Gilles Sadowski
parent
e39ad3c984
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f49e77a806
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/*
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* Licensed to the Apache Software Foundation (ASF) under one or more
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* contributor license agreements. See the NOTICE file distributed with
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* this work for additional information regarding copyright ownership.
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* The ASF licenses this file to You under the Apache License, Version 2.0
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* (the "License"); you may not use this file except in compliance with
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* the License. You may obtain a copy of the License at
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*
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* http://www.apache.org/licenses/LICENSE-2.0
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*
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* Unless required by applicable law or agreed to in writing, software
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* distributed under the License is distributed on an "AS IS" BASIS,
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* WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
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* See the License for the specific language governing permissions and
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* limitations under the License.
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*/
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package org.apache.commons.math4.optim.nonlinear.scalar.noderiv;
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import org.apache.commons.math4.analysis.MultivariateFunction;
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import org.apache.commons.math4.exception.MathUnsupportedOperationException;
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import org.apache.commons.math4.optim.InitialGuess;
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import org.apache.commons.math4.optim.MaxEval;
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import org.apache.commons.math4.optim.PointValuePair;
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import org.apache.commons.math4.optim.SimpleBounds;
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import org.apache.commons.math4.optim.SimpleValueChecker;
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import org.apache.commons.math4.optim.nonlinear.scalar.GoalType;
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import org.apache.commons.math4.optim.nonlinear.scalar.ObjectiveFunction;
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import org.apache.commons.math4.optim.nonlinear.scalar.SimulatedAnnealing;
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import org.apache.commons.math4.optim.nonlinear.scalar.noderiv.MultiDirectionalSimplex;
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import org.apache.commons.math4.optim.nonlinear.scalar.noderiv.NelderMeadSimplex;
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import org.apache.commons.math4.optim.nonlinear.scalar.noderiv.SimplexOptimizer;
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import org.apache.commons.math4.util.FastMath;
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import org.apache.commons.math4.util.MathArrays;
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import org.junit.Assert;
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import org.junit.Test;
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import org.junit.Ignore;
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public class SimplexOptimizerMultiDirectionalTest {
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private static final int DIM = 13;
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@Test(expected=MathUnsupportedOperationException.class)
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public void testBoundsUnsupported() {
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SimplexOptimizer optimizer = new SimplexOptimizer(1e-10, 1e-30);
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final OptimTestUtils.FourExtrema fourExtrema = new OptimTestUtils.FourExtrema();
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optimizer.optimize(new MaxEval(100),
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new ObjectiveFunction(fourExtrema),
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GoalType.MINIMIZE,
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new InitialGuess(new double[] { -3, 0 }),
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new NelderMeadSimplex(new double[] { 0.2, 0.2 }),
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new SimpleBounds(new double[] { -5, -1 },
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new double[] { 5, 1 }));
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}
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@Test
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public void testMinimize1() {
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SimplexOptimizer optimizer = new SimplexOptimizer(1e-11, 1e-30);
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final OptimTestUtils.FourExtrema fourExtrema = new OptimTestUtils.FourExtrema();
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final PointValuePair optimum
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= optimizer.optimize(new MaxEval(200),
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new ObjectiveFunction(fourExtrema),
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GoalType.MINIMIZE,
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new InitialGuess(new double[] { -3, 0 }),
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new MultiDirectionalSimplex(new double[] { 0.2, 0.2 }));
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Assert.assertEquals(fourExtrema.xM, optimum.getPoint()[0], 4e-6);
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Assert.assertEquals(fourExtrema.yP, optimum.getPoint()[1], 3e-6);
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Assert.assertEquals(fourExtrema.valueXmYp, optimum.getValue(), 8e-13);
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Assert.assertTrue(optimizer.getEvaluations() > 120);
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Assert.assertTrue(optimizer.getEvaluations() < 150);
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// Check that the number of iterations is updated (MATH-949).
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Assert.assertTrue(optimizer.getIterations() > 0);
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}
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@Test
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public void testMinimize2() {
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SimplexOptimizer optimizer = new SimplexOptimizer(1e-11, 1e-30);
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final OptimTestUtils.FourExtrema fourExtrema = new OptimTestUtils.FourExtrema();
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final PointValuePair optimum
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= optimizer.optimize(new MaxEval(200),
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new ObjectiveFunction(fourExtrema),
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GoalType.MINIMIZE,
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new InitialGuess(new double[] { 1, 0 }),
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new MultiDirectionalSimplex(new double[] { 0.2, 0.2 }));
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Assert.assertEquals(fourExtrema.xP, optimum.getPoint()[0], 2e-8);
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Assert.assertEquals(fourExtrema.yM, optimum.getPoint()[1], 3e-6);
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Assert.assertEquals(fourExtrema.valueXpYm, optimum.getValue(), 2e-12);
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Assert.assertTrue(optimizer.getEvaluations() > 120);
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Assert.assertTrue(optimizer.getEvaluations() < 150);
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// Check that the number of iterations is updated (MATH-949).
