The New Version of CPT, an Optimal Temporal POCL Planner based on Constraint Programming

CPT is a domain-independent temporal planner that combines a branching scheme based on Partial Order Causal Link (POCL) Planning with powerful and sound pruning rules implemented as constraints. Unlike other recent approaches that build on POCL planning (Nguyen & Kambhampati 2001; Younes & Simmons 2003), CPT is an optimal planner that minimizes makespan. The details of the planner and its underlying formulation are described in (Vidal & Geffner 2004; Vidal & Geffner 2006). CPT competed in the optimal track of IPC-4, where it got a second place. The development of CPT is motivated by the limitation of heuristic state approaches to parallel and temporal planning that suffer from a high branching factor (Haslum & Geffner 2001) and thus have difficulties matching the performance of planners built on SAT techniques such as Blackbox (Kautz & Selman 1999). In CPT, all branching decisions (resolution of open supports, support threats, and mutex threats), generate binary splits, and nodes σ in the search correspond to ‘partial plans’ very much as in POCL planning. While ideally, one would like to have informative lower bounds f(σ) on the makespan f∗(σ) of the best complete plans that expand σ, so that the partial plan σ can be pruned if f(σ) 6≤ B for a given boundB, such lower bounds are not easy to come by in the POCL setting. CPT thus models the planning domain as a temporal constraint satisfaction problem, adds the constraint f∗(σ) ≤ B for a suitable bound B on the makespan, and performs limited form of constraint propagation in every node σ of the search tree. The novelty of CPT in relation to other temporal POCL planners such as IXTET (Laborie & Ghallab 1995) and RAX (Jonsson et al. 2000), that also rely on constraint propagation (and Dynamic CSP approaches such as (Joslin & Pollack 1996)), is the formulation that enables CPT to reason about actions a that are not yet in the plan. Often a lot can be inferred about such actions including restrictions about their possible starting times and supports. Some of this information can actually be inferred before any commitments are made; the lower bounds on the starting times of all actions as computed in GRAPHPLAN being one example (Blum & Furst 1995). CPT thus reasons with CSP variables that involve all the actions a in the domain and not only those present in the current plan, and for each such action, it deals with two variables S(p, a) and T (p, a) that stand for the possibly undetermined action supporting precondition p of a, and the possibly undetermined starting time of such an action. A causal link a′[p]a thus becomes a constraint S(p, a) = a′, which in turn implies that the supporter a′ of precondition p of a starts at time T (p, a) = T (a′). A number of constraints enforce the correspondences among these variables. At the same time, the heuristic functions for estimating costs in a temporal setting, as introduced in (Haslum & Geffner 2001), are used to initialize variables domains and some ‘distances’ between actions (Van Beek & Chen 1999). Currently, the semantics of the optimal temporal plans computed by CPT follows the one in (Smith & Weld 1999) where interfering actions (actions that delete a precondition or an effect of another one) are not allowed to overlap in time. This condition has been relaxed in PDDL 2.1 where interfering actions may overlap sometimes (e.g., when preconditions do not have to be preserved throughout the execution of the action). This restriction can in some domains produce slightly longer plans.