A hybridofNestedPartition,BinaryAntSystem,andLinearProgrammingforthe multidimensional knapsackproblem

This workpresentsahybridalgorithmofNestedPartition(NP),BinaryAntSystem(BAS),andLinear Programming (LP)tosolvethemultidimensionalknapsackproblem(MKP).ThehybridNP+BAS+LPalgo- rithm takesadvantageoftheglobalsearchstrategiesoftheNPalgorithm;theabilityofBAStoquickly generate goodsolutionsandincorporatesinformationobtainedfromsolvingaLPrelaxationoftheMKPto help guidethesearch.Itthusincorporatesboththelowerbounds(LB),foundbytheBAS,andtheupper bounds (UB),foundbysolvingtherelaxedLP,intothesearchbyembeddingbothintheNPframework. An adjustablecomputationbudgetisimplementedwherethenumberofsamplesincreasesiftheLB and theUBpointtodifferentpromisingsubregions.Theproposedhybridiscomparedtostate-of-the-art solution techniquesandisfoundtobeoneofthebestalgorithmsintermsofthequalityofsolutions obtained andCPUtimerequirements.