Chuong 4 - Tim kiem heuristic.pdf

Tr Tu Nhn To

Nguyn Nht Quang

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Vin Cng ngh Thng tin v Truyn thngTrng i hc Bch Khoa H Ni

Nm hc 2009-2010

Ni dung mn hc:

Gii thiu v Tr tu nhn to

Tc t

Gii quyt vn : Tm kim, Tha mn rng buc Tm kim vi tri thc b sung (Informed search)

Logic v suy din

Biu din tri thc

Suy din vi tri thc khng chc chny g

Hc my

Lp k hoch Lp k hoch

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Nhc li: Tm kim theo cu trc cy

Mt chin lc (phng php) tm kim = Mt cch xc nh (p g p p) th t xt cc nt ca cy

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Tm kim vi tri thc b sungg Cc chin lc tm kim c bn (uninformed search

strategies) ch s dng cc thng tin cha trong nh nghastrategies) ch s dng cc thng tin cha trong nh ngha ca bi ton Khng ph hp vi nhiu bi ton thc t (do i hi chi ph qu

cao v thi gian v b nh)cao v thi gian v b nh)

Cc chin lc tm kim vi tri thc b sung (informed search strategies) s dng cc tri thc c th ca bi ton Qustrategies) s dng cc tri thc c th ca bi ton Qu trnh tm kim hiu qu hn Best-first search algorithms (Greedy best-first, A*)

( S Local search algorithms (Hill-climbing, Simulated annealing, Local beam, Genetic algorithms)

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Best-first search tng: S dng mt hm nh gi f(n) cho mi nt ca

cy tm kimcy tm kim nh gi mc ph hp ca nt Trong qu trnh tm kim, u tin xt cc nt c mc ph hp

cao nhtcao nht

Ci t gii thut Sp th t cc nt trong cu trc fringe theo trt t gim dn v

mc ph hp

Cc trng hp c bit ca gii thut Best-first searchGreedy best first search Greedy best-first search

A* search

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Greedy best-first search

Hm nh gi f(n) l hm heuristic h(n)

Hm heuristic h(n) nh gi chi ph i t nt hin ti nn nt ch (mc tiu)

V d: Trong bi ton tm ng i t Arad n Bucharest, s dng: hSLD(n) = c lng khong cch ng thng (chim bay) t thnh ph hin ti n nng thng ( chim bay ) t thnh ph hin ti n n Bucharest

Phng php tm kim Greedy best-first search s xt Phng php tm kim Greedy best first search s xt (pht trin) nt c v gn vi nt ch (mc tiu) nht

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Greedy best-first search V d (1)y ( )

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Greedy best-first search V d (2)

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Greedy best-first search Cc c im

Tnh hon chnh?Khng V c th ng (cht tc) trong cc ng lp ki nh Khng V c th vng (cht tc) trong cc vng lp kiu nh: Iasi Neamt Iasi Neamt

phc tp v thi gian? phc tp v thi gian? O(bm) Mt hm heuristic tt c th mang li ci thin ln

phc tp v b nh? O(bm) Lu gi tt c cc nt trong b nh

Tnh ti u? Khngg

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A* search

tng: Trnh vic xt (pht trin) cc nhnh tm kim h ( h thi i hi t i) l hi h xc nh (cho n thi im hin ti) l c chi ph cao

S dng hm nh gi f(n) = g(n) + h(n)

g(n) = chi ph t nt gc cho n nt hin ti n

h(n) = chi ph c lng t nt hin ti n ti ch( ) p g

f(n) = chi ph tng th c lng ca ng i qua nt hin ti nn ch

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A* search V d (1)

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A* search V d (2)

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A* search V d (3)

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A* search V d (4)

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A* search V d (5)

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A* search V d (6)

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A* search Cc c im Nu khng gian cc trng thi l hu hn v c gii

php trnh vic xt (lp) li cc trng thi th giiphp trnh vic xt (lp) li cc trng thi, th gii thut A* l hon chnh (tm c li gii) nhng khng m bo l ti u

Nu khng gian cc trng thi l hu hn v khng c gii php trnh vic xt (lp) li cc trng thi, th gii

* ( thut A* l khng hon chnh (khng m bo tm c li gii)

N kh i t thi l h th ii th t A* Nu khng gian cc trng thi l v hn, th gii thut A* l khng hon chnh (khng m bo tm c li gii)

