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Java example source code file (BOBYQAOptimizerTest.java)

This example Java source code file (BOBYQAOptimizerTest.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

ackley, basis, cigar, cigtab, dim, elli, ellirotated, multivariatefunction, pointvaluepair, rastrigin, rosen, tablet, test, twoaxes, util

The BOBYQAOptimizerTest.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.optimization.direct;

import java.util.Arrays;
import java.util.Random;

import org.apache.commons.math3.analysis.MultivariateFunction;
import org.apache.commons.math3.exception.DimensionMismatchException;
import org.apache.commons.math3.exception.TooManyEvaluationsException;
import org.apache.commons.math3.exception.NumberIsTooLargeException;
import org.apache.commons.math3.exception.NumberIsTooSmallException;
import org.apache.commons.math3.optimization.GoalType;
import org.apache.commons.math3.optimization.PointValuePair;
import org.apache.commons.math3.optimization.InitialGuess;
import org.apache.commons.math3.optimization.SimpleBounds;
import org.apache.commons.math3.util.FastMath;
import org.junit.Assert;
import org.junit.Ignore;
import org.junit.Test;

/**
 * Test for {@link BOBYQAOptimizer}.
 */
@Deprecated
public class BOBYQAOptimizerTest {

    static final int DIM = 13;

    @Test(expected=NumberIsTooLargeException.class)
    public void testInitOutOfBounds() {
        double[] startPoint = point(DIM, 3);
        double[][] boundaries = boundaries(DIM, -1, 2);
        doTest(new Rosen(), startPoint, boundaries,
                GoalType.MINIMIZE,
                1e-13, 1e-6, 2000, null);
    }

    @Test(expected=DimensionMismatchException.class)
    public void testBoundariesDimensionMismatch() {
        double[] startPoint = point(DIM, 0.5);
        double[][] boundaries = boundaries(DIM + 1, -1, 2);
        doTest(new Rosen(), startPoint, boundaries,
               GoalType.MINIMIZE,
               1e-13, 1e-6, 2000, null);
    }

    @Test(expected=NumberIsTooSmallException.class)
    public void testProblemDimensionTooSmall() {
        double[] startPoint = point(1, 0.5);
        doTest(new Rosen(), startPoint, null,
               GoalType.MINIMIZE,
               1e-13, 1e-6, 2000, null);
    }

    @Test(expected=TooManyEvaluationsException.class)
    public void testMaxEvaluations() {
        final int lowMaxEval = 2;
        double[] startPoint = point(DIM, 0.1);
        double[][] boundaries = null;
        doTest(new Rosen(), startPoint, boundaries,
               GoalType.MINIMIZE,
               1e-13, 1e-6, lowMaxEval, null);
     }

    @Test
    public void testRosen() {
        double[] startPoint = point(DIM,0.1);
        double[][] boundaries = null;
        PointValuePair expected = new PointValuePair(point(DIM,1.0),0.0);
        doTest(new Rosen(), startPoint, boundaries,
                GoalType.MINIMIZE,
                1e-13, 1e-6, 2000, expected);
     }

    @Test
    public void testMaximize() {
        double[] startPoint = point(DIM,1.0);
        double[][] boundaries = null;
        PointValuePair expected = new PointValuePair(point(DIM,0.0),1.0);
        doTest(new MinusElli(), startPoint, boundaries,
                GoalType.MAXIMIZE,
                2e-10, 5e-6, 1000, expected);
        boundaries = boundaries(DIM,-0.3,0.3);
        startPoint = point(DIM,0.1);
        doTest(new MinusElli(), startPoint, boundaries,
                GoalType.MAXIMIZE,
                2e-10, 5e-6, 1000, expected);
    }

    @Test
    public void testEllipse() {
        double[] startPoint = point(DIM,1.0);
        double[][] boundaries = null;
        PointValuePair expected =
            new PointValuePair(point(DIM,0.0),0.0);
        doTest(new Elli(), startPoint, boundaries,
                GoalType.MINIMIZE,
                1e-13, 1e-6, 1000, expected);
     }

    @Test
    public void testElliRotated() {
        double[] startPoint = point(DIM,1.0);
        double[][] boundaries = null;
        PointValuePair expected =
            new PointValuePair(point(DIM,0.0),0.0);
        doTest(new ElliRotated(), startPoint, boundaries,
                GoalType.MINIMIZE,
                1e-12, 1e-6, 10000, expected);
    }

