廣東工業(yè)大學最優(yōu)化課程設(shè)計.doc

最優(yōu)化理論方法課 程 實 驗 報 告 項目名稱：最優(yōu)化學生班級：學生姓名：學生學號：完成日期：2015-11-01問題：1用黃金分割法求解，已知初始單谷區(qū)間，要求精度2用拋物線插值法求解，已知初始單谷區(qū)間解法：1、 本次計算采用java語言編程根據(jù)題意，定下如下變量變量與方法符號數(shù)據(jù)類型說明Gold_Optimal()String遞歸方法主體，完成求解，輸出最優(yōu)解坐標Function()double命題函數(shù)，返回函數(shù)值a_k,b_kdouble區(qū)間值，初始值為0，a_k,b_k表示區(qū)間a_n,b_ndouble兩個探測點，無初始值，a_n-0.382,b_n-0.618GOLD_LINE_UPfinal double0.618GOLD_LINE_DOWMfinal double0.382Ldouble精確度，定值為0.001主體遞歸如下public static String Gold_Optimal(double a,double b,double l) a_k = a ; /給區(qū)間賦值 b_k = b ; /給區(qū)間賦值 if(a_n=0) a_n = a_k + GOLD_LINE_DOWM*(b_k - a_k) ; /給探測點賦初始值 if(b_n=0) b_n = a_k + GOLD_LINE_UP*(b_k - a_k) ; /給探測點賦初始值 if(b_k - a_k)funtion(b_n)/遞歸分類，計算探測點b_n型 a_k = a_n ; a_n = b_n ; b_n = a_k + GOLD_LINE_UP*(b_k - a_k) ; else/遞歸分類，計算探測點a_n型 b_k = b_n ; b_n = a_n ; a_n = a_k + GOLD_LINE_DOWM*(b_k - a_k) ; return Gold_Optimal(a_k,b_k,l) ; 以上實現(xiàn)了計算最小值的遞歸操作，給初始探測點賦值也并到遞歸中，但設(shè)定了條件，他們都只能執(zhí)行一次，在遞歸中也分成了兩個類別。但是還差一個函數(shù)值，其實現(xiàn)如下：public static double funtion(double a) return a*(a + 2) ; 接著是主方法如下：public static void main(String args) System.out.println(Gold_Optimal(-3f,5f,0.001f); 輸出如下：2、本題同樣是采用java語言編程實現(xiàn)。題目采用以拋物線去逼近三次方程，找出最小值，由于計算xk比較繁瑣，同時又要多次計算，于是將其封裝于一個類中，如下：public class GetParabolaData private static double x1 , x2 , x3 ; /定義三個變量 private static double x_k ; /定義二次函數(shù)極小值點 public static double Funtion2(double x)/函數(shù)返回值 return 8 * x * x * x - 2 * x * x - 7 * x + 3 ; public GetParabolaData(double x1, double x2, double x3) /構(gòu)造函數(shù) this.x1 = x1; this.x2 = x2; this.x3 = x3; public static double getB1() /獲得B1 return (x2 * x2 - x3 * x3) * Funtion2(x1) ; public static double getB2()/獲得B2 return (x3 * x3 - x1 * x1) * Funtion2(x2) ; public static double getB3()/獲得B3 return (x1 * x1 - x2 * x2) * Funtion2(x3) ; public static double getC1()/獲得C1 return (x2 - x3) * Funtion2(x1) ; public static double getC2()/獲得C2 return (x3 - x1) * Funtion2(x2) ; public static double getC3()/獲得C3 return (x1 - x2) * Funtion2(x3) ; public static double getX_k() /獲得函數(shù)極小值 x_k = (getB1() + getB2() + getB3() / (2 * (getC1() + getC2() + getC3() ; return x_k; 如此一來，每次循環(huán)的時候只要通過3個變量實例化class GetParabolaData的對象即可，其遞歸方法如下：public static double Parabola_Optimal(double x1, double x2, double x3) paraboladata = new GetParabolaData(x1,x2,x3) ; /實例化，執(zhí)行全部計算 double x_k = paraboladata.getX_k() ; /獲得拋物線極小值點 /判斷是否遞歸結(jié)束 if(Math.abs(GetParabolaData.Funtion2(x_k) - GetParabolaData.Funtion2(x2)L) return x_k ; else /遞歸繼續(xù) if(x2GetParabolaData.Funtion2(x2) x3 = x_k ; / x1 x2 x_k else / x2 x_k x3 x1 = x2 ; x2 = x_k ; else / x1 x_k x2 x3 if(GetParabolaData.Funtion2(x_k)GetParabolaData.Funtion2(x2) x1 = x_k ; / x_k x2 x3 else / x1 x_k x2 x3 = x2 ; x2 = x_k ; return Parabola_Optimal(x1,x2,x3) ; 之后再配上主方法有： public static void main(String args)System.out.println(Parabola_Optimal(0f, 1f,2f); 顯示為：項目二 常用無約束最優(yōu)化方法（一）實驗目的編寫最速下降法、Newton法（修正Newton法）的程序。編程解決以下問題：1用最速下降法求2用Newton法求，初始點問題1.