简介：Thispaperaimsatprovidinganuncertainbilevelknapsackproblem(UBKP)model,whichisatypeofBKPsinvolvinguncertainvariables.AndthenanuncertainsolutionfortheUBKPisproposedbydefiningPENashequilibriumandPEStackelbergNashequilibrium.Inordertoimprovethecomputationalefficiencyoftheuncertainsolution,severaloperators(binarycodingdistance,inversionoperator,explosionoperatorandbinarybacklearningoperator)areappliedtothebasicfireworksalgorithmtodesignthebinarybackwardfireworksalgorithm(BBFWA),whichhasagoodperformanceinsolvingtheBKP.Asanillustration,acasestudyoftheUBKPmodelandthePEuncertainsolutionisappliedtoanarmamentstransportationproblem.

简介：Adiscretedifferentialevolutionalgorithmcombinedwiththebranchandboundmethodisdevelopedtosolvetheintegerlinearbilevelprogrammingproblems,inwhichbothupperlevelandlowerlevelvariablesareforcedtobeinteger.Anintegercodingforupperlevelvariablesisadopted,andthenadiscretedifferentialevolutionalgorithmwithanimprovedfeasibility-basedcomparisonisdevelopedtodirectlyexploretheintegersolutionattheupperlevel.Foragivenupperlevelintegervariable,thelowerlevelintegerprogrammingproblemissolvedbytheexistingbranchandboundalgorithmtoobtaintheoptimalintegersolutionatthelowerlevel.Inthesameframeworkofthealgorithm,twootherconstrainthandlingmethods,i.e.thepenaltyfunctionmethodandthefeasibility-basedcomparisonmethodarealsotested.Theexperimentalresultsdemonstratethatthediscretedifferentialevolutionalgorithmwithdifferentconstrainthandlingmethodsiseffectiveinfindingtheglobaloptimalintegersolutions,buttheimprovedconstrainthandlingmethodperformsbetterthantwocomparedconstrainthandlingmethods.