Kernel search:Ageneralheuristicforthemulti-dimensionalknapsackproblem

In thispaperweapplythekernelsearchframeworktothesolutionofthestronglyNP-hardmulti- dimensionalknapsackproblem(MKP).Kernelsearchisaheuristicframeworkbasedonthe identificationofarestrictedsetofpromisingitems(kernel) andontheexactsolutionofILP sub-problems.Initially,thecontinuousrelaxationoftheMKP,solvedonthecompletesetofavailable items, isusedtoidentifytheinitialkernel.Then,asequenceofILPsub-problemsaresolved,whereeach sub-problemisrestrictedtothepresentkernelandtoasubsetofotheritems.EachILPsub-problem may findbettersolutionswithrespecttothepreviousoneandidentifyfurtheritemstoinsertintothe kernel.Thekernelsearchwasinitiallyproposedtosolveacomplexportfoliooptimizationproblem.In this paperweshowthatthemethodhasgeneralkeyfeaturesthatmakeitappropriatetosolveother combinatorialproblemsusingbinaryvariablestomodelthedecisionstoselectornotitems.Weadapt the kernelsearchtothesolutionofMKPandshowthatthemethodisveryeffectiveandefficientwith respecttoknownproblem-specificapproaches.Moreover,thebestknownvaluesofsomeMKP benchmarkproblemsfromtheMIPLIBlibraryhavebeenimproved.