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摘要遗传算法起源于对生物系统所进行的计算机模拟。美国密执安大学的Holland教授及其学生受到这种生物模拟技术的启发，创造出了一种基于生物遗传和进化机制的适合于复杂系统优化计算的自适应概率优化技术---遗传算法。证券投资组合优化问题的实质就是有限的资产在具有不同风险收益特性的证券之间的优化配置问题。因此，本文根据上述要求把交易成本和股票的整手买卖引入含有风险偏好的Markowitz组合投资模型，并对证券组合进行分类约束来降低风险，从而构造了含有约束的混合整数非线性规划模型。遗传算法是一类模拟自然界生物进化过程与机制，求解问题的自组织和自适应的人工智能技术。由于其运行简单和解决问题的有效能力而被广泛应用到众多领域。但是它也容易产生早熟现象以及局部搜索能力比较差，所以对很多问题而言，基本遗传算法并不是解决问题的最有效方法。因此本文对基本遗传算法的一些算子进行了改进，获得了较满意的结果。本文提出的组合投资模型在求解上存在一定的难度，采用遗传算法求解。在计算机上用Matlab7.0编程实现。关键字：遗传算法；生物模拟；投资组合；交易成本；ABSTRACTGeneticalgorithmoriginatedinbiologicalsystemsthroughthecomputersimulations.HollandMichiganUniversityprofessorandhisstudentsaresubjecttothisbiologicalsimulationtechnologyinspiredtocreateabio-basedgeneticandevolutionaryoptimizationofcomplexsystemsforadaptiveprobabilitycalculation---geneticalgorithmoptimizationtechnique.PortfolioOptimizationessenceoftheproblemisthelimitedassetswithdifferentriskandreturncharacteristicsoftheoptimalallocationbetweenthesecuritiesissue.Therefore,thispaperaccordingtotherequirementsofthetransactioncostsandstockscontainingwholelotintroducingriskappetiteMarkowitzportfoliomodel,andclassifyconstraintsportfoliotoreducerisk,whichisconstructedwithconstrainedmixed-integernonlinearprogrammingmodelGeneticalgorithmsareaclassofsimulationofnaturalbiologicalevolutionandmechanismsforsolvingtheproblemofself-organizationandadaptiveartificialintelligencetechnology.Becauseofitsoperationalsimplicityandabilitytosolveproblemseffectivelybeenwidelyappliedtomanyfields.Butitisalsopronetoprematureandrelativelypoorlocalsearchability,somanyproblems,thebasicgeneticalgorithmisnotthemosteffectivewaytosolvetheproblem.Thisarticleonsomeofthebasicgeneticalgorithmhasbeenimprovedoperatortoobtainamoresatisfactoryresult.Theproposedmodelforportfolioinvestmentinthesolutionthereisacertaindegreeofdifficulty,usinggeneticalgorithm.OnacomputerusingMatlab7.0programming.Keyword：geneticalgorithm；biologicalsimulations；Investmentportfolio；Transactioncosts；目录引言-------------------------------------------------------------------------------------------------------4第一章遗传算法概述-------------------------------------------------------------------------------------51.1遗传算法的形式------------------------------------------------------------------------------------51.2遗传算法的运算过程------------------------------------------------------------------------------61.3基本遗传算法的构成------------------------------------------------------------------------------71.4基本遗传算法的形式化定义---------------------------------------------------------------------7第二章遗传算法的基本实现技术----------------------------------------------------------------------82.1遗传算法的编码原则-----------------------------------------------------------------------------82.1.1二进制编码方法---------------------------------------------------------------------------82.1.2浮点数编码方法：------------------------------------------------------------------------92.2遗传算法的适应度函数--------------------------------------------------------------------------92.2.1乘幂尺度变换-----------------------------------------------------------------------------102.2.2指数尺度变换-----------------------------------------------------------------------------102.3遗传算法的选择算子----------------------------------------------------------------------------102.3.1比例选择-----------------------------------------------------------------------------------102.3.2最优保存策略-----------------------------------------------------------------------------102.3.3确定式采样选择--------------------------------------------------------------------------112.4交叉算子-------------------------------------------------------------------------------------------112.4.1单点交叉-----------------------------------------------------------------------------------112.4.2算数交叉-----------------------------------------------------------------------------------112.5变异算子-------------------------------------------------------------------------------------------122.5.1基本位变异--------------------------------------------------------------------------------122.5.2均匀变异-----------------------------------------------------------------------------------12第三章投资组合------------------------------------------------------------------------------------------133.1投资组合理论的提出----------------------------------------------------------------------------133.2证券组合投资理论-------------------------------------------------------------------------------143.3马克威茨的均值—方差模型--------------------------------------------------------------------143.3.1单个资产的收益、风险和资产间的相互关系-------------------------------------143.3.2资产组合的收益和风险-----------------------------------------------------------------153.4现代投资理论的组成和发展-------------------------------------------------------------------183.5投资组合的应用----------------------------------------------------------------------------------18第四章基于改进遗传算法的有交易成本的组合投资问题---------------------------------------204.1模型的建立与分析-------------------------------------------------------------------------------214.1.1股票交易额不可分割及无风险投资-------------------------------------------------214.1.2交易成本------------------------