Enhancing Search for Satisficing Temporal Planning with Objective-driven Decisions

1. Enhancing Search for Satisficing Temporal Planning with Objective-driven Decisions Patrick Eyerich Subbarao Kambhampati J. Benton

2. g-value plateaus in Temporal Planning • Common temporal planning objective function (:metric (minimize (total-time))) • Makespan as the evaluation function is inefficient for satisificing search • g-value plateaus • Leads to worst case cost-variance between search operations • The usual approach: Use a Surrogate Search • Choose a surrogate evaluation function that allows for scalability, improving the cost-variance between search states • Objective Function ≠ Evaluation Function • We want to improve “keeping track” of objective function

3. Temporal Fast Downward • Temporal Fast Downward (TFD) Objective Function Corresponding Evaluation Function Surrogate Evaluation Function

4. Temporal Fast Downward Search 5 @ start @ end eff @ end eff @ end eff 3 2 4 @ end eff @ start @ end eff 2 6

5. Temporal Fast Downward Search 5 … @ start @ end eff @ end eff @ end eff 3 2 4 @ end eff @ start @ end eff 2 6

6. Find the Better Path • Force consideration of better-makespan path • Should maintain surrogate evaluation function’s scalability • Our idea: Determine whether operators are useful according to makespan and force their expansion

7. Useful Operators • Related to Wehrle et al.’s useless actions • At parent state s • Remove operator o from the domain • Find heuristic value for , • Apply operator o to generate • Find heuristic value for , • If then operator is possibly useful • Its degree of usefulness is

8. Makespan-Usefulness Example An optimal plan Get all trucks to

9. Makespan-Usefulness Example

10. Lookahead on Useful Operators • Force expansion of most makespan-useful state before other states • Remove ‘best’ node from queue • Analyze for child states for makespan-usefulness • Expand state given by most useful operator • Evaluate each resulting grandchild state according to the surrogate evaluation function and push into queue

11. Useful Operator Lookahead 5 … @ start @ end eff @ end eff @ end eff 3 2 4 @ end eff @ start @ end eff 2 6

12. Empirical Evaluation • 4 Anytime search variations • TFD • TFD with useful lookahead, • TFD with lazy evaluation followed by TFD with useful lookahead (and without lazy evaluation), • TFD with lazy evaluation followed by TFD without lazy evaluation, • Makespan heuristic using STN • 30 minute timeout • Compared on IPC score

13. Results Over Time

14. Results Over Time

15. At 30 Minutes

16. Quality Change

17. Summary • Used notion of operator usefulness • Lookahead on most useful operator • Use in combination with surrogate search • Shown to improve plan quality in some domains • Continues to help when combined with a portfolio-like approach

18. Future Work • Lookahead more than one step • k-deep local lookaheads on most useful operators combined with best-first search • Use relaxed solutions • YAHSP-style lookahead but stop when no makespan-useful operators are applicable