reported in [11] for LBBD are much longer than those obtained in earlier st...