1Chng 3: Cc k thut tm kim Heuristics

2Ni dung Khi nim Tm kim tt nht trc Phng php leo i Ci t hm nh gi Thu gim rng buc Gii thut ct ta -

3Gii hn ca duyt h thng 8-puzzle

Li gii cn trung bnh 22 cp (depth) rng ca bc ~ 3 Tm kim vt cn cho 22 cp cn

3.1 x 1010 states Nu ch gii hn d=12, cn trung bnh 3.6

triu trng thi[24 puzzle c 1024 trng thi]

Cn chin lc tm kim heuristic

4Khi nim: Heuristic Heuristics: l cc phng on, c chng da

trn kinh nghim, trc gic (kin thc b sung) Cc h gii quyt AI s dng heuristic trong hai

tnh hung c bn: Bi ton c nh ngha chnh xc nhng chi ph tm

li gii vt cn l khng th chp nhnVD: S bng n khng gian trng thi (KGTT) trong tr chi c vua

Vn vi nhiu s m h trong li pht biu bi ton hay d liu cng nh tri thc sn cVD: Chn on trong y hc

5Khi nim: Gii thut Heuristics Mt gii thut heuristic c th c xem gm 2

phn: Php o heuristic: th hin qua hm nh gi heuristic

(evaluation function f(n) - EF), dng nh gi cc c im ca mt trng thi trong KGTT

Gii thut tm kim heuristic: TK tt nht (best-first search) A* search Gii thut leo ni (hill-climbing)

6V d php o Heuristics

7V d php o Heuristics (tt)

Heuristic S ng thng nhiu nht (theo cc ng cho trn bn c) p dng cho cc con c u tn t vo bn c trong bn c tic-tac-toe

8V d php o Heuristics (tt)

9Gii thut leo i (Hill climbing) Gii thut

Xt trng thi bt u Nu l ch dng Ngc li: thit lp khi u nh TT hin ti

Lp n khi: gp ch hoc khng cn lut no cha c p dng vo TT hin ti La mt lut p dng vo TT hin ti sinh ra mt

TT mi Xem xt TT mi ny

Nu l ch dng Nu khng l ch, nhng tt hn TT hin ti thit

lp TT mi l TT hin ti Nu khng tt hn th lp tip tc

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Gii thut leo i (tt) Gii hn

Gii thut c khuynh hng b sa ly nhng cc i cc b Li gii tm c khng ti u Khng tm c li gii mc d c tn ti li gii

Gii thut c th gp vng lp v hn do khng lu gi thng tin v cc trng thi duyt

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Gii thut leo i (tt) Bi ton 8 Hu

Trng thi bt u: mi Hu trn 1 ct Trng thi ch: cc Hu khng th tn cng nhau Php o Heuristic h(n): s lng cc cp hu i khng

nhau

H(n) = 17 h(n) = 1

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Tm kim tt nht (BFS) L phng php dung ho ca BrFS v DFS C s dng nh gi u th ca mi trng thi, c th

l c lng t n n TT ch Ti mi bc, gii thut s chn trng thi m n cho

rng l c u th nht trong s cc trng thi sinh ra c n thi im

Khc vi gii thut leo i c ci tin ch: c lu tt c nhng TT pht sinh n thi im chn TT xt tip

Dng hai danh sch: OPEN: cha cc TT s c xt. CLOSED: cha cc TT xt qua.

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Tm kim tt nht (BFS) Gii thut

OPEN = [TT u] Lp n khi: gp ch hoc OPEN rng

Ly TT tt nht t OPEN Pht sinh cc con ca n Vi mi con:

Nu n cha c pht sinh: gn n tr nh gi, a vo OPEN, ghi nhn TT cha ca n

Nu c pht sinh trc: Nu t n bi ng khc tt hn ghi nhn li TT cha ca n, cp nht li tr nh gi ca n vca cc con ca n

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Tm kim tt nht (BFS)1. open = [A5]; closed = [ ]2. nh gi A5; open = [B4,C4,D6];

closed = [A5]3. nh gi B4;

open = [C4,E5,F5,D6]; closed = [B4,A5]

4. nh gi C4; open = [H3,G4,E5,F5,D6]; closed = [C4,B4,A5]

5. nh gi H3; open = [O2,P3,G4,E5,F5,D6]; closed = [H3,C4,B4,A5]

6. nh gi O2; open = [P3,G4,E5,F5,D6]; closed = [O2,H3,C4,B4,A5]

7. nh gi P3; tm c li gii!

Open l queue, xp theo Heuristic tng dn

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Ci t hm nh gi (EF) Xt tr chi 8-, mi trng thi n, mt gi tr f(n):

f(n) = g(n) + h(n) g(n) = khong cch thc s t n n trng thi bt u h(n) = hm heuristic nh gi khong cch t trng thi

n n mc tiu.

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start

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goal

g(n) = 0

g(n) = 1

6 4 6f(n) =

h(n): s lng cc v tr cn sai;

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V d

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V d

18

V d

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Heuristic trong tr chi i khng Gii thut minimax

Hai u th trong tr chi c gi l MIN v MAX. Mi nt l c gi tr:

1 nu l MAX thng, 0 nu l MIN thng.

Minimax s truyn cc gi tr ny ln cao dn trn th, qua cc nt cha m k tip theo cc lut sau: Nu trng thi cha m l MAX, gn cho n gi tr ln nht c

trong cc trng thi con. Nu trng thi cha m l MIN, gn cho n gi tr nh nht c

trong cc trng thi con.

