Flow-Based combinatorial chance constraints

Authors:
Andre A. Cire;Elvin Coban;Willem-Jan van Hoeve
Affiliations:
Tepper School of Business, Carnegie Mellon University, Pittsburgh, PA;Tepper School of Business, Carnegie Mellon University, Pittsburgh, PA;Tepper School of Business, Carnegie Mellon University, Pittsburgh, PA
Venue:
CPAIOR'12 Proceedings of the 9th international conference on Integration of AI and OR Techniques in Constraint Programming for Combinatorial Optimization Problems
Year:
2012

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Abstract

We study stochastic variants of flow-based global constraints as combinatorial chance constraints. As a specific case study, we focus on the stochastic weighted alldifferent constraint. We first show that determining the consistency of this constraint is NP-hard. We then show how the combinatorial structure of the alldifferent constraint can be used to define chance-based filtering, and to compute a policy. Our propagation algorithm can be extended immediately to related flow-based constraints such as the weighted cardinality constraint. The main benefits of our approach are that our chance-constrained global constraints can be integrated naturally in classical deterministic CP systems, and are more scalable than existing approaches for stochastic constraint programming.