2. TADA Transition Aligned Domain Analysis T J. Benton and Kartik Talamadupula and Subbarao Kambhampati

3. Motivation Multi-valued Variables (at truck-1 loc-1): false (at truck-1 loc-2): true (at truck-1 loc-3): false (at truck-1 loc-4): false (at truck-1 loc-5): false (at truck-1 loc-6): false locations: loc-1 … loc-6 truck: truck-1 (= (loc truck-1) loc-2) (and (at ?t ?loc1) (at ?t ?loc2)) (= (?loc1 ?loc2))

4. Motivation Action Interleaving Durative actions may execute concurrently with each other; need to model this to extract accurate heuristics 2 2 T T 1 1 l start (T,2) l start (T,2) l end (T,2) l end (T,2) ul start (T,1) ul start (T,1) ul end (T,1) ul end (T,1)

5. Motivation Lookahead during search, following a YAHSP- style approach

6. Deadline Goals with Utility Give an estimate of establishment time e T – as against the actual deadline e D Model reward or penalty in terms of their difference Reward = min(0, [R - k (e T – e D )]) – R is the reward accrued for achieving the deadline goal. – If achieved by time e D, full reward. Else diminishing reward until 0.

7. Example Problem 1 1 2 2 1 1 2 2 I G truck package (load/unload) Causal Graph

8. Deadline Goals Example 2 2 T T 1 1 2 2 1 1 package truck load start /unload start unload start load start unload end load end m start (1,2) m start (1,2) m end (1,2) m end (1,2) move start move end move start move end l start (T,2) l start (T,2) l end (T,2) l end (T,2) ul start (T,1) ul start (T,1) ul end (T,1) ul end (T,1) m start (2,1) m start (2,1) m end (2,1) m end (2,1) 10 44 8 time counter t=0 t=10 P=14 t=22 t=26 deadline: t=20

9. FUTURE WORK International Planning Competition 2008 Tracks: Sequential Net-Benefit Temporal Problem decomposition for better analysis and more accurate estimates Considering a goal ordering based on causal dependencies in the domain

10. Summary Planning with multi-valued variables Domain Transition Graph representation Extended DTGs to handle durative actions Useful to estimate deadline establishment times; can be used for soft deadline goals with diminishing utility Implement a lookahead strategy for search Try to find a satisficing solution quickly Make effective use of action interleaving Handles net-benefit and temporal problems.