Value ordering for quantified CSPs

We investigate the use of value ordering in backtracking search for Quantified Constraint Satisfaction problems (QCSPs). We consider two approaches for ordering heuristics. The first approach is solution-focused and is inspired by adversarial search: on existential variables we prefer values that maximise the chances of leading to a solution, while on universal variables we prefer values that minimise those chances. The second approach is verification-focused, where we prefer values that are easier to verify whether or not they lead to a solution. In particular, we give instantiations of this approach using QCSP-Solve's pure-value rule Gent et al. (QCSP-solve: A solver for quantified constraint satisfaction problems. In Proceedings of IJCAI, pp. 138-143, 2005). We show that on dense 3-block problems, using QCSP-Solve, the solution-focused adversarial heuristics are up to 50% faster than lexicographic ordering, while on sparse loose interleaved problems, the verification-focused pure-value heuristics are up to 50% faster. Both types are up to 50% faster on dense interleaved problems, with one pure-value heuristic approaching an order of magnitude improvement.