ttnt-02-heuristic_and_astart

8/7/2019 TTNT-02-Heuristic_and_Astart

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TR TU NHN T OTm ki m c thng tin heuristic, A*

Ref: http://www.cs.cmu.edu/~awm/tutorials


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N i dung trnh byTm ki m c thng tin heuristic t t nh t

Nh ng i m khng thch h p c a tm ki m t t nh tM o: tnh lun chi ph i n tr ng thi hi n t i.Vi c tm ki m k t thc khi no?

2

eur s c c p n n cTm ki m A* l y Tm ki m A* lun d ngKhuy t i m c a A*Ti t ki m nhi u b nh v i IDA* (Iterative Deepening A*)


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Tm ki m v i thng tin heuristicCc phng php tm ki m m (blind search):

thng tin v tr ng thi ch khng ng vai trtrong vi c tm ki m.S Nn i

n no?

3

C th s d ng c l ng kho ng cch n ch

gi a cc tr ng thi tm ng i?

a b c

G


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Tm ki m v i thng tin heuristic (tt)Gi s ngoi vi c c t tm ki m chu n ta cng c m t

heuristic .M t hm heuristic nh x m t tr ng thi thnh m t c l ng v chi ph n

4

.B n c th ngh ra v d v heuristics?

VD. i v i bi ton 8-puzzle?VD. l p ng i trong ma tr n?

K hi u heuristic b ng m t hmh(s)


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5

Heuristic theo Kho ng cch Euclide

GOAL

b c

a2

81

22

5h=11

h=8

h=5 h=4

h=0

START

d

pq

e

h

f

r

9 913

5

34

4

15

1

2

h=12

h=8

h=6

h=9

h=4

h=6h=11


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6

Tm ki m v i thng tin heuristic t t nh t

(Best-first)GOAL

b c

a2

81

22

5h=11

h=8

h=5 h=4

h=0

START

d

pq

e

h

f

r

9 913

5

34

4

15

1

2

h=12

h=8

h=6

h=9

h=4

h=6h=11


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7

Tm ki m t t nh t (tt)

GOAL

b c

a2

81

22

5h=11

h=8

h=5 h=4

h=0

h=9

START

d

pq

e

h

f

r

9 913

5

34

4

15

1

2

h=12

h=8

h=6

h=4

h=6h=11

PQ = {(Start,12)}


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8


GOAL

b c

a2

81

22

5h=11

h=8

h=5 h=4

h=0

h=12

PQ = {(e,4),(d,8),(p,11)}

START

d

pq

e

h

f

r

9 913

5

34

4

15

1

2

h=8

h=6

h=9

h=4

h=6h=11


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9


h=0

GOAL

b c

a2

81

22

5h=11

h=8

h=5 h=4

PQ = {(h,6),(r,6),(d,8),(p,11)}

START

d

pq

e

h

f

r

9 913

5

34

4

15

1

2

h=12

h=8

h=6

h=9

h=4

h=6h=11


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10


GOAL

b c

a2

81

22

5h=11

h=8

h=5 h=4

h=0

PQ = {(r,6),(d,8),(q,9),(p,11)}

START

d

pq

e

h

f

r

9 913

5

34

4

15

1h=12

h=8

h=6

h=9

h=4

h=6h=11

d

p


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Heuristic trong bi ton 8-puzzleTheo s n m sai v tr

1 2 31 52 6 3 h = 6

11

7 87 4 8


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Heuristic trong bi ton 8-puzzle (tt)Theo t ng kho ng cch Manhattan

1 5 1 2 3

12

2 6 37 4 8

4 5 67 8

h = 0 + 2 + 1 + 2 + 2 + 1 +0 + 1 = 9

h = 9

d = dx + dy


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Thu t ton tm ki m t t nh tInit-PriQueue(PQ)Insert-PriQueue(PQ,START,h(START))while (PQ khc r ng v PQ khng ch a tr ng thi ch)

(s , h ) := Pop-least(PQ)V i m i s trong succs(s)N u s khn c tron PQ v s cha c vi n tr c bao

13

gi Insert-PriQueue(PQ,s,h(s))

M t vi c i ti n c a thu t ton ny c th lm cho m i vi ct t p hn. N l th m chng ta g i l: A*.

* Vi c s d ng heuristic lm thay i B

Thu t ton T i u Th i gian Khng gianBestFS Best First

SearchC K O(min(N,BLMAX )) O( min(N,BLMAX ))


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Hy Xem t t nh t ng ng n th no!

S A CB G2

4

11 2

14

Tm ki m t t nh t r rng khng m b o tmth y ng i t i uCu h i: Chng ta c th lm g trnh l ing ng n ny?

h=3 h=2 h=1h=4 h=0


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A* - t ng C b nBest-first: Khi b n m m t noden, l y node conn' v

t n vo PriQueue v i u tinh(n' )A*: Khi b n m m t noden, l y node conn' v t nvo PriQueue v i u tin

15

(Chi ph i nn' ) + h(n' ) (1)

t g (n) = Chi ph i nn (2)

v nh ngha

f (n) = g (n) + h(n) (3)


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A* khng ng ng n!

