Perturbing Branching Heuristics in Constraint Solving.

Variable ordering heuristics are one of the key settings for an efficient constraint solver. During the last two decades, a considerable effort has been spent for designing dynamic heuristics that iteratively change the order of variables as search progresses. At the same time, restart and randomization methods have been devised for alleviating heavy-tailed phenomena that typically arise in backtrack search. Despite restart methods are now well-understood, choosing how and when to randomize a given heuristic remains an open issue in the design of modern solvers. In this paper, we present several conceptually simple perturbation strategies for incorporating random choices in constraint solving with restarts. The amount of perturbation is controlled and learned in a bandit-driven framework under various stationary and non-stationary exploration policies, during successive restarts. Our experimental evaluation shows significant performance improvements for the perturbed heuristics compared to their classic counterpart, establishing the need for incorporating perturbation in modern constraint solvers.