    @Test
    public void testCigar() {
        double[] startPoint = point(DIM,1.0);
        double[][] boundaries = null;
        PointValuePair expected =
            new PointValuePair(point(DIM,0.0),0.0);
        doTest(new Cigar(), startPoint, boundaries,
                GoalType.MINIMIZE,
                1e-13, 1e-6, 100, expected);
    }

    @Test
    public void testTwoAxes() {
        double[] startPoint = point(DIM,1.0);
        double[][] boundaries = null;
        PointValuePair expected =
            new PointValuePair(point(DIM,0.0),0.0);
        doTest(new TwoAxes(), startPoint, boundaries,
                GoalType.MINIMIZE, 2*
                1e-13, 1e-6, 100, expected);
     }

    @Test
    public void testCigTab() {
        double[] startPoint = point(DIM,1.0);
        double[][] boundaries = null;
        PointValuePair expected =
            new PointValuePair(point(DIM,0.0),0.0);
        doTest(new CigTab(), startPoint, boundaries,
                GoalType.MINIMIZE,
                1e-13, 5e-5, 100, expected);
     }

    @Test
    public void testSphere() {
        double[] startPoint = point(DIM,1.0);
        double[][] boundaries = null;
        PointValuePair expected =
            new PointValuePair(point(DIM,0.0),0.0);
        doTest(new Sphere(), startPoint, boundaries,
                GoalType.MINIMIZE,
                1e-13, 1e-6, 100, expected);
    }

    @Test
    public void testTablet() {
        double[] startPoint = point(DIM,1.0);
        double[][] boundaries = null;
        PointValuePair expected =
            new PointValuePair(point(DIM,0.0),0.0);
        doTest(new Tablet(), startPoint, boundaries,
                GoalType.MINIMIZE,
                1e-13, 1e-6, 100, expected);
    }

    @Test
    public void testDiffPow() {
        double[] startPoint = point(DIM/2,1.0);
        double[][] boundaries = null;
        PointValuePair expected =
            new PointValuePair(point(DIM/2,0.0),0.0);
        doTest(new DiffPow(), startPoint, boundaries,
                GoalType.MINIMIZE,
                1e-8, 1e-1, 21000, expected);
    }

    @Test
    public void testSsDiffPow() {
        double[] startPoint = point(DIM/2,1.0);
        double[][] boundaries = null;
        PointValuePair expected =
            new PointValuePair(point(DIM/2,0.0),0.0);
        doTest(new SsDiffPow(), startPoint, boundaries,
                GoalType.MINIMIZE,
                1e-2, 1.3e-1, 50000, expected);
    }

    @Test
    public void testAckley() {
        double[] startPoint = point(DIM,0.1);
        double[][] boundaries = null;
        PointValuePair expected =
            new PointValuePair(point(DIM,0.0),0.0);
        doTest(new Ackley(), startPoint, boundaries,
                GoalType.MINIMIZE,
                1e-7, 1e-5, 1000, expected);
    }

    @Test
    public void testRastrigin() {
        double[] startPoint = point(DIM,1.0);

        double[][] boundaries = null;
        PointValuePair expected =
            new PointValuePair(point(DIM,0.0),0.0);
        doTest(new Rastrigin(), startPoint, boundaries,
                GoalType.MINIMIZE,
                1e-13, 1e-6, 1000, expected);
    }

    @Test
    public void testConstrainedRosen() {
        double[] startPoint = point(DIM,0.1);

        double[][] boundaries = boundaries(DIM,-1,2);
        PointValuePair expected =
            new PointValuePair(point(DIM,1.0),0.0);
        doTest(new Rosen(), startPoint, boundaries,
                GoalType.MINIMIZE,
                1e-13, 1e-6, 2000, expected);
    }

    // See MATH-728
    // TODO: this test is temporarily disabled for 3.2 release as a bug in Cobertura
    //       makes it run for several hours before completing
    @Ignore @Test
    public void testConstrainedRosenWithMoreInterpolationPoints() {
        final double[] startPoint = point(DIM, 0.1);
        final double[][] boundaries = boundaries(DIM, -1, 2);
        final PointValuePair expected = new PointValuePair(point(DIM, 1.0), 0.0);

        // This should have been 78 because in the code the hard limit is
        // said to be
        //   ((DIM + 1) * (DIM + 2)) / 2 - (2 * DIM + 1)
        // i.e. 78 in this case, but the test fails for 48, 59, 62, 63, 64,
        // 65, 66, ...
        final int maxAdditionalPoints = 47;

        for (int num = 1; num <= maxAdditionalPoints; num++) {
            doTest(new Rosen(), startPoint, boundaries,
                   GoalType.MINIMIZE,
                   1e-12, 1e-6, 2000,
                   num,
                   expected,
                   "num=" + num);
        }
    }

