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Distribution Optimization in Constraint Programming

Authors Guillaume Perez , Gaël Glorian , Wijnand Suijlen , Arnaud Lallouet

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Guillaume Perez
  • Huawei Technologies Ltd, CSI Paris, Boulogne-Billancourt, France
Gaël Glorian
  • Huawei Technologies Ltd, CSI Paris, Boulogne-Billancourt, France
Wijnand Suijlen
  • Huawei Technologies Ltd, CSI Paris, Boulogne-Billancourt, France
Arnaud Lallouet
  • Huawei Technologies Ltd, CSI Paris, Boulogne-Billancourt, France

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Guillaume Perez, Gaël Glorian, Wijnand Suijlen, and Arnaud Lallouet. Distribution Optimization in Constraint Programming. In 29th International Conference on Principles and Practice of Constraint Programming (CP 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 280, pp. 29:1-29:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)
https://doi.org/10.4230/LIPIcs.CP.2023.29

Abstract

Stochastic Constraint Programming introduces stochastic variables following a probability distribution to model uncertainty. In the classical setting, probability distributions are given and constant. We propose a framework in which random variables are given a set of possible distributions and only one should be selected. A solution is obtained when all variable distributions are assigned, and all decision variables are assigned too. In such a setting, a constraint on random variables limits the possible distributions its random variables may take. We generalize the notion of chance as the probability of satisfaction of a constraint, called probabilization, given variable distributions. Probabilization can be seen as a generalization of reification in a random setting whose result is a random variable. We define minimal arithmetic to work with stochastic variables having a variable distribution. Using the introduced representation, our framework can in theory save an exponential number of decisions, and represents problems that were previously not representable with finite integer domains. Finally, we model and solve two industrial problems that require this extension - virtual network configuration and assignment of chemical delivery - and show improvement in terms of quality of solution and speed.

Subject Classification

ACM Subject Classification
  • Theory of computation → Constraint and logic programming
  • Mathematics of computing → Solvers
  • Computing methodologies → Probabilistic reasoning
Keywords
  • Constraint Programming
  • Optimization
  • Stochastic Optimization

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