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Java example source code file (SimplexOptimizerMultiDirectionalTest.java)

This example Java source code file (SimplexOptimizerMultiDirectionalTest.java) is included in the alvinalexander.com "Java Source Code Warehouse" project. The intent of this project is to help you "Learn Java by Example" TM.

Learn more about this Java project at its project page.

Java - Java tags/keywords

epsilon, fourextrema, gaussian2d, global, initialguess, local, maxeval, multidirectionalsimplex, multivariatefunction, objectivefunction, pointvaluepair, simplexoptimizer, simplexoptimizermultidirectionaltest, test

The SimplexOptimizerMultiDirectionalTest.java Java example source code

/*
 * 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.
 */

package org.apache.commons.math3.optim.nonlinear.scalar.noderiv;

import org.apache.commons.math3.analysis.MultivariateFunction;
import org.apache.commons.math3.optim.MaxEval;
import org.apache.commons.math3.optim.InitialGuess;
import org.apache.commons.math3.optim.PointValuePair;
import org.apache.commons.math3.optim.SimpleValueChecker;
import org.apache.commons.math3.optim.SimpleBounds;
import org.apache.commons.math3.optim.nonlinear.scalar.GoalType;
import org.apache.commons.math3.optim.nonlinear.scalar.ObjectiveFunction;
import org.apache.commons.math3.exception.MathUnsupportedOperationException;
import org.apache.commons.math3.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() {
                    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() {
                    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.

        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();
        }

        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;
}

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