An Adaptive Model Restarts Heuristic

Symmetry is an important but often problematic feature of constraint satisfaction problems. One way to deal with symmetry is to add constraints to eliminate symmetric solutions [1–7]. Posting static symmetry breaking constraints has both good and bad features. On the positive side, static constraints are easy to post, and a few simple constraints can eliminate most symmetry in a problem. On the negative side, static symmetry breaking constraints pick out particular solutions in each symmetry class, and this may conflict with the branching heuristic. An alternative is a dynamic approach that modifies the search method to ignore symmetric states [8–11]. Whilst this reduces the conflict with the branching heuristic, we may get less propagation. In particular there is no pruning of symmetric values deeper in the search tree. An effective method to tackle this tension is model restarts [12]. This restarts search frequently with new and different symmetry breaking constraints. The hope is that we will find symmetry breaking constraints that do not clash with the branching heuristic. The original model restarts method proposed a random choice of symmetry breaking constraints. We show here that we can improve performance with an adaptive heuristic that aligns symmetry breaking with the dynamic branching heuristic.