Class Note for CMPSCI 683 at UMass(8)
Class Note for CMPSCI 683 at UMass(8)
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Date Created: 02/06/15
Jiaying Shen CMPSCI 683 Fall 2002 Example tracing All with two dill39erent heuristics m m mm mmilullrat tiu mm mmlnhmn ixinu Space and time variations of A rutmm Slhmbrnw limi wllilm Problem How to handle the exponential growth of memory used by admissible search algorithms such as A Solutions DA Korf1985 RBFS Korf1993 SMA Russell1992 wath summer Lamtlii39 tim Beginning with an fbound equal to the fvalue of the 39 al state perform a depth rst search bounded by the fbound instead of a depth bound Unless the goal is found increase the fbound to the lowest fvalue found in the previous search that exceeds the previous fbound and restart the depth rst search DQVWW saitasuincvusa DiAPSElnXJ The more Informed a heuristic the more the contours will be stretched toward the goal they will be more focused around the optimal path DQVWW saitasuincvusa DiAPSElnXJ Algorithm lterativeDeepeningA 1 Set THRESHOLD the heuristic evaluation ofthe start state 2 Conduct a depth rst search based on minimal cost from current node pruning any branch when its total cost function g h39 exceeds THRESHOLD If a solution path is found during the search return it 3 Otherwise increment THRESHOLD by the minimum amount it was exceeded during the previous step and then go to Step 2 start state always on path so initial estimate is always overestimate and never decreasing dinm s lebusmin vtgsss DiAPsElnXJ am nmm 1mm R 39 VG awc tark 2i an i x m moms 7 3911 39 Mum lama my arm Izmm lmiw as 2m 26 cum no we ago 35 algae Nodes are labeled with f g h The h values are the straightline distances to Bucharest What is the next Contour dinm s lebusmin vtgsss DiAPsElnXJ lDA is asymptotically same time as A but only Od in Mimics beSt39 rSt searCh With linear space versus Ob for A Space 7 Avoids overhead of sorted queue of nodes Similar to recursive depthfirst Limits recursion by keeping track of the fvalue of lDA is simpler to implement no closed lists limited open the best alternative path from any ancestor node 5039 If current node exceeds this value recursion unwinds back to the alternative path ln Korfs 15puzzle experiments lDA solved all problems As recursion unwinds replaces fvalue of node ran faster even though it generated more nodes than A With bes f39Vallle 0f Children 7 A solved no problems due to insuf cient space ran slower 5 W5 remember Whe herm re39eXPam Path 5 mequot than IDA quot39quote Wm mmnevoss wwscinxa 9 mm smbmnevoss wwscinxa m mm 1 RLCURslvrrBEsTrFlRSTrSEARCulmobum relllrns a solution 01 mm RnFSlMA KLVom llm l m s w rpm715mm t39llnrliml mam pmblanlndeX mill wturns a salmon or failure and a new frcosl mm ifGOALTESTDimblumllxlulw um rulurn mth vuummrl p m m mnmlepmhim n mamaw llt empty then return Willi1m l39or eacllsiusuucessm do islemm Ho nodah repeal 2w yr the luwcsl frulluu node in mmmu if m gt lmm thequot return az391um mm ulumumHhe Semndrlmwsl frmllle among tutacme mum Mm 7m Slymlilwiibcsl uliuf nmr alrcmaivcl ifemlz 7 mm lhen return mm WM and cow va somech msmm M naem swimmech msmm 2 mm mm m m m mm x mm ml mum MN m in mm ywuvmwlmsmm aiidcwml up mm m 515 am wwan SlharshinLllmu mum is Enzqu sawinqu swim to Uses a given amount ofmemory to remember nodes so that they don t have to be repeatedly regenerated More efficient than IDA and still optimal It will utilize whatevermemory is made available to it Like DA suffers from excessive node regeneration Note mind changes in example lt avoids repeated states as faras its memory allows It is complete provided the available memory is sufficient to store the shallowest solution path It is optimal ifenough memory is available to store IDAquot and RBFS not good for graphs the shallowest optimal solution path Othenivise it Can t check for repeated states otherthan those on mums the be SOIUtiOquot if anvlthat can be reached current path with the available memory When enough memory is available forthe entire search tree its behavior replicates that ofAquot wwan summing 2mm 5 Enzqu sawinqu 2mm in a sh of Am wArwAAwtntmmAwmAw Wm WM tpmbh tn mm lam nwmd mtnwttmtht Aw 1 Expand deepest lowest I cost leafnode um umde m555555me WA 2 Update cost of nodes whose successors ff g wf jfE m j v have higher Least trr methnmlumtmerx xtSunmwut it Amhlrtxutltlt u mwnnmmttmu 3 Drop shallowest amp highest I cost leaf node W 5 remember best forgotten descendant twmwm mrmmmmmmw Munw mm mm mm 4 Paths longerthan node IImIt get on cost quotSumwwmttmamattwnmurnlmmwm m mum Antith tnyrmtamm zm twu mumAwhww WAWWW WWW a Emwmt szmmmy 2mm w mum smwm 2mm rx A A A A A t2 tZ 13 t3t5 545 35 t3 E 3 3 t5 5 t3 t3 H 525 Mm m tEI mt E 3n 535 ammo 2mm NAME Emwmt szmmmy 2mm w mum snuusmcvm 2mm in l5 ism A tum ZEIUnl ZEI Why oon lwe need in Search anymore alierlmmng D comm Snmencvmy 2mm Staged search involves periodically pruning unpromising paths SMA is an example of a staged search llode expansion may be so costly because the branching factor is high or the cost to apply operators is high that exhaustive node expansion is not practical a mum summon cmch 22 Use a generator approach to incrementally