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ID:41281319
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时间:2019-08-21
《AdvancedComputerGraphics-Virginia:先进的计算机图形-弗吉尼亚》由会员上传分享,免费在线阅读,更多相关内容在教育资源-天天文库。
1、AdvancedComputerGraphicsSpring2002ProfessorBroganSimulatedAnnealingMonteCarloapproachforminimizingmultivariatefunctionsMonteCarlo=Random=StochasticRequiresone‘goodness’metric–resultofevaluationfunctionMultivariate–selectsmultipleparametervaluestominimizeevaluationfunctionAl
2、gorithmOutlineSelectsomeinitialguessofevaluationfunctionparameters:x0Evaluateevaluationfunction,E(x0)=vComputearandomdisplacement,x’0TheMonteCarloeventEvaluateE(x’0)=v’Ifv’3、tisAnnealing?Usedtotreatwork-hardenedpartsmadeoutoflow-carbonsteelsHeattoaspecifictemperature,thensoak,andthencoolslowlyThermodynamics–moleculescanmovearoundwhentheyareathightemps.SlowcoolingpermitsselforganizationintominimumenergyconfigurationsBacktoourSituationWeapproxima4、tenature’salignmentofmoleculesbyallowinguphilltransitionsexp(-E/kT)BoltzmannProbabiltyDistributionEvenwhenTissmall,adisruptionispossibleexp(-(E2-E1)/kT)MetropolisStepTherateatwhichTisdecreasedandtheamountitisdecreasedisprescribedbyanannealingscheduleWhathavewegot?Alwaysm5、ovedownhillifpossibleSometimesgouphillOptimalityguaranteedwithslowannealingscheduleNoneedforsmoothsearchspaceNoderivativesCanbediscretesearchspaceTravelingsalesmanproblemOptimizationGiven:Whatvalueofminimizesf()?Expensivetocomputerf()?Expensivetocomputepartialsoff()=Jacobia6、n?Globalvs.localsolutionsConstrainedOptimizationMinimizeSubjectto:ThereareapriorilimitationsonthepossiblevaluesoftheindependentvariablesLinearProgrammingSpecialtypeofconstrainedoptimizationFunctionf()andconstraintsarelinear
3、tisAnnealing?Usedtotreatwork-hardenedpartsmadeoutoflow-carbonsteelsHeattoaspecifictemperature,thensoak,andthencoolslowlyThermodynamics–moleculescanmovearoundwhentheyareathightemps.SlowcoolingpermitsselforganizationintominimumenergyconfigurationsBacktoourSituationWeapproxima
4、tenature’salignmentofmoleculesbyallowinguphilltransitionsexp(-E/kT)BoltzmannProbabiltyDistributionEvenwhenTissmall,adisruptionispossibleexp(-(E2-E1)/kT)MetropolisStepTherateatwhichTisdecreasedandtheamountitisdecreasedisprescribedbyanannealingscheduleWhathavewegot?Alwaysm
5、ovedownhillifpossibleSometimesgouphillOptimalityguaranteedwithslowannealingscheduleNoneedforsmoothsearchspaceNoderivativesCanbediscretesearchspaceTravelingsalesmanproblemOptimizationGiven:Whatvalueofminimizesf()?Expensivetocomputerf()?Expensivetocomputepartialsoff()=Jacobia
6、n?Globalvs.localsolutionsConstrainedOptimizationMinimizeSubjectto:ThereareapriorilimitationsonthepossiblevaluesoftheindependentvariablesLinearProgrammingSpecialtypeofconstrainedoptimizationFunctionf()andconstraintsarelinear
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