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Using Abstraction for Planning in Sokoban

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Title: Using Abstraction for Planning in Sokoban


1
Using Abstraction for Planning in Sokoban
  • Adi Botea, Martin Müller, Jonathan Schaeffer
  • University of Alberta
  • CG 2002

2
Outline
  • What is Sokoban
  • Motivation
  • Planning Abstraction in Sokoban
  • Experimental Results
  • Future Work
  • Conclusion

3
What is Sokoban
4
Previous Work in Sokoban
  • Rolling Stone
  • Deepgreen
  • Standard 90 problem suite

5
Motivation
  • Heuristic Search is not Enough
  • Why Planning?
  • Why Abstraction?

6
Heuristic Search is not Enough
  • Sokoban is hard
  • Large branching factor (can be gt 100)
  • Long solutions (can be gt 600)
  • Deadlocks
  • Expensive evaluation function
  • Humans create hard problems

7
Why Planning?
  • Humans not only search but also plan
  • Significant progress in AI planning recently
  • AIPS planning competition
  • Few results published about planning in games
    (even fewer successful results!)

8
Why Abstraction?
  • Non-abstracted planning in Sokoban is limited
  • Abstraction can reduce branching factor, solution
    length, and likelihood of encountering a deadlock
  • Actions ? atomic moves
  • Humans also abstract problems

9
Maze Abstraction
  • Maze Rooms Tunnels

10
Maze Preprocessing
11
Sokoban as a Planning Domain
BEFORE
AFTER
82
MOVE
81
80
Position(80) Position(81) Position(82) CanPush(82,
81, 80)
StoneAt(81) ManCanGoTo(82) !StoneAt(80)
!StoneAt(81) ManAt(81) StoneAt(80)
12
Planning Abstraction
TLPlan
13
Plain Sokoban
  • TLPlan
  • General purpose planner
  • Supports domain-specific
  • knowledge
  • Domain-specific knowledge
  • Distance heuristic Minmatching
  • Deadlock database
  • World equivalence
  • 0 real problems solved

14
Tunnel Sokoban
  • Abstracted tunnels
  • Non-abstracted rooms
  • Planning actions
  • Simple push moves inside rooms
  • Macro moves for tunnels
  • Push a stone across a tunnel
  • Park a stone to a tunnel
  • Un-park a stone from a tunnel
  • 1 real problem solved

Abstracted Rooms
Abstracted Tunnels
Domain Specific Knowledge
TLPlan
15
Abstract Sokoban
  • Abstracted both rooms and tunnels
  • Planning actions
  • Move a stone from one
  • room/tunnel to another room/tunnel
  • Shuffle stones inside a room
  • so that the man can walk
  • between two entrances
  • No simple push moves anymore
  • 17 real problems solved

Abstracted Rooms
Abstracted Tunnels
Domain Specific Knowledge
TLPlan
16
Planning Move - Example
MOVE AT THE ABSTRACT LEVEL
WHAT ACTUALLY HAPPENS
17
Problem Decomposition
  • One global abstract problem
  • Several local abstract problems
  • (one for each room)

T0
T3
R2
R0
R3
T1
R2
T2
R1
R0
GLOBAL PROBLEM
LOCAL PROBLEMS
R3
R1
R3
R0
R1
R2
18
Local Problems
  • Two main goals
  • Compute planning preconditions
  • Detect local deadlocks
  • Rooms
  • Small ? complete knowledge
  • Large ? on demand search

19
Local Abstraction
SAME ABSTRACT STATE OF A ROOM
SAME ABSTRACT STATE OF A TUNNEL
20
Experimental Results
SP stone pushes in RS solution
Solution length
Problem number
21
Experimental Results
Expanded nodes
Number of stones
22
Experimental Results
  • Compare Abstract Sokoban (AS) to Tunnel Sokoban
    (TS) and Rolling Stone (RS)
  • Abstract Sokoban
  • 17/90 problems solved so far
  • Each abstraction step reduces search complexity
    by orders of magnitude
  • Promise to overcome limitations of heuristic
    search approaches

23
Future Work
  • Solve more problems
  • Maze decomposition
  • Global deadlock detection
  • Parallel Sokoban
  • Automatic abstraction of planning domains
  • Planning abstraction in other domains, such as
    Go

24
Conclusion
  • Abstract Sokoban
  • Highly abstracted representation as a planning
    domain
  • Experimental Results
  • Exponential reduction of initial search space
  • Promise to overcome limitations of heuristic
    search approaches
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