美赛2012b题outstanding

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1、Control#15421SUMMARYInthispaperwepresentamethodofoptimallyschedulingtripstravellingdownBigLongRiver.Ourmodeltakesthenumberofcampsitesandtherelativedistributionoftypesoftripsasparametersandgeneratesaschedulethatmaximizesthenumberoftripsanddetermineswheneachshouldbelaun

2、ched.WedeterminetheoptimallaunchdateofeachtripbymodelingthecollectionoftripsasachemicalsystemofcrystallizingmoleculesandusethemethodofSimulatedAnnealingtogeneratealaunchscheduleinwhichhumaninteractionsareminimized.Startingwithamathematicallyderivedupperboundonthenumbe

3、roftripswereducethenumberoftripsuntilwefindanamountwhichallowsthemodeltoproduceavalidschedule.Inthispaperwetakeintoaccountusercomfortandemergencyneedsbyschedulingthreecampsitespertrippernight.Thispaperalsodiscussestheflexibilityofourmodelandpresentssampleoutputforause

4、r-definedinput.Team15421Page2of16CrystallizationofMetalParticlesasaModelforOptimalRiverRaftingControl#15421February13,2012InthispaperwepresentamethodofoptimallyschedulingtripstravellingdownBigLongRiver.Ourmodeltakesthenumberofcampsitesandtherelativedistributionoftypes

5、oftripsasparametersandgeneratesaschedulethatmaximizesthenumberoftripsanddetermineswheneachshouldbelaunched.WedeterminetheoptimallaunchdateofeachtripbymodelingthecollectionoftripsasachemicalsystemofcrystallizingmoleculesandusethemethodofSimulatedAnnealingtogeneratealau

6、nchscheduleinwhichhumaninteractionsareminimized.Startingwithamathematicallyderivedupperboundonthenumberoftripswereducethenumberoftripsuntilwefindanamountwhichallowsthemodeltoproduceavalidschedule.Inthispaperwetakeintoaccountusercomfortandemergencyneedsbyschedulingthre

7、ecampsitespertrippernight.Thispaperalsodiscussestheflexibilityofourmodelandpresentssampleoutputforauser-definedinput.Team15421Page3of16Contents1.AssumptionsandRepresentations4a)GlobalAssumptions4b)ModelingaSingleTrip42.ModelingaSystemofTrips5a)AnnealingandCrystallizat

8、ioninChemistryandMetallurgy5b)Energy6c)SimulatedAnnealing:Overview6d)InputParameters7e)SimulatedAnnealing:Specifics7f)ThePro