响应式网站开发实例,河南建设工程造价管理协会网站,友情链接交换形式,人工做流量的网站版权声明#xff1a;本文为博主原创文章#xff0c;未经博主同意不得转载#xff0c;博客主页 http://blog.csdn.net/i_love_home https://blog.csdn.net/zstu_wangrui/article/details/36242529 外点惩处函数法约束优化问题 外点法惩处函数#xff08;r添加#xff0c;SU… 版权声明本文为博主原创文章未经博主同意不得转载博客主页 http://blog.csdn.net/i_love_home https://blog.csdn.net/zstu_wangrui/article/details/36242529 外点惩处函数法·约束优化问题 外点法惩处函数r添加SUMT.java用于求解约束优化问题。解题过程例如以下 Step1 输入目标函数与约束方程构建外点惩处函数法求解方程求解初始化。 Step2 对求解方程进行一次无约束优化方法求解鲍威尔BWE得到新解。 Step3 新解与原解求误差。如误差满足精度要求则输出解否则添加因子r运行Step 2。 鲍威尔法BWE.java是N维无约束求解方法。须要调用一维求解方法。一维求解方法採用黄金切割法GSM.java。 在实现算法的代码中我去掉了输入处理人为地将输入确定下来。可降低代码篇幅。 我会将文件打包放入我的下载欢迎大家一起交流。 1外点法惩处函数 SUMT.java package ODM.Method;import java.util.Arrays;
/** 无约束优化方法惩处函数法·外点法*/
public class SUMT {private int n 6; // 维数变量个数private final double eps 1e-5; // 精度private final double c 5; // 递增系数private double r 0.1; // 惩处因子趋向无穷public SUMT(){Finit();AlgorithmProcess();AnswerOutput();}// 结果private double[] xs; private double ans;private void Finit(){xs new double[n];Arrays.fill(xs, 0);ans -1;//xs[0] xs[1] xs[2] xs[4] 1; xs[3] 3; xs[5] 5;}// 算法主要流程private void AlgorithmProcess(){int icnt 0; // 迭代次数double[] x new double[n]; // 转化为无约束优化问题的解while(true){icnt;BWE temp new BWE(n, r, xs); // 採用鲍威尔方法求函数最优解x temp.retAns();if(retOK(x) eps){ // 满足精度要求for(int i 0; i n; i)xs[i] x[i];ans temp.mAns();break;}r c * r;for(int i 0; i n; i)xs[i] x[i];}System.out.println(迭代次数 icnt);}// 收敛条件仅仅有一个不完好private double retOK(double[] x){double sum 0;for(int i 0; i n; i){sum Math.pow(x[i] - xs[i], 2);}return Math.sqrt(sum);}// 结果输出private void AnswerOutput(){for(int i 0; i n; i)System.out.printf(%.6f\t, xs[i]);System.out.printf(%.6f\n, ans);}public static void main(String[] args) {// TODO Auto-generated method stubnew SUMT();}}2鲍威尔法 BWE.java package ODM.Method;import java.util.Arrays;public class BWE {private double r;// 初始化变量private double[] x0; // 初始解集private double[][] e; // 初始方向private int N;final private double eps 1e-5;private Func F;// 初始化初始点, 初始矢量(n 个n*n 矩阵), 维数private void Init(int n){this.x0 new double[n];if(r -1)Arrays.fill(this.x0, 0);else{}this.e new double[n][n];for(int i 0; i n; i){for(int j 0; j n; j){if(i ! j)e[i][j] 0;else e[i][j] 1;}}this.N n;if(r ! -1)F new Func(r);elseF new Func();}// 搜索点, 方向矢量private double[][] x;private double[][] d;// 方向重排, 队列操作private void queueDir(double[] X){// 删去首方向for(int i 0; i N-1; i){for(int j 0; j N; j){d[i][j] d[i1][j];}}// 新方向插入队尾for(int i 0; i N; i)d[N-1][i] X[i];}private void Process(){x new double[N1][N];d new double[N][N];for(int j 0; j N; j)x[0][j] x0[j];for(int i 0; i N; i){for(int j 0; j N; j){d[i][j] e[i][j];}}int k 0; // 迭代次数while(k N){for(int i 1; i N; i){GSM t new GSM(F, x[i-1], d[i-1]);x[i] t.getOs();}double[] X new double[N];for(int i 0; i N; i)X[i] x[N][i] - x[0][i];queueDir(X);GSM t new GSM(F, x[N], X);x[0] t.getOs();k;}}// 答案打印private void AnswerOutput(){for(int i 0; i N; i){System.out.printf(x[%d] %.6f\n, i1, x[0][i]);
