solving delete-relaxed planning tasks by using cut...

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?