Optimal decision-making under constraints and uncertainty

We present an extensive study of methods for exactly solving stochastic constraint (optimisation) problems (SCPs) in network analysis. These problems are prevalent in science, governance and industry. Both our proposed solving methods aim to strike a good balance between convenience, generality, and speed. The first method we study is generic and decomposes stochastic constraints into a multitude of smaller local constraints that are solved using a constraint programming (CP) or mixed-integer programming (MIP) solver. However, many SCPs are formulated on probability distributions with a monotonic property, meaning that adding a positive decision to a partial solution to the problem cannot cause a decrease in solution quality. The second method is specifically designed for solving global stochastic constraints on monotonic probability distributions (SCMDs) in CP. Both methods use knowledge compilation to obtain a decision diagram encoding of the relevant probability distributions, where we focus on ordered binary decision diagrams (OBDDs). We discuss theoretical advantages and disadvantages of these methods and evaluate them experimentally. We conclude that, while the decomposition method is easy to implement and can be used to solve and SCP, the global stochastic constraint solves problems faster, and is still widely applicable due to the prevalence of monotonicity in real-world problems.This research was funded by the Netherlands Organisation for Scientific Research (NWO).Algorithms and the Foundations of Software technolog

Combining Stochastic Constraint Optimization and Probabilistic Programming

Algorithms and the Foundations of Software technolog

Stochastic Constraint Propagation for Mining Probabilistic Networks

A number of data mining problems on probabilistic networks can be modelled as Stochastic Constraint Optimisation and Satisfaction Problems, i.e., problems that involve objectives or constraints with a stochastic component. Earlier methods for solving these problems used Ordered Binary Decision Diagrams (OBDDs) to represent constraints on probability distributions, which were decomposed into sets of smaller constraints and solved by Constraint Programming (CP) or Mixed Integer Programming (MIP) solvers. For the specific case of monotonic distributions, we propose an alternative method: a new propagator for a global OBDD-based constraint. We show that this propagator is efficient and maintains domain consistency. We experimentally evaluate this global constraint in comparison to existing decomposition-based approaches. As test cases we use problems from the data mining literature.Algorithms and the Foundations of Software technolog