Search Strategies for an Anytime Usage of the Branch and Prune PDF
Preview Search Strategies for an Anytime Usage of the Branch and Prune
TheBranchandPruneAlgorithm TheMostDistantFirstStrategy TheDepthandMostDistantFirstStrategy Experiments ConclusionandFutureWork Search Strategies for an Anytime Usage of the Branch and Prune Algorithm R.Chenouard1, A. Goldsztejn2 andC. Jermann1 SWIM2009 1LinaUMRCNRS6241,UniversityofNantes,France 2CNRS,LinaUMRCNRS6241,France lin LABORATOIRED'INFORMATIQUE DENANTESATLANTIQUE R.Chenouard,A.GoldsztejnandC.Jermann SearchStrategiesforanAnytimeUsageoftheBPA 1/16 TheBranchandPruneAlgorithm TheMostDistantFirstStrategy Introduction TheDepthandMostDistantFirstStrategy ExistingStrategies Experiments IdealStrategyforanAnytimeUsage ConclusionandFutureWork The Branch and Prune Algorithm Alternatessearch(branch)andfiltering (prune). ⇒ setof e -boxescoveringthesolutionset. L I Boxes to beprocessed: e S I Computed -boxes: (can bepost-processed) Search Issue L Howto choosethenext box to processin ? R.Chenouard,A.GoldsztejnandC.Jermann SearchStrategiesforanAnytimeUsageoftheBPA 2/16 TheBranchandPruneAlgorithm TheMostDistantFirstStrategy Introduction TheDepthandMostDistantFirstStrategy ExistingStrategies Experiments IdealStrategyforanAnytimeUsage ConclusionandFutureWork Breadth-First Search Principle of BFS L Selectsboxes in followingaFIFO strategy. Main behavior Exploresuniformelythewhole searchspace. ⇒ Attime T no e -boxesare computed. i R.Chenouard,A.GoldsztejnandC.Jermann SearchStrategiesforanAnytimeUsageoftheBPA 3/16 TheBranchandPruneAlgorithm TheMostDistantFirstStrategy Introduction TheDepthandMostDistantFirstStrategy ExistingStrategies Experiments IdealStrategyforanAnytimeUsage ConclusionandFutureWork Depth-First Search Principle of DFS L Selectsboxes in followingaLIFO strategy. Main behavior e Descendsrapidlyto -boxesthenfinds themby neighborhood. ⇒ Attime T manysimiliare -boxesare computed. i R.Chenouard,A.GoldsztejnandC.Jermann SearchStrategiesforanAnytimeUsageoftheBPA 4/16 TheBranchandPruneAlgorithm TheMostDistantFirstStrategy Introduction TheDepthandMostDistantFirstStrategy ExistingStrategies Experiments IdealStrategyforanAnytimeUsage ConclusionandFutureWork Ideal Search Strategy for an Anytime Usage Principle L Selectsboxes in mixingBFSand DFSprinciples. Main behavior Exploresuniformelythewhole searchspaceandfind e well-ditributed -boxesat earlystage ofthe search. R.Chenouard,A.GoldsztejnandC.Jermann SearchStrategiesforanAnytimeUsageoftheBPA 5/16 TheBranchandPruneAlgorithm Principle TheMostDistantFirstStrategy MinDistEvaluationExample TheDepthandMostDistantFirstStrategy ASimpleExample Experiments TheoreticalProperty ConclusionandFutureWork Most Distant First Strategy Principle of MDFS L e S Selectin the mostdistantbox to -boxesin . Distance evaluation MinDist(x)=min{d(x,[x ]),...,d(x,[x ])}, (1) 1 m [x1],...,[xm] whered isthe maximaldistancebetweenpointsof two boxes. R.Chenouard,A.GoldsztejnandC.Jermann SearchStrategiesforanAnytimeUsageoftheBPA 6/16 TheBranchandPruneAlgorithm Principle TheMostDistantFirstStrategy MinDistEvaluationExample TheDepthandMostDistantFirstStrategy ASimpleExample Experiments TheoreticalProperty ConclusionandFutureWork MinDist Evaluation Example MinDist(A)=min{d(A,[s ]),d(A,[s ])}=d(A,[s ]), 1 2 1 [s1],[s2] MinDist(B)=min{d(B,[s ]),d(B,[s ])}=d(B,[s ]). 1 2 2 [s1],[s2] R.Chenouard,A.GoldsztejnandC.Jermann SearchStrategiesforanAnytimeUsageoftheBPA 7/16 TheBranchandPruneAlgorithm Principle TheMostDistantFirstStrategy MinDistEvaluationExample TheDepthandMostDistantFirstStrategy ASimpleExample Experiments TheoreticalProperty ConclusionandFutureWork MDFS : a simple example R.Chenouard,A.GoldsztejnandC.Jermann SearchStrategiesforanAnytimeUsageoftheBPA 8/16 TheBranchandPruneAlgorithm Principle TheMostDistantFirstStrategy MinDistEvaluationExample TheDepthandMostDistantFirstStrategy ASimpleExample Experiments TheoreticalProperty ConclusionandFutureWork MDFS Theoretical Property e The nextcomputed -boxx satisfies: m+1 |d∗ − MinDist(x )|≤e , m+1 [x1],...,[xm] whered∗ is theglobal maximumof MinDist. Therefore: lim MinDist(x )=d∗ m+1 e →0[x1],...,[xm] ⇒ Slowdiscoveryof e -boxesdue to breadthexploration. R.Chenouard,A.GoldsztejnandC.Jermann SearchStrategiesforanAnytimeUsageoftheBPA 9/16 TheBranchandPruneAlgorithm TheMostDistantFirstStrategy Principle TheDepthandMostDistantFirstStrategy ASimpleExample Experiments DMDFSandMDFSTheoreticalcomparison ConclusionandFutureWork Depth and Most Distant First Strategy Principle of DMDFS e MixingMDFSand DFSto quickenthediscoveryof -boxes: I Selectboxes in L followinga LIFO∗ strategy. L S I Sort wrt.(1) aftereach insertionin . ∗HeuristicbasedonMinDistfor depthsearch. R.Chenouard,A.GoldsztejnandC.Jermann SearchStrategiesforanAnytimeUsageoftheBPA 10/16
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