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Assert.assertTrue(optimizer.getIterations() > 0);
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}
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@Test
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public void testMaximize1() {
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SimplexOptimizer optimizer = new SimplexOptimizer(1e-11, 1e-30);
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final OptimTestUtils.FourExtrema fourExtrema = new OptimTestUtils.FourExtrema();
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final PointValuePair optimum
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= optimizer.optimize(new MaxEval(200),
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new ObjectiveFunction(fourExtrema),
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GoalType.MAXIMIZE,
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new InitialGuess(new double[] { -3.0, 0.0 }),
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new MultiDirectionalSimplex(new double[] { 0.2, 0.2 }));
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Assert.assertEquals(fourExtrema.xM, optimum.getPoint()[0], 7e-7);
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Assert.assertEquals(fourExtrema.yM, optimum.getPoint()[1], 3e-7);
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Assert.assertEquals(fourExtrema.valueXmYm, optimum.getValue(), 2e-14);
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Assert.assertTrue(optimizer.getEvaluations() > 120);
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Assert.assertTrue(optimizer.getEvaluations() < 150);
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// Check that the number of iterations is updated (MATH-949).
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Assert.assertTrue(optimizer.getIterations() > 0);
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}
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@Test
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public void testMaximize2() {
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SimplexOptimizer optimizer = new SimplexOptimizer(new SimpleValueChecker(1e-15, 1e-30));
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final OptimTestUtils.FourExtrema fourExtrema = new OptimTestUtils.FourExtrema();
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final PointValuePair optimum
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= optimizer.optimize(new MaxEval(200),
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new ObjectiveFunction(fourExtrema),
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GoalType.MAXIMIZE,
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new InitialGuess(new double[] { 1, 0 }),
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new MultiDirectionalSimplex(new double[] { 0.2, 0.2 }));
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Assert.assertEquals(fourExtrema.xP, optimum.getPoint()[0], 2e-8);
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Assert.assertEquals(fourExtrema.yP, optimum.getPoint()[1], 3e-6);
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Assert.assertEquals(fourExtrema.valueXpYp, optimum.getValue(), 2e-12);
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Assert.assertTrue(optimizer.getEvaluations() > 180);
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Assert.assertTrue(optimizer.getEvaluations() < 220);
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// Check that the number of iterations is updated (MATH-949).
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Assert.assertTrue(optimizer.getIterations() > 0);
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}
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@Test
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public void testRosenbrock() {
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final OptimTestUtils.Rosenbrock rosenbrock = new OptimTestUtils.Rosenbrock();
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SimplexOptimizer optimizer = new SimplexOptimizer(-1, 1e-3);
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PointValuePair optimum
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= optimizer.optimize(new MaxEval(100),
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new ObjectiveFunction(rosenbrock),
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GoalType.MINIMIZE,
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new InitialGuess(new double[] { -1.2, 1 }),
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new MultiDirectionalSimplex(new double[][] {
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{ -1.2, 1.0 },
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{ 0.9, 1.2 },
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{ 3.5, -2.3 } }));
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Assert.assertTrue(optimizer.getEvaluations() > 50);
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Assert.assertTrue(optimizer.getEvaluations() < 100);
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Assert.assertTrue(optimum.getValue() > 1e-2);
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}
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@Test
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public void testPowell() {
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final OptimTestUtils.Powell powell = new OptimTestUtils.Powell();
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SimplexOptimizer optimizer = new SimplexOptimizer(-1, 1e-3);
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PointValuePair optimum
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= optimizer.optimize(new MaxEval(1000),
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new ObjectiveFunction(powell),
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GoalType.MINIMIZE,
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new InitialGuess(new double[] { 3, -1, 0, 1 }),
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new MultiDirectionalSimplex(4));
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Assert.assertTrue(optimizer.getEvaluations() > 800);
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Assert.assertTrue(optimizer.getEvaluations() < 900);
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Assert.assertTrue(optimum.getValue() > 1e-2);
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}
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@Test
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public void testMath283() {
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// fails because MultiDirectional.iterateSimplex is looping forever
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// the while(true) should be replaced with a convergence check
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SimplexOptimizer optimizer = new SimplexOptimizer(1e-14, 1e-14);
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final OptimTestUtils.Gaussian2D function = new OptimTestUtils.Gaussian2D(0, 0, 1);
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PointValuePair estimate = optimizer.optimize(new MaxEval(1000),
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new ObjectiveFunction(function),
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GoalType.MAXIMIZE,
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new InitialGuess(function.getMaximumPosition()),
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new MultiDirectionalSimplex(2));
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final double EPSILON = 1e-5;
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final double expectedMaximum = function.getMaximum();
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final double actualMaximum = estimate.getValue();
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Assert.assertEquals(expectedMaximum, actualMaximum, EPSILON);
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final double[] expectedPosition = function.getMaximumPosition();
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final double[] actualPosition = estimate.getPoint();
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Assert.assertEquals(expectedPosition[0], actualPosition[0], EPSILON );
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Assert.assertEquals(expectedPosition[1], actualPosition[1], EPSILON );
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}
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@Test
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public void testRosen() {
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doTest(new OptimTestUtils.Rosen(),
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OptimTestUtils.point(DIM, 0.1),
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GoalType.MINIMIZE,
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183861,
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new PointValuePair(OptimTestUtils.point(DIM, 1.0), 0.0),
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1e-4);
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}
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@Test
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public void testEllipse() {
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doTest(new OptimTestUtils.Elli(),
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OptimTestUtils.point(DIM, 1.0),
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GoalType.MINIMIZE,
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873,
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new PointValuePair(OptimTestUtils.point(DIM, 0.0), 0.0),
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1e-14);
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}
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//@Ignore
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@Test
