MDDs: Sampling and Probability Constraints

Perez, Guillaume; Régin, Jean‐Charles

doi:10.1007/978-3-319-66158-2_15

Cited by 8 publications

(4 citation statements)

References 19 publications

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“…This line of works generated many theoretical and algorithmic results [73], as well as fruitful collaborations with other CP researchers. Jean-Charles Régin and Guillaume Perez, in particular, reformulated a number of our algorithms in the framework of Multi-valued Decision Diagrams (MDD), yielding substantial gains in efficiency [82,81].…”

Section: Sampling Methodsmentioning

confidence: 99%

Assisted music creation with Flow Machines: towards new categories of new

François¹,

Roy²,

Benoit³

2020

Preprint

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This chapter reflects on about 10 years of research in AIassisted music composition, in particular during the Flow Machines project. We reflect on the motivations for such a project, its background, its main results and impact, both technological and musical, several years after its completion. We conclude with a proposal for new categories of "new", created by the many uses of AI techniques to generate novel material.

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Section: Sampling Methodsmentioning

confidence: 99%

Assisted music creation with Flow Machines: towards new categories of new

François¹,

Roy²,

Benoit³

2020

Preprint

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“…Andersen et al (2007) propagator to ensure that the probability of every feasible assignment is inside a pre-defined range. The authors extended this constraint to consider probability distributions given by a Markov chain process (Perez and Régin 2017b).…”

Section: Cp Propagationmentioning

confidence: 99%

Decision Diagrams for Discrete Optimization: A Survey of Recent Advances

Castro¹,

Ciré²,

Beck³

2022

Preprint

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In the last decade, decision diagrams (DDs) have been the basis for a large array of novel approaches for modeling and solving optimization problems. Many techniques now use DDs as a key tool to achieve stateof-the-art performance within other optimization paradigms, such as integer programming and constraint programming. This paper provides a survey of the use of DDs in discrete optimization, particularly focusing on recent developments. We classify these works into two groups based on the type of diagram (i.e., exact or approximate) and present a thorough description of their use. We discuss the main advantages of DDs, point out major challenges, and provide directions for future work.

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“…At the beginning of this century stochastic constraint programming has been defined (Walsh 2002). Some problems involving Confidence constraints, coined "chance constraints" at that time (Rossi et al 2008;Hnich et al 2012), Markov or probability distribution constraints (Perez and Régin 2017a) have already been solved. Until recently the Confidence constraint lacked a generic filtering algorithm.…”

Section: Introductionmentioning

confidence: 99%

“…For many problems, this is not true, for example, in music generation, the succession of musical notes is often described by Markov chains (Pachet and Roy 2011). In this paper, working with MDDs allows to use the polynomial-size transformation of an MDD and a Markov chain to an MDD with layer-independent probabilities (Perez and Régin 2017a). This gives the Confidence constraint the capability to handle a broad new range of problems.…”

Section: Introductionmentioning

confidence: 99%

Generalized Confidence Constraints

Perez

Malalel

Glorian

et al. 2023

AAAI

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In robust optimization, finding a solution that solely respects the constraints is not enough. Usually, the uncertainty and unknown parameters of the model are represented by random variables. In such conditions, a good solution is a solution robust to most-likely assignments of these random variables. Recently, the Confidence constraint has been introduced by Mercier-Aubin et al. in order to enforce this type of robustness in constraint programming. Unfortunately, it is restricted to a conjunction of binary inequalities In this paper, we generalize the Confidence constraint to any constraint and propose an implementation based on Multi-valued Decision Diagrams (MDDs). The Confidence constraint is defined over a vector of random variables. For a given constraint C, and given a threshold, the Confidence constraint ensures that the probability for C to be satisfied by a sample of the random variables is greater than the threshold. We propose to use MDDs to represent the constraints on the random variables. MDDs are an efficient tool for representing combinatorial constraints, thanks to their exponential compression power. Here, both random and decision variables are stored in the MDD, and propagation rules are proposed for removing values of decision variables that cannot lead to robust solutions. Furthermore, for several constraints, we show that decision variables can be omitted from the MDD because lighter filtering algorithms are sufficient. This leads to gain an exponential factor in the MDD size. The experimental results obtained on a chemical deliveries problem in factories – where the chemicals consumption are uncertain – shows the efficiency of the proposed approach.

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MDDs: Sampling and Probability Constraints

Cited by 8 publications

References 19 publications

Assisted music creation with Flow Machines: towards new categories of new

Assisted music creation with Flow Machines: towards new categories of new

Decision Diagrams for Discrete Optimization: A Survey of Recent Advances

Generalized Confidence Constraints

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