Extended Critical Paths in Temporal Planning

Timed initial literals refer to a recently added feature to the problem domain description language PDDL. Besides the modelling perspective to express exogenous events, this language extension allows to impose deadlines to action execution and to select temporal plans of high quality. For efficiently solving problems with explicit timing requirements, the work in this paper extends a two-stage planning/scheduling system where the sequential plan is built followed by a critical path scheduling phase to find a parallel arrangement. Timed initial literals are included into the plan finding and scheduling process in form of time windows for action execution. Compared to earlier work, the temporal model is refined to include slack and to allow overlappings of dependent actions. The apparently simple scheduling phase is faster than other approaches to establish parallel plans, but expressive enough to cope with current benchmark problems. Through its efficiency, it applies not only to schedule complete plans, but also partial and relaxed plans. Correctness and optimality of the algorithms are shown, and limitations of the approach are discussed. Empirical evidence is given by providing plans for many temporal planning problems.