修正单纯形法·优化算法实现·Java

修正单纯性法

代码如下：

舍去了输入转化的内容，主要包含算法关键步骤。

public class LPSimplexM {private static final double inf = 1e9;private int n;// 约束个数private double[][] A;// 输入函数参数private double[] b;// 约束值private double[] c;// 目标函数系数private double Z;// 目标值private void InitF() {// 初始化 First/* problem 1. * max Z = 5*x1 + 4*x2;  min Z = -5*x1 - 4*x2; * x1   + 3*x2 <= 90;x1 + 3*x2 +  x3= 90; * 2*x1 + x2   <= 80;=>  2*x1 +   x2     + x4= 80; * x1   + x2   <= 45;x1 +   x2     + x5 = 45; * xi >= 0 *//* problem 2. * min Z = -7*x1 - 12*x2; * 9*x1 + 4*x2  + x3          = 360; * 4*x1 + 5*x2       +x4   = 200;   * 3*x1 + 10*x2 + x5 = 300; *   xi >= 0 */n = 3;A = new double[n+1][n+1];b = new double[n+1];//c = new double[n<<1];Z = inf;// 约束初始条件A[1][1] = 1;A[1][2] = 3;A[2][1] = 2;A[2][2] = 1;A[3][1] = 1;A[3][2] = 1;// 条件值// problem 1.//b[1] = 90;//b[2] = 80;//b[3] = 45;// problem 2.b[1] = 360;b[2] = 200;b[3] = 300;//for(int i = 1; i <= n; i++)System.out.println("b[" + i + "] = " + b[i]);// 目标函数系数//c[1] = -5;c[2] = -4;}int m;private double[][] p;private double[][] e, oe;private double[][] E, oE;private double[] X;private boolean[] G;private int[] S;private void InitS() {m = 2;p = new double[n+1][n+m+1];e = new double[n+1][n+1];oe = new double[n+1][n+1];E = new double[n+1][n+1];oE = new double[n+1][n+1];X = new double[n+1];G = new boolean[n+m+1];S = new int[n+1];c = new double[n+m+1];// problem 1.//c[1] = -5;c[2] = -4;c[3] = 0;c[4] = 0;c[5] = 0;// problem 2.c[1] = -7;c[2] = -12;c[3] = 0;c[4] = 0;c[5] = 0;// problem 1.//p[1][1] = 1;p[1][2] = 3;p[1][3] = 1;p[1][4] = 0;p[1][5] = 0;//p[2][1] = 2;p[2][2] = 1;p[2][3] = 0;p[2][4] = 1;p[2][5] = 0;//p[3][1] = 1;p[3][2] = 1;p[3][3] = 0;p[3][4] = 0;p[3][5] = 1;// problem 2.p[1][1] = 9;p[1][2] = 4;p[1][3] = 1;p[1][4] = 0;p[1][5] = 0;p[2][1] = 4;p[2][2] = 5;p[2][3] = 0;p[2][4] = 1;p[2][5] = 0;p[3][1] = 3;p[3][2] = 10;p[3][3] = 0;p[3][4] = 0;p[3][5] = 1;for(int i = 1; i <= n; i++)for(int j = 1; j <= n; j++)if(i == j)E[i][j] = oE[i][j] = 1;else E[i][j] = oE[i][j] = 0;for(int i = 1; i <= n; i++)X[i] = b[i];G[1] = false;G[2] = false;G[3] = true;G[4] = true;G[5] = true;S[1] = 3;S[2] = 4;S[3] = 5;}public LPSimplexM() {InitF();InitS();AlgorithmProcess();solve();}private void AlgorithmProcess() {double[] coE = new double[n+1];// c * E^-1double[] r = new double [n+m+1];// c - c * E^-1 * pdouble[] oEp = new double[n+1];// E^-1 * p;boolean flag = false;while(true) {// x = E^-1 * bfor(int i = 1; i <= n; i++){X[i] = 0;for(int j = 1; j <= n; j++)X[i] += oE[i][j]*b[j];}// c * E^-1for(int i = 1; i <= n; i++){coE[i] = 0;for(int j = 1; j <= n; j++)coE[i] += c[S[j]]*oE[j][i];}// r = c - c * E^-1 * p     => min r' id -> kint k = -1;flag = false;for(int i = 1; i <= n+m; i++)if(!G[i]){double ans = 0;for(int j = 1; j <= n; j++)ans += coE[j]*p[j][i];r[i] = c[i] - ans;if(!flag && r[i] < 0){k = i;flag = true;}else if(flag && r[i] < r[k]){k = i;}}if(k == -1)return ;// solution output 1（X, S 为最优解）// E^-1 * p;=> min theta>0' id -> sint s = -1;flag = false;for(int i = 1; i <= n; i++){oEp[i] = 0;for(int j = 1; j <= n; j++){oEp[i] += oE[i][j]*p[j][k];}if(oEp[i] > 0){if(!flag){s = i;flag = true;}else if(flag && X[i]/oEp[i] < X[s]/oEp[s]){s = i;}}}if(!flag)return ; // no solution 1（无允许解）if(s == -1)return ;// no solution 2（该问题有无解集）// p[s] = p[k], 形成新的矢量基 EG[S[s]] = false;G[k] = true;S[s] = k;//System.out.println("k = " + k + "; s = " + s);for(int i = 1; i <= n; i++){p[i][k] = -1.0*oEp[i]/oEp[s];if(i == s)p[i][k] = 1/oEp[s];}for(int i = 1; i <= n; i++){int id = S[i];for(int j = 1; j <= n; j++){if(i == s){e[j][i] = p[j][k];}else{if(j == i){e[j][i] = 1;}else{e[j][i] = 0;}}}}//for(int i = 1; i <= n; i++){//for(int j = 1; j <= n; j++){//System.out.print(oE[i][j] + " ");//}System.out.println();//}System.out.println("{oE}");//for(int i = 1; i <= n; i++){//for(int j = 1; j <= n; j++){//System.out.print(e[i][j] + " ");//}System.out.println();//}System.out.println("{e}");for(int i = 1; i <= n; i++){for(int j = 1; j <= n; j++){oe[i][j] = 0;for(int t = 1; t <= n; t++){oe[i][j] += e[i][t]*oE[t][j];}}}for(int i = 1; i <= n; i++){for(int j = 1; j <= n; j++){oE[i][j] = oe[i][j];//System.out.print(oE[i][j] + " ");}//System.out.println();}//System.out.println();}}// 最优解输出private void solve() {Z = 0;for(int i = 1; i <= n; i++){int id = S[i];Z += c[id]*X[i];System.out.println(id + " : " + X[i] + " * " + -c[id]);}System.out.println("Z = " + -Z);}public static void main(String[] args) {new LPSimplexM();}}

如有问题，请网友指正。

希望网友的交流，共同进步。