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* http://www.apache.org/licenses/LICENSE-2.0
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package org.apache.commons.math4.optim.nonlinear.scalar.noderiv;
import org.apache.commons.math4.analysis.MultivariateFunction;
import org.apache.commons.math4.exception.MathUnsupportedOperationException;
import org.apache.commons.math4.optim.InitialGuess;
import org.apache.commons.math4.optim.MaxEval;
import org.apache.commons.math4.optim.PointValuePair;
import org.apache.commons.math4.optim.SimpleBounds;
import org.apache.commons.math4.optim.SimpleValueChecker;
import org.apache.commons.math4.optim.nonlinear.scalar.GoalType;
import org.apache.commons.math4.optim.nonlinear.scalar.ObjectiveFunction;
import org.apache.commons.math4.optim.nonlinear.scalar.noderiv.MultiDirectionalSimplex;
import org.apache.commons.math4.optim.nonlinear.scalar.noderiv.NelderMeadSimplex;
import org.apache.commons.math4.optim.nonlinear.scalar.noderiv.SimplexOptimizer;
import org.apache.commons.math4.util.FastMath;
import org.junit.Assert;
import org.junit.Test;
public class SimplexOptimizerMultiDirectionalTest {
@Test(expected=MathUnsupportedOperationException.class)
public void testBoundsUnsupported() {
SimplexOptimizer optimizer = new SimplexOptimizer(1e-10, 1e-30);
final FourExtrema fourExtrema = new FourExtrema();
optimizer.optimize(new MaxEval(100),
new ObjectiveFunction(fourExtrema),
GoalType.MINIMIZE,
new InitialGuess(new double[] { -3, 0 }),
new NelderMeadSimplex(new double[] { 0.2, 0.2 }),
new SimpleBounds(new double[] { -5, -1 },
new double[] { 5, 1 }));
}
@Test
public void testMinimize1() {
SimplexOptimizer optimizer = new SimplexOptimizer(1e-11, 1e-30);
final FourExtrema fourExtrema = new FourExtrema();
final PointValuePair optimum
= optimizer.optimize(new MaxEval(200),
new ObjectiveFunction(fourExtrema),
GoalType.MINIMIZE,
new InitialGuess(new double[] { -3, 0 }),
new MultiDirectionalSimplex(new double[] { 0.2, 0.2 }));
Assert.assertEquals(fourExtrema.xM, optimum.getPoint()[0], 4e-6);
Assert.assertEquals(fourExtrema.yP, optimum.getPoint()[1], 3e-6);
Assert.assertEquals(fourExtrema.valueXmYp, optimum.getValue(), 8e-13);
Assert.assertTrue(optimizer.getEvaluations() > 120);
Assert.assertTrue(optimizer.getEvaluations() < 150);
// Check that the number of iterations is updated (MATH-949).
Assert.assertTrue(optimizer.getIterations() > 0);
}
@Test
public void testMinimize2() {
SimplexOptimizer optimizer = new SimplexOptimizer(1e-11, 1e-30);
final FourExtrema fourExtrema = new FourExtrema();
final PointValuePair optimum
= optimizer.optimize(new MaxEval(200),
new ObjectiveFunction(fourExtrema),
GoalType.MINIMIZE,
new InitialGuess(new double[] { 1, 0 }),
new MultiDirectionalSimplex(new double[] { 0.2, 0.2 }));
Assert.assertEquals(fourExtrema.xP, optimum.getPoint()[0], 2e-8);
Assert.assertEquals(fourExtrema.yM, optimum.getPoint()[1], 3e-6);
Assert.assertEquals(fourExtrema.valueXpYm, optimum.getValue(), 2e-12);
Assert.assertTrue(optimizer.getEvaluations() > 120);
Assert.assertTrue(optimizer.getEvaluations() < 150);
// Check that the number of iterations is updated (MATH-949).
Assert.assertTrue(optimizer.getIterations() > 0);
}
@Test
public void testMaximize1() {
SimplexOptimizer optimizer = new SimplexOptimizer(1e-11, 1e-30);
final FourExtrema fourExtrema = new FourExtrema();
final PointValuePair optimum
= optimizer.optimize(new MaxEval(200),
new ObjectiveFunction(fourExtrema),
GoalType.MAXIMIZE,
new InitialGuess(new double[] { -3.0, 0.0 }),
new MultiDirectionalSimplex(new double[] { 0.2, 0.2 }));
Assert.assertEquals(fourExtrema.xM, optimum.getPoint()[0], 7e-7);
Assert.assertEquals(fourExtrema.yM, optimum.getPoint()[1], 3e-7);
Assert.assertEquals(fourExtrema.valueXmYm, optimum.getValue(), 2e-14);
Assert.assertTrue(optimizer.getEvaluations() > 120);
Assert.assertTrue(optimizer.getEvaluations() < 150);
// Check that the number of iterations is updated (MATH-949).
