如何使用joptimizer进行线性规划

Question

我正在使用joptimizer解决一个线性规划问题。

我的问题是：

Maximize (x1*f1 + x2*f2 + x3*f3)

such that (x1*v1 + x2*v2 + x3*v3) <= h

我要找到x1，x2和x3。

我不知道如何从上面的方程式创建一个joptimizer输入。

Answer 1

Java文档可以在这里找到http://www.joptimizer.com/apidocs/index.html

简单示例最小化3x+4y，使得2x+3y >= 8，5x+2y >= 12，x >= 0，y >= 0

我用来解决简单线性规划问题的示例代码如下：

package test_joptimizer;

import com.joptimizer.functions.ConvexMultivariateRealFunction;
import com.joptimizer.functions.LinearMultivariateRealFunction;
import com.joptimizer.optimizers.JOptimizer;
import com.joptimizer.optimizers.OptimizationRequest;
import org.apache.log4j.BasicConfigurator;

/**
 * @author K.P.L.Kanchana
 */

public class Main {

    public static void main(String[] args) throws Exception {

        // Objective function (plane)
        LinearMultivariateRealFunction objectiveFunction = new LinearMultivariateRealFunction(new double[] {3.0, 4.0}, 0); //minimize 3x+4y

        //inequalities (polyhedral feasible set G.X<H )
        ConvexMultivariateRealFunction[] inequalities = new ConvexMultivariateRealFunction[4];
        // x >= 0
        inequalities[0] = new LinearMultivariateRealFunction(new double[]{-1.0, 0.00}, 0.0);  // focus: -x+0 <= 0 
        // y >= 0
        inequalities[1] = new LinearMultivariateRealFunction(new double[]{0.0, -1.00}, 0.0);  // focus: -y+0 <= 0
        // 2x+3y >= 8
        inequalities[2] = new LinearMultivariateRealFunction(new double[]{-2.0, -3.00}, 8.0); // focus: -2x-3y+8 <= 0
        // 5x+2y >= 12
        inequalities[3] = new LinearMultivariateRealFunction(new double[]{-5.0, -2.00}, 12.0);// focus: -5x-2y+12 <= 0

        //optimization problem
        OptimizationRequest or = new OptimizationRequest();
        or.setF0(objectiveFunction);
        or.setFi(inequalities);
        //or.setInitialPoint(new double[] {0.0, 0.0});//initial feasible point, not mandatory
        or.setToleranceFeas(1.E-9);
        or.setTolerance(1.E-9);

        //optimization
        JOptimizer opt = new JOptimizer();
        opt.setOptimizationRequest(or);
        int returnCode = opt.optimize();

        double[] sol = opt.getOptimizationResponse().getSolution();

        System.out.println("Length: " + sol.length);
        for (int i=0; i<sol.length/2; i++){
            System.out.println( "X" + (i+1) + ": " + Math.round(sol[i]) + "\ty" + (i+1) + ": " + Math.round(sol[i+1]) );
        }
    }

}

Answer 2

也许你也想看看下面的示例代码。

不要忘记从http://www.joptimizer.com/downloadWithAdd.html导入依赖项。

您应该手动下载三个外部jar文件( /joptimizer-4.0.0.jar、/joptimizer-4.0.0-dependencies.zip、/joptimizer-4.0.0-sources.jar)并将其导入到您的项目中。.zip文件也需要解压缩。

import java.util.Arrays;
import com.joptimizer.optimizers.*;

public class LCLP {
    // min (x) for J = C'*X;
    // s.t.
    // A*X = b;
    // X <= 0;
    // X = [x1;x2;x3;...xN]
    public static void main(String[] args) throws Exception {

        // Example from http://www.joptimizer.com/linearProgramming.html

        //Objective function
        double[] c = new double[] { -1., -1. };
        //Inequalities constraints
        double[][] G = new double[][] {{4./3., -1}, {-1./2., 1.}, {-2., -1.}, {1./3., 1.}};
        double[] h = new double[] {2., 1./2., 2., 1./2.};
        //Bounds on variables
        double[] lb = new double[] {0 , 0};
        double[] ub = new double[] {10, 10};
        //optimization problem
        LPOptimizationRequest or = new LPOptimizationRequest();
        or.setC(c);
        or.setG(G);
        or.setH(h);
        or.setLb(lb);
        or.setUb(ub);
        or.setDumpProblem(true); 
        //optimization
        LPPrimalDualMethod opt = new LPPrimalDualMethod();
        opt.setLPOptimizationRequest(or);
        opt.optimize();
        double[] sol = opt.getOptimizationResponse().getSolution();
        System.out.println("Solution = " + Arrays.toString(sol));
    }
}