1. June 6 th, 2005 ICAPS-2005 Workshop on Constraint Programming for Planning and Scheduling 1/12 Stratified Heuristic POCL Temporal Planning based on Planning Graphs and Constraint Programming Ioannis Refanidis University of Macedonia, Thessaloniki, Greece

2. June 6 th, 2005 ICAPS-2005 Workshop on Constraint Programming for Planning and Scheduling 2/12 Introduction Our context: –Deadline goals –Durative actions with the effects at the end of the duration Innovations: –Simplified way to create the temporal planning graph –POCL heuristic temporal planning with disjunctive constraints No quantization of time, no-op actions Threats by emutex and cmutex relations –Heuristic guidance based on temporal planning graph –Completeness preserving pruning rules

3. June 6 th, 2005 ICAPS-2005 Workshop on Constraint Programming for Planning and Scheduling 3/12 Temporal planning graphs Citation: –Smith, D., and Weld., D. 1999. Temporal planning with mutual exclusion reasoning. Proc. of the 16th Intern. Joint Conf. on Artificial Intelligence, 326,333. Planning graph nodes: Actions and Propositions –action(A,T) –prop(P,T) Relations: –emutex(N1,N2) –cmutex(N1,N2,T) Events: –new_prop(P,T) –end_cmutex(P,Q,T)

4. June 6 th, 2005 ICAPS-2005 Workshop on Constraint Programming for Planning and Scheduling 4/12 Algorithm outline Main loop add_effects new_emutex_relations cmutex_action_prop1 cmutex_actions cmutex_props stop_cmutex_props cmutex_action_prop2 update_cmutex_props update_cmutex_action_prop update_cmutex_actions

5. June 6 th, 2005 ICAPS-2005 Workshop on Constraint Programming for Planning and Scheduling 5/12 Efficient planning graph construction Computing cmutex between actions: The most costly part of the temporal planning graph construction. Idea: Do not compute cmutex between actions during planning graph construction. –Omit calls to cmutex_actions and update_cmutex_actions. Choices: –Compute them once only, after the temporal planning graph construction. –Compute them on demand, during the POCL planning phase. Depending on the problem, significant savings in overall planning time.

6. June 6 th, 2005 ICAPS-2005 Workshop on Constraint Programming for Planning and Scheduling 6/12 Plan extraction as a CS problem Temporal constraint variables for: –Open goals,  G,T  –Actions in the plan,  A,T A  –Persistence conditions,  G,T 1,T 2  Algorithm outline: –Call the CSP solver when Agenda is empty. –Three ways to support open goals Initial state, current plan, new actions –Potential conflicts between persistence conditions (existing and new) and actions (existing and new).

7. June 6 th, 2005 ICAPS-2005 Workshop on Constraint Programming for Planning and Scheduling 7/12 Conflict resolution Threats are detected based on emutex and cmutex relations. Suppose two conflicting persistence conditions: –  G 1,T 11,T 12  –  G 2,T 21,T 22  Let T be the time where the mutex relations ends. Two cases for T: T=inf –T 11 ≥T 22 or T 21 ≥T 12 T<inf –T 11 ≥T 22 or T 21 ≥T 12 or T 11 ≥T or T 21 ≥T

8. June 6 th, 2005 ICAPS-2005 Workshop on Constraint Programming for Planning and Scheduling 8/12 Heuristic POCL Temporal Planning Adapted by: –Younes, L.S.H., and Simmons, R.G. 2003. VHPOP: Versatile Heuristic Partial Order Planner. Journal of Artificial Intelligence Research, 20, 405-430. For each set of open goals: –We do not consider duplicate goals. –We do not consider goals that can potentially be supported by actions already inserted in the plan. –From the remaining goals, we sum the maximum of the heuristic values for each "cluster" of goals that are emutexed or cmutexed until the infinite to each other. –In the above sum, we add the number of the goals (tie breaking mechanism). Subgoal selection: Most costly first. Tie breaking: Select the newest plans.

9. June 6 th, 2005 ICAPS-2005 Workshop on Constraint Programming for Planning and Scheduling 9/12 Repeated subgoal pruning Def. 1: A primitive subgoal chain PCHAIN(G n ) is an ordered list of subgoals  G n, G n-1, …G 0 , where each subgoal G i has been inserted in Agenda as a precondition of action A i, where action A i was initially inserted in the plan to support subgoal G i-1. Subgoal G 0 is an original goal of the problem instance. Repeated subgoal pruning rule: A new action A with G  Eff(A), cannot be inserted in a plan to support a specific subgoal G, if there is any proposition P  Precs(A) such that P  PCHAIN(G). switch on off on switch off on off clean on dirty clean dirty initial off clean goal off

10. June 6 th, 2005 ICAPS-2005 Workshop on Constraint Programming for Planning and Scheduling 10/12 Deleted supports Suppose two actions in a plan, A and B, such that: –P  Prec(A), P  Prec(B) –A and B are supported by the same proposition instance P. Then: –If neither A nor B deletes P, no constraint is posted. –If A deletes P but B preserves it, A is demoted after B. –If B deletes P but A preserves it, B is demoted after A. –If both A and B delete P, the plan is discarded. The use of disjunctive constraints renders this inconsistency undetectable, so it must be checked explicitly.

11. June 6 th, 2005 ICAPS-2005 Workshop on Constraint Programming for Planning and Scheduling 11/12 Preliminary results Preliminary implementation in ECLiPSe 5.8. Time limit 300 secs. Occasionally solve problems by the Airport and Pipesworld domains. #FullOlder-Pruning 1-Pruning 1, Older STP timemakesp an timemakesp an timemakesp an timemakesp an timemakesp an satellite11.11771.726981.8319843.3269 374.47323 satellite210.44538.8182--13.88182-- satellite310.744113.4251--15.5251-- satellite443.1501-------- satellite5246.3688--------

12. June 6 th, 2005 ICAPS-2005 Workshop on Constraint Programming for Planning and Scheduling 12/12 Future work Partially instantiated actions. Stronger propagation rules for disjunctive constraints. –e.g. A#>B, A# C ⊨ A#>C Expreriments/results in other domains.