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Cc c lng chp nhn cg p Mt c lng (heuristic) h(n) c xem l chp nhnc nu i vi mi nt n: 0 h(n) h*(n) trong c nu i vi mi nt n: 0 h(n) h (n), trong h*(n) l chi ph tht (thc t) i t nt n n ch

Mt c lng chp nhn c khng bao gi nh gi qu cao (overestimate) i vi chi ph i ti ch

Thc cht, c lng chp nhn c c xu hng nh gilc quan

V d: c lng hSLD(n) khng bao gi nh gi qucao khong cch ng i thc t

nh l: Nu h(n) l nh gi chp nhn c, thphng php tm kim A* s dng gii thut TREE-SEARCH l ti uSEARCH l ti u

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Tnh ti u ca A* - Chng minh (1)g Gi s c mt ch khng ti u (suboptimal goal) G2 c sinh ra

v lu trong cu trc fringe. Gi n l mt nt cha xt trong cu trcv lu trong cu trc fringe. Gi n l mt nt cha xt trong cu trcfringe sao cho n nm trn mt ng i ngn nht n mt ch tiu (optimal goal) G

Ta c: f(G2) = g(G2) v h(G2) = 0 Ta c: g(G2) > g(G) v G2 l ch khng ti u Ta c: f(G) = g(G) v h(G) = 0 Suy ra: f(G2) > f(G) y ( 2) ( )

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Tnh ti u ca A* - Chng minh (2)g

Ta c: h(n) h*(n) v h l c lng chp nhn c Suy ra: g(n) + h(n) g(n) + h*(n) Suy ra: g(n) + h(n) g(n) + h (n) Ta c: f(n) f(G) v n nm trn ng i ti G

V vy: f(G2) > f(n). Tc l, th tc A* khng bao gi xt G2

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Cc c lng chp nhn c (1)g pV d i vi tr chi ch 8 s:

h1(n) = s cc ch nm sai v tr (so vi v tr ca ch y trng thi ch)

h2(n) = khong cch dch chuyn (,,,) ngn nht dchh h i t t chuyn cc ch nm sai v tr v v tr ng

h (S) = ? h1(S) = ?

h2(S) = ?

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Cc c lng chp nhn c (2)g pV d i vi tr chi ch 8 s:

h1(n) = s cc ch nm sai v tr (so vi v tr ca ch y trng thi ch)

h2(n) = khong cch dch chuyn (,,,) ngn nht dchh h i t t chuyn cc ch nm sai v tr v v tr ng

h (S) = 8 h1(S) = 8

h2(S) = 3+1+2+2+2+2+2+3+3+2 = 18

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c lng u thg c lng h2 c gi l u th hn / tri hn (dominate) c

lng h1 nu:h (n) v h (n) u l cc c lng chp nhn c v h1(n) v h2(n) u l cc c lng chp nhn c, v

h2(n) h1(n) i vi tt c cc nt n Nu c lng h2 u th hn c lng h1, th h2 tt hn (nn c s dng hn) cho qu trnh tm kimc s dng hn) cho qu trnh tm kim

Trong v d ( ch 8 s) trn: Chi ph tm kim = S lng trung bnh ca cc nt phi xt: Vi su d =12 Vi su d =12

IDS (Tm kim su dn): 3.644.035 nt phi xt A*(s dng c lng h1): 227 nt phi xt A*(s dng c lng h2): 73 nt phi xt ( g g 2) p

Vi su d =24 IDS (Tm kim su dn): Qu nhiu nt phi xt A*(s dng c lng h1): 39.135 nt phi xt

A*( d l h ) 1 641 t hi t A*(s dng c lng h2): 1.641 nt phi xt

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Cc c lng kin nhg Mt c lng c xem l kin nh (consistent), nu vi mi nt n

v vi mi nt tip theo n' ca n (c sinh ra bi hnh ng a):h(n) c(n,a,n') + h(n')

Nu c lng h l kin nh ta c: Nu c lng h l kin nh, ta c:f(n') = g(n') + h(n')

= g(n) + c(n,a,n') + h(n') g(n) + h(n) g(n) + h(n) = f(n)

Ngha l: f(n) khng gim trong bt k ng i (tm kim) noi qua n

nh l: Nu h(n) l kin nh, th phng php tm kim A* s dng gii thut GRAPH SEARCH l ti ugii thut GRAPH-SEARCH l ti u

