外文翻译-α-β剪枝& Zobrist散列.docx

外文翻译-α-β剪枝& Zobrist散列.docx

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外文文献

Alpha–betapruning&Zobristhashing

Alpha–betapruning

Alpha–betapruningisasearchalgorithmthatseekstodecreasethenumberofnodesthatareevaluatedbytheminimaxalgorithminitssearchtree.Itisanadversarialsearchalgorithmusedcommonlyformachineplayingoftwo-playergames（Tic-tac-toe,Chess,Go,etc.）.Itstopscompletelyevaluatingamovewhenatleastonepossibilityhasbeenfoundthatprovesthemovetobeworsethanapreviouslyexaminedmove.Suchmovesneednotbeevaluatedfurther.Whenappliedtoastandardminimaxtree,itreturnsthesamemoveasminimaxwould,butprunesawaybranchesthatcannotpossiblyinfluencethefinaldecision.

Thebenefitofalpha–betapruningliesinthefactthatbranchesofthesearchtreecanbeeliminated.Thisway,thesearchtimecanbelimitedtothe'morepromising'subtree,andadeepersearchcanbeperformedinthesametime.Likeitspredecessor,itbelongstothebranchandboundclassofalgorithms.Theoptimizationreducestheeffectivedepthtoslightlymorethanhalfthatofsimpleminimaxifthenodesareevaluatedinanoptimalornearoptimalorder（bestchoiceforsideonmoveorderedfirstateachnode）.

Withan（averageorconstant）branchingfactorofb,andasearchdepthofdplies,themaximumnumberofleafnodepositionsevaluated（whenthemoveorderingispessimal）isO（b*b*...*b）=O（bd）–thesameasasimpleminimaxsearch.Ifthemoveorderingforthesearchisoptimal（meaningthebestmovesarealwayssearchedfirst）,thenumberofleafnodepositionsevaluatedisaboutO（b*1*b*1*...*b）forodddepthandO（b*1*b*1*...*1）foreven

depth,or.Inthelattercase,wheretheplyofasearchiseven,the

effectivebranchingfactorisreducedtoitssquareroot,or,equivalently,thesearchcangotwiceasdeepwiththesameamountofcomputation.[10]Theexplanationofb*1*b*1*...isthatallthefirstplayer'smovesmustbestudiedtofindthebestone,butforeach,onlythebestsecondplayer'smoveisneededtorefuteallbutthefirst（andbest）firstplayermove–alpha–betaensuresnoothersecondplayermovesneedbeconsidered.Whennodesareorderedatrandom,theaveragenumberofnodesevaluatedisroughly.

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Normallyduringalpha–beta,thesubtreesaretemporarilydominatedbyeitherafirstplayeradvantage（whenmanyfirstplayermovesaregood,andateachsearchdepththefirstmovecheckedbythefirstplayerisadequate,butallsecondplayerresponsesarerequiredtotrytofindarefutation）,orviceversa.Thisadvantagecanswitchsidesmanytimesduringthesearchifthemoveorderingisincorrect,eachtimeleadingtoinefficiency.Asthenumberofpositionssearcheddecreasesexponentiallyeachmovenearerthecurrentposition,itisworthspendingconsiderableeffortonsortingearlymoves.Animprovedsortatanydepthwillexponentiallyreducethetotalnumberofpositionssearched,butsortingallpositionsatdepthsneartherootnodeisrelativelycheapastherearesofewofthem.Inpractice,themoveorderingisoftendeterminedbytheresultsofearlier,smallersearches,suchasthroughiterativedeepening.

Thealgorithmmaintainstwovalues,alphaandbeta,whichrepresentthemaximumscorethatthemaximizingplayerisassuredofandtheminimumscorethattheminimizingplayerisassuredofrespectively.Initiallyalphaisnegativeinfinityandbetaispositiveinfinity,i.e.bothplayersstartwiththeirlowestpossiblescore.Itcanhappenthatwhenchoosingacertainbranchofacertainnodetheminimumscorethattheminimizingplayerisassuredofbecomeslessthanthemaximumscorethatthemaximizingplayerisassuredof（beta<=alpha）.Ifthisisthecase,theparentnodeshouldnotchosethethisnode,becauseitwillmakethescorefortheparentnodeworse.Therefore,theotherbranchesofthenodedonothavetobeexplored.

Additionally,thisalgorithmcanbetriviallymodifiedtoreturnanentireprincipalvariationinadditiontothescore.SomemoreaggressivealgorithmssuchasMTD（f）donoteasilypermitsuchamodification.

Furtherimprovementcanbeachievedwithoutsacrificingaccuracy,byusingorderingheuristicstosearchpartsofthetreethatarelikelytoforcealpha–betacutoffsearly.Forexample,inchess,movesthattakepiecesmaybeexaminedbeforemovesthatdonot,ormovesthathavescoredhighlyinearlierpassesthroughthegame-treeanalysismaybeevaluatedbeforeothers.Anothercommon,andverycheap,heuristicisthekillerheuristic,wherethelastmovethatcausedabeta-cutoffatthesamelevelinthetreesearchisalways

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examinedfirst.Thisideacanbegeneralizedintoasetofrefutationtables.

Alpha–betasearchcanbemadeevenfasterbyconsideringonlyanarrowsearchwindow（generallydeterminedbyguessworkbasedonexperience）.Thisisknownasaspirationsearch.Intheextremecas