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commons-math-legacy/src/test/java/org/apache/commons/math4/legacy/optim/nonlinear/scalar/noderiv/SimplexOptimizerMultiDirectionalTest.java.NEW
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/*
* Licensed to the Apache Software Foundation (ASF) under one or more
* contributor license agreements. See the NOTICE file distributed with
* this work for additional information regarding copyright ownership.
* The ASF licenses this file to You under the Apache License, Version 2.0
* (the "License"); you may not use this file except in compliance with
* the License. You may obtain a copy of the License at
*
* http://www.apache.org/licenses/LICENSE-2.0
*
* Unless required by applicable law or agreed to in writing, software
* distributed under the License is distributed on an "AS IS" BASIS,
* WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
* See the License for the specific language governing permissions and
* limitations under the License.
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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.SimulatedAnnealing;
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.apache.commons.math4.util.MathArrays;
import org.junit.Assert;
import org.junit.Test;
import org.junit.Ignore;
public class SimplexOptimizerMultiDirectionalTest {
private static final int DIM = 13;
@Test(expected=MathUnsupportedOperationException.class)
public void testBoundsUnsupported() {
SimplexOptimizer optimizer = new SimplexOptimizer(1e-10, 1e-30);
final OptimTestUtils.FourExtrema fourExtrema = new OptimTestUtils.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 OptimTestUtils.FourExtrema fourExtrema = new OptimTestUtils.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 OptimTestUtils.FourExtrema fourExtrema = new OptimTestUtils.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 OptimTestUtils.FourExtrema fourExtrema = new OptimTestUtils.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 OptimTestUtils.FourExtrema fourExtrema = new OptimTestUtils.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() {
final OptimTestUtils.Rosenbrock rosenbrock = new OptimTestUtils.Rosenbrock();
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.assertTrue(optimizer.getEvaluations() > 50);
Assert.assertTrue(optimizer.getEvaluations() < 100);
Assert.assertTrue(optimum.getValue() > 1e-2);
}
@Test
public void testPowell() {
final OptimTestUtils.Powell powell = new OptimTestUtils.Powell();
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.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 OptimTestUtils.Gaussian2D function = new OptimTestUtils.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 );
}
@Test
public void testRosen() {
doTest(new OptimTestUtils.Rosen(),
OptimTestUtils.point(DIM, 0.1),
GoalType.MINIMIZE,
183861,
new PointValuePair(OptimTestUtils.point(DIM, 1.0), 0.0),
1e-4);
}
@Test
public void testEllipse() {
doTest(new OptimTestUtils.Elli(),
OptimTestUtils.point(DIM, 1.0),
GoalType.MINIMIZE,
873,
new PointValuePair(OptimTestUtils.point(DIM, 0.0), 0.0),
1e-14);
}
//@Ignore
@Test
public void testElliRotated() {
doTest(new OptimTestUtils.ElliRotated(),
OptimTestUtils.point(DIM, 1.0),
GoalType.MINIMIZE,
873,
new PointValuePair(OptimTestUtils.point(DIM, 0.0), 0.0),
1e-14);
}
@Test
public void testCigar() {
doTest(new OptimTestUtils.Cigar(),
OptimTestUtils.point(DIM, 1.0),
GoalType.MINIMIZE,
925,
new PointValuePair(OptimTestUtils.point(DIM,0.0), 0.0),
1e-14);
}
@Test
public void testTwoAxes() {
doTest(new OptimTestUtils.TwoAxes(),
OptimTestUtils.point(DIM, 1.0),
GoalType.MINIMIZE,
1159,
new PointValuePair(OptimTestUtils.point(DIM, 0.0), 0.0),
1e-14);
}
@Test
public void testCigTab() {
doTest(new OptimTestUtils.CigTab(),
OptimTestUtils.point(DIM, 1.0),
GoalType.MINIMIZE,
795,
new PointValuePair(OptimTestUtils.point(DIM, 0.0), 0.0),
1e-14);
}
@Test
public void testSphere() {
doTest(new OptimTestUtils.Sphere(),
OptimTestUtils.point(DIM, 1.0),
GoalType.MINIMIZE,
665,
new PointValuePair(OptimTestUtils.point(DIM, 0.0), 0.0),