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Cc c im ca A*

Tnh hon chnh?C (tr khi c rt nhi cc nt c chi ph f f(G) ) C (tr khi c rt nhiu cc nt c chi ph f f(G) )

phc tp v thi gian? Bc ca hm m S lng cc nt c xt l hm m ca

di ng i ca li gii

h t b h? phc tp v b nh? Lu gi tt c cc nt trong b nh

Tnh ti u? C

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A* vs. UCS

Tm kim vi chi ph cctiu (UCS) pht trin theo

Tm kim A* pht trin ch yu th h ti h htiu (UCS) pht trin theo

mi hngtheo hng ti ch, nhng m bo tnh ti u

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Cc gii thut tm kim cc bg Trong nhiu bi ton ti u, ng i ti ch khng

quan trng m quan trng l trng thi chq g q g g Trng thi ch = Li gii ca bi ton

Khng gian trng thi = Tp hp cc cc cu hnh hon chnhchnh

Mc tiu: Tm mt cu hnh tha mn cc rng buc V d: Bi ton n qun hu (b tr n qun hu trn mt bn c

k h th h h kh h )kch thc nxn, sao cho cc qun hu khng n nhau)

Trong nhng bi ton nh th, chng ta c th s dng cc gii thut tm kim cc bg

Ti mi thi im, ch lu mt trng thi hin thi" duy nht Mc tiu: c gng ci thin trng thi (cu hnh) hin thi ny i vi mt tiu ch no (nh trc)hin thi ny i vi mt tiu ch no (nh trc)

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V d: Bi ton n qun huq

B tr n (=4) qun hu trn mt bn c c kch thc h kh 2 h t hnn, sao cho khng c 2 qun hu no trn cng hng,

hoc trn cng ct, hoc trn cng ng cho

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Tm kim leo i Gii thut

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Tm kim leo i Bi ton ch (1) 2 8 31 6 4

1 38 4

2start goal h = 0h = -4

7 5 7 6 5g

-5 -5 -22 8 31 4

1 38 42

h = -3 h = -17 6 5 7 6 5

-4-32 31 8 47 6 5

31 8 47 6 5

2h = -2

7 6 5 7 6 5h = -3 -4f(n) = -(S lng cc ch nm sai v tr) 33

Tm kim leo i Bi ton ch (2)

1 2 547 4

8 6 3

-4

start goal

1 2 57 4

1 2 57 4

1 2 57 4 -4 0

8 6 3 8 6 38 6 3

1 2 5-3

7 48 6 3

-4

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Tm kim leo i Bi ton 8 qun hu (1)

c lng h = tng s cc cp qun hu n nhau, hoc l trc tip hoc gin tip

Trong trng thi (bn c) trn: h =17 Trong trng thi (bn c) trn: h =17

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Tm kim leo i Bi ton 8 qun hu (2)

Trng thi bn c trn l mt gii php ti u cc b (a local minimum) Vi c lng h =1 (vn cn 1 cp hu n nhau)

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Tm kim leo i Minh ha Nhc im: Ty vo trng thi u, gii thut tm kim leo i c

th tc cc im cc i cc b (local maxima) Khng tm c li gii ti u ton cc (global optimal solution)

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Simulated annealing search Da trn qu trnh ti (annealing process): Kim loi ngui i

v lnh cng li thnh cu trc kt tinhv lnh cng li thnh cu trc kt tinh

Phng php tm kim Simulated Annealing c th trnh c cc im ti u cc b (local optima)

Phng php tm kim Simulated Annealing s dng chin lc tm kim ngu nhin, trong chp nhn cc thay i lm tng gi tr hm mc tiu (i e cn ti u) v cng chplm tng gi tr hm mc tiu (i.e., cn ti u) v cng chp nhn (c hn ch) cc thay i lm gim

Phng php tm kim Simulated Annealing s dng mt tham s iu khin T (nh trong cc h thng nhit ) Bt u th T nhn gi tr cao, v gim dn v 0

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Simulated annealing search Gii thut

tng: Thot khi (vt qua) cc im ti u cc b bng cch cho php c cc dch chuyn ti t trng thi hin thi, nhngcho php c cc dch chuyn ti t trng thi hin thi, nhng gim dn tn xut ca cc di chuyn ti ny

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Simulated annealing search Cc c im

