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Runningtitle:lietal.on….

animprovedshuffledfrog-leapingalgorithmforknapsackp roblem

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abstract

shuffledfrog-leapingalgorithm(sFla)haslongbeenconsi deredasnewevolutionaryalgorithmofgroupevolution,and hasahighcomputingperformanceandexcellentabilityforg lobalsearch.knapsackproblemisatypicalnp-completepro

blem.Forthediscretesearchspace,thispaperpresentsthe improvedsFla,andsolvestheknapsackproblembyusingthea lgorithm.experimentalresultsshowthefeasibilityandef fectivenessofthismethod.

keywords:shuffledfrog-leapingalgorithm;knapsackprob lem;optimizationproblem

0introduction

knapsackproblem(kp)isaverytypicalnp-hardprobleminco mputerscience,whichwasfirstproposedandstudiedbydant zinginthe1950s.therearemanyalgorithmsforsolvingthek napsackproblem.classicalalgorithmsforkparethebranch andboundmethod(babm),dynamicprogrammingmethod（分支界定法和动态规划

法）,etc.however,mostofsuchalgorithmsareover-relian ceonthefeaturesofproblemitself,thecomputationalvolu meofthealgorithmincreasesbyexponentially,andthealgo rithmneedsmoresearchingtimewiththeexpansionofthepro blem.intelligentoptimizationproblemforsolvingnparet heantcolonyalgorithm,greedyalgorithm,etc.suchalgori thmsdonotdependonthecharacteristicsoftheproblemitse

lf,andhavethestrongglobalsearchability.Relatedstudi eshaveshownthatitcaneffectivelyimprovetheabilitytos earchfortheoptimalsolutionbycombiningtheintelligent optimizationalgorithmwiththelocalheuristicsearching algorithm.

shuffledfrog-leapingalgorithmisanewintelligentoptim izationalgorithm,itcombinestheadvantagesofmemealgor ithmbasedongeneticevolutionandparticleswarmalgorith mbasedongroupbehavior.ithasthefollowingcharacterist ics:simpleinconcept,fewparameters,thecalculationspe ed,globaloptimizationability,easytoimplement,etc.an dhasbeeneffectivelyusedinpracticalengineeringproble ms,suchasresourceallocation,jobshopprocessarrangeme nts,travelingsalesmanproblem,0/1knapsackproblem,etc .however,thebasicleapfrogalgorithmiseasytoblendinto localoptimum,andthusthispaperimprovedtheshuffledfro g-leapingalgorithmtosolvecombinatorialoptimizationp roblemssuchasknapsackproblem.experimentalresultssho wthatthealgorithmis

effectiveinsolvingsuchproblems.

1themathematicalmodelofknapsackproblem

knapsackproblemisanp-completeproblemaboutcombinator ialoptimization,whichisusuallydividedinto0/1knapsac kproblem,completeknapsackproblem,multipleknapsackpr oblem,mixedknapsackproblem,thelatterthreekindscanbe transformedintothefirst,therefore,thepaperonlydiscu ssedthe0/1knapsackproblem.themathematicalmodelof0/1 knapsackproblemcanbedescribedas:

nmaxxivii0nxwc(x1or0,i1,2,...,n)iiii0

where:nisthenumberofobjects;wiistheweightoftheithob ject(i=1,2…

n);viisthevalueoftheithobject;xiisthechoicestatusof theithobject;whentheithobjectisselectedintoknapsack ,definingvariablexi=1,otherwisexi=0;cisthemaximumca pacityofknapsack.

2thebasicshuffledfrog-leapingalgorithm

itgeneratespfrogsrandomly,eachfrogrepresentsasoluti onoftheproblem,denotedbyui,whichisseenastheinitialp opulation.calculatingthefitnessofallthefrogsinthepo pulation,andarrangingthefrogaccordingtothedescendin