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Combining Novelty-Guided and Heuristic-Guided Search
Master ThesisArtificial Intelligence Group
Dario Maggi 29th July 2016
Examiner: Prof. Dr. Malte HelmertSupervisor: Dr. Thomas Keller
29.07.16 Dario Maggi 2
Overview
● 1. Introduction– Planning Task
– Heuristic Guided Search: Greedy Best-First Search
● 2. Novelty– What is novel?
– Iterated Width
● 3. Heuristic- and Novelty- Guided Search● 4. Experiments● 5. Conclusion
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1. Introduction
A Z
B
C
D
E
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Planning Task
A Z
B
C
D
E
● VariablesTruck: A, B, C, D, E, ZPackage 1: A, Truck, Z...
● OperatorsdriveA→B, driveA→C ...load1, load2, load3unload1, unload2, unload3
● Initial State● Goal State
Truck at APackage 1 in APackage 2 at APackage 3 at A
AAAAload1
ATAA ZZZZ
Packet 1 in Truck
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Breadth-First Search
A Z
B
C
D
E
AAAA
ATAA
load1 load2 load3
AATA AAAT
BTAA CTAA
ETAA
DTAA ZTAA
BATA CATA
EATA
DATA ZATA
BAAT CAAT
EAAT
DAAT ZAAT
ZZAA
BAAA CAAA
EAAA
DAAA ZAAA
ZAZA ZAAZ
driveA→B driveA→C
ZZZZ
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Breadth-First Search
A Z
B
C
D
E
AAAA
ATAA
load1 load2 load3
AATA AAAT
BTAA CTAA
ETAA
DTAA ZTAA
BATA CATA
EATA
DATA ZATA
BAAT CAAT
EAAT
DAAT ZAAT
ZZAA
BAAA CAAA
EAAA
DAAA ZAAA
ZAZA ZAAZ
driveA→B driveA→C
ZZZZ
Plan:load1,driveA→C,driveC→E,driveE→Z,unload1,...
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Heuristic Guided Search
● Heuristic h: Distance to Goal Estimator
● h: #Packets + #Packets in A - #Packets in Z
ATAA
AAAAh( ) = 4 + 4 - 0 = 8
h( ) = 4 + 3 - 0 = 7
A Z
B
C
D
E
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Greedy Best-First Search (GBFS)
h = 8
h = 7
AAAA
ATAA
load1 load2 load3
AATA AAAT
BTAA CTAA
ETAA
DTAA ZTAA
BATA CATA
EATA
DATA ZATA
BAAT CAAT
EAAT
DAAT ZAAT
ZZAA
BAAA
CAAA
driveA→B
driveA→C
h = 6
A Z
B
C
D
E
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Greedy Best-First Search (GBFS)
h = 8
h = 7
AAAA
ATAA
load1 load2 load3
AATA AAAT
BTAA CTAA
ETAA
DTAA ZTAA
BATA CATA
EATA
DATA ZATA
BAAT CAAT
EAAT
DAAT ZAAT
ZZAA
BAAA
CAAA
driveA→B
driveA→C
h = 6
A Z
B
C
D
E
Uninformed Heuristic Region (UHR)
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GBFS and UHRs
● Two Problems:– No Guidance in UHRs
– GBFS might expand multiple UHRs simultaneously
● What do we do?
Change the approach in UHRs
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2. Novelty
● How ''new'' is a state?
Truck Package 1 Package 2 Package 3 Novelty
A A A A 1
A T A A 1
A A T A 1
A A A T 1
B T A A 1
B A T A 2
A A A A 5
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Iterated Width
29.07.16 Dario Maggi 13
Iterated Width
AAAA
ATAA
load1 load2 load3
AATA AAAT
BTAA CTAA
ETAA
DTAA ZTAA
BATA CATA
EATA
DATA ZATA
BAAT CAAT
EAAT
DAAT ZAAT
ZZAA
BAAA CAAA
EAAA
DAAA ZAAA
ZAZA ZAAZ
driveA→B driveA→C
IW(1)
A Z
B
C
D
E
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Iterated Width
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Iterated Width +
● Extension for IW● Compute relaxed plan● Novelty Check on different Layers● Layer is the number of the relaxed plan facts that
were made true on a path
Iterated Width +
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Iterated Width +
AAAA
ATAA
load1 load2 load3
AATA AAAT
BTAA CTAA BATA CATA BAAT CAAT
BAAACAAA
EAAA
driveA→B driveA→C
Relaxed Plan:
Truck: B, E, D, ZPacket1: T Packet2: TPacket3: T
EAAA
A Z
B
C
D
E
layer: 0
layer: 1
layer: 2
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3. Heuristic- and Novelty- Guided Search
● Detect UHRs → UHR Threshold● In UHR: Start local IW● Expand nodes at maximum once
GBFS
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3. Heuristic- and Novelty- Guided Search
● Detect UHRs● In UHR: Start local IW● Expand nodes at maximum once
● Star Approach
GBFS
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Star Approach
s0 g
UHR
UHR
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Star Approach
s0 g
UHR
UHR
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Star Approach
s0 g
IW(1)
UHR
UHR
Szenario 1
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Star Approach
s0 g
UHR
UHR
Szenario I
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Star Approach
s0 g
UHR
UHR
Szenario I
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s0 g
IW(1)
UHR
UHR
Star Approach
Szenario 2
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Star Approach
s0 g
IW(1)
IW(2)
UHR
UHR
Szenario 2
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Star Approach
s0 g
IW(1)
IW(2)
UHR
UHR
Szenario 2
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Star Approach
s0 g
IW(1)
IW(2)
UHR
UHR
Szenario 3
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Star Approach
s0 g
UHR
UHR
Szenario 3,GBFS takes over again
IW(1)
IW(2)
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4. Experiments
● Implemented in Fast Downward● 46 Domains, total of 1456 Problems● Star Approach
● vs GBFS and GBFSpreferred (ff-heuristic)
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Coverage: Star Approach
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Comparison
1'456
1'000
GBFS1'075
GBFSpreferred1'171
Star: IW+(1), UHRsize(10)1'251
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5. Conclusion
● Helpful to switch to IW● Start more, smaller local searches
● Even Closer Coupling by only using IW to escape UHRs?
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Lessons Learned
● Fast Downward, Novelty, Data Structure
● Lessons I wish I had finally learned– Branching Strategy
– Setup Testing Environment
– Carefulness
– Don't Panic
– Daily Routine
Thank You
Thank You for your attention
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