S A CB G2

411 2

16

h=3 h=2 h=1h=4 h=0


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A* d ng khi no? t ng: Ngay khi n pht sinh c tr ng thi ch?

Xem v d sau:

S1 11

h = 3

17

D

CA

G

1

77

h = 7

h = 1

h = 2

h = 0

h = 8


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Quy t c D ng A* ng n:A* D ng Ch Khi m t Tr ng Thi ch c L y ra

kh i Priority QueueS1 1

1h = 3

18

D

CA

G

1

7

7

h = 7

h = 1

h = 2

h = 0

h = 8


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Cc tr ng thi quay l i A*M t cu h i khc:i u g x y ra n u A* quay l i m t tr ngthi m , v tm c m t ng ng n hn?

S1 11

h = 3

19

D

CA

G

1

7

h = 7

h = 1

h = 2

Trong v d ny m t tr ngthi m c m l i.Nh th no v t i sao ?

1/2

h = 8


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i u g n u A* thm m t tr ng thi c trong hng i?

S1 11

h = 3

h = 8

Cc tr ng thi quay l i A*20

D

CA

G

1

7

h = 7

h = 1

h = 8

Trong v d ny m t tr ng thi c trong hng i v ang i mc u tin tng v t ln. Nhth no v t i sao?

1/2

lu r ng gi tr h ny thay i so v i trang tr c.


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Thu t ton A*

Priority queuePQ ban u r ng.V (= t p cc (b ba (state,f ,backpointer )) thm tr c b t u lr ng. t S vo PQ v V v i u tinf (s) = g (s) + h(s)PQ r ng?

C? Khn c l i i i.

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Khng? Lo i b node v if (n) th p nh t kh i queue. G i nl n.N un l m t ch, d ng v bo thnh cng.M n : V i m i n' trongsuccs (n)

tf

=g (n'

) +h

(n'

) =g

(n) +

cost (n,n'

) +h

(n'

)N u n' cha th y tr c , hayn' m v i f (n' )>f , hay n' hi n trongPQ v i f (n' )>f Th t/C p nh tn' trong PQ v i u tinf v c p nh tV bao g m (state=n' , f , BackPtr =n).Ng c l i b qua n'


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A* C B o m Tm th y ng i T iu?

A1

1h = 6 h = 0

22

G3

Khng. V v d sau cho th y t i sao.

h = 7


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Heuristic ch p nh n c t h*(n) = chi ph t i thi u th p nh t tn n

ch.M t heuristich l ch p nh n cn u

h n


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24

V d 8-Puzzle

1 5

2 6 37 4 8

1 2 3

4 5 67 8

Tr ng thiv d

Tr ng thich

h(n) = S n m sai v tr trong

tr ng thin h(n) = 0 h(n) = T ng kho ng cch

Manhattan gi a m i so v i v trch

h(n) = 1

h(n) = min (2,h*(n)) h(n) = h*(n) h(n) = max (2,

h*(n))


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A* v i heuristic ch p nh n c b o m ng i t i u

Ch ng minh n gi n

(B n c th t ch ng minh?)

25


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So snh L p Su d n v i A*Trong sch c a Russell and Norvig, trang 107, Hnh4.8

V i 8-puzzle, s tr ng thi cm trung bnh trong 100 bi ton c ch n ng u nhin trong n i t i u di

26

4 b c 8 b c 12 b c

L p Su d n 112 6,300 3.6 x 106

Tm ki m A* dngs sai vtrlm heuristic

13 39 227

A* dngT ng kho ng cchManhattanlm heuristic

12 25 73


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27 A* : Khuy t i mA* c th dng nhi u b nh .

Trn l thuy t:O(s tr ng thi)

s l n, A* s dng h t b nh .


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IDA* : Tm ki m V i B nh Gi i h n

A* l p v i su tng d n. Th t s , r t khc so v i A*. Gi s chiph l s nguyn.

1. Th c hi n l p-khng dng DFS, khng m r ng node no cf (n) > 0. C tm th y ch? N u c, d ng.2. Th c hi n l p-khng dng DFS, khng m r ng node no c

f (n) > 1. C tm th y ch? N u c, d ng.-

28

. ,f (n) > 2. C tm th y ch? N u c, d ng.

4. Th c hi n l p-khng dng DFS, khng m r ng node no cf (n) > 3. C tm th y ch? N u c, d ng.

l p l i i u ny, tng ng ngf (n) ln m t 1 m i l n, cho n khi d ng.

Ci ny y B o m tm c l i gi i t i uNi chung t n chi ph nhi u hn A*.


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i u c n n mHi u th u o A*.C th ch y tay cc v d th c thi A*n gi n.

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Hi u c tnh ch p nh n c c aheuristics. Ch ng minh tnh y ,b o m tnh t i u c a ng i.C th nh n xt v cc nh gi.


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Th c m c30

ttnt-02-heuristic_and_astart

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