apache commons LinearObjectiveFunction算法

Question

apache commons数学库如何计算给定不等式约束的目标函数的最小值和最大值。

e.g

maximize 3x1+5x2 
given - 2x1+8x2<=13
5x1-x2<=11
x1>=0,x2>=0

apache commons库对此应用了什么算法。

Answer 1

在Apache commons数学中有一个Simplex求解器。

你可以使用这个库来解决你的问题：

@Test
public void testMathStackOverflow() {
    //      maximize 3x1+5x2
    //      subject to
    //          2x1+8x2<=13
    //          5x1-x2<=11
    //              x1>=0
    // x2>=0

    LinearObjectiveFunction f = new LinearObjectiveFunction(new double[] { 3, 5}, 0);

    ArrayList<LinearConstraint> constraints = new ArrayList<>();

    constraints.add(new LinearConstraint(new double[] {2, 8}, Relationship.LEQ, 13));
    constraints.add(new LinearConstraint(new double[] {5, -1}, Relationship.LEQ, 11));

    double epsilon = 1e-6;
    SimplexSolver solver = new SimplexSolver();
    PointValuePair solution = solver.optimize(f, new LinearConstraintSet(constraints),
            GoalType.MAXIMIZE,
            new NonNegativeConstraint(true),
            PivotSelectionRule.BLAND);
    System.out.printf("x1: %f; x2: %f; max: %f", solution.getPoint()[0], solution.getPoint()[1], solution.getValue());
}

结果是：

x1: 2.404762; x2: 1.023810; max: 12.333333

我使用了以下依赖项：

<groupId>org.apache.commons</groupId>
<artifactId>commons-math4</artifactId>
<version>4.0-SNAPSHOT</version>

有关此库中Simplex求解器用法的更多示例，请下载源代码并检查包中的单元测试：

org.apache.commons.math4.optim.linear