produce successors in order by quality must have operatorordering function Limit expansion so that only likely successors are generated often called plausiblemove generator Prune unpromising successors immediately following node expansion 39 Delay state computation until expansion time when possible must be able to compute hvvithout state only on operatorlprevious state comm Snmencvmy 2mm Practical and theoretical dif culties Agents have limited computational power They must react within an acceptable time Computation time normally reduces the value of the result There is a high degree of uncertainty regarding the rate of progress The appropriate level of deliberation is situation dependent 2 mm summon cmch 2 A theory of rationality that does not give an account of problem solving in the face of complexity is sadly incomplete It is worse than incomplete it can be seriously misleading by providing solutions that are without operational signi cance The global optimization problem is to nd the least cost or bestreturn decision net of computational costs Herbert Simon 1958 mm s mbmnavueg msmm 25 A Scottish word which means satisfying Denotes decision making that searches until an alternative is found that is satisfactory by the agent39s aspiration level criterion Heuristic search as satisficing Formalizing the notion of satisficing mm s mbmnavueg msmm za It appears probable that however adaptive the behavior of organisms in learning and choice situations this adaptiveness falls far short of the ideal quotmaximizingquot postulated in economic theory Evidently organisms adapt well enough to satis ce they do not in general optimize quot mm s mbmnavueg msmm 27 In complex realworld situations optimization becomes approximate optimization since the description of the real world is radically simpli ed until reduced to a degree of complication that the decision maker can handle Satis cing seeks simplification in a somewhat different direction retaining more of the detail of the realworld situation but settling fora satisfactory rather than approximatebest decision 0 Which approach is preferable mm s mbmnavueg msmm 23 Goal reduce the execution time ofA Method limit the search horizon ofA and select an action single move in constant time Make decision about next move in realWorld Without a complete plan path to reach goal state liitermik partial search With execution of action Two stages Make indivrdual move decision Perform minimin search With alpha priming Make a sequence of decisions to arrive at a solution recovering from inappropriate actions avoid loops WWW samenevmi EllElm z ha s ga to c hc s ha 7 assuming you need to go to rna gasstare mm 5 mm a As a result of ex lorin in the search space from ato c you can re lace 3Wl the better more Informed estimate gFa to c c This leads to a more informed decisionat 5 whether to take the action inthe real world of movmgquot to either state y a or X WWW samenevmi EllElm Jl Minimin lookhead search see next slide 7 Relumsbackruplvaluelnr a nodelmmlnnking area in ine ireniier node aiine nerizen 7 Viewed as simply a mere accurate and computationally expensive neurisiie Motion 7 Reasen iiine neurisiieiuneiien n is consistent and admissible inen ine errer in ine backedrup cost estimate cannot increase Wiin searen depth Alpha pruning e llcurrenl minimum iei nerizen node is iessinan ieian intermediate node ine intermediate node and any successors can be eiiminaiea iremiuriner consideration 7 Reason lismnnolonicand you are only searchinglo nerizen don t need goal state in prime miner summing 2mm air procedure evalualelmoveJimm a return hackedup estimate r imovei hy pnming search to depth Ilmi 1 Open moveu w z llmove qlmovel e n imovei 3 While lopequot not emptyl do i node poplonenl 5 expand node hr each child olnoile do a q iciiiiiii q inoiei e movecost 7 llchildl qlchildl e n iciiiiiii Prune child iiiieiiiiiii gt 1 a illlchildllt dn 9 ii iieptii rim or goallchildll then m iieiiiiiii iii else put child on Open oil oil oil 11 Return at unwiememmmim a aasic Principle Ma39nta39nsin a hash table a list olthose nodcsthat have been One should backtrack to a previously visited state when the 5quot Va 1quot quot W39 M mm W estimate ol solving the problem born that state plus the 39 M eayh 991th wran status expanded am he heuris p cost or returning to that state is less than the estimated cost M i 395 WWW olpoinplorwardlromthecurrentstatequotKorl lhe wluelol oleadr naghhorlng state rs conputad by aldrnp the hvalue plusthecost olthelinlt to thecurrent state 39 Merit 039 every node nl aim Mm is mm quotmm 0 The neighbor with the nininum value is chosen lorthe current the current poshion olthe problem solver in the realworld up 7 rnrlral slate is irrelevant The second best value is stored in thehash table lor the cunent state pm mm mm a rmly mm mapme my 7 Replesemslhe esrrmaredhresrelsehrnpthe plumeme rerurnrnp then it needs to talre into account that one already has 9 quot 5 5 3 9 talren actionthere a Setnn beslavm slnnps rvalue Mslale ls maxi basil conmr smenwr cumm 1 mm snnmenauua curscrm at AnytimeA Hierarchical A conmr smenwr cumm I new snnmenauua curscrm no
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