    /**
     * @param func Function to optimize.
     * @param startPoint Starting point.
     * @param boundaries Upper / lower point limit.
     * @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 point / value.
     */
    private void doTest(MultivariateFunction func,
                        double[] startPoint,
                        double[][] boundaries,
                        GoalType goal,
                        double fTol,
                        double pointTol,
                        int maxEvaluations,
                        PointValuePair expected) {
        doTest(func,
               startPoint,
               boundaries,
               goal,
               fTol,
               pointTol,
               maxEvaluations,
               0,
               expected,
               "");
    }

    /**
     * @param func Function to optimize.
     * @param startPoint Starting point.
     * @param boundaries Upper / lower point limit.
     * @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 additionalInterpolationPoints Number of interpolation to used
     * in addition to the default (2 * dim + 1).
     * @param expected Expected point / value.
     */
    private void doTest(MultivariateFunction func,
                        double[] startPoint,
                        double[][] boundaries,
                        GoalType goal,
                        double fTol,
                        double pointTol,
                        int maxEvaluations,
                        int additionalInterpolationPoints,
                        PointValuePair expected,
                        String assertMsg) {

//         System.out.println(func.getClass().getName() + " BEGIN"); // XXX

        int dim = startPoint.length;
//        MultivariateOptimizer optim =
//            new PowellOptimizer(1e-13, FastMath.ulp(1d));
//        PointValuePair result = optim.optimize(100000, func, goal, startPoint);
        final double[] lB = boundaries == null ? null : boundaries[0];
        final double[] uB = boundaries == null ? null : boundaries[1];
        final int numIterpolationPoints = 2 * dim + 1 + additionalInterpolationPoints;
        BOBYQAOptimizer optim = new BOBYQAOptimizer(numIterpolationPoints);
        PointValuePair result = boundaries == null ?
            optim.optimize(maxEvaluations, func, goal,
                           new InitialGuess(startPoint)) :
            optim.optimize(maxEvaluations, func, goal,
                           new InitialGuess(startPoint),
                           new SimpleBounds(lB, uB));
//        System.out.println(func.getClass().getName() + " = "
//              + optim.getEvaluations() + " f(");
//        for (double x: result.getPoint())  System.out.print(x + " ");
//        System.out.println(") = " +  result.getValue());
        Assert.assertEquals(assertMsg, expected.getValue(), result.getValue(), fTol);
        for (int i = 0; i < dim; i++) {
            Assert.assertEquals(expected.getPoint()[i],
                                result.getPoint()[i], pointTol);
        }

//         System.out.println(func.getClass().getName() + " END"); // XXX
    }

    private static double[] point(int n, double value) {
        double[] ds = new double[n];
        Arrays.fill(ds, value);
        return ds;
    }

    private static double[][] boundaries(int dim,
            double lower, double upper) {
        double[][] boundaries = new double[2][dim];
        for (int i = 0; i < dim; i++)
            boundaries[0][i] = lower;
        for (int i = 0; i < dim; i++)
            boundaries[1][i] = upper;
        return boundaries;
    }

    private static class Sphere implements MultivariateFunction {

        public double value(double[] x) {
            double f = 0;
            for (int i = 0; i < x.length; ++i)
                f += x[i] * x[i];
            return f;
        }
    }

    private static class Cigar implements MultivariateFunction {
        private double factor;

        Cigar() {
            this(1e3);
        }

        Cigar(double axisratio) {
            factor = axisratio * axisratio;
        }

        public double value(double[] x) {
            double f = x[0] * x[0];
            for (int i = 1; i < x.length; ++i)
                f += factor * x[i] * x[i];
            return f;
        }
    }

    private static class Tablet implements MultivariateFunction {
        private double factor;

        Tablet() {
            this(1e3);
        }

        Tablet(double axisratio) {
            factor = axisratio * axisratio;
        }

        public double value(double[] x) {
            double f = factor * x[0] * x[0];
            for (int i = 1; i < x.length; ++i)
                f += x[i] * x[i];
            return f;
        }
    }

    private static class CigTab implements MultivariateFunction {
        private double factor;

