Efficient Operations Between MDDs and Constraints

Jung, Victor; Régin, Jean‐Charles

doi:10.1007/978-3-031-08011-1_13

Cited by 2 publications

(1 citation statement)

References 15 publications

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“…To do so, we perform the intersection between the MDD with higher precision and MDD M , but without computing the entire constraint: we only need the parts in common with MDD M . In order to do so, we perform the on the fly intersection [5]. This allows us to compute higher precision only for the parts of the MDD that need it, without wasting time and memory to recompute a large amount of solutions.…”

Section: On the Fly Intersectionmentioning

confidence: 99%

Dealing with the Product Constraint

Malalel

Jung

Régin

et al. 2022

Integration of Constraint Programming, Artificial Intelligence, and Operations Research

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The product constraint ensures that the product of some variables will be greater than a given value, that is Π n i=1 xi ≥ w. With the emergence of stochastic problems, this constraint appears more and more frequently in practice. The variables are most often probability variables that represent the probability that an event will occur and the minimum bound is the minimum probability that must be satisfied. This is often done to guarantee a certain level of security or a certain quality of service. To deal with this constraint, it is tempting as proposed by many authors to take the logarithm of the sum and the bound in order to transform the product into a sum. In this article we show that this idea creates many problems and forbids an exact calculation. We propose and compare different representations allowing to compute the set of solutions of this problem exactly or up to a certain precision. We also give an efficient method to represent that constraint by a Multi-valued Decision Diagram (MDD) in order to combine this constraint with some others MDDs.

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Section: On the Fly Intersectionmentioning

confidence: 99%

Dealing with the Product Constraint

Malalel

Jung

Régin

et al. 2022

Integration of Constraint Programming, Artificial Intelligence, and Operations Research

Self Cite

View full text Add to dashboard Cite

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On Aligning Non-Order-Associated Binary Decision Diagrams

Bochkarev

Smith

2023

INFORMS Journal on Computing

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Recent studies employ collections of binary decision diagrams (BDDs) to solve combinatorial optimization problems. This paper focuses on the problem of optimally aligning two BDDs, that is, transforming them to enforce a common order of variables while keeping the total size of the diagrams as small as possible. We address this problem, which is known to be NP-hard, by introducing and studying a simplified problem instead of working with the more complex original diagrams. We discuss some basic properties of the simplified problem, design a corresponding heuristic for the original problem, and show empirically that this approach yields good quality alignments while significantly reducing the complexity of intermediate diagram transformations. We highlight the practicality of this approach in the context of a variation of the uncapacitated facility location problem. History: Accepted by Andrea Lodi, Area Editor for Design and Analysis of Algorithms–Discrete Funding: This work was supported by the Office of Naval Research [Grant N00014-17-1-2421]. Supplemental Material: The online appendices are available at https://doi.org/10.1287/ijoc.2023.1293 .

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Efficient Operations Between MDDs and Constraints

Cited by 2 publications

References 15 publications

Dealing with the Product Constraint

Dealing with the Product Constraint

On Aligning Non-Order-Associated Binary Decision Diagrams

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