Chapter

Integration of AI and OR Techniques in Contraint Programming for Combinatorial Optimzation Problems

Volume 7298 of the series Lecture Notes in Computer Science pp 129-145

Flow-Based Combinatorial Chance Constraints

  • Andre A. CireAffiliated withLancaster UniversityTepper School of Business, Carnegie Mellon University
  • , Elvin CobanAffiliated withLancaster UniversityTepper School of Business, Carnegie Mellon University
  • , Willem-Jan van HoeveAffiliated withLancaster UniversityTepper School of Business, Carnegie Mellon University

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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.