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public void testElliRotated() {
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doTest(new OptimTestUtils.ElliRotated(),
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OptimTestUtils.point(DIM, 1.0),
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GoalType.MINIMIZE,
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873,
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new PointValuePair(OptimTestUtils.point(DIM, 0.0), 0.0),
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1e-14);
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}
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@Test
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public void testCigar() {
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doTest(new OptimTestUtils.Cigar(),
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OptimTestUtils.point(DIM, 1.0),
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GoalType.MINIMIZE,
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925,
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new PointValuePair(OptimTestUtils.point(DIM,0.0), 0.0),
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1e-14);
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}
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@Test
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public void testTwoAxes() {
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doTest(new OptimTestUtils.TwoAxes(),
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OptimTestUtils.point(DIM, 1.0),
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GoalType.MINIMIZE,
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1159,
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new PointValuePair(OptimTestUtils.point(DIM, 0.0), 0.0),
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1e-14);
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}
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@Test
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public void testCigTab() {
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doTest(new OptimTestUtils.CigTab(),
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OptimTestUtils.point(DIM, 1.0),
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GoalType.MINIMIZE,
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795,
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new PointValuePair(OptimTestUtils.point(DIM, 0.0), 0.0),
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1e-14);
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}
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@Test
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public void testSphere() {
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doTest(new OptimTestUtils.Sphere(),
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OptimTestUtils.point(DIM, 1.0),
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GoalType.MINIMIZE,
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665,
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new PointValuePair(OptimTestUtils.point(DIM, 0.0), 0.0),
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1e-14);
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}
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@Test
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public void testTablet() {
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doTest(new OptimTestUtils.Tablet(),
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OptimTestUtils.point(DIM, 1.0),
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GoalType.MINIMIZE,
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873,
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new PointValuePair(OptimTestUtils.point(DIM, 0.0), 0.0),
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1e-14);
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}
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@Test
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public void testDiffPow() {
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doTest(new OptimTestUtils.DiffPow(),
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OptimTestUtils.point(DIM, 1.0),
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GoalType.MINIMIZE,
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614,
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new PointValuePair(OptimTestUtils.point(DIM, 0.0), 0.0),
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1e-14);
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}
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@Test
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public void testSsDiffPow() {
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doTest(new OptimTestUtils.SsDiffPow(),
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OptimTestUtils.point(DIM / 2, 1.0),
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GoalType.MINIMIZE,
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656,
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new PointValuePair(OptimTestUtils.point(DIM / 2, 0.0), 0.0),
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1e-15);
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}
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@Ignore
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@Test
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public void testAckley() {
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doTest(new OptimTestUtils.Ackley(),
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OptimTestUtils.point(DIM, 1.0),
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GoalType.MINIMIZE,
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587,
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new PointValuePair(OptimTestUtils.point(DIM, 0.0), 0.0),
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0);
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}
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@Ignore
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@Test
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public void testAckleyWithSimulatedAnnealing() {
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doTestWithSimulatedAnnealing(new OptimTestUtils.Ackley(),
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OptimTestUtils.point(DIM, 1.0),
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GoalType.MINIMIZE,
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100000,
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new PointValuePair(OptimTestUtils.point(DIM, 0.0), 0.0),
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0);
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}
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@Ignore
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@Test
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public void testRastrigin() {
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doTest(new OptimTestUtils.Rastrigin(),
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OptimTestUtils.point(DIM, 1.0),
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GoalType.MINIMIZE,
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535,
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new PointValuePair(OptimTestUtils.point(DIM, 0.0), 0.0),
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0);
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}
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@Ignore
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@Test
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public void testRastriginWithSimulatedAnnealing() {
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doTestWithSimulatedAnnealing(new OptimTestUtils.Rastrigin(),
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OptimTestUtils.point(DIM, 1.0),
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GoalType.MINIMIZE,
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100000,
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new PointValuePair(OptimTestUtils.point(DIM, 0.0), 0.0),
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0);
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}
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/**
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* @param func Function to optimize.
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* @param startPoint Starting point.
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* @param goal Minimization or maximization.
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* @param fTol Tolerance relative error on the objective function.
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* @param pointTol Tolerance for checking that the optimum is correct.
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* @param maxEvaluations Maximum number of evaluations.
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* @param expected Expected optimum.
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*/
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private void doTest(MultivariateFunction func,
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double[] startPoint,
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GoalType goal,
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int maxEvaluations,
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PointValuePair expected,
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double tol) {
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final int dim = startPoint.length;
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final SimplexOptimizer optim = new SimplexOptimizer(1e-10, 1e-12);
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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);
|
|
||||||
}
|
|
||||||
}
|
|
||||||
Loading…
Reference in New Issue