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带系数线性比式和问题的全局优化方法(英文).docx

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带系数线性比式和问题的全局优化方法(英文) GlobalOptimizationMethodforLinearRatioEquationsandProblemswithCoefficients Linearratioequationsareatypeofequationsthatinvolveratiosoflinearexpressionsandarecommonlyusedtomodelreal-worldsituations.Theseequationscancomeindifferentforms,suchascontinuousratioequationsordiscreteratioequations.Thecoefficientsintheseequationsrepresentthefactorsthatinfluencetheratiosandoftenplayacrucialroleindeterminingthesolutions. Inrecentyears,therehasbeenagrowinginterestindevelopingglobaloptimizationmethodsforlinearratioequationswithcoefficients.Suchmethodsaimtofindtheglobalminimumormaximumofalinearratioequationoveragivendomain.Thisisachallengingtaskduetothenonlinearityandnon-convexityoftheequationsinvolved,aswellasthehighdimensionalityofthesolutionspace. Oneapproachtoglobaloptimizationoflinearratioequationsisbasedonconvexrelaxationtechniques.Theideaistotransformtheoriginalnon-convexoptimizationproblemintoaconvexonebyrelaxingtheconstraintsontheratiosandintroducingauxiliaryvariables.Thisallowsfortheuseofpowerfulconvexoptimizationalgorithms,suchassemidefiniteprogrammingorconvexprogramming,tofindtheglobalsolution. Anotherpopularmethodforglobaloptimizationoflinearratioequationsisbasedongeneticalgorithms.Thesealgorithmsareinspiredbytheprocessofnaturalselectionandevolutionandareparticularlywell-suitedforsolvingnonlinear,non-smooth,andnon-convexoptimizationproblems.Thekeyideaistogenerateapopulationofcandidatesolutionsandletthemevolveovertimethroughaseriesofselection,crossover,andmutationoperations.Thebestsolutionsareretainedforthenextgeneration,whiletheworstonesarediscarded.Thisprocesscontinuesuntilasatisfactorysolutionisfound. Otherglobaloptimizationmethodsforlinearratioequationswithcoefficientsincludesimulatedannealing,particleswarmoptimization,anddifferentialevolution.Thesemethodsarebasedondifferentoptimizationprinciplesandhavetheirownstrengthsandweaknesses.Thechoiceofmethoddependsonthespecificproblemathand,thecharacteristicsofthesolutionspace,andthecomputationalresour