Ni dungBiu din bi ton trong Khng Gian Trng ThiCc chin lc tm kim Tm kim mTm kim kinh nghim (heuristic).Tm kim trn khng gian trng thi: Tm kim theo chiu rng (breath first search)Tm kim theo chiu su (depth first search)Tm kim su bng cch o su nhiu ln (depth first search with iterative deepening)S dng khng gian trng thi biu din suy lun vi php tnh v t: th V/Hoc (And/Or Graph)

Gii quyt vn bng tm kim Khi biu din mt vn nh l mt th khng gian trng thi, chng ta c th s dng l thuyt th phn tch cu trc v phc tp ca cc vn cng nh cc th tc tm kim.H thng cu thnh ph Konigsberg v biu din th tng ng

Bi ton tm kim Tm kim: l tm mt i tng tho mn mt s i hi no , trong mt tp hp rng ln cc i tng Cc k thut tm kim uc p dng rng ri trong lnh vc TTNT:Tm kim m: khng c hiu bit g v cc i tng hng dn tm kimTm kim kinh nghim (heuristic): da vo kinh nghim v hiu bit v vn cn gii quyt xy dng hm nh gi hng dn s tm kim.Tm kim ti uTm kim c i th: tm kim nc i trong cc tr chi hai ngi (c vua, c tng,...)

Khng gian trng thi Khng gian tm kim: bao gm tt c cc i tngm ta cn quan tm tm kim (c th l khng gian lin tc (khng gian cc vc t thc n chiu) hoc khng gian cc i tng ri rc.

Ton t: m t hnh ng hoc php bin i a mt trng thi ti trng thi khcV d: Bi ton tm ng i: cc con ng ni cc thnh ph s c biu din bi cc ton t --->Gii bi ton bng tm mt dy cc ton t a trng thi ban u (im xut pht) v trng thi kt thc (im ch)

Biu din mt bi ton trong khng gian trng thi, cn xc nh cc yu t:+ Trng thi ban u+ Mt tp hp cc ton t+ Mt tp hp cc trng thi kt thc (trng thi ch).

Khng gian trng thi c th c biu din bi mt th c hng: mi nh ca th tng ng vi mt trng thi, nu ton t R bin i trng thi u thnh trng thi v th cung (u,v) c gn nhn R

Mt phn KGTT trin khai trong Tic-tac-toe th c hng khng lp (directed acyclic graph - DAG)

Tr 8 hay 15 Trng thi ban u Trng thi chTr 15

Tr 8

Cn biu din KGTT cho bi ton ny nh th no?

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KGTT ca 8-puzzle sinh ra bng php di chuyn trngC kh nng xy ra vng lp khng?

Mt v d ca bi ton TSP

Cn biu din KGTT cho bi ton ny nh th no?

KGTT ca bi ton TSPMi cung c nh du bng tng gi ca con ng t nt bt u n nt hin ti.

Cy tm kimQu trnh tm kim c xem nh qu trnh xy dng cy tm kim.Cy tm kim: Gc = trng thi ban unh = trng thi ca khng gian trng thi

Cc chin lc tm kimTm kim m: khng c s hng dn no cho tm kim, ch pht trin cc trng thi ban u cho ti khi gp mt trng thi ch no .Tm kim kinh nghim (heuristic): tm kim da vo hiu bit v cc vn , da vo kinh nghim, trc gic nh gi cc trng thi

Tm kim theo b rngTrng thi chn pht trin l trng thi c sinh ra trc cc trng thi ch pht trin khcThut ton:Procedure Breadth_first_Search;begin1. Khi to dsch L ch cha trng thi ban u;2. Loop do2.1 if L rng then {thng bo tm kim tht bi; stop};2.2 Loi trng thi u u danh sch L;2.3 if u l trng thi kt thc then{thng bo tm kim thnh cng; stop};2.4 for mi trng thi v k u do{t v vo cui danh sch L;father(v) u};end;

nh gi thut tonDanh sch L c x l nh hng iNu bi ton c nghim (tn ti ng i t trng thi ban u ti trng thi ch) th thut ton s tm ra nghim v ng i l ngn nht.Nu bi ton v nghim, khng gian trng thi hu hn, thut ton dng v thng bo v nghim.Gi b l nhn t nhnh, nghim ca bi ton l ng i c di d, phc tp O(bd).

Tm kim theo suTrng thi chn pht trin l trng thi c sinh ra sau cng.Thut ton:Procedure Depth_first_Search;begin1. Khi to dsch L ch cha trng thi ban u;2. Loop do2.1 if L rng then {thng bo tm kim tht bi; stop};2.2 Loi trng thi u u danh sch L;2.3 if u l trng thi kt thc then{thng bo tm kim thnh cng; stop};2.4 for mi trng thi v k u do{t v vo u danh sch L;father(v) u};end;

nh gi thut tonNu bi ton c nghim, khng gian trng thi hu hn th thut ton s tm ra nghim. Nu khng gian trng thi v hn th c th khng tm ra nghim khng nn dng thut ton ny vi bi ton c cy tm kim cha cc nhnh v hn.Nghim bi ton l ng i c di d, cy tm kim c nhn t nhnh b, phc tp trong trng hp ti nht O(bd), phc tp khng gian l O(db).

