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改进的细菌觅食优化算法求解0-1背包问题.docx

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改进的细菌觅食优化算法求解0-1背包问题 Title:ImprovedBacteriaForagingOptimizationAlgorithmforSolvingthe0-1KnapsackProblem Abstract: The0-1KnapsackProblemisacombinatorialoptimizationproblemwidelystudiedincomputerscienceandmathematics.Itinvolvesselectingasubsetofitemswithvaryingweightsandvaluestomaximizethetotalvaluewhilekeepingthetotalweightwithinagivencapacity.Inrecentyears,theBacteriaForagingOptimizationAlgorithm(BFOA)hasgainedattentionasanefficientmetaheuristicalgorithmforsolvingcomplexoptimizationproblems.Inthispaper,weproposeanimprovedversionoftheBFOAforsolvingthe0-1KnapsackProblem.Experimentalresultsshowthattheproposedalgorithmoutperformsexistingapproachesintermsofsolutionqualityandconvergencespeed. 1.Introduction The0-1KnapsackProblem(KP)isaclassicNP-hardproblemwithbroadapplicationsinvariousfieldssuchasresourceallocation,productionplanning,andfinancialportfoliooptimization.Theprobleminvolvesselectingasubsetofitemsfromagivenset,eachwithaweightandavalue,tomaximizethetotalvaluewithoutexceedingtheknapsack'scapacity.TheKPisachallengingtaskduetoitscombinatorialnature,andtraditionaloptimizationalgorithmsoftenstruggletofindoptimalsolutionswithinareasonabletimeframe. 2.BacteriaForagingOptimizationAlgorithm(BFOA) TheBFOAisabio-inspiredstochasticoptimizationalgorithminspiredbytheforagingbehaviorofbacteria.Itmimicsthemovementandinteractionofbacteriainanutrient-richenvironment.Thealgorithmcomprisesfourmainsteps:chemotaxis,swarming,reproduction,andelimination-dispersal.Ineachstep,thebacteriaadjusttheirpositionsbasedonthelocalsearch,communicationwithneighbors,andreproduction. 3.ProposedImprovedBFOAforKP Inthissection,wepresentthedetailsoftheproposedimprovedBFOAforsolvingtheKP.Themainmodificationsincludetheintroductionofalocalsearchmechanismandarecombinationoperatortoenhanceexploitationandexplorationabilities.Additionally,adynamicpenaltyfunctionisintegratedtohandletheconstraintviolationissues.TheimprovedBFOAaimstostrikeabalancebetweenexplorationandexploitationtoimprovethesearchqualityandconver