Stratified Heuristic POCL Temporal Planning based on Planning Graphs and Constraint Programming

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

2. 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 ICAPS-2005 Workshop on Constraint Programming for Planning and Scheduling

3. 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) ICAPS-2005 Workshop on Constraint Programming for Planning and Scheduling

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

5. 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. ICAPS-2005 Workshop on Constraint Programming for Planning and Scheduling

6. Plan extraction as a CS problem • Temporal constraint variables for: • Open goals, G,T • Actions in the plan, A,TA • Persistence conditions, G,T1,T2 • 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). ICAPS-2005 Workshop on Constraint Programming for Planning and Scheduling

7. Conflict resolution • Threats are detected based on emutex and cmutex relations. • Suppose two conflicting persistence conditions: • G1,T11,T12 • G2,T21,T22 • Let T be the time where the mutex relations ends. • Two cases for T: • T=inf • T11≥T22 or T21≥T12 • T<inf • T11≥T22 or T21≥T12 or T11≥T or T21≥T ICAPS-2005 Workshop on Constraint Programming for Planning and Scheduling

8. 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. ICAPS-2005 Workshop on Constraint Programming for Planning and Scheduling

9. switch on goal switch off initial on off off off on off dirty clean clean on dirty clean Repeated subgoal pruning • Def. 1: A primitivesubgoal chain PCHAIN(Gn) is an ordered list of subgoals Gn, Gn-1, …G0, where each subgoal Gi has been inserted in Agenda as a precondition of action Ai, where action Ai was initially inserted in the plan to support subgoal Gi-1. Subgoal G0 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). ICAPS-2005 Workshop on Constraint Programming for Planning and Scheduling

10. 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. ICAPS-2005 Workshop on Constraint Programming for Planning and Scheduling

11. Preliminary results • Preliminary implementation in ECLiPSe 5.8. • Time limit 300 secs. • Occasionally solve problems by the Airport and Pipesworld domains. ICAPS-2005 Workshop on Constraint Programming for Planning and Scheduling

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