Learning When to Use Automatic Tabulation in Constraint Model Reformulation

Combinatorial optimisation has numerous practi- cal applications, such as planning, logistics, or cir- cuit design. Problems such as these can be solved by approaches such as Boolean Satisfiability (SAT) or Constraint Programming (CP). Solver perfor- mance is affected significantly by the model cho- sen to represent a given problem, which has led to the study of model reformulation. One such method is tabulation: rewriting the expression of some of the model constraints in terms of a single table constraint. Successfully applying this process means identifying expressions amenable to trans- formation, which has typically been done manu- ally. Recent work introduced an automatic tab- ulation using a set of hand-designed heuristics to identify constraints to tabulate. However, the per- formance of these heuristics varies across problem classes and solvers. Recent work has shown learn- ing techniques to be increasingly useful in the con- text of automatic model reformulation. The goal of this study is to understand whether it is possi- ble to improve the performance of such heuristics, by learning a model to predict whether or not to activate them for a given instance. Experimental results suggest that a random forest classifier is the most robust choice, improving the performance of four different SAT and CP solvers.