How does apache commons math library calculate minimum and maximum value of objective function given inequality constraint.
e.g
maximize 3x1+5x2
given - 2x1+8x2<=13
5x1-x2<=11
x1>=0,x2>=0
what algorithm does apache commons library applies for this.
There is a Simplex solver in Apache commons math.
You can solve your problem like this using this library:
@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());
}
The result is:
x1: 2.404762; x2: 1.023810; max: 12.333333
I have used these dependencies:
<groupId>org.apache.commons</groupId>
<artifactId>commons-math4</artifactId>
<version>4.0-SNAPSHOT</version>
For more examples of the usage of the Simplex solver in this library download the source code and check the unit tests in package:
org.apache.commons.math4.optim.linear
