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3Heuristic Search1.

(Sequencial Search) 2 (Blind Search) (Heuristic Search)

2. (Blind search)

(Depth first search) (Breadth first search)

2.1

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(Root node) (Terminal node) 1

1

8 142

6 93 15 1712

5 74 11 1310 18 1916

1

( ) (pop)

AB

DC

F

E

G

H

2 A B C A

C C C D F (Push) B D F C F

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G B D G (A C F G H E D B) 1

A B CC B D FF B D GG B D HH B D EE B DD BB

1

1 2 STACK 3 1. 1 STACK 22. STACK 3

4 STACK 0 1 () 2 STACK 2

3. 4.

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2.2

( 0) 1 1 2 3

1

3 42

6 75 9 108

12 1311 15 1614 18 1917

3 (Queue)

AB

DC

F

E

G

H

4

A B C A B D E B D E B (A B C D E F G H) 2

A B CB C D E

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C D E FD E F G HE F G HF G HG HH

2

1 2 QUEUE 3 1. 1 QUEUE 22. QUEUE 3

4 QUEUE 0 1 () 2 QUEUE 2

3. 4.

3. (heuristic search)

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(heuristic function) (aspects) Weak Methods Weak Methods (general-purposecontrol stategies)

3.1 (Branch and bound)

(Traveling Salesman)

n (n-1) * (n-2) * (n-3) 1 (n-1)! 10

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10! 3,628,800 25

(Branch and bound)

A B C DA 0 20 30 50B 0 15 20C 0 10D 0

3

A B C D 4 A B C D

A B C D = 20 + 15 + 10 = 45 A C B B

A C B = 30 + 15 = 45

A C B A C D B 60

A C D B = 30 + 10 + 20 = 60 A D

A D = 50 A D A B C D

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1. 2.

2.1 2.2

3

(complete path)

3.2 (Generate and Test)

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1.

path 2.

path 3. 2

1 5

O @

@ @ O O

@ O

2 1. 1 2. 1

O O @ @

5 @ O

(path) 6

@ @ O O @ @ O O @ O @ O @ O @ O @ O O @

@ O O @

6

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7

@ @ O O @ @ O O @ O @ O @ O @ O @ O O @

O @ @ O O @ @ O

@ O O @

7 2 O @ @ O

8

@ @ O O @ @ O O @ O @ O @ O @ O @ O O @

O @ @ O O @ @ O

@ O @ O

O @ @ O

O @ O @

O @ O @ O O @ O O O @ @

@ O O @

7 2 O O @ @

9

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@ @ O O @ @ O O @ O @ O

@ O @ O

O @ @ O

O @ O @

O @ O @ O O @ O O O @ @

(path)

9

(complete path) (Depth first search) (back tracking)

British Museum Algorithm

(Heuristic function)

3.2 (Hill Climbing)(Hill climbing)

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generate-and-test generate and test (test function) yes no hill climbing

3.2.1 Simple Hill Climbing1.

(current state) 2

2.

2.1

2.2

2

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OO @@@@ OO @@ OO

@ O

@@ OO

12

11

@ O@O 9

O@ O@ 8

O O@@ 6

@ O@O 8

@O O@ 6

@O @O 4

@O @O 3

O @@O 1

OO @@ 0

O@ @O 6

O@ @O 5

1

2

3

4

5

6

7

8

9

10

11

12

13

3.2.2 (Steepest-Ascent Hill Climbing)1.

(current state) 2

2.

2.1 SUCC 2.2

SUCC SUCC

2.3 SUCC SUCC

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@@ OO

@@ OO

12

11

@ O@O 9

O@ O@ 8 @ O@O 8

@O O@ 6

@O @O 4

@O @O 3

O @@O 1

OO @@ 0

1

2

3

4

5

6

7

8

9

@@ OO 11

@@ OO 10

steepest ascent

Hill climbing generate andtest

!!!! (Local Maximum): (a) 1 B C B C B C 1 C E 1 B

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!!!! (Plateau): (b) 3 A

!!!! (Ridge):

3.2.3 (Simulated Annealing)

(Kritpatrick., 1983) (annealing) ()

A

G

CB

ED F

5 7

8910 11

A

DB 7 7C 7

(b)

(a)

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p = e - E/KT

E K Boltmann T

K T

p = e - E/T

T T P ( local maximum) T ( local maximum) T T T annealing schedule localmaximum (problem space) local maximum T T T simulated annealing

1. (current state) 2

2. BEST (pointer) SUCC 3. annealing schedule T4. SUCC

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a) SUCCb)

return

SUCC BEST

E = - p 0-1 1 p p p p SUCC

c) T annealing schedule5. return BEST

3.3 (Best-first search) (Depth first

search) (Breadth first search) (most promising) 2.7 1 (root node) 2 B C B C 3 1 C ( ) C 3 D E 4 6 (terminal node) B 3 ( )

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4 F G 6 5

A A

CB 3 1

A

CB 3

D E 64A

CB 3

D E 64F G 56

: 1. OPEN 2. OPEN

OPEN

i) OPEN

ii)

3.3.1 (Greedy Algorithm) (Best first search)

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1. 2. 3.

