solving delete-relaxed planning tasks by using cut...
TRANSCRIPT
Solving Delete-Relaxed
Planning Tasks by Using Cut SetsBACHELOR THESIS PRESENTATION
BY MARVIN BUFF
Overview
Classical Planning
What is the Problem?
The Flow-Cut Algorithm
Experiments /Results
Conclusion
Classical Planning
City
B
City
D
City
C
City
E
City
F
Island Problem
City
A
Island 1
Island 2
Island 3
City
G
Classical Planning
Fact B
Fact D
Fact C
Fact E
Fact F
Fact A
Causal Graph
GFact
What is the Problem?
Exponential Growth!
City
A
City
B
Island Problem – 10 Cities
City
…
City
J➢ ~3 mio expanded states
City
K➢ ~40 mio expanded states
City
L➢ ~500 mio expanded states
Flow-Cut Algorithm
The Idea
O(2𝑛)
Island Problem
Island Problem 1
Island Problem 2
O(2𝑛/2)
O(2𝑛/2)
SplittingSplit Problem
O(2 ∗ 2𝑛/2)
Flow-Cut Algorithm
Given Problem
City
B
City
D
City
C
City
E
City
F
City
A
Island 1
Island 2
Island 3
City
G
Flow-Cut Algorithm
Derive Causal Graph
Fact B
Fact D
Fact C
Fact E
Fact F
Fact A
Fact G
Flow-Cut Algorithm
Determine SCC’s
Fact B
Fact D
Fact C
Fact E
Fact F
Fact A
Fact G
Flow-Cut Algorithm
Simplify
Fact B
Fact D
Fact C
Fact E
Fact F
Fact A
Fact G
Fact X
Flow-Cut Algorithm
Initial Cut
Fact B
Fact D
Fact C
Fact E
Fact F
Fact A
Fact G
Left SCC Middle SCCs Right SCC= Initial Cut
Fact D
Fact E
Fact F
Flow-Cut Algorithm
Minimize Cut
Fact B
Fact D
Fact C
Fact E
Fact F
Fact A
Fact G
Fact D
Fact E
Fact F
Flow-Cut Algorithm
Create Sub-Problems
Fact B
Fact D
Fact C
Fact E
Fact F
Fact A
Fact G
Fact D
Left ProblemRight Problem
Fact H
Flow-Cut Algorithm
Create Sub-Problems
Left Problem 1 Cut = {} Right Problem 1
Flow-Cut Algorithm
Create Sub-Problems
Left Problem 2 Cut = {D} Right Problem 2
Solution = 3 + 2
Flow-Cut Algorithm
Create Sub-Problems
Left Problem 3 Cut = {H} Right Problem 3
Solution = 3 + 2
Flow-Cut Algorithm
Create Sub-Problems
Left Problem 4 Cut = {D,H} Right Problem 4
Solution = 4 + 2
Experiments
Setup
Implemented in C++
Tested on IPC Benchmark
Run over 60 minutes per problem
Results
Type A: Solvable
Type B: Big Cut
Type C: No Cut
Experiments
Type A: Solvable
Suitable Domains
miconic
pathways
satellite
40% 40%
Cut RightLeft
20%
Experiments
Type A: Solvable
Unbalanced Domains
Mystery
Rovers
trucks-strips
50%
Cut RightLeft
49%1%
Experiments
Type B: Big Cut
Domains with Big Cut
childsnack
no-mystery
parcprinter
tidybot
40% 40%
Cut > 20 RightLeft
20%
Experiments
Type B: Big Cut
Domains with Big Cut
childsnack
no-mystery
parcprinter
tidybot
Cut = 1 SCC RightLeft
98%1% 1%
Experiments
Type B: Big Cut
Domains with Big Cut
childsnack
no-mystery
parcprinter
tidybot
Cut = x SCCs RightLeft
98%1% 1%
Experiments
Type C: No Cut
Single SCCsOnly One SCCs No Middle SCC’s
Single Single Left RightSingle
Conclusion
What did we do?
Algorithm to compute ℎ+
What could be done different?
No SCCs
Undirected Structure
Multiple Left- /Right-Parts
Questions?