java 线性规划 和lingo 比较

model:
max=13*A+ 23*B;

5*A + 15*B <480 ;
4*A + 4 *B <160 ;
35* A + 20 *B <1190 ;

end

Variable Value Reduced Cost
A 12.00000 0.000000
B 28.00000 0.000000

Row Slack or Surplus Dual Price
1 800.0000 1.000000
2 0.000000 1.000000
3 0.000000 2.000000
4 210.0000 0.000000

public static void test0() {
double[][] A = {
{ 5,  15 },
{  4, 4 },
{  35,  20  }

};
double[] c = { 13, 23 };
double[] b = { 480,160,1190};
test(A, b, c);
}

value = 800.0
x[0] = 11.999999999999998
x[1] = 28.0
y[0] = 1.0
y[1] = 2.0
y[2] = -0.0

package 线性规划;

/**
* Created by han on 2016/5/5.
*/

import java.io.PrintStream;

/*************************************************************************
*  Compilation:  javac Simplex.java
*  Execution:    java Simplex
*
*  Given an M-by-N matrix A, an M-length vector b, and an
*  N-length vector c, solve the  LP { max cx : Ax <= b, x >= 0 }.
*  Assumes that b >= 0 so that x = 0 is a basic feasible solution.
*
*  Creates an (M+1)-by-(N+M+1) simplex tableaux with the
*  RHS in column M+N, the objective function in row M, and
*  slack variables in columns M through M+N-1.
*
*************************************************************************/

public class Simplex {
private static final double EPSILON = 1.0E-10;
private double[][] a;   // tableaux
private int M;          // number of constraints
private int N;          // number of original variables

private int[] basis;    // basis[i] = basic variable corresponding to row i
private static PrintStream StdOut=System.out;
// only needed to print out solution, not book

// sets up the simplex tableaux
public Simplex(double[][] A, double[] b, double[] c) {
M = b.length;
N = c.length;
a = new double[M+1][N+M+1];
for (int i = 0; i < M; i++)
for (int j = 0; j < N; j++)
a[i][j] = A[i][j];
for (int i = 0; i < M; i++) a[i][N+i] = 1.0;
for (int j = 0; j < N; j++) a[M][j]   = c[j];
for (int i = 0; i < M; i++) a[i][M+N] = b[i];

basis = new int[M];
for (int i = 0; i < M; i++) basis[i] = N + i;

solve();

// check optimality conditions
assert check(A, b, c);
}

// run simplex algorithm starting from initial BFS
private void solve() {
while (true) {

// find entering column q
int q = bland();
if (q == -1) break;  // optimal

// find leaving row p
int p = minRatioRule(q);
if (p == -1) throw new RuntimeException("Linear program is unbounded");

// pivot
pivot(p, q);

// update basis
basis[p] = q;
}
}

// lowest index of a non-basic column with a positive cost
private int bland() {
for (int j = 0; j < M + N; j++)
if (a[M][j] > 0) return j;
return -1;  // optimal
}

// index of a non-basic column with most positive cost
private int dantzig() {
int q = 0;
for (int j = 1; j < M + N; j++)
if (a[M][j] > a[M][q]) q = j;

if (a[M][q] <= 0) return -1;  // optimal
else return q;
}

// find row p using min ratio rule (-1 if no such row)
private int minRatioRule(int q) {
int p = -1;
for (int i = 0; i < M; i++) {
if (a[i][q] <= 0) continue;
else if (p == -1) p = i;
else if ((a[i][M+N] / a[i][q]) < (a[p][M+N] / a[p][q])) p = i;
}
return p;
}

// pivot on entry (p, q) using Gauss-Jordan elimination
private void pivot(int p, int q) {

// everything but row p and column q
for (int i = 0; i <= M; i++)
for (int j = 0; j <= M + N; j++)
if (i != p && j != q) a[i][j] -= a[p][j] * a[i][q] / a[p][q];

// zero out column q
for (int i = 0; i <= M; i++)
if (i != p) a[i][q] = 0.0;

// scale row p
for (int j = 0; j <= M + N; j++)
if (j != q) a[p][j] /= a[p][q];
a[p][q] = 1.0;
}

// return optimal objective value
public double value() {
return -a[M][M+N];
}

// return primal solution vector
public double[] primal() {
double[] x = new double
;
for (int i = 0; i < M; i++)
if (basis[i] < N) x[basis[i]] = a[i][M+N];
return x;
}

// return dual solution vector
public double[] dual() {
double[] y = new double[M];
for (int i = 0; i < M; i++)
y[i] = -a[M][N+i];
return y;
}

// is the solution primal feasible?
private boolean isPrimalFeasible(double[][] A, double[] b) {
double[] x = primal();

// check that x >= 0
for (int j = 0; j < x.length; j++) {
if (x[j] < 0.0) {
StdOut.println("x[" + j + "] = " + x[j] + " is negative");
return false;
}
}

// check that Ax <= b
for (int i = 0; i < M; i++) {
double sum = 0.0;
for (int j = 0; j < N; j++) {
sum += A[i][j] * x[j];
}
if (sum > b[i] + EPSILON) {
StdOut.println("not primal feasible");
StdOut.println("b[" + i + "] = " + b[i] + ", sum = " + sum);
return false;
}
}
return true;
}

