A Hierarchical Goal-Based - PowerPoint Presentation

Slide1

A Hierarchical Goal-Based Formalism and Algorithm for Single-Agent PlanningAAMAS ‘12

Utku

Şirin

1560838

Slide2

OutlinePlanning and Domain ModelsHierarchical Goal Network (HGN) Planner formalism and proof of its capabilitiesAn algorithm for HGN planning

,

Goal

Decomposition

Planner (GDP)

Experimental

Results

Comments

and

Conclusions

Slide3

Automated PlanningWhat is automated planning?There is goal and current situation, aim is to achieve

the

goal

by

executing

possible

actions

Current

situation

is

defined

by

states

Repeatedly

;

execute

an

executable

action

,

apply

the

changes

to

the

state

and

check

whether

the

goal

is

satisfied

How

to

do

these

automatically

,

fast

,

and

in

less

number

of

steps

?

Important ability for

computurized

agents

Robotic Agents

Game-Playing Agents

Web-service Agents

etc...

Slide4

Domain ModelsPlanner should have a domain model defining the states, actions and the relation between the

actions

and

states

How

to

build

domain

models

?

Hand-crafted

planner

module

Huge

development

effort

!

Domain-

configurable

planner

Utilization

of a domain-model file

Most

of

the

uses

are

Hierarchical

Task

Network (HTN) Planning

There

are

methods

dividing

tasks

into

subtasks

(

will

be

analyzed

deeper

)

Does

not

focus

on

goals

, but

tasks

Just

apply

the

tasks

until

there

is

no

remaining

tasks

Easier

with

respect

to

hand-crafted

planning

module

Problem of

lacking

of

task

and

goal

correspondence

makes

it hard

to

translate

classical

planning

domains

into

HTN

domains

,

hence

to

prove

soundness

Can

we

do

better

?

Hierarchical

Goal

Network (HGN)

Planner

Similar

to

HTN

formalism

, but

easier

to

develop

domain

models

More

flexible

Integrates

domain-

independent

heuristics

Decomposes

goals

rather

than

tasks

Provably

HGN has

same

expressivity

power

as HTN, is

sound

and

complete

Slide5

FormalismClassical PlanningDomain D is a finite-state transition systemS is a set of states, each state is a finite set of ground atomsEx:

onTable

(block1), on(block2,block1)

G is

the

specification

of

the

goal

state

comprised

of a set

of

ground

atoms

O is a set of

operators

which

is a

triple

(

head

(o),

pre

(o),

eff

(o))

Each

action

is a

ground

instance

of an

operator

An

action

a

is

executable

in a

state

s

if

s╞

pre

(a) (s

entails

pre

(a))

Meaning

that

s

satisfies

the

preconditions

of

action

a

After

execution

an

action

a,

the

new

state

s’ is

s’ = (s -

eff

-

(a))

∪

eff

+

(a)

A plan  = <a

1

, …, a

n

> is

executable

in s

if

each

action

a

i

is

executable

in

the

state

produced

by

a

i-1

.

A

solution

to

a

classical

planning

problem

P = (D, s

0

, g)

is ,

if

δ

(

s

0

,

)

╞

g,

where

D is

the

domain,

s

0

is

the

initial

state

and

g is a

goal

definition

Slide6

Hierarchical Goal Network (HGN) PlanningSimilar to classical planning but have methods additionallyA HGN method m is a quadruple (

head

(m),

pre

(m),

sub

(m), post(m))

head

(m)

and

pre

(m)

same

as

the

ones

in

operators

for

classical

planning

sub

(m)

list

of

goals

<g

1

, …,

g

k

>

where

each

g

i

is a

goal

formula

post(m) =

g

k

;

if

sub

(m) is

non-empty

post(m) =

pre

(m) ;

otherwise

Relevance

:

An

action

a

or

a

method

m is

relevant

for

a

goal

formula

g

if

eff

(a)

or

post(m)

entails

at

least

one

literal

in

g

.

Provides

smaller

search

space

than

a

classical

planner

A HGN domain is D’ = (D,M)

where

D is a

classical

planning

domain

and

M is

the

set of

methods

Slide7

ProofsHGN planning is sound and complete. These are proved by mapping HGN planning problem to classical

planning

problem

Soundness

:

HGN

planning

domain is

D = (D

’,

M

),

where

D’

is a

classical

planning

domain

Every

action

executable

in D is

also

executable

in D’

Hence

,

every

solution

to

problem

P = (D,

s

0

, g)

is

also

a

solution

to

P = (D’,

s

0

, g)

Hence

, HGN

planning

is

sound

.

