预览加载中，请您耐心等待几秒...

求线性比试和问题的确定性全局优化算法(英文).docx

预览
1/2
2/2

在线预览结束，喜欢就下载吧，查找使用更方便

下载提示 文本预览

如果您无法下载资料，请参考说明：

1、部分资料下载需要金币，请确保您的账户上有足够的金币

2、已购买过的文档，再次下载不重复扣费

3、资料包下载后请先用软件解压，在使用对应软件打开

求线性比试和问题的确定性全局优化算法(英文) Introduction: Optimizationproblemsareubiquitousinvariousfields,includingengineering,computerscience,economics,andmanyotherfields.Linearprogrammingisawidelyusedoptimizationtechniquethatcanhandlebothlinearobjectivesandconstraints.However,linearprogrammingmaynotprovidethebestsolutionforallcases,especiallywhendealingwithcomplexnonlinearproblems.Insuchcases,globaloptimizationalgorithmsarerequiredtofindthebestsolution. Thispaperpresentsareviewofdeterministicglobaloptimizationalgorithms.Thesealgorithmsareclassifiedasinterval-basedmethods,branch-and-boundmethods,andconvexification-basedmethods.Foreachclass,wediscussthemainfeatures,advantages,andlimitations. Interval-BasedMethods: Interval-basedmethodsarebasedonenclosureoffeasibleregions.Thefeasiblesolutionspaceisdividedintoasetofboxes,wheretheminimumandmaximumvaluesoftheobjectivefunctionarecalculatedforeachbox.Thealgorithmtheneliminatesboxesthatcannotcontaintheoptimalsolutionandcontinuessearchingtheremainingboxesuntilthebestsolutionisfound.Interval-basedmethodsarerobustandcanhandleglobaloptimizationproblemswithmultiplelocaloptima. Themainadvantageofinterval-basedmethodsistheirabilitytofindtheglobalminimumofnonlinearfunctionswithguaranteedconvergence.However,thesemethodscanbecomputationallyexpensivesincetheyrequirethecalculationoffunctionvaluesforallboxes.Moreover,interval-basedmethodscanbehighlysensitivetothechoiceofinitialboxsizeandpartitioning. Branch-and-BoundMethods: Branch-and-boundmethodsarewidelyusedinglobaloptimizationduetotheirabilitytohandlenonlinearandnon-convexoptimizationproblems.Thealgorithmdividesthesearchspaceintoasetofsub-regionsandtheniterativelysolvesthesub-regionsusinglinearprogramming.Thealgorithmmaintainsalowerboundontheobjectivefunction,andifasub-region'slowerboundexceedsthecurrentglobalupperbound,thesub-regioniseliminatedfromfurtherconsideration. Theadvantageofbranch-and-boundmethodsistheirabilitytoprovidereliableglobaloptimizationresults,especiallyfornon-convexproblemswithmany