eng
Schloss Dagstuhl – Leibniz-Zentrum für Informatik
Leibniz International Proceedings in Informatics
1868-8969
2023-09-22
29:1
29:19
10.4230/LIPIcs.CP.2023.29
article
Distribution Optimization in Constraint Programming
Perez, Guillaume
1
https://orcid.org/0000-0001-6473-583X
Glorian, Gaël
1
https://orcid.org/0000-0002-0843-5987
Suijlen, Wijnand
1
https://orcid.org/0000-0001-6450-5620
Lallouet, Arnaud
1
https://orcid.org/0000-0002-4318-356X
Huawei Technologies Ltd, CSI Paris, Boulogne-Billancourt, France
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.
https://drops.dagstuhl.de/storage/00lipics/lipics-vol280-cp2023/LIPIcs.CP.2023.29/LIPIcs.CP.2023.29.pdf
Constraint Programming
Optimization
Stochastic Optimization