(C th chng minh c) Nu gi tr ca tham s T (xc nh mc gim tn xut i vi cc di chuyn ti) gim chm, th phng php tm kim Simulated Annealing Search s tm c li gii ti u ton cc viAnnealing Search s tm c li gii ti u ton cc vi xc sut xp x 1

Phng php tm kim Simulated Annealing Search rt Phng php tm kim Simulated Annealing Search rt hay c s dng trong cc lnh vc: thit k s bng mch VLSI, lp lch bay,

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Local beam search

mi thi im (trong qu trnh tm kim), lun lu gi kthay v ch 1 trng thi tt nht thay v ch 1 trng thi tt nht

Bt u gii thut: Chn k trng thi ngu nhin

mi bc tm kim, sinh ra tt c cc trng thi k tip ca k trng thi ny

Nu mt trong s cc trng thi l trng thi ch, th gii thut kt thc (thnh cng); nu khng, th chn k trng thi tip theo tt nht (t tp cc trng thi tip theo) vthi tip theo tt nht (t tp cc trng thi tip theo), v lp li bc trn

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Gii thut di truyn Gii thiu Da trn (bt chc) qu trnh tin ha t nhin trong sinh hc p dng phng php tm kim ngu nhin (stochastic search) p g p g p p g ( ) tm c li gii (vd: mt hm mc tiu, mt m hnh phn lp, ) ti u

Gii thut di truyn (Generic Algorithm GA) c kh nng tm Gii thut di truyn (Generic Algorithm GA) c kh nng tm c cc li gii tt thm ch ngay c vi cc khng gian tm kim (li gii) khng lin tc rt phc tpMi kh li ii bi di b h i h Mi kh nng ca li gii c biu din bng mt chui nh phn (vd: 100101101) c gi l nhim sc th (chromosome)

Vic biu din ny ph thuc vo tng bi ton c th

GA cng c xem nh mt bi ton hc my (a learning bl ) d t t h ti h ( ti i ti )problem) da trn qu trnh ti u ha (optimization)

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Gii thut di truyn M t Xy dng (khi to) qun th (population) ban u

To nn mt s cc gi thit (kh nng ca li gii) ban uMi gi thit khc cc gi thit khc (vd: khc nhau i vi cc gi tr ca mt Mi gi thit khc cc gi thit khc (vd: khc nhau i vi cc gi tr ca mt s tham s no ca bi ton)

nh gi qun thnh gi (cho im) mi gi thit ( d bng cch kim tra chnh c ca nh gi (cho im) mi gi thit (vd: bng cch kim tra chnh xc ca h thng trn mt tp d liu kim th)

Trong lnh vc sinh hc, im nh gi ny ca mi gi thit c gi l ph hp (fitness) ca gi thit ph hp (fitness) ca gi thit

Xp hng cc gi thit theo mc ph hp ca chng, v ch gi li cc gi thit tt nht (gi l cc gi thit ph hp nht survival of the fittest)

Sn sinh ra th h tip theo (next generation) Sn sinh ra th h tip theo (next generation) Thay i ngu nhin cc gi thit sn sinh ra th h tip theo (gi l cc

con chu offspring) Lp li qu trnh trn cho n khi mt th h no c gi thit tt nht c Lp li qu trnh trn cho n khi mt th h no c gi thit tt nht c

ph hp cao hn gi tri ph hp mong mun (nh trc)

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GA(Fitness, , n, rco, rmu)Fit A f ti th t d th (fit ) i h th iFitness: A function that produces the score (fitness) given a hypothesis

: The desired fitness value (i.e., a threshold specifying the termination condition)

n: The number of hypotheses in the population

rco: The percentage of the population influenced by the crossover operator at each step

rmu: The percentage of the population influenced by the mutation operator at each step

Initialize the population: H Randomly generate hypothesesInitialize the population: H Randomly generate n hypothesesEvaluate the initial population. For each hH: compute Fitness(h)while (max{hH}Fitness(h) < ) do{hH}

Hnext Reproduction (Replication). Probabilistically select (1-rco).n hypotheses of H to add to HnextH to add to Hnext.The probability of selecting hypothesis hi from H is:

= n

j

ii

)Fitness(h

)Fitness(h)P(h

=j 1

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GA(Fitness, , n, rco, rmu)

Crossover.Probabilistically select (rco.n/2) pairs of hypotheses from H, according to the probability computation P(h ) given abovethe probability computation P(hi) given above.For each pair (hi, hj), produce two offspring (i.e., children) by applying the crossover operator. Then, add all the offspring to Hnext.

