B.Y. Title: Solving Problems b y Sear hing ✫ ✬ Choueiry AIMA: Chapter 3 (Se tions 3.1, 3.2 and 3.3) In tro du tion to Arti� ial In telligen e CSCE 476-876, Spring 2016 URL: www. se.unl.edu/~ ho uei ry/ S1 6-4 76- 87 6 1 Berthe Y. Choueiry (Sh u-w e-ri) (402)472-5444 Instru tor's Jan uary notes 29, 2016 #5 ✪ ✩
Summary B.Y. ✫ ✬ In telligen t Agen ts Choueiry Designing in telligen t agen ts: P AES T yp es of In telligen t Agen ts 1. Self Re�ex • 2. ? 3. ? • 4. ? 2 T yp es of en vironmen ts: observ able (fully or partially), deterministi or sto hasti , episo di or sequen tial, stati vs. dynami , dis rete vs. on tin uous, single agen t vs. m ultiagen t Instru tor's • Jan uary notes 29, 2016 #5 ✪ ✩
Outline B.Y. ✫ ✬ Choueiry Problem-solving agen ts F orm ulating problems � Problem omp onen ts • � Imp ortan e of mo deling • Sear h � basi elemen ts/ omp onen ts 3 � Uninformed sear h (Se tion 3.4) � Informed (heuristi ) sear h (Se tion 3.5) • Instru tor's Jan uary notes 29, 2016 #5 ✪ ✩
Simple re�ex agen t unable to plan ahead B.Y. ✫ ✬ - a tions limited b y urren t p er epts Choueiry - no kno wledge of what a tions do - no kno wledge of what they are trying to a hiev e Problem-solving agen t: goal-based agen t Giv en: - a problem form ulation: a set of states and a set of a tions - a goal to rea h/a omplish 4 Find: - a sequen e of a tions leading to goal Instru tor's Jan uary notes 29, 2016 #5 ✪ ✩
Example: Holida y in Romania B.Y. ✫ ✬ On holida y in Romania, urren tly in Arad, w an t to go to Bu harest Choueiry 5 Instru tor's Jan uary notes 29, 2016 #5 ✪ ✩
B.Y. Example: On holida y in Romania, urren tly in Arad, w an t to go ✫ ✬ Choueiry to Bu harest F orm ulate goal : b e in Bu harest F orm ulate problem : states : v arious ities a tions : (op erators, su essor fun tion) driv e b et w een ities 6 Find solution : sequen e of ities, e.g. Arad, Sibiu, F agaras, Bu harest Instru tor's Jan uary notes 29, 2016 #5 ✪ ✩
Driv e to Bu harest... ho w man y roads out of Arad? B.Y. ✫ ✬ Choueiry Oradea 71 Neamt 87 Zerind 151 75 Iasi Arad 140 92 Sibiu Fagaras 99 118 Vaslui 80 Rimnicu Vilcea 7 Timisoara 142 211 111 Pitesti Lugoj 97 70 98 Hirsova 85 146 Mehadia 101 Use map to onsider h yp otheti al journeys through Urziceni ea h road un til 86 75 138 Bucharest rea hing Bu harest 120 Dobreta Instru tor's 90 Eforie Craiova Giurgiu Jan uary notes 29, 2016 #5 ✪ ✩
B.Y. ✫ ✬ Choueiry Oradea 71 Neamt 87 Zerind 151 75 Iasi Arad 140 92 Sibiu Fagaras 99 118 Vaslui 80 Rimnicu Vilcea Timisoara 142 211 111 Pitesti Lugoj 97 Lo oking for a sequen e of a tions − sear h 70 98 Hirsova 85 146 Mehadia 101 Urziceni 8 Sequen e of a tions to goal − solution 86 75 138 Bucharest 120 Dobreta 90 Carrying out a tions − exe ution phase Eforie Craiova Giurgiu F orm ulate, sear h, exe ute → → Instru tor's → Jan uary notes 29, 2016 #5 ✪ ✩
F orm ulate, sear h, exe ute B.Y. ✫ ✬ Choueiry Up date-State F orm ulate-goal 9 F orm ulate-Problem Sear h Re ommendation = �rst, and Remainder = rest Assumptions for en vironmen t: observ able, stati , dis rete, deterministi sequen tial, single-agen t × × √ √ Instru tor's Jan uary notes 29, 2016 #5 ✪ ✩
Problem form ulation A pr oblem is de�ned b y the follo wing items: B.Y. 1. initial state : In ( Arad ) ✫ ✬ Choueiry 2. su essor fun tion S ( x ) (op erators, a tions) Example, S ( In ( Arad )) = {� Go ( Sibiu ) , In ( Sibiu ) � , 3. go al test , an b e expli it, e.g., x = In ( Bucharest ) or a prop ert y NoDirt ( x ) 4. step ost : assumed non-negativ e � Go ( Timisoara ) , In ( Timisoara ) � , � Go ( Zerind ) , In ( Zerind ) �} 5. p ath ost (additiv e) 10 e.g. , sum of distan es, n um b er of op erators exe uted, et . A solution is a sequen e of op erators leading from the initial state to a goal state. Solution qualit y , optimal solutions. Instru tor's Jan uary notes 29, 2016 #5 ✪ ✩
