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1、ComputationalOptimizationandApplications,18,295–309,2001°c2001KluwerAcademicPublishers.ManufacturedinTheNetherlands.IntegratingSQPandBranch-and-BoundforMixedIntegerNonlinearProgrammingSVENLEYFFERsleyffer@mcs.dundee.ac.ukDepartmentofMathematics,UniversityofDundee,Dundee,U.K.ReceivedNovember
2、9,1998;AcceptedAugust31,1999Abstract.ThispaperconsidersthesolutionofMixedIntegerNonlinearProgramming(MINLP)problems.ClassicalmethodsforthesolutionofMINLPproblemsdecomposetheproblembyseparatingthenonlinearpartfromtheintegerpart.Thisapproachislargelyduetotheexistenceofpackagedsoftwareforsolv
3、ingNonlinearProgramming(NLP)andMixedIntegerLinearProgrammingproblems.Incontrast,anintegratedapproachtosolvingMINLPproblemsisconsideredhere.Thisnewalgorithmisbasedonbranch-and-bound,butdoesnotrequiretheNLPproblemateachnodetobesolvedtooptimality.Instead,branchingisallowedaftereachiterationof
4、theNLPsolver.Inthisway,thenonlinearpartoftheMINLPproblemissolvedwhilstsearchingthetree.ThenonlinearsolverthatisconsideredinthispaperisaSequentialQuadraticProgrammingsolver.Anumericalcomparisonofthenewmethodwithnonlinearbranch-and-boundispresentedandafactorofupto3improvementoverbranch-and-b
5、oundisobserved.Keywords:mixedintegernonlinearprogramming,branch-and-bound,sequentialquadraticprogramming1.IntroductionThispaperconsidersthesolutionofMixedIntegerNonlinearProgramming(MINLP)prob-lems.Problemsofthistypearisewhensomeofthevariablesarerequiredtotakeintegervalues.ApplicationsofMI
6、NLPproblemsincludethedesignofbatchplants(e.g.[17]and[21]),thesynthesisofprocesses(e.g.[7]),thedesignofdistillationsequences(e.g.[27]),theoptimalpositioningofproductsinamulti-attributespace(e.g.[7]),theminimizationofwasteinpapercutting[29]andtheoptimizationofcorereloadpatternsfornuclearreac
7、tors[25].ForacomprehensivesurveyofMINLPapplicationsseeGrossmannandKravanja[16].MINLPproblemscanbemodelledinthefollowingform8>:x2X;y2Yinteger;whereyaretheintegervariablesmodellingforinstancedecisions(y2f0;1g),numbersofequi