// System.out.print(x[0][i] );}System.out.printf(最小值%.6f\n, F.fGetVal(x[0]));
// System.out.println(: F.fGetVal(x[0]));}public BWE(int n){this.r -1;Init(n);Process();AnswerOutput();}public BWE(int n, double r, double[] x){this.r r;Init(n);for(int i 0; i n; i)x0[i] x[i];Process();}// 返回结果解向量和最优值public double[] retAns(){return x[0];}public double mAns(){return F.fGetVal(x[0], 0);}/*public static void main(String[] args) {// TODO Auto-generated method stubnew BWE(2);}*/}3黄金切割 GSM.java package ODM.Method;
/** 黄金切割法*/
public class GSM {private int N; // 维度private final double landa (Math.sqrt(5)-1)/2; // 0.618private double[] x1;private double[] x2;private double[] os;private final double eps 1e-5; // 解精度private ExtM EM; // 用于获取外推法结果// 最优值输出public double[] getOs() {return os;}// 函数, 初始点, 方向矢量public GSM(Func Sample, double[] x, double[] e) {//for(int i 0; i e.length; i)System.out.print(e[i] );System.out.println();initial(Sample, x, e);process(Sample);AnswerPrint(Sample);}// 结果打印private void AnswerPrint(Func Sample) {os new double[N];for(int i 0; i N; i)os[i] 0.5*(x1[i] x2[i]);// System.out.println(os os[0] os[1]);
// System.out.println(ans Sample.fGetVal(os));}// 向量范值private double FanZhi(double[] b, double[] a){double sum 0;for(int i 0; i N; i){if(b[i] - a[i] ! 0 b[i] 0)return eps*(1e10);if(b[i] 0)continue;sum Math.pow((b[i] - a[i]) / b[i], 2);}return Math.pow(sum, 0.5);}// 算法主流程private void process(Func Sample) {double[] xx1 new double[N];SubArraysCopy(xx1);double yy1 Sample.fGetVal(xx1);double[] xx2 new double[N];AddArraysCopy(xx2);double yy2 Sample.fGetVal(xx2);// 迭代过程while(true){if(yy1 yy2){ArraysCopy(xx1, x1);ArraysCopy(xx2, xx1); yy1 yy2;AddArraysCopy(xx2);yy2 Sample.fGetVal(xx2);}else{ArraysCopy(xx2, x2);ArraysCopy(xx1, xx2); yy2 yy1;SubArraysCopy(xx1);yy1 Sample.fGetVal(xx1);}//System.out.println(FanZhi(x2, x1) / Math.abs((yy2 - yy1)/yy2));if(FanZhi(x2, x1) eps Math.abs(yy2 - yy1) eps)break;}}// 获得外推法结果左右边界private void initial(Func Sample, double[] x, double[] e) {N x.length;EM new ExtM(Sample, x, e);x1 EM.getX1();x2 EM.getX3();}// 向量赋值private void ArraysCopy(double[] s, double[] e){for(int i 0; i N; i)e[i] s[i];}// landaprivate void AddArraysCopy(double[] arr){for(int i 0; i N; i)arr[i] x1[i] landa*(x2[i] - x1[i]);}// - landaprivate void SubArraysCopy(double[] arr){for(int i 0; i N; i)arr[i] x2[i] - landa*(x2[i] - x1[i]);}/*public static void main(String[] args) {// TODO Auto-generated method stubdouble[] C {0, 0};double[] d {1, 0};new GSM(new Func(), C, d);}*/
