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.