Completeness

For

a

path

x

in

classical

domain

D

,

there

can be

constructed

a

method

m

that

specifies

each

state

in

x

as a

sub-goal

in

its

sub

(m).

Then

a

single

action

will

achieve

each

subgoal

completing

the

path

Hence

for

each

classical

planning

problem

P = (

D, s

0

,

g),

there

is a HGN

planning

problem

P’ = ((D, M),

s

0

,

g)

where

P

and

P’

have

same

set of

solution

Slide8

ProofsHGN formalism expressivity power is equal to HTN formalismFrom HGN formalism construct HTN formalismMap

subgoals

to

subtasks

with

same

preconditions

<g

1

, … ,

g

k

>

mapped

directly

to

<t

g1

,

… ,

t

gk

>

In

HTN,

however

, it is

needed

to

define

primitive

tasks

as

well

.

So

, define a

new

primitive

task

for

each

t

gi

having

same

precondition

as

g

i

and

no

subtasks

(

that’s

why

it is

primitive

,

indeed

).

From

HTN

formalism

construct

HGN

formalism

Map

subtasks

to

subgoals

with

same

preconditions

<t

1

, … ,

t

k

>

mapped

directly

to

<fin

t

1

,

…

,

fin

t

k

>

Slide9

A little Bit HTN

Associate

methods

with

networks

Critics

for

different

types

of network

Slide10

Algorithm, Goal decomposition planning (GDP)

Slide11

GDP is sound and complete Soundness, if GDP returns a plan, it is a solution indeed.Induction on length of the solution

n

For

n = 0, it

means

s

0

╞ g

If



is a

solution

of

length

k < n

returned

by GDPThen ’ of length k+1 returned by GDP is also a solution as

line 11 appends a relevant action/method u to the planCompleteness, if there is a solution, then GDP will

return itInduction on length of

the solution nFor n = 0, GDP

will return it as s0╞ gAssume there is a solution

of

length

k

and

GDP

returns

it

Then

GDP

returns

solutions

of

length

k+1 as at

line

11 GDP

appends

relevant

action

/

method

Slide12

Domain-independent heuristicsOne of the most important contribution of HGN planning formalismLine 9-13 was choosing action/

methods

nondeterministically

,

however

, it can be

chosen

based

on a

heruistic

value

So

,

line

9-13

will

be replaced as below:

Slide13

Domain-independent heuristicsHow to calculate heruistic value for each action/method:

First

propositional

level

in

which

p

appears

in

Plannig

Graph

States-Levels

Action-

L

evels

PLANNING GRAPH

Slide14

ExperimentsAn HTN planner SHOP2, a classical planner FF and the HGN planner GDP are compared in five different domainsDOMAINs

:

Logistics

Transportation

Domain:

There

several

cities

.

At

each

city

there

are several post-officesAim is to move specified number of packages

to different citiesIntracity transportation is done via trucksIntercity transportation is done via airplanesTrucks and airplanes

are unlimitedBlocks-World:

There are n-many blocks

in a specified configurationConvert the initial configuration

to

goal

configuration

by

obeying

the

following

rules

:

Move

one block at a timeA block

may be put on another block or

tableDepots:Combination of Logistics and Blocks-World domainTrucks have hoist just like the arms of robots

in Blocks-World domainStacking the crates becomes Blocks-World domainTowers of Hanoi:There are three sticks in which

several disks are places on itDisks are put in such a way that each disk is smaller than the disk that it is put on itMove

disks from one stick

to

other

by

obeying

the

following

rules

Move

one

disk at a time

No disk

may

be put

onto

a

smaller

disk

3-City Routing

The

only

newly

written

domain,

hence

it is a

weak

domain model

There

are

3

cities

Each

city

has

several

locations

and

locations

are

connected

with

roads

arbitrarily

in

the

cities

There

is

one

random

road

connected

city1

to

city3

and

one

random

road

connected

city2

to

city3

Aim

is

to

go

from

city1

or

city3

to

city2

Slide15

ResultsLogistics Domain ResultsFor n = 15, 20, …, 60 packagesGDP-h does not bring much overhead for heuristic

function

calculation

FF has

strong

heuristics

Slide16

Results Blocks-World Domain ResultsFor n = 10, 20, …, 100 blocksFF has known problems with Blocks-WorldGDP-h has heuristic

value

calcuation

time

overhead

GDP-h

results

in a bit

smaller

plans

Slide17

ResultsThe Depots Domain ResultsFor n = 10, 20, …, 80 cratesFF cannot solve more than 24 crates