M t tiMutation.Select (rmu.n) hypotheses of Hnext, with uniform probability.For each selected hypothesis, invert one randomly chosen bit (i.e., 0 to 1, or 1 to 0) in the hypothesiss representationor 1 to 0) in the hypothesis s representation.

Producing the next generation: H HnextEvaluate the new population. For each hH: compute Fitness(h)

end while

return argmax{hH}Fitness(h)

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Gii thut di truyn Minh ha

[Duda et al., 2000]

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Cc ton t di truyn3 ton t di truyn c s dng sinh ra cc c th con chu

(offspring) trong th h tip theo Nhng ch c 2 ton t lai ghp (crossover) v t bin (mutation) to nn

s thay i

Ti sn xut (Reproduction)Ti sn xut (Reproduction) Mt gi thit c gi li (khng thay i)

Lai ghp (Crossover) sinh ra 2 c th miGhp (phi hp") ca hai c th cha m Ghp ( phi hp ) ca hai c th cha m

im lai ghp c chn ngu nhin (trn chiu di ca nhim sc th) Phn u tin ca nhim sc th hi c ghp vi phn sau ca nhim

sc th hj v ngc li sinh ra 2 nhim sc th misc th hj, v ngc li, sinh ra 2 nhim sc th mit bin (Mutation) sinh ra 1 c th mi

Chn ngu nhin mt bit ca nhim sc th, v i gi tr (01 / 10)Ch t t th i h hi i i t th h ! Ch to nn mt thay i nh v ngu nhin i vi mt c th cha m!

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Cc ton t di truyn V dCha m Th h

hin tiCon chu Th

h tip theo

11101001000 11111000000 11101010101

Ti sn xut: 11101001000 11101001000

11101001000

00001010101

11111000000(crossover mask)

11101010101

00001001000

Lai ghp ti 1 im:

11101001000

00001010101

11001011000

00101000101

Lai ghp ti 2 im:

00111110000(crossover mask)

t bin: 11101001000 11101011000

[Mitchell, 1997]

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Ton t lai ghp V d

Bi ton b tr 8 qun hu trn bn c - Ton t lai ghp (crossover)

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Tm kim c i th

Cc th tc tm kim su dn (IDS) v tm kim A* hu dng i vi cc bi ton (tm kim) lin quan n mtdng i vi cc bi ton (tm kim) lin quan n mt tc t

Th t t ki h bi t li 2 t t Th tc tm kim cho cc bi ton lin quan n 2 tc t c mc tiu i nghch nhau (xung t vi nhau)? Tm kim c i th (Adversarial search)( )

Phng php tm kim c i th c p dng ph bin trong cc tr chi (games)bin trong cc tr chi (games)

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Cc vn ca tm kim trong tr chi Khng th d on trc c phn ng ca i th

Cn xc nh (xt) mt nc i ph hp i vi mi phn ng Cn xc nh (xt) mt nc i ph hp i vi mi phn ng (nc i) c th ca i th

Gii hn v thi gian (tr chi c tnh gi) Thng kh (hoc khng th) tm c gii php ti u Xp x

Tm kim c i th i hi tnh hiu qu (gia cht l i thi i hi h) l t lng ca nc i v thi gian chi ph) y l mt yu cu kh khn

Nguyn tc trong cc tr chi i khng Nguyn tc trong cc tr chi i khng Mt ngi chi thng = Ngi chi kia thua Mc (tng im) thng ca mt ngi chi = Mc (tng

im) thua ca ngi chi kia

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Tr chi c ca-r

Tr chi c ca-r l mt v d ph bin trong AI minh ha v tm kim c i thha v tm kim c i th Vd: http://www.ourvirtualmall.com/tictac.htm

L t h i i kh i 2 i ( i l MAX MIN) L tr chi i khng gia 2 ngi (gi l MAX v MIN) Thay phin nhau i cc nc (moves) Kt thc tr chi: Ngi thng c thng (im), ngi thua g g g ( ) g

b pht (im)

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Biu din bi ton tr chi i khngg Tr chi bao gm cc thng tin

Trng thi bt u (Initial state): Trng thi ca tr chi + Ngi Trng thi bt u (Initial state): Trng thi ca tr chi + Ngi chi no c i nc u tin