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p dng GT Minimax vo Tr Chi NIMMIN

MIN

MIN

MAX

MAX

MAX

1

1 1 1

1 1

1

0 0

0

0

0

01

KT QU CA MIN

KT QU CA MAX

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Minimax vi su lp c nh Minimax i vi mt KGTT gi nh

3 l gi tr max ca cc nt con

2 l gi tr min ca cc nt con

Cc nt l c gn cc gi tr heuristic no Cn gi tr ti cc nt trong l cc gi tr nhn c da trn gii thut Minimax (min hay max cua cc nt con)

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Heuristic trong tr chi tic-tac-toe

Hm Heuristic: E(n) = M(n) O(n)Trong : M(n) l tng s ng thng c th ca ti

O(n) l tng s ng thng c th ca i thE(n) l tr s nh gi tng cng cho trng thi n

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Minimax 2 lp c p dng vo nc i m u trong tic-tac-toe

Max (X) c 5 ng thng,

Min(O) c 4, hm heuristic l -1

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Thu gim bi ton th AND-OR :

c dng biu din KGTT cho bi ton gii c bng cch phn r ra cc bi ton nh hn

Khi bi ton c phn r thnh N bi ton con, m tt c chng phi c gii hon thnh bi ton ln th c biu din thnh cung AND ch n N trng thi con

Nhiu cch gii cho bi ton c th c dng th c th biu din bi cung OR

A c th c thng qua hai cch:- Gii B, hoc- Gii c C v D

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Thu gim bi ton (tt) th AND-OR :

Nu dng gii thut BFS cho vic tm li gii trn th AND-OR th c l khng thch hp v nh xem xt th sau:

Nu gi tr ghi k bn trng thi l tr c lng cho trng thi . Theo BFS th trng thi k tip c chn l C, nh:

Khi chn cch gii qua C th bt buc phi gii c D. Do vy tng chi ph cho cch gii ny l: C+D+ 2 = 9, 2 l gi tr ca hm g trong BFS

Trong khi nu chn cch gii qua B th chi ph ch l: B+1 = 6.

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Thu gim bi ton (tt) GT thu gim bi ton

Khi ng th l TT bt u. Lp n khi: TT u c gn nhn l SOLVED hoc chi ph

vt qua ngng FUTILITY: Duyt th bt u t TT u, theo con ng tt nht hin ti,

tch lu tp trng thi trn con ng m n cha c m rng hoc c gn nhn SOLVED.

Ly mt TT cha m rng v m rng n. Nu khng c con th gn FUTILITY bng tr ca TT ny. Ngc li, thm cc con vo th v mi chng tnh f (s dng ch h, b qua g). Nu f =0th gn nhn cho TT l SOLVED.

Thay i f ca TT c m rng phn nh thng tin c cung cp bi con ca n. Lan truyn tr ny ngc ln th. Nu mt TT c cung m tt c cc con ca n c gn nhn SOLVED th n cng c gn nhn SOLVED. Khi lan truyn ngc ln th nh du cung no l tt nht nh l phn ca con ng tt nht hin ti.

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Thu gim bi ton (tt) GT Thu gim (tt.) - tng bc:

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Thu gim bi ton (tt) GT Thu gim (tt.) - tng bc:

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Gii thut ct ta - Tm kim theo kiu depth-first. Nt MAX c 1 gi tr (lun tng) Nt MIN c 1 gi tr (lun gim) Tm kim c th kt thc di bt k:

Nt MIN no c ca bt k nt cha MAX no. Nt MAX no c ca bt k nt cha MIN no.

Gii thut ct ta - th hin mi quan h gia cc nt lp n v n+2, m ti ton b cy c gc ti lp n+1 cth ct b.

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Ct ta (v tr MAX)S

A C

MAX

MIN

B

C gi tr >=

- cut

C gi tr =

MAX

C gi tr gi tr Biu kin 3: X, Y, .. , Z v tr MaxB nhng cy con c gc l X,Y,, Z

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Ct ta (v tr Min)S

A C

MIN

MAX

B

- cutMIN

C gi tr =

C gi tr = k

X Y . Z

iu kin 1: Ch cn bit gi tr ti A v Biu kin 2: Gi tr A < gi tr Biu kin 3: X, Y, .. , Z v tr MinB nhng cy con c gc l X,Y,, Z

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Ct ta -: v d

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Bi tp: bi 1 (tr 8 nh)

Dng cc hm lng gi heuristic sau h1 = s lng cc v tr sai khc so vi trng thi goal. h2 = tng s di ngn nht ca cc v v tr ng (khong cch

Manhattan)Hy trin khai khng gian trng thi ca bi ton n mc 5 (nu cha tm c

goal): a) Theo gii thut leo ni b) Theo gii thut tm kim rngc) Theo gii thut tm kim sud) Theo gii thut tm kim tt nht u tin

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Trong cy tm kim di y, mi nt c 2 gi tr i km: gi tr bn tri ca nt (in nghing) th hin gi tr heuristic ca nt, v gi tr bn phi nt th hin th t nt c duyt qua. Vi mi chin lc tm kim di y, hy vit danh sch th t cc nt c duyt, so snh v cho bit ta dng gii thut tm kim no trn cy :

a) Tm kim rng BFS b) Tm kim su DFS c) Tm kim tt nht u tin BFSd) Tm kim leo ni

Bi tp: bi 2 (duyt th)

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Lit k danh sch cc nt c duyt theo tm kim DFS. Thc hin gii thut Minimax trn cy.

S c g khc bit nu nh ta dng gii thut ct ta alpha beta nh tr nt gc cho cy?

Bi tp: bi 3 (minimax)