Cc chin lc cho TK-KGTTTK hng t d liu (Data-driven Search)Suy din tin (forward chaining)TK hng t mc tiu (Goal-driven Search)Suy din li (backward chaining)

TK hng t d liuVic tm kim i t d liu n mc tiu

Thch hp khi:Tt c hoc mt phn d liu c cho t u.C nhiu mc tiu, nhng ch c mt s t cc php ton c th p dng cho mt trng thi bi ton. Rt kh a ra mt mc tiu hoc gi thuyt ngay lc u.

TK hng t mc tiuVic tm kim i t mc tiu tr v d liu.

Thch hp khi:C th a ra mc tiu hoc gi thuyt ngay lc u.C nhiu php ton c th p dng trn 1 trng thi ca bi ton => s bng n s lng cc trng thi. Cc d liu ca bi ton khng c cho trc, nhng h thng phi t c trong qu trnh tm kim.

Cc phng php tm kim trn th KGTT:Pht trin t gii thut quay lui (back tracking):Tm kim rng (breath-first search)Tm kim su (depth-first search)TK su bng cch o su nhiu ln (depth-first search with iterative deepening)

Tm kim theo chiu rngOpen = [A]; closed = []Open = [B,C,D]; closed = [A]Open = [C,D,E,F];closed = [B,A]Open = [D,E,F,G,H];closed = [C,B,A]Open = [E,F,G,H,I,J];closed = [D,C,B,A]Open = [F,G,H,I,J,K,L]; closed = [E,D,C,B,A]Open = [G,H,I,J,K,L,M];(v L c trong open);closed = [F,E,D,C,B,A]

Tm kim theo chiu suOpen = [A]; closed = []Open = [B,C,D]; closed = [A]Open = [E,F,C,D];closed = [B,A]Open = [K,L,F,C,D];closed = [E,B,A]Open = [S,L,F,C,D];closed = [K,E,B,A]Open = [L,F,C,D]; closed = [S,K,E,B,A]Open = [T,F,C,D];closed = [L,S,K,E,B,A]Open = [F,C,D]; closed = [T,L,S,K,E,B,A]

Tm kim Su hay Rng? (1)C cn thit tm mt ng i ngn nht n mc tiu hay khng?S phn nhnh ca khng gian trng thiTi nguyn v khng gian v thi gian sn cKhong cch trung bnh ca ng dn n trng thi mc tiu.Yu cu a ra tt c cc li gii hay ch l li gii tm c u tin.

Tm kim su bng cch o su nhiu ln(depth-first iterative deepening) su gii hn (depth bound): gii thut TK su s quay lui khi trng thi ang xt t n su gii hn nh.TK Su bng cch o su nhiu ln: TK su vi su gii hn l 1, nu tht bi, n s lp li GT TK su vi su l 2, GT tip tc cho n khi tm c mc tiu, mi ln lp li tng su ln 1.GT ny c phc tp v thi gian cng bc vi TK Rng v TK Su.

Tr chi 8-puzzleThe 8-puzzle searched by a production system with loop detection and depth bound 5

th V/HocS dng KGTT biu din suy lun vi php tnh v tL phng php qui bi ton v cc bi ton con.Mt tp hp cc mnh / cu v t to thnh mt th V/Hoc (And/Or graph) hay siu th (hypergraph).Trong th V/Hoc:Cc nt AND biu th s phn chia bi ton, tt c cc bi ton con phi c chng minh l ng.Cc nt OR biu th cc chin lc gii quyt bi ton khc nhau, ch cn chng minh mt chin lc ng l C th p dng TK theo kiu hng t d liu hay t mc tiu.Trong gii thut cn ghi nhn din tin ca qu trnh.

V d th V/HocGi s mt tnh hung vi cc mnh sau:abcabdacebdffgaeh

Hy tr li cc cu hi sau:h c ng khng?h c cn ng nu b sai?

Cy nghimGc ca cy ng vi bi ton cn giiCc l l cc nh kt thc (ng vi cc bi ton s cp)Nu u l nh trong ca cy, th cc nh con ca u l cc nh k u theo mt ton t no .Cc nh c gn nhn gii c hoc khng gii cnh gii c:nh kt thcnh khng kt thc nhng c ton t R sao cho tt c cc nh k ca n theo R u gii c.nh khng gii c:nh khng kt thc v khng c nh ku khng phi nh kt thc v mi ton t R p dng c ti u u c nh v k u theo R khng gii c.

Tm kim trn th V/HOCS dng k thut tm kim theo chiu su nh du cc nhFunction Solvable(u);Begin1. If u l nh kt thc then {Solvable true; stop};2. If u khng l nh kt thc v khng c nh k then {Solvable false; stop};3. For mi ton t R p dng c ti u do{OKtrue; for mi v k u theo R do if Solvable(v) = false then {OKfalse; exit}; if OK then {Solvable(u)true; operator(u)R; stop} }4. Solvable(u)false;End;

V d: H T Vn Ti Chnh Th And/Or biu din phn KGTT duyt qua i n li gii

V D TH AND/OR:Cho mt bi ton c m t bng cc cu v t:Hy v th AND/OR biu din phn KGTK tr li cu hi: Fred ang u? (p dng suy din li)

TTNT. p.*

Bi Tp Chng 3