Using Satisfiability for Non-optimal Temporal Planning

Abstract

AI planning is one of the research fields that has benefited from employing satisfiability checking methods. These methods have been proved to be very effective in finding optimal plans for both classical and temporal planning. It is also known that by using planning-based heuristic information in solving SAT formulae, one can develop SAT-based planners that are competitive with state-of-the-art non-optimal planners in classical planning domains. However, using satisfiability for non-optimal temporal planning has not been investigated so far. The main difficulty in using satisfiability in temporal planning is the representation of time, which is a continuous concept. Previously introduced SAT-based temporal planners employed an explicit representation of time in the SAT formulation, which made the formulation too large for even very small problems. To overcome this problem, we introduce a novel method for converting temporal problems into a SAT encoding. We show how the size of the encoding can be reduced by abstracting out durations of planning actions. We also show that the new formulation is powerful enough to encode fully concurrent plans. We first use an off-the-shelf SAT solver to extract an abstract initial plan out of the new encoding. We then add the durations of actions to a relaxed version of the initial plan and verify the resulting temporally constrained plan by testing consistency of a certain related Simple Temporal Problem (STP). In the case of an inconsistency, a negative cycle within the corresponding Simple Temporal Network (STN) is detected and encoded into the SAT formulation to prevent the SAT solver from reproducing plans with similar cycles. This process is repeated until a valid temporal plan will be achieved. Our empirical results show that the new approach, while not using a planning-based heuristic function of any kind, is competitive with POPF, which is the state-of-the-art of expressively temporal heuristic planners.