1e-14);
}
@Test
public void testTablet() {
doTest(new OptimTestUtils.Tablet(),
OptimTestUtils.point(DIM, 1.0),
GoalType.MINIMIZE,
873,
new PointValuePair(OptimTestUtils.point(DIM, 0.0), 0.0),
1e-14);
}
@Test
public void testDiffPow() {
doTest(new OptimTestUtils.DiffPow(),
OptimTestUtils.point(DIM, 1.0),
GoalType.MINIMIZE,
614,
new PointValuePair(OptimTestUtils.point(DIM, 0.0), 0.0),
1e-14);
}
@Test
public void testSsDiffPow() {
doTest(new OptimTestUtils.SsDiffPow(),
OptimTestUtils.point(DIM / 2, 1.0),
GoalType.MINIMIZE,
656,
new PointValuePair(OptimTestUtils.point(DIM / 2, 0.0), 0.0),
1e-15);
}
@Ignore
@Test
public void testAckley() {
doTest(new OptimTestUtils.Ackley(),
OptimTestUtils.point(DIM, 1.0),
GoalType.MINIMIZE,
587,
new PointValuePair(OptimTestUtils.point(DIM, 0.0), 0.0),
0);
}
@Ignore
@Test
public void testAckleyWithSimulatedAnnealing() {
doTestWithSimulatedAnnealing(new OptimTestUtils.Ackley(),
OptimTestUtils.point(DIM, 1.0),
GoalType.MINIMIZE,
100000,
new PointValuePair(OptimTestUtils.point(DIM, 0.0), 0.0),
0);
}
@Ignore
@Test
public void testRastrigin() {
doTest(new OptimTestUtils.Rastrigin(),
OptimTestUtils.point(DIM, 1.0),
GoalType.MINIMIZE,
535,
new PointValuePair(OptimTestUtils.point(DIM, 0.0), 0.0),
0);
}
@Ignore
@Test
public void testRastriginWithSimulatedAnnealing() {
doTestWithSimulatedAnnealing(new OptimTestUtils.Rastrigin(),
OptimTestUtils.point(DIM, 1.0),
GoalType.MINIMIZE,
100000,
new PointValuePair(OptimTestUtils.point(DIM, 0.0), 0.0),
0);
}
/**
* @param func Function to optimize.
* @param startPoint Starting point.
* @param goal Minimization or maximization.
* @param fTol Tolerance relative error on the objective function.
* @param pointTol Tolerance for checking that the optimum is correct.
* @param maxEvaluations Maximum number of evaluations.
* @param expected Expected optimum.
*/
private void doTest(MultivariateFunction func,
double[] startPoint,
GoalType goal,
int maxEvaluations,
PointValuePair expected,
double tol) {
final int dim = startPoint.length;
final SimplexOptimizer optim = new SimplexOptimizer(1e-10, 1e-12);
final PointValuePair result = optim.optimize(new MaxEval(Integer.MAX_VALUE), // XXX
//new MaxEval(maxEvaluations), // XXX
new ObjectiveFunction(func),
goal,
new InitialGuess(startPoint),
new MultiDirectionalSimplex(dim, 0.1));
final double dist = MathArrays.distance(expected.getPoint(),
result.getPoint());
System.out.println("==> " + func.getClass().getName()); // XXX
System.out.println(" N=" + optim.getEvaluations()); // XXX
System.out.println(" d=" + dist); // XXX
System.out.println(" v(r)=" + func.value(result.getPoint())); // XXX
System.out.println(" v(e)=" + func.value(expected.getPoint())); // XXX
Assert.assertEquals(0d, dist, tol);
}
/**
* @param func Function to optimize.
* @param startPoint Starting point.
* @param goal Minimization or maximization.
* @param fTol Tolerance relative error on the objective function.
* @param pointTol Tolerance for checking that the optimum is correct.
* @param maxEvaluations Maximum number of evaluations.
* @param expected Expected optimum.
*/
private void doTestWithSimulatedAnnealing(MultivariateFunction func,
double[] startPoint,
GoalType goal,
int maxEvaluations,
PointValuePair expected,
double tol) {
final int dim = startPoint.length;
final SimplexOptimizer optim = new SimplexOptimizer(1e-14, 1e-15);
final PointValuePair result = optim.optimize(new MaxEval(Integer.MAX_VALUE), // XXX
//new MaxEval(maxEvaluations), // XXX
new ObjectiveFunction(func),
goal,
new InitialGuess(startPoint),
new MultiDirectionalSimplex(dim, 0.1),
new SimulatedAnnealing(OptimTestUtils.rng(),
maxEvaluations));
final double dist = MathArrays.distance(expected.getPoint(),
result.getPoint());
System.out.println("++> " + func.getClass().getName()); // XXX
System.out.println(" N=" + optim.getEvaluations()); // XXX
System.out.println(" d=" + dist); // XXX
System.out.println(" v(r)=" + func.value(result.getPoint())); // XXX
System.out.println(" v(e)=" + func.value(expected.getPoint())); // XXX
Assert.assertEquals(0d, dist, tol);
}
}