Imp ortan e of mo deling (for problem form ulation) Real art of problem solving is mo deling, B.Y. ✫ ✬ state des ription Choueiry de iding what's in a tion des ription ho osing the righ t lev el of abstra tion State abstra tion: road maps, w eather fore ast, tra v eling ompanions, s enery , radio programs, ... A tion abstra tion: generate p ollution, slo wing do wn/sp eeding 11 up, time duration, turning on the radio, .. Com binatorial explosion. Abstra tion b y remo ving irrelev an t detail mak e the task easier to handle Instru tor's Jan uary notes 29, 2016 #5 ✪ ✩
B.Y. ✫ ✬ State spa e vs. state set Choueiry R 1 2 L R L 12 S S 3 4 R R L R L R L L S S 5 6 S S R L R L 7 8 Instru tor's S S Jan uary notes 29, 2016 #5 ✪ ✩
Example problems B.Y. ✫ ✬ T o y Problems: Choueiry on epts in tended to illustrate or exer ise problem-solving metho ds an b e giv e on ise, exa t des ription resear hers an ompare p erforman e of algorithms 8 < → yield metho ds that rarely s ale-up : ma y re�e t realit y ina urately (or not at all) √ √ Real-w orld Problems: 13 more di� ult but whose solutions p eople a tually are ab out × more redible, useful for pra ti al settings × di� ult to mo del, rarely agreed-up on des riptions → Instru tor's √ Jan uary × notes 29, 2016 #5 ✪ ✩
T o y problem: v a uum Single state ase B.Y. ✫ ✬ Choueiry States: Initial State: 14 Su essor fun tion: Goal test: P ath ost: Instru tor's With 2 lo ations: 2 . 2 2 states. With n lo ations: n. 2 n states Jan uary notes 29, 2016 #5 ✪ ✩
T o y problem: 8-puzzle B.Y. ✫ ✬ Choueiry States: Initial state: Su essor fun tion: Goal test: 15 P ath ost: instan e of sliding-blo k puzzles, kno wn to b e NP - omplete Optimal solution of n -puzzle NP -hard so far, nothing b etter than sear h 8-puzzle, 15-puzzle traditionally used to test sear h algorithms Instru tor's → Jan → uary → notes 29, → 2016 #5 ✪ ✩
T o y problem: n -Queens B.Y. ✫ ✬ Choueiry F orm ulation: in remen tal vs. omplete-state States: An y arrangemen t of x ≤ 8 queens on b oard Initial state: → Su essor fun tion: add a queen (alt., mo v e a queen) 16 Goal test: 8 queens not atta king one another P ath ost: irrelev an t (only �nal state matters) p ossible states, but ∃ other more e�e tiv e form ulations Instru tor's Jan uary notes 29, → 64 8 2016 #5 ✪ ✩
B.Y. ✫ ✬ Choueiry T o y problems: requiring sear h 8 puzzles -queens v a uum √ Others: Missionaries & annibals, farmer's dilemma, et . √ n 17 √ Instru tor's Jan uary notes 29, 2016 #5 ✪ ✩
Real-w orld problems: requiring sear h Route �nding: state = lo ations, a tions = transitions B.Y. routing omputer net w orks, tra v el advisory , et . ✫ ✬ Choueiry T ouring: start in Bu harest, visit ev ery it y at least on e T ra v eling salesp erson problem (TSP) (exa tly on e, shortest tour) • VLSI la y out: ell la y out, hannel la y out minimize area and onne tion lengths to maximize sp eed • Rob ot na vigation ( on tin uous spa e, 2D, 3D, ldots ) Assem bly b y rob ot-arm • States: rob ot join t angles, rob ot and parts o ordinates 18 Su essor fun tion: on tin uous motions of the rob ot joins • goal test: omplete assem bly • path ost: time to exe ute + protein design, in ternet sear h, et . ( he k AIMA) Instru tor's Jan uary notes 29, • 2016 #5 ✪ ✩
Problem solving p erforman e Measures for e�e tiv eness of sear h: B.Y. ✫ ✬ Choueiry 1. Do es it �nd a solution? omplete 2. Is it a go o d solution? path ost lo w 3. Sear h ost? time & spa e T otal ost = Sear h ost + P ath ost problem? 19 Example: Arad to Bu harest P ath ost: total mileage, fuel, tire w ear f (route), et . − → Sear h ost: time, omputer at hand, et . Instru tor's Jan uary notes 29, 2016 #5 ✪ ✩
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