The Confidence Constraint: A Step Towards Stochastic CP Solvers

Mercier-Aubin, Alexandre; Dumetz, Ludwig; Gaudreault, Jonathan; Quimper, Claude-Guy

doi:10.1007/978-3-030-58475-7_44

Cited by 2 publications

(6 citation statements)

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“…We consider problems involving random variables for which the probability distribution is known. Recently, the Confidence constraint has been defined (Mercier-Aubin et al 2020). Let γ ∈ [0, 1] be a value.…”

Section: Generalized Confidencementioning

confidence: 99%

“…A stick MDD is an MDD such that each layer contains 1 node. Proposition 2 Algorithm Conf idence ≤ and a stick MDD on the random variables is equivalent to the Confidence filtering algorithm defined in (Mercier-Aubin et al 2020).…”

Section: Particular Casesmentioning

confidence: 99%

“…Optimization and satisfaction problems involving random variables and searching for robust solutions are ubiquitous in modern continuous flux applications. Vehicle sharing, organ transplant, textile manufactures, and deliveries are just a few of the many industrial areas where robust optimization is necessary (Lin, Janak, and Floudas 2004;Parra et al 2005;Kargar et al 2020;Mercier-Aubin et al 2020). In such setting, the chance constrained problem is usually defined as follow: minimize…”

Section: Introductionmentioning

confidence: 99%

“…A first attempt had been made in 2015 (Rossi et al 2015). In 2020, some filtering algorithms (Mercier-Aubin et al 2020) were finally presented but they can handle only conjunction of binary inequality constraints.…”

Section: Introductionmentioning

confidence: 99%

“…Probability distributions used in constraint programming are often independent and directly represented by their probability mass functions (Mercier-Aubin et al 2020). 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).…”

Section: Introductionmentioning

confidence: 99%

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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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Section: Generalized Confidencementioning

confidence: 99%

Section: Particular Casesmentioning

confidence: 99%