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Transition-Aligned Domain Analysis for Multi-Valued Variables

Planning with multi-valued variables using Domain Transition Graph representation for accurate deadline estimates and goal ordering based on causal dependencies. Implement lookahead strategy for search efficiency.

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Transition-Aligned Domain Analysis for Multi-Valued Variables

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

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

  3. Motivation • Action Interleaving • Durative actions may execute concurrently with each other; need to model this to extract accurate heuristics 2 lstart (T,2) lend (T,2) 1 ulstart (T,1) ulend (T,1) T

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

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

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

  7. Deadline Goals Example package deadline: t=20 truck loadstart/unloadstart 2 2 unloadend movestart time counter moveend loadstart 1 t=0 t=10 1 P=14 moveend movestart t=22 unloadstart t=26 T loadstart/unloadstart loadend 4 4 lstart (T,2) lend (T,2) ulstart (T,1) ulend (T,1) 8 10 mstart (1,2) mend (1,2) mstart (2,1) mend (2,1)

  8. 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

  9. 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.

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