Exact stochastic constraint optimisation with applications in network analysis

doi:10.1016/j.artint.2021.103650

Exact stochastic constraint optimisation with applications in network analysis

2022-03-01

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DOI：10.1016/j.artint.2021.103650

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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. 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 observed that global approaches to solving SCMDs outperform decomposition approaches from CP, and perform complementarily to MIPbased decomposition approaches, while scaling much more favourably with instance size. Both methods have many alternative design choices, as both knowledge compilation and constraint solvers are used in a single pipeline. To identify which configurations work best, we apply programming by optimisation. Specifically, we show how an automated algorithm configurator can be used to find optimised configurations of our pipeline. After configuration, our global SCMD solving pipeline outperforms its closest competitor (a MIPbased decomposition pipeline) on all test sets we considered by up to two orders of magnitude in terms of PAR10 scores. (c) 2021 The Author(s). Published by Elsevier B.V.

Keyword:

Constraint programming

Probabilistic inference

Stochastic constraints

Ordered binary decision diagrams

Monotonic probability distributions

Global constraints

Automated algorithm configuration

Probabilistic networks

Exact stochastic constraint optimisation with applications in network analysis

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