GDP-h

heuristic

overhead

is

significant

,

also

have

almost

same

plans

with

the other planners

Slide18

ResultsTowers of Hanoi Domain ResultsFor n = 3, …, 14 ringsSHOP2 could not solve problems

for

n > 12

and

GDP

and

GDP-h

cound

not

solve

problems

for

n > 14

Both

is due to stack overflow, hence thought as implementation

issue, FF did not use a stackFF has very bad planning results while the others have

almost optimal path results

Slide19

Results3-City Routing Domain ResultsAll previous domains are strong and very well defined

domains

This

one

is

constructed

as a

weak

domain model

having

only

one

method

for

HGN and three corresponding methods for HTNFor n = 10, 20, …, 100

citiesGDP and SHOP2 could not solve except for n = 10 FF may solve

the problems up

to n = 60, after that

point it even could not parse the problem file

GDP-h

solved

all

problems

quickly

and

nearly

optimal

The

reason

for

the success

of the GDP-h is the guided

search thanks to the heuristicsAs the model is weak, the other planners do not have enough

information to constraint the search space and do a lot of backtrackings, however, GDP-h uses heuristic to

be able to guide its search and narrow its search spaceAs a conclusion, we can say that

if there is a strong domain model,

heuristic

calculation

most

probably

will

result

in a

overhead

and

give not significantly better result; however, if the model is weak than contribution of heuristic function is crucial

Slide20

Results Domain AuthoringSubjective to developersMeasures as number of lisp symbols and compared for GDP

and

SHOP2

planners

GDP

almost

always

have

less

number

of

symbols

HTN

specifies

more than one task to achieve a goal

formula. It defines a decomposition task, several primitive tasks and deletion-check conditions, while

, GDP only needs to

speficify those as goals

and let the planner choose the

appropriate

action

to

do

with

respect

to

the

goal

.

There

is a need

for different

base cases for each method in HTN, however, GDP does not need such

bases cases as the semantic of a goal provides to do nothing if a

goal is true.

Slide21

Comments and ConclusionsNo cross-domain explanations for the experiments. For example, why FF is unsuccessfull is not answered

.

Just

the

results

are

shown

and

it is

said

that

GDP is

capable

enough the others, even produces better results for weak domain models

. Almost everything is compared with HTN but HTN is not explained, at least in principle. Moreover, main difference is not shown algorithmically. What

was doing HTN and now

what is the thing that

HGN is not doing, thereby resulting better. For example, can

we

use

heuristics

in SHOP2

planner

. I

guess

we

can,

and

if

we

can, it

may also produce

similar results. HGN is more intutive when

comparing both, hence, seems good contribution to the literature (since 1974). However, HTN is being used many many years, hence

more comprehensive comparison is expectedSo the only contribution of HGN is the easy development domain models, which is even

a subjective criteria.

Slide22

ReferencesV. Shivashankar, U. Kuter, D. S. Nau, and R. Alford. A hierarchical goal-based formalism and algorithm for single-agent planning. In Eleventh Internat. Conf. on Autonomous Agents and Multiagent Systems (AAMAS), 2012Kutluhan Erol, James A.

Hendler

, and Dana S.

Nau

. UMCP: A sound and complete procedure for hierarchical task-network planning. In

Proceedings of the International Conference on AI Planning & Scheduling (AIPS)

, pages 249–254, 1994.

J. Hoffmann and B.

Nebel

. The FF planning system. JAIR

,

14:253–302

, 2001.

D. S.

Nau

, T.-C. Au, O.

Ilghami

, U.

Kuter, J. W. Murdock, D. Wu, and F. Yaman. SHOP2: An HTN planning system. JAIR, 20:379–404, Dec. 2003.

M. M. Veloso. Learning by analogical reasoning in general problem solving. PhD thesis CMU-CS-92-174, Carnegie Mellon University, 1992.F. Bacchus. The AIPS ’00 planning competition. AI Mag., 22(1):47–56, 2001.M. Fox and D. Long. International planning competition, 2002

. http://planning.cis.strath.ac.uk/competition.

Hui Li. Technical Report: Relaxed Plan Graph Heuristic Cost

Estimation. 2006.

Slide23

Any Comments or Questions ?