Assert.assertTrue(optimizer.getIterations() > 0);
}
@Test
public void testMaximize2() {
SimplexOptimizer optimizer = new SimplexOptimizer(new SimpleValueChecker(1e-15, 1e-30));
final FourExtrema fourExtrema = new FourExtrema();
final PointValuePair optimum
= optimizer.optimize(new MaxEval(200),
new ObjectiveFunction(fourExtrema),
GoalType.MAXIMIZE,
new InitialGuess(new double[] { 1, 0 }),
new MultiDirectionalSimplex(new double[] { 0.2, 0.2 }));
Assert.assertEquals(fourExtrema.xP, optimum.getPoint()[0], 2e-8);
Assert.assertEquals(fourExtrema.yP, optimum.getPoint()[1], 3e-6);
Assert.assertEquals(fourExtrema.valueXpYp, optimum.getValue(), 2e-12);
Assert.assertTrue(optimizer.getEvaluations() > 180);
Assert.assertTrue(optimizer.getEvaluations() < 220);
// Check that the number of iterations is updated (MATH-949).
Assert.assertTrue(optimizer.getIterations() > 0);
}
@Test
public void testRosenbrock() {
MultivariateFunction rosenbrock
= new MultivariateFunction() {
@Override
public double value(double[] x) {
++count;
double a = x[1] - x[0] * x[0];
double b = 1.0 - x[0];
return 100 * a * a + b * b;
}
};
count = 0;
SimplexOptimizer optimizer = new SimplexOptimizer(-1, 1e-3);
PointValuePair optimum
= optimizer.optimize(new MaxEval(100),
new ObjectiveFunction(rosenbrock),
GoalType.MINIMIZE,
new InitialGuess(new double[] { -1.2, 1 }),
new MultiDirectionalSimplex(new double[][] {
{ -1.2, 1.0 },
{ 0.9, 1.2 },
{ 3.5, -2.3 } }));
Assert.assertEquals(count, optimizer.getEvaluations());
Assert.assertTrue(optimizer.getEvaluations() > 50);
Assert.assertTrue(optimizer.getEvaluations() < 100);
Assert.assertTrue(optimum.getValue() > 1e-2);
}
@Test
public void testPowell() {
MultivariateFunction powell
= new MultivariateFunction() {
@Override
public double value(double[] x) {
++count;
double a = x[0] + 10 * x[1];
double b = x[2] - x[3];
double c = x[1] - 2 * x[2];
double d = x[0] - x[3];
return a * a + 5 * b * b + c * c * c * c + 10 * d * d * d * d;
}
};
count = 0;
SimplexOptimizer optimizer = new SimplexOptimizer(-1, 1e-3);
PointValuePair optimum
= optimizer.optimize(new MaxEval(1000),
new ObjectiveFunction(powell),
GoalType.MINIMIZE,
new InitialGuess(new double[] { 3, -1, 0, 1 }),
new MultiDirectionalSimplex(4));
Assert.assertEquals(count, optimizer.getEvaluations());
Assert.assertTrue(optimizer.getEvaluations() > 800);
Assert.assertTrue(optimizer.getEvaluations() < 900);
Assert.assertTrue(optimum.getValue() > 1e-2);
}
@Test
public void testMath283() {
// fails because MultiDirectional.iterateSimplex is looping forever
// the while(true) should be replaced with a convergence check
SimplexOptimizer optimizer = new SimplexOptimizer(1e-14, 1e-14);
final Gaussian2D function = new Gaussian2D(0, 0, 1);
PointValuePair estimate = optimizer.optimize(new MaxEval(1000),
new ObjectiveFunction(function),
GoalType.MAXIMIZE,
new InitialGuess(function.getMaximumPosition()),
new MultiDirectionalSimplex(2));
final double EPSILON = 1e-5;
final double expectedMaximum = function.getMaximum();
final double actualMaximum = estimate.getValue();
Assert.assertEquals(expectedMaximum, actualMaximum, EPSILON);
final double[] expectedPosition = function.getMaximumPosition();
final double[] actualPosition = estimate.getPoint();
Assert.assertEquals(expectedPosition[0], actualPosition[0], EPSILON );
Assert.assertEquals(expectedPosition[1], actualPosition[1], EPSILON );
}
private static class FourExtrema implements MultivariateFunction {
// The following function has 4 local extrema.
final double xM = -3.841947088256863675365;
final double yM = -1.391745200270734924416;
final double xP = 0.2286682237349059125691;
final double yP = -yM;
final double valueXmYm = 0.2373295333134216789769; // Local maximum.
final double valueXmYp = -valueXmYm; // Local minimum.
final double valueXpYm = -0.7290400707055187115322; // Global minimum.
final double valueXpYp = -valueXpYm; // Global maximum.
@Override
public double value(double[] variables) {
final double x = variables[0];
final double y = variables[1];
return (x == 0 || y == 0) ? 0 :
FastMath.atan(x) * FastMath.atan(x + 2) * FastMath.atan(y) * FastMath.atan(y) / (x * y);
}
}
private static class Gaussian2D implements MultivariateFunction {
private final double[] maximumPosition;
private final double std;
public Gaussian2D(double xOpt, double yOpt, double std) {
maximumPosition = new double[] { xOpt, yOpt };
this.std = std;
}
public double getMaximum() {
return value(maximumPosition);
}
public double[] getMaximumPosition() {
return maximumPosition.clone();
}
@Override
public double value(double[] point) {
final double x = point[0], y = point[1];
final double twoS2 = 2.0 * std * std;
return 1.0 / (twoS2 * FastMath.PI) * FastMath.exp(-(x * x + y * y) / twoS2);
}
}
private int count;
}