同樣采用java語言編寫，也包括一個屬于該問題的工具類與一個在主類里執(zhí)行的方法，工具類如下：/* * 最速下降法 */public class Adapter1 private double x1,x2; public Adapter1(double x1, double x2) this.x1 = x1;this.x2 = x2; public double Fution() return x1 * x1 + 25 * x2 *x2 ; public double derivativeFoution() double a = new double2 ; a0 = 2*x1 ; a1 = 50 * x2 ; return a ; public double derivativeFoution_D()return derivativeFoution() ;public boolean isCommuntinue(double e)double d = derivativeFoution_D()0 * derivativeFoution_D()0+ derivativeFoution_D()1 * derivativeFoution_D()1;return d (e * e); /truepublic double vual_y()return -(2 * x1 * derivativeFoution_D()0 + 50 * x2* derivativeFoution_D()1)/ (2 * derivativeFoution_D()0 + 50 * derivativeFoution_D()1);主類里調(diào)用該工具類的方法如下：/* * 最速下降法 */public double Lower(double x1 ,double x2)adapter1 = new Adapter1(x1, x2) ;double a = x1,x2 ;if(adapter1.isCommuntinue(E)/E=0.01double b = x1 + adapter1.vual_y() * adapter1.derivativeFoution_D()0,x2 + adapter1.vual_y() * adapter1.derivativeFoution_D()1 ;return Lower(b0,b1) ;elsereturn a ;結(jié)果顯示如下：問題2，同樣采用java語言編寫，也包括一個屬于該問題的工具類與一個在主類里執(zhí)行的方法，工具類如下：/* * 牛頓 */public class Adapter2 private double x1,x2 ;public Adapter2(double x1, double x2) this.x1 = x1;this.x2 = x2;/* * 一階梯度 */public double fDerivativeFoution() double a = new double2 ; a0 = 2* x1 - x2 - 10 ; a1 = 2 * x2 - x1 - 4 ; return a ; /* * 二階梯度 */public double tDerivativeFoution() double a =2,-1,-1,2 ; return a ; /* * 二階梯度的逆 * 一階梯度 */public double vual_Y()double a = new double2 ;a0 = (2 * fDerivativeFoution()0 + fDerivativeFoution()1) /3 ;a1 = (2 * fDerivativeFoution()1 + fDerivativeFoution()0) /3 ;return a ;public boolean isComtinue(double e)return (vual_Y()1 * vual_Y()1 + vual_Y()0 * vual_Y()0) (e * e);調(diào)用方法如下： /* * 牛頓法 */public static double Newton1(double x1 ,double x2)double a = new double2 ;adapter2 = new Adapter2(x1, x2) ;if(adapter2.isComtinue(E)a0 = x1 - adapter2.vual_Y()0 ;a1 = x2 - adapter2.vual_Y()1 ;return Newton1(a0 ,a1) ;elsea0 = x1 ;a1 = x2 ;return a;顯示結(jié)果如下：項目三 常用無約束最優(yōu)化方法（二）實驗目的編寫共軛梯度法、變尺度法（DFP法和BFGS法）程序。編程解決以下問題：1用共軛梯度法求得，取初始點，2用共軛梯度法求，自定初始點，3用DFP法求，初始點問題1，實現(xiàn)共軛梯度法的工具類如下：/* * 共軛 */public class Adapter4 private double x1,x2,y1,y2 ; private boolean val = false ;public Adapter4(double x1, double x2) public double getD(double e,double x)double a = - getG(x)0 + getP(e,x) * e0,- getG(x)1 + getP(e,x) * e1 ;return a;public double setNextG(double k1,double k2)double a = 2 * k1,4 * k2 ;return a ;/* * 獲取g */public double getG(double x)double a = 2 * x0,4 * x1 ;return a ;/* * 計算 */public double getP(double e,doublex)return (getG(x)0 * getG(x)0 + getG(x)1 * getG(x)1)/(e0 * e0 + e1 * e1) ;/* * A */public double getA()double a = 2,0,0,8 ;return a;public double vaul_Y(double e)return (e0 * e0 + e1 * e1 )/(2 *e0 * e0 + 8 * e1 * e1);public boolean isComtinue(double e,double r)return (r0 * r0 + r1 * r1) (e * e) ;調(diào)用方法如下：/* * 共軛 */public static double GongE(double x,double e)adapter4 = new Adapter4(x0, x1) ;if(adapter4.isComtinue(E,e)double a = new double2 ;double d = new double2 ;a0 = x0 + adapter4.vaul_Y(e) * e0 ;a1 = x1 + adapter4.vaul_Y(e) * e1 ;d = adapter4.getD(e,a) ;return GongE(a , d) ;elsereturn