Hm chuyn trng thi (Sucessor function): Tr v thng tin gm (nc i trng thi)(nc i, trng thi) Tt c cc nc i hp l t trng thi hin ti Trng thi mi (l trng thi chuyn n sau nc i)

Kim tra kt thc tr chi (Terminal test) Hm tin ch (Utility function) nh gi cc trng

thi kt thcthi kt thc

Trng thi bt u + Cc nc i hp l = Cy biu din tr chi (Game tree)biu din tr chi (Game tree)

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Cy biu din tr chi c ca-r

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Cc chin lc ti u Mt chin lc ti u l mt chui cc nc i gip a n trng thi ch mong mun (vd: chin thng)n trng thi ch mong mun (vd: chin thng)

Chin lc ca MAX b nh hng (ph thuc) vo cc nc i ca MIN v ngc lig

MAX cn chn mt chin lc gip cc i ha gi tr hm mc tiu vi gi s l MIN i cc nc i ti u MIN cn chn mt chin lc gip cc tiu ha gi tr hm mc

tiu

Chin lc ny c xc nh bng vic xt gi tr Chin lc ny c xc nh bng vic xt gi tr MINIMAX i vi mi nt trong cy biu din tr chi Chin lc ti u i vi cc tr chi c khng gian trng thi xc h (d t i i ti t t )nh (deterministic states)

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Gi tr MINIMAX

MAX chn nc i ng vi gi tr MINIMAX cc i ( t c gi tr cc i ca hm mc tiu)t c gi tr cc i ca hm mc tiu)

Ngc li, MIN chn nc i ng vi gi tr MINIMAX cc tiucc tiu

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Gii thut MINIMAX

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Gii thut MINIMAX Cc c im Tnh hon chnh

C (nu cy biu din tr chi l hu hn) C (nu cy biu din tr chi l hu hn)

Tnh ti u C (i vi mt i th lun chn nc i ti u)

phc tp v thi gian O(bm)

h t b h phc tp v b nh O(bm) (khm ph theo chin lc tm kim theo chiu su)

i vi tr chi c vua, h s phn nhnh b 35 v h s mc su ca cy biu din m100 Chi ph qu cao Khng th tm kim chnh xc nc i ti u Chi ph qu cao Khng th tm kim chnh xc nc i ti u

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Ct ta tm kim

Vn : Gii thut tm kim MINIMAX vp phi vn bng n (mc hm m) cc kh nng nc i cn phibng n (mc hm m) cc kh nng nc i cn phi xt khng ph hp vi nhiu bi ton tr chi thc t

Chng ta c th ct ta (b i khng xt n) mt s Chng ta c th ct ta (b i khng xt n) mt s nhnh tm kim trong cy biu din tr chi

Phng php ct ta - (Alpha-beta prunning) Phng php ct ta - (Alpha-beta prunning) tng: Nu mt nhnh tm kim no khng th ci thin i

vi gi tr (hm tin ch) m chng ta c, th khng cn xt n nhnh tm kim na!nhnh tm kim na!

Vic ct ta cc nhnh tm kim (ti) khng nh hng n kt qu cui cng

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Ct ta - V d (1)(

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Ct ta - V d (2)(

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Ct ta - V d (3)(

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Ct ta - V d (4)(

63Tr tu nhn to

Ct ta - V d (5)(

64Tr tu nhn to

Ti sao c gi l ct ta -?g l gi tr ca nc i

tt nht i vi MAX (gitt nht i vi MAX (gi tr ti a) tnh n hin ti i vi nhnh tm kim

Nu v l gi tr ti hn , MAX s b qua nc i

ng vi v Ct ta nhnh ng vi vCt t a g

c nh ngha tng t i vi MINg

65Tr tu nhn to

Gii thut ct ta - (1)(

66Tr tu nhn to

Gii thut ct ta - (2)(

67Tr tu nhn to

Ct ta - i vi cc tr chi c khng gian trng thi ln, th

phng php ct ta vn khng ph hpphng php ct ta - vn khng ph hp Khng gian tm kim (kt hp ct ta) vn ln

C th h h kh i t ki b h d C th hn ch khng gian tm kim bng cch s dng cc tri thc c th ca bi ton Tri thc cho php nh gi mi trng thi ca tr chip p g g Tri thc b sung (heuristic) ny ng vai tr tng t nh l hm c lng h(n) trong gii thut tm kim A*

68Tr tu nhn to

Documents

Chuong 4 - Tim kiem heuristic.pdf