// is the solution dual feasible?
private boolean isDualFeasible(double[][] A, double[] c) {
double[] y = dual();

// check that y >= 0
for (int i = 0; i < y.length; i++) {
if (y[i] < 0.0) {
StdOut.println("y[" + i + "] = " + y[i] + " is negative");
return false;
}
}

// check that yA >= c
for (int j = 0; j < N; j++) {
double sum = 0.0;
for (int i = 0; i < M; i++) {
sum += A[i][j] * y[i];
}
if (sum < c[j] - EPSILON) {
StdOut.println("not dual feasible");
StdOut.println("c[" + j + "] = " + c[j] + ", sum = " + sum);
return false;
}
}
return true;
}

// check that optimal value = cx = yb
private boolean isOptimal(double[] b, double[] c) {
double[] x = primal();
double[] y = dual();
double value = value();

// check that value = cx = yb
double value1 = 0.0;
for (int j = 0; j < x.length; j++)
value1 += c[j] * x[j];
double value2 = 0.0;
for (int i = 0; i < y.length; i++)
value2 += y[i] * b[i];
if (Math.abs(value - value1) > EPSILON || Math.abs(value - value2) > EPSILON) {
StdOut.println("value = " + value + ", cx = " + value1 + ", yb = " + value2);
return false;
}

return true;
}

private boolean check(double[][]A, double[] b, double[] c) {
return isPrimalFeasible(A, b) && isDualFeasible(A, c) && isOptimal(b, c);
}

// print tableaux
public void show() {
StdOut.println("M = " + M);
StdOut.println("N = " + N);
for (int i = 0; i <= M; i++) {
for (int j = 0; j <= M + N; j++) {
StdOut.printf("%7.2f ", a[i][j]);
}
StdOut.println();
}
StdOut.println("value = " + value());
for (int i = 0; i < M; i++)
if (basis[i] < N) StdOut.println("x_" + basis[i] + " = " + a[i][M+N]);
StdOut.println();
}

public static void test(double[][] A, double[] b, double[] c) {
Simplex lp = new Simplex(A, b, c);
StdOut.println("value = " + lp.value());
double[] x = lp.primal();
for (int i = 0; i < x.length; i++)
StdOut.println("x[" + i + "] = " + x[i]);
double[] y = lp.dual();
for (int j = 0; j < y.length; j++)
StdOut.println("y[" + j + "] = " + y[j]);
}
public static void test0() {
double[][] A = {
{ 5,  15 },
{  4, 4 },
{  35,  20  }

};
double[] c = { 13, 23 };
double[] b = { 480,160,1190};
test(A, b, c);
}
public static void test1() {
double[][] A = {
{ -1,  1,  0 },
{  1,  4,  0 },
{  2,  1,  0 },
{  3, -4,  0 },
{  0,  0,  1 },
};
double[] c = { 1, 1, 1 };
double[] b = { 5, 45, 27, 24, 4 };
test(A, b, c);
}

// x0 = 12, x1 = 28, opt = 800
public static void test2() {
double[] c = {  13.0,  23.0 };
double[] b = { 480.0, 160.0, 1190.0 };
double[][] A = {
{  5.0, 15.0 },
{  4.0,  4.0 },
{ 35.0, 20.0 },
};
test(A, b, c);
}

// unbounded
public static void test3() {
double[] c = { 2.0, 3.0, -1.0, -12.0 };
double[] b = {  3.0,   2.0 };
double[][] A = {
{ -2.0, -9.0,  1.0,  9.0 },
{  1.0,  1.0, -1.0, -2.0 },
};
test(A, b, c);
}

// degenerate - cycles if you choose most positive objective function coefficient
public static void test4() {
double[] c = { 10.0, -57.0, -9.0, -24.0 };
double[] b = {  0.0,   0.0,  1.0 };
double[][] A = {
{ 0.5, -5.5, -2.5, 9.0 },
{ 0.5, -1.5, -0.5, 1.0 },
{ 1.0,  0.0,  0.0, 0.0 },
};
test(A, b, c);
}

// test client
public static void main(String[] args) {
try                 { test0();             }
catch (Exception e) { e.printStackTrace(); }
StdOut.println("--------------------------------");

try                 { test1();             }
catch (Exception e) { e.printStackTrace(); }
StdOut.println("--------------------------------");

try                 { test2();             }
catch (Exception e) { e.printStackTrace(); }
StdOut.println("--------------------------------");

try                 { test3();             }
catch (Exception e) { e.printStackTrace(); }
StdOut.println("--------------------------------");

try                 { test4();             }
catch (Exception e) { e.printStackTrace(); }
StdOut.println("--------------------------------");

int M = Integer.parseInt(args[0]);
int N = Integer.parseInt(args[1]);
double[] c = new double
;
double[] b = new double[M];
double[][] A = new double[M]
;
for (int j = 0; j < N; j++)
c[j] = StdRandom.uniform(1000);
for (int i = 0; i < M; i++)
b[i] = StdRandom.uniform(1000);
for (int i = 0; i < M; i++)
for (int j = 0; j < N; j++)
A[i][j] = StdRandom.uniform(100);
Simplex lp = new Simplex(A, b, c);
StdOut.println(lp.value());
}

private static class StdRandom {
public static double uniform(int i) {
return Math.random()*i;
}
}
}