Disjoint Pattern Database Heuristics
Disjoint Pattern Database Heuristics
Disjoint Pattern Database Heuristics
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eratedfewernodesandincurredlessoverheadpernode.FortheTwenty-Four Puzzle,the2-and3-tiledatabasesusuallygeneratedfewernodesthanthe compute,itincurredalargerconstanttimepernode,andthustheactual disjointdatabase.Again,however,sincethisheuristicismorecomplexto<br />
foundin[2]. databaseheuristicsarebothsimplerandperformbetter,thedetailsofour experimentswiththe2-and3-tiledatabasesareomittedhere,butcanbe runningtimewasgreaterthanforthedisjointdatabases.Sincethedisjoint<br />
and3-tiledatabaseswasgreaterfortheFifteenPuzzlethantheTwenty- asingledatabase,butonlyaquarteroftheTwenty-FourPuzzletiles.For FourPuzzle,probablybecausewecouldstorehalftheFifteenPuzzletilesin Theperformancedierencebetweenthedisjointdatabasesandthe2-<br />
thesetwoproblems,thedisjointdatabaseheuristicsarebothsimplerand moreeective,buttheymaynotbeforlargerversionsoftheproblemor otherdomains.<br />
WehavefoundoptimalsolutionstoftyrandominstancesoftheTwenty- FourPuzzle,aproblemwithalmost1025states.Thebranchingfactorofthe 6 Summary,Conclusions,andFurtherWork<br />
problemis2.3676,andoptimalsolutionsaverageabout100moves.Wealso Thisisbyfarthebestperformanceontheseproblemstodate. ndoptimalsolutionstotheFifteenPuzzlein27millisecondsonaverage. functions,basedonpatterndatabases[1].Ratherthancomputingthecosts ofsolvingindividualsubgoalsindependently,apatterndatabaseheuristic considersthecostsofsolvingseveralsubgoalssimultaneously,takinginto Toachievethis,weimplementedIDA*withnewadmissibleheuristic<br />
admissibleheuristicsisalwaysanotheradmissibleheuristic. values.Thisisthemostgeneralapproach,sincethemaximumofanytwo accounttheinteractionsbetweenthem.CulbersonandSchaeer[1]combined heuristicsfromdierentpatterndatabasesbytakingthemaximumoftheir<br />
values.Adisjointpatterndatabasepartitionsthesetofsubgoalsintodisjoint ferentdatabasestobeaddedtogether,resultinginmoreaccurateheuristic groups,andthenaddstogetherthecostsofsolvingallthesubgoalsineach Weintroduceddisjointpatterndatabasestopermitthevaluesfromdif-<br />
group.Thisrequiresthatthegroupsbedisjoint,andthatasingleoperator 16
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