Learning SAT Encodings for Constraint Satisfaction Problems

Constraint programming addresses many interesting and challenging problems in
\nour world, including recent applications to contexts as diverse as allocating
\nrefugee relief funds, short-term mine planning and hardware circuit design.
\n
\nUsers define their problems in high-level modelling languages which include
\ndescriptive global constraints. One of the most effective ways to solve
\nconstraint satisfaction problems (CSPs) is by translating them into instances
\nof the Boolean Satisfiability Problem (SAT). For some global constraints in
\nCSPs there exist many algorithms which encode the constraint into SAT;
\nchoosing an appropriate SAT encoding can alter the ultimate solving time
\ndramatically.
\n
\nWe investigate the problem of selecting the best SAT encoding for
\npseudo-Boolean and linear integer constraints. Many machine learning
\ntechniques are explored, applied and evaluated to aid this selection. The
\nresult is a significant improvement in performance compared to the default
\nchoice and to the single best choice from a training set. The approach is
\nsuccessful even for previously unseen problem classes and it greatly
\noutperforms a sophisticated general algorithm selection and configuration
\ntool.
\n
\nThis work provides a thorough empirical study and detailed analysis of each
\nstage in the machine learning process as applied to choosing SAT encodings.
\nIt does this in three phases: firstly by using generic CSP instance features
\nto select an encoding per constraint type for each instance, then by
\nintroducing new features which focus on the constraint types in question, and
\nfinally by learning to select encodings for individual constraints.
\n
\nWe find that even generic instance features can produce good predictions, but
\nthat the specialised features introduced give more robust performance
\nespecially when predicting for unseen problem classes. Training to predict
\nper constraint shows potential and leads to better performance for some
\nproblem classes, but per-instance selection is still competitive across the
\ncorpus of problems as a whole.

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