x;結(jié)果顯示如下：問題2，同問題1，計算得結(jié)果如下：X1 = 0 ，x 2 = 0 ；問題3：DFP法，其工具類如下：/* * DPF * author 風飄絮 * */public class Adapter5 private double x1, x2;private double h;public Adapter5(double x1, double x2, double h) this.x1 = x1;this.x2 = x2;this.h = h; /* * 獲得G1 */private double getG() double a = 8 * x1 - 40, 2 * x2 - 12 ;return a;/* *計算D */public double getD() double a = - h0 * getG()0 - h1 * getG()1,-h2 * getG()0 - h3 * getG()1 ;return a;/* * 計算r */public double values() return (40 * getD()0 + 12 * getD()1 - 8 * getD()0 * x1 - 2* getD()1 * x2)/ (8 * getD()0 * getD()0 + 2 * getD()1 * getD()1);/* * 計算G2,進而計算H2 */private double getG2(double x) double a = 8 * x0 - 40, 2 * x1 - 12 ;return a;/* *獲得P */private double getP() double a = values() * getD()0, values() * getD()1 ;return a;/* * 計算Q，需要下一個x值 */private double getQ(double x) double a = getG2(x)0 - getG()0, getG2(x)1 - getG()1 ;return a;/* * H2 = w -M/T M=V*H1 */private double getw(double x) double a = h0+ (getP()0 * getP()0) / (getP()0 * getQ(x)0 + getP()1* getQ(x)1),h1+ (getP()0 * getP()1) / (getP()0 * getQ(x)0 + getP()1* getQ(x)1),h2+ (getP()1 * getP()0) / (getP()0 * getQ(x)0 + getP()1* getQ(x)1),h3+ (getP()1 * getP()1) / (getP()0 * getQ(x)0 + getP()1* getQ(x)1) ;return a;/* * 計算V */private double getV(double x)double a = getQ(x)0 * getQ(x)0 * h0 + getQ(x)0 * getQ(x)1 * h1 , getQ(x)0 * getQ(x)1 * h0 + getQ(x)1 * getQ(x)1 * h1 , getQ(x)0 * getQ(x)1 * h3 + getQ(x)0 * getQ(x)0 * h2, getQ(x)1 * getQ(x)0 * h2 + getQ(x)1 * getQ(x)1 * h3 ;return a;/* * 計算T */private double getT(double x)return getQ(x)0 * getQ(x)0 * h0 + getQ(x)0 * getQ(x)1 * h2 + getQ(x)0 * getQ(x)1 * h1 +getQ(x)1 * getQ(x)1 * h3 ;/* * 計算M */private double getM(double x)double a = getV(x)0 * h0 + getV(x)1 * h2, getV(x)0 * h1 + getV(x)1 * h3, getV(x)2 * h0 + getV(x)3 * h2, getV(x)2 * h1 + getV(x)3 * h3, ;return a;/* * 計算H */public double getH2(double x)double a = getw(x)0 - getM(x)0/getT(x), getw(x)1 - getM(x)1/getT(x), getw(x)2 - getM(x)2/getT(x), getw(x)3 - getM(x)3/getT(x) ;return a;/* * 判斷條件 */public boolean isComtinue(double e)return (getG()0 * getG()0 + getG()1 * getG()1) (e * e) ;調(diào)用方法如下：/* * DFP */private static double DFP(double x1, double x2, double h)double a = x1,x2 ;adapter5 = new Adapter5(x1, x2, h) ;if(adapter5.isComtinue(E)a0 = x1 + adapter5.values() * adapter5.getD()0 ;a1 = x2 + adapter5.values() * adapter5.getD()1 ;double H = adapter5.getH2(a) ;return DFP(a0, a1, H) ;elsereturn a;結(jié)果顯示如下：項目四 常用約束最優(yōu)化方法實驗目的編寫外點罰函數(shù)法、外點罰函數(shù)法的程序。編程解決以下問題：1用外點罰函數(shù)法編程計算精度 2用內(nèi)點罰函數(shù)法編程計算初始點取為，初始障礙因子取，縮小系數(shù)取問題1，鑒于ln x 編程求解比較麻煩，需要用泰勒展開式去必進球近似解，一旦求解，便會使目的變更，將會大邊幅地計算ln x ，所以將兩年ln x 變化為等價的x2 -1=0，進行求解，同樣，工具類如下：/* * 外罰 * author 風飄絮 * */public class Adapter6 private double x1,x2 ; public Adapter6(double x1,double x2) this.x1 = x1 ; this.x2 = x2 ; public double FuntionP(double e) double a = (x1 + x2 - 1) * (x1 + x2 - 1) + (x2-1)* (x2-1); System.out.println(a); return e*a; public void printFuntion() System.out.println(x1=+ x1 + ,x2= + x2); System.out.println(函數(shù)最小值 = + (x2 - x1); public Boolean ifComuntinue(double E,double