1. Heuristic POCL Planning Håkan L. S. Younes Carnegie Mellon University

2. POCL Planning Search through plan-space Record only essential action orderings and variable bindings Partial order Lifted actions Causal links track reasons for having an action in a plan

3. Early to mid 1990s: Glory-Days of POCL Planning Dominating planning paradigm in early 1990s SNLP (McAllester & Rosenblitt 1991) UCPOP (Penberthy & Weld 1992) Theoretically appealing, but remained inefficient despite significant research effort until mid 1990s

4. Paradigm Shift Planning graph analysis Graphplan (Blum & Furst 1995) Planning as propositional satisfiability SATPLAN (Kautz & Selman 1996) Heuristic search planning HSP (Bonet & Geffner 1998) FF (Hoffman & Nebel 2001)

5. Revival of POCL Planning RePOP (Nguyen & Kambhampati 2001) Distance-based heuristic derived from serial planning graph Disjunctive ordering constraints Restricted to ground actions

6. VHPOP (2002) Additive heuristic (HSP-r) for ranking partial plans Implements many novel flaw selection strategies Joint parameter domain constraints when planning with lifted actions (Younes & Simmons 2002)

7. Search Control in POCL Planning Plan selection Flaw selection

8. Additive Heuristic for POCL Planning Key assumption: Subgoal independence Heuristic value for open condition p: Zero if p unifies with an initial condition Minimum over heuristic values for ground actions having some effect unifying with p Heuristic value for partial plan: Sum of heuristic values for open conditions

9. Accounting for Reuse Assign zero heuristic value to open condition that can be linked to some effect of an existing action

10. Accounting for Reuse (Example) A B pre: p add: p Additive heuristic: 1With reuse: 0

11. No Reuse vs. Reuse ProblemMW-LocMW-Loc-ConfLCFR-LocLCFR-Loc-Conf h add h r add h add h r add h add h r add h add h r add 68.650.164.410.1387.582.01-1.16 73.660.340.630.1721.151.281.570.22 8--110.261.48-177.27-2.05 9-0.33-0.28---- 104.132.110.710.763.790.641.300.83 6-0.9317.412.9025.090.9511.242.82 7---37.81---33.10 8-15.48-37.99---6.45 9-86.21-11.53-33.3726.339.49 10-26.59-21.22-21.20-18.22 DriverLog ZenoTravel

12. No Reuse vs. Reuse ProblemMW-LocMW-Loc-ConfLCFR-LocLCFR-Loc-Conf h add h r add h add h r add h add h r add h add h r add 60.360.220.370.240.320.210.400.24 70.490.370.540.840.550.510.62- 81.09-1.290.840.850.831.250.68 92.41-2.11-1.84-2.50- 101.531.121.951.111.501.362.081.37 Satellite

13. Estimated Effort Estimate of total number of open conditions that will have to be resolved Estimated effort for fully resolving an open condition p: Like additive heuristic, but with value one if p unifies with an initial condition Use as tie-breaker

14. Estimated Effort (Example) Init B pre: q add: p, q A pre: p Init B pre: q add: p, q C pre: p, q Additive heuristic: 0 Estimated effort: 2 Additive heuristic: 0 Estimated effort: 3 add: radd: sadd: radd: s

15. Estimated Effort as Tie-Breaker Problemh add with efforth r add with effortRePOP gripper-8705449*** gripper-101359795*** gripper-1223591294*** gripper-20122045558*** rocket-ext-a2581020028245072032117768 rocket-ext-b200341936315919670551540 logistics-a301287621317191 logistics-b488404694326436 logistics-c4223466292272468 logistics-d139813842525682*

16. Old Flaw Selection Strategies UCPOP: Threats before open conditions DSep: Delay separable threats DUnf: Delay unforced threats LCFR: Least cost flaw repair ZLIFO: Zero commitment LIFO

17. Issues in Flaw Selection Focus on subgoal achievement Global vs. local flaw selection Sensitivity to precondition order

18. New Flaw Selection Strategies Early commitment through flaw selection Heuristic flaw selection Local flaw selection Conflict-driven flaw selection

19. Early Commitment through Flaw Selection Select static open conditions first Static preconditions must be linked to the initial conditions The initial conditions contain no variables Therefore, linking static open conditions will bind action parameters to objects Can lead to fewer generated plans (Younes & Simmons 2002)

20. Heuristic Flaw Selection Use distance-based heuristic to rank open conditions Build plan from goals to start state Most heuristic cost first Most estimated effort first Build plan from start state to goals Least cost/effort first

21. Local Flaw Selection Only select from open conditions of most recently added action with remaining open conditions Helps maintain subgoal focus Can be combined with other strategies LCFR-Loc MW-Loc

22. Global vs. Local Flaw Selection ProblemUCPOPLCFRLCFR-Loc / n / n / n 60.20200.01200.0120 70.23200.10200.3220 80.2817-00.001 90.6270.00100.4514 100.3316-00.0720 60.27200.0370.2220 70.238-00.1816 80.2911-00.1519 90.2217-00.2118 100.2618-00.2217 DriverLog ZenoTravel

23. Global vs. Local Flaw Selection ProblemMCMC-LocMWMW-Loc / n / n / n / n 60.18200.23200.02200.0220 70.13180.2520-00.0520 8-0-0-0-0 9-00.0120-00.0120 10-00.0820-00.0820 6-00.0020-00.0020 7-00.1616-00.1616 8-00.1820-00.1820 9-00.1920-00.1920 10-00.1519-00.1519 DriverLog ZenoTravel

24. Conflict-Driven Flaw Selection Select unsafe open conditions first An open condition is unsafe if a link to it would be threatened Helps expose inconsistencies and conflicts early

25. Conflict-Driven Flaw Selection (Results) ProblemMW-LocMW-Loc-ConfLCFR-LocLCFR-Loc-Conf h add h r add h add h r add h add h r add h add h r add 68.650.164.410.1387.582.01-1.16 73.660.340.630.1721.151.281.570.22 8--110.261.48-177.27-2.05 9-0.33-0.28---- 104.132.110.710.763.790.641.300.83 6-0.9317.412.9025.090.9511.242.82 7---37.81---33.10 8-15.48-37.99---6.45 9-86.21-11.53-33.3726.339.49 10-26.59-21.22-21.20-18.22 DriverLog ZenoTravel

26. Planning with Durative Actions Replace ordering constraints with simple temporal network VHPOP currently uses same plan and flaw selection heuristics for temporal planning as for classical planning

27. Future of VHPOP Tailored heuristic functions for temporal planning Support for durations as functions of action parameters Use of landmarks

28. VHPOP: Versatile Heuristic Partial Order Planner www.cs.cmu.edu/~lorens/vhpop.html