}以上算法文件包括函数方程黄金切割时有一维搜索的外推法确定“高低高”区间。 函数方程 Func.java。外推法 ExtM.java。 Func.java package ODM.Method;public class Func {private int N; // N 维private double[] left; // 函数左边界private double[] right; // 函数右边界private double r;public Func() {r -1;}public Func(double r) {this.r r;}// 定义函数与函数值返回public double fGetVal(double[] x){if(r ! -1)return fGetVal(x, r);// 10*(x1x2-5)^2 (x1-x2)^2return 10*Math.pow(x[0]x[1]-5, 2) Math.pow(x[0]-x[1], 2);//}private double max(double a, double b){return a b ? a : b;}public double fGetVal(double[] x, double r){double ret 0;
// function f1
// ret Math.pow(x[0]-5, 2) 4*Math.pow(x[1]-6, 2)
// r * (
// Math.pow(max(64-x[0]*x[0]-x[1]*x[1], 0), 2)
// Math.pow(max(x[1]-x[0]-10, 0), 0)
// Math.pow(max(x[0]-10, 0), 2)
// );// function f2
// ret x[0]*x[0] x[1]*x[1] r*(1-x[0]0 ? 1-x[0] : 0)*(1-x[0]0 ? 1-x[0] : 0); // function f3 ret Math.pow(x[0]-x[3], 2) Math.pow(x[1]-x[4], 2) Math.pow(x[2]-x[5], 2) r * ( Math.pow(max(x[0]*x[0]x[1]*x[1]x[2]*x[2]-5, 0), 2) Math.pow(max(Math.pow(x[3]-3, 2)x[4]*x[4]-1, 0), 2) Math.pow(max(x[5]-8, 0), 2) Math.pow(max(4-x[5], 0), 2) ); return ret; } } ExtM.java package ODM.Method;/** 外推法确定“高-低-高”区间*/
public class ExtM {private int N; // 函数维数private double[] x1;private double[] x2;private double[] x3;private double y1;private double y2;private double y3;private double h; // 步长private double[] d; // 方向矢量public double[] getX1() {return x1;}public double[] getX2() {return x2;}public double[] getX3() {return x3;}public double getH() {return h;}// 函数, 初始点方向public ExtM(Func Sample, double[] x, double[] e) {initial(Sample, x, e);process(Sample);AnswerPrint();}// 初始化阶段private void initial(Func Sample, double[] x, double[] e){N x.length;x1 new double[N];x2 new double[N];x3 new double[N];h 0.01;d new double[N];ArraysCopy(e, 0, d);//for(int i 0; i d.length; i)System.out.print(d[i]);System.out.println();ArraysCopy(x, 0, x1);y1 Sample.fGetVal(x1);ArraysCopy(x, h, x2);y2 Sample.fGetVal(x2);}// 循环部分private void process(Func Sample){if(y2 y1){h -h;ArraysCopy(x1, 0, x3);y3 y1;}else{ArraysCopy(x2, h, x3); y3 Sample.fGetVal(x3);}while(y3 y2){h 2*h;
// System.out.println(h h);ArraysCopy(x2, 0, x1); y1 y2;ArraysCopy(x3, 0, x2); y2 y3;ArraysCopy(x2, h, x3); y3 Sample.fGetVal(x3);
// System.out.println(x1 x1[0] x1[1] y1 y1);
// System.out.println(x2 x2[0] x2[1] y2 y2);
// System.out.println(x3 x3[0] x3[1] y3 y3);}}// 打印算法结果private void AnswerPrint(){
// System.out.println(x1 x1[0] x1[1] y1 y1);
// System.out.println(x2 x2[0] x2[1] y2 y2);
// System.out.println(x3 x3[0] x3[1] y3 y3);}// 向量转移private void ArraysCopy(double[] s, double c, double[] e){for(int i 0; i s.length; i)e[i] d[i]*c s[i];}/*public static void main(String[] args) {// TODO Auto-generated method stub// new ExtM();}*/}转载于:https://www.cnblogs.com/ldxsuanfa/p/10761431.html
