Investigating the Effect of Relevance and Reachability Constraints on SAT Encodings of Planning

Recently, satisfiability (SAT) techniques have been shown to be more efficient at extracting solutions from a planning graph in Graphplan (Blum & Furst 1995) than the standard backward search(Kautz & Selman 1998). Graphplan gains efficiency from forward propagation and backward use of mutual exclusion constraints. The utility of SAT techniques for solution extraction raises two important questions: (a) Are the mutual exclusion constraints equally useful for solution extraction with SAT encodings? (b) If so, are there additional types of propagated constraints that can benefit them even more? Our ongoing research investigates these two questions. The mutual exclusion relations (mutex) used in the standard Graphplan, that we shall refer to as fmutex constraints, are propagated by the following rules: Two facts and are fmutex if all actions supporting are pair-wise fmutex with all actions supporting . Two actions are fmutex if action deletes another action ’s preconditions or effects, or if preconditions of are pairwise fmutex with preconditions of . Fmutex relations propagate forward from the initial state to provide “reachability” information to the backward search. Though they increase the size of the SAT encoding with a quadratic number of additional clauses, the overall encoding is simplified through unit-propagation based methods. E.g., fmutexes helps an 11 step/73 action logistics problem that takes 6 min 30 sec on Blackbox to solve in 7sec (60x speedup). It is also possible to propagate “relevance” relations starting from the goals. Such constraints would not be useful for standard Graphplan, unless it conducts the search in the forward direction. In contrast, the search in SAT encodings is “directionless” in that it neither goes exclusively backward from goals nor exclusively forward from the initial state. Any variable that has the best heuristic properties (smallest live domain (Tsang 1993), maximum unit propagation (Li & Anbulagan 1997)) is selected, irrespective of its position in the corresponding planning graph. This means that the solver can potentially exploit mutex relations based on reachability as well as relevance. With this insight, we developed two types of constraints that can be propagated in backward direction, and carry relevance information: Backward mutex (bmutex): Bmutex constraints attempt to capture the idea that two actions (or propositions) are never relevant together. Facts in the goal level are not bmutex. If actions and give the same set of facts at the next level, then is bmutex with . Moreover, if all the