3.1 3.2

4. 2

A B C D 3

A

DB C20 30 50

DC 15 20

D 10

D

B C

A

20

50

30

15

20 10

13

13 A B C D A 20 30 50 B B C D 15 20 C C D 10 D A 20 + 15 + 10 + 50 = 95

3.3.2 A*

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A* A* A* 2 f g cost h' cost

f = g + h A*(A* algorithm) A*

(description) (indicator) (pointer) parent (list) parent-link recover

2 + OPEN priority queue QUEUE + CLOSE

f' f' 2 g = cost h'= cost

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f=g+h' g

1. OPEN (initial node) 0 g = 0 h' f=h'+0 CLOSED 2. :

2.1 OPEN fail2.2 OPEN f BESTNODE

OPEN CLOSED BESTNODE

2.3 BESTNODE BESTNODE BESTNODE

BESTNODE

g(SUCCESSOR) = g(BESTNODE) + cost BESTNODE SUCCESSOR

cost SUCCESSOR cost OPEN : OLD SUCCESSOR OLD BESTNODE parent link OLD BESTNODE ( SUCCESSOR OLD ) parent SUCCESSOR BESTNODE SUCCESSOR g OLD SUCCESSOR parent OLD BESTNODE g(OLD) update f(OLD)

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SUCCESSOR OPEN CLOSE OLD OLD BESTNODE's successor ( ) parent g f' OLD (propagate) OLD OLD SUCCESSOR (terminal node) OPEN (propagate cost) depth-first traverse tree OLD g (f' ) traverse parent link parent parent g g current parent current parent parent

SUCCESSOR OPEN CLOSE OPEN BESTNODE

f'(SUCCESSOR) = g(SUCCESSOR) + h'(SUCCESSOR)

A* 8-puzzle g h g h

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2 8 3

1 6 4

7 5

1 2 3

4 5 6

7 8 9

2 3

1 8 4

7 6 5

1 2 3

8 4

7 6 5

g 1 0 1 2 3 4 0 5 1 8 1 1=0, 2=0, 3=0, 4=0, 5=1, 6=0, 7=0, 8=1, 9=0 g=2 h' 1=1, 2=0, 3=0, 4=1, 5=1, 6=0, 7=0, 8=0, 9=0 h'=3f = 2 + 3 = 5

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2 8 3

1 6 4

7 5

2 8 3

1 6 4

7 5

2 8 3

1 4

7 6 5

2 8 3

1 6 4

7 5

2 8 3

1 4

7 6 5

2 3

1 8 4

7 6 5

2 8 3

1 4

7 6 5

2 8 3

7 1 4

6 5

2 3

1 8 4

7 6 5

2 3

1 8 4

7 6 5

1 2 3

8 4

7 6 5

1 2 3

8 4

7 6 5

1 8 3

7 8 4

6 5

8 3

2 1 4

7 6 5

f=0+4

f=1+5f=1+3f=1+5

f=2+3 f=2+3 f=2+4

f=3+3

f=3+4 f=3+2 f=3+4

f=4+1

f=5+0 f=5+2

8-puzzle A*

1.

g=0

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( 1)

2. h' h () h' perfect estimator h, A* algorithm

h'= h'= 0 g g=0 random g 1 breadth-first

3.3.2 Agendas Best-First Search: 1. most promising task 2. task (resource) time space task task (successor node)

- agenda (justification) task agenda - task task

3.3.3 Problem Reduction

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AND-OR AND AND AND-OR

2.8 AND

Traverse 1. traverse (initial node) expand 2. f'( h' ) 3. f' 2 arcs (mostpromising)

2.9 cost AND

cost cost = 1 A ->B cost = 5+1 = 6 A ->C & D cost = 3+4+1+1 = 9

AO*(AO* algorithm) 1. G INIT h'(INIT) 2. INIT SOLVED h' INIT FUTILITY

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- Trace mark INIT NODE - NODE FUTILITY h' NODE NODE + SUCCESSOR G + SUCCESSOR SOLVED h'=0 + SUCCESSOR h' 3. S SOLVED h' parent S NODE S

3.4 Constrain satisfaction

3.5 Mean-End Analysis Mean-end analysis

General Problem Solver(GPS) Mean end analysis Mean-End Analysis (precondition)

Operator Precondition ResultPUSH(obj, loc) at(robot,obj)^

large(obj)^clear(obj)^armempty

at(obj, loc)^at(robot, loc)

CARRY(obj.loc) at(robot,obj)^amall(obj)

at(obj, loc)^at(robot, loc)

WALK(loc) none at(robot, loc)

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PICKUP(loc) at(robot, obj) holding(obj)PUTDOWN(obj) holding(obj) ~holding(obj)PLACE(obj1,obj2) at(robot,obj2)^

holding(obj1)on(obj1, obj2)

9

Push Carry Walk Pickup Putdown PlaceMove object * *Move robot *Clear object *Get object on object *Get arm empty * *Be holding object *

2.10

2

A walk pick up put down pick up put down B push C E place D

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Heuristic Search 5 O @ simulated annealing