比式和问题的全局优化算法

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1、equivalentproblem，weestablisharelaxationlinearprogramminganddevelopacceleratingmeasures((DT)and(BTT))toproposeanewacceleratingglobaloptimizationalgorithm．Themeasuresareincorporatedintothebranch-and-boundprocessasanacceleratingde-vice，80thatthesolutionprocedureisenhance

2、dandtheproposedalgorithmhasbetterperformance．Numericalexperimentsshowthatcomputationalefficiencycanbeimprovedobviously,specially,thenumberofthebrangchingoperationscanbesignificantlyreduced．Finally,wecombinetheglobaloptimizationmethodproposedbySheneta1．withasuitabledele

3、tingtechniquetoproposeanewacceleratingtrapezoidalalgorithmforsolvingnonlinearsum-of-ratiosproblem(SRP)overaconvexset．Thistechniqueoffersapos-sibilitytocutawayalloralargepartofthecurrentlyinvestigatedregioninwhichtheoptimalsolutionoftheproblemof(SRP)doesnotexist，andcanb

4、eseenasanacceleratingdevicefortheglobaloptimizationalgorithmofthenonlinearsum-of—ratiosproblem．Thecomparedresultsinthenumbericalexperimentsshowthatthecomputa-tionalefficiencyisobviouslyimprovedbyusingthisnewtechnique．KEYWORDS：Globaloptimization，Sum-of-ratios，Branch-and

5、-bound，Concaveenve-lope，Deletingtechnique，BoundingtighteningtechniqueIV摘要ABSTRACT第一章§1．1§1．2§1．3目录IIII绪论1全局优化算法概述．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．1本文所研究问题的背景和现状．．．．．．．．．．．．．．．．．．．．．．．．4基本理论知识．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．5第二章求解线性比式和问题的加速梯形算法9鹭。⋯§2．1引言．．．．．．。．．．．．．．．．．

6、．．．．．．．．．．．．．．．．．．．．．．9§2．2预备知识．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．§2．3加速技术．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．§2．3．1删除技术(DT)．．．．．．．．．．．．．．．．．．．．．．．．．．．．．§2．3．2界紧技术(BTT)．．．．．．．．．．．．．．．．．．．．．．．．．．．．§2．4算法及其收敛性．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．§2．5数值结果．．．．．．．．．．．．．．．．．．．．．

7、．．．．．．．．．．．．．．．§2．6小结．．．．．．．．．．．．．．。．．．．．．．．．．．．．．．．．．．．．．．．第三章§3．1§3．2§3．3一类非线性比式和问题的全局求解方法35引言．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．35删除技术．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．35算法及其收敛性分析．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．41V9"M均组嬲∞§3．3．1算法步骤．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．

8、．4l§3．3．2算法收敛性分析．．．．．．．．．．．．．．．．．．．．．．．．．．．．42§3．4数值实验．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．43结论参考文献致谢攻读硕士学位期间写作或接受的论文独