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Flexible Planning Ian Miguel AI Group Department of Computer Science University of York
AI Planning ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]
Example – Initial State ,[object Object],[object Object],[object Object],[object Object],[object Object],c 1 c 2 c 4 c 3 r 1 r 2 r 3 m 1 m 2 pkg 1 pkg 2 guard 1 ,[object Object],[object Object],[object Object]
Example - Operators ,[object Object],[object Object],[object Object],[object Object],[object Object],c 1 c 2 c 4 c 3 r 1 r 2 r 3 m 1 m 2 pkg 1 pkg 2 guard 1
Example – Solution ,[object Object],[object Object],c 1 c 2 c 4 c 3 r 1 r 2 r 3 m 1 m 2 pkg 1 pkg 2 guard 1
Example - Solution ,[object Object],[object Object],c 1 c 2 c 4 c 3 r 1 r 2 r 3 m 1 m 2 pkg 1 pkg 2 guard 1
Example - Solution ,[object Object],[object Object],[object Object],[object Object],c 1 c 2 c 4 c 3 r 1 r 2 r 3 m 1 m 2 pkg 1 pkg 2 guard 1
Example - Solution ,[object Object],[object Object],c 1 c 2 c 4 c 3 r 1 r 2 r 3 m 1 m 2 guard 1 pkg 1 pkg 2
Solving Planning Problems ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]
The Planning Graph ,[object Object],[object Object],[object Object],[object Object],Initial Conditions Actions 1 Propositions 1 . . . . . . . . . Goals
Mutual Exclusion Constraints ,[object Object],[object Object]
Mutual Exclusion Constraints ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]
Mutual Exclusion Constraints ,[object Object],[object Object],[object Object],[object Object],[object Object],a b
Finding a Valid Plan ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]
The Constraint Satisfaction Problem ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],Specify allowed combinations of assignments of values to variables.
The CSP Viewpoint ,[object Object],[object Object],[object Object],[object Object],[object Object],Goal Sub-problem
Memoisation ,[object Object],[object Object],[object Object],[object Object],Goal Sub-problem
Memoset Propagation ,[object Object],[object Object],Goal Sub-problem
A Weakness of Classical Planning ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]
Flexible Planning Problems ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]
Truth Degree ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]
Flexible Plan Quality ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]
Flexible Example ,[object Object],[object Object],[object Object],[object Object],[object Object],c 1 c 2 c 4 c 3 r 1 r 2 r 3 m 1 m 2 pkg 1 pkg 2 guard 1 L={l   , l 1 , l 2 , l T }
Flexible Example ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],c 1 c 2 c 4 r 1 r 2 r 3 m 1 m 2 pkg 1 pkg 2 guard 1 L={l   , l 1 , l 2 , l T }
Flexible Planning Graph ,[object Object],[object Object],[object Object],Actions 1 Propositions 1 . . . . . . . . . l 2 l 3 l 1
Finding Valid Flexible Plans: Flexible Graphplan ,[object Object],[object Object],[object Object],[object Object],Goal Sub-problem
Short Compromise Plan ,[object Object],[object Object],[object Object],[object Object],c 1 c 2 c 4 c 3 r 1 r 2 r 3 m 1 m 2 pkg 1 pkg 2 guard 1 L={l   , l 1 , l 2 , l T } 4-steps ( l 1 )
Longer Plan, Fewer Compromises ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],c 1 c 2 c 4 c 3 r 1 r 2 r 3 m 1 m 2 pkg 1 pkg 2 guard 1 L={l   , l 1 , l 2 , l T } 6-steps ( l 2 )
Limited Graph Expansion ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]
Satisfaction Degree Propagation ,[object Object],[object Object],[object Object],[object Object],l 1 Action1 Action2 Level a Level a+1
Satisfaction Degree Propagation ,[object Object],[object Object],l 1 Action1 Action3 Level a Level a+1 l 2 l 2
Satisfaction Degree Propagation ,[object Object],[object Object],l 1 Action1 Action3 Level a Level a+1 l 2 l 2 l 2
Results: FGP vs Boolean Solving ,[object Object]
Utility of Limited Graph Expansion/Satisfaction Propagation ,[object Object]
Flexible Graphplan: Observations ,[object Object],[object Object],[object Object],[object Object]
Drowning and Leximin Ordering ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]
Solution (Leximin) ,[object Object],[object Object],[object Object],[object Object],[object Object],c 1 c 2 c 4 c 3 r 1 r 2 r 3 m 1 m 2 pkg 1 pkg 2 guard 1 L={l   , l 1 , l 2 , l T } 5-steps ( l 1 ,  l 2 ,  l 2 ,  l 2 ) Also finds 2 more plans that FGP misses.
Finding Leximin-optimal Plans: Leximin FGP ,[object Object],[object Object],[object Object],[object Object],Goal Sub-problem
Enhancements ,[object Object],[object Object],[object Object],[object Object],{ l 1 ,  l 2 } Action1 Action3 Level a Level a+1 { l 2 ,  l 3 } { l 2 ,  l 3 } { l 1 }
Satisfaction Degree Vector Propagation ,[object Object],[object Object],[object Object],{ l 1 ,  l 2 } Action1 Action3 Level a Level a+1 { l 2 ,  l 3 } { l 2 ,  l 3 } { l 1 ,  l 2 ,  l 3 } Action2
Removing Duplicates ,[object Object],[object Object],[object Object],[object Object],[object Object],{ l 1 } Action1 Action2 Level a Level a+1 {?,  l 3 } { l 1 } { l 1 }
Results: BBFGP vs. LFGP ,[object Object]
Results: BBFGP vs. LFGP ,[object Object]
Results: BBFGP vs. LFGP ,[object Object]
Results: Flexible Logistics ,[object Object],[object Object]
Utility of Satisfaction Degree Vector Propagation ,[object Object],[object Object],[object Object],[object Object],[object Object]
Leximin FGP: Observations ,[object Object],[object Object],[object Object],[object Object],[object Object]
Conclusions ,[object Object],[object Object],[object Object],[object Object]
Related Work ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]
Future Work ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]
Acknowledgements ,[object Object],[object Object]
Resources ,[object Object],[object Object],[object Object],[object Object]

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