        CigTab() {
            this(1e4);
        }

        CigTab(double axisratio) {
            factor = axisratio;
        }

        public double value(double[] x) {
            int end = x.length - 1;
            double f = x[0] * x[0] / factor + factor * x[end] * x[end];
            for (int i = 1; i < end; ++i)
                f += x[i] * x[i];
            return f;
        }
    }

    private static class TwoAxes implements MultivariateFunction {

        private double factor;

        TwoAxes() {
            this(1e6);
        }

        TwoAxes(double axisratio) {
            factor = axisratio * axisratio;
        }

        public double value(double[] x) {
            double f = 0;
            for (int i = 0; i < x.length; ++i)
                f += (i < x.length / 2 ? factor : 1) * x[i] * x[i];
            return f;
        }
    }

    private static class ElliRotated implements MultivariateFunction {
        private Basis B = new Basis();
        private double factor;

        ElliRotated() {
            this(1e3);
        }

        ElliRotated(double axisratio) {
            factor = axisratio * axisratio;
        }

        public double value(double[] x) {
            double f = 0;
            x = B.Rotate(x);
            for (int i = 0; i < x.length; ++i)
                f += FastMath.pow(factor, i / (x.length - 1.)) * x[i] * x[i];
            return f;
        }
    }

    private static class Elli implements MultivariateFunction {

        private double factor;

        Elli() {
            this(1e3);
        }

        Elli(double axisratio) {
            factor = axisratio * axisratio;
        }

        public double value(double[] x) {
            double f = 0;
            for (int i = 0; i < x.length; ++i)
                f += FastMath.pow(factor, i / (x.length - 1.)) * x[i] * x[i];
            return f;
        }
    }

    private static class MinusElli implements MultivariateFunction {
        private final Elli elli = new Elli();
        public double value(double[] x) {
            return 1.0 - elli.value(x);
        }
    }

    private static class DiffPow implements MultivariateFunction {
//        private int fcount = 0;
        public double value(double[] x) {
            double f = 0;
            for (int i = 0; i < x.length; ++i)
                f += FastMath.pow(FastMath.abs(x[i]), 2. + 10 * (double) i
                        / (x.length - 1.));
//            System.out.print("" + (fcount++) + ") ");
//            for (int i = 0; i < x.length; i++)
//                System.out.print(x[i] +  " ");
//            System.out.println(" = " + f);
            return f;
        }
    }

    private static class SsDiffPow implements MultivariateFunction {

        public double value(double[] x) {
            double f = FastMath.pow(new DiffPow().value(x), 0.25);
            return f;
        }
    }

    private static class Rosen implements MultivariateFunction {

        public double value(double[] x) {
            double f = 0;
            for (int i = 0; i < x.length - 1; ++i)
                f += 1e2 * (x[i] * x[i] - x[i + 1]) * (x[i] * x[i] - x[i + 1])
                + (x[i] - 1.) * (x[i] - 1.);
            return f;
        }
    }

    private static class Ackley implements MultivariateFunction {
        private double axisratio;

        Ackley(double axra) {
            axisratio = axra;
        }

        public Ackley() {
            this(1);
        }

        public double value(double[] x) {
            double f = 0;
            double res2 = 0;
            double fac = 0;
            for (int i = 0; i < x.length; ++i) {
                fac = FastMath.pow(axisratio, (i - 1.) / (x.length - 1.));
                f += fac * fac * x[i] * x[i];
                res2 += FastMath.cos(2. * FastMath.PI * fac * x[i]);
            }
            f = (20. - 20. * FastMath.exp(-0.2 * FastMath.sqrt(f / x.length))
                    + FastMath.exp(1.) - FastMath.exp(res2 / x.length));
            return f;
        }
    }

    private static class Rastrigin implements MultivariateFunction {

        private double axisratio;
        private double amplitude;

        Rastrigin() {
            this(1, 10);
        }

        Rastrigin(double axisratio, double amplitude) {
            this.axisratio = axisratio;
            this.amplitude = amplitude;
        }

        public double value(double[] x) {
            double f = 0;
            double fac;
            for (int i = 0; i < x.length; ++i) {
                fac = FastMath.pow(axisratio, (i - 1.) / (x.length - 1.));
                if (i == 0 && x[i] < 0)
                    fac *= 1.;
                f += fac * fac * x[i] * x[i] + amplitude
                * (1. - FastMath.cos(2. * FastMath.PI * fac * x[i]));
            }
            return f;
        }
    }

    private static class Basis {
        double[][] basis;
        Random rand = new Random(2); // use not always the same basis

        double[] Rotate(double[] x) {
            GenBasis(x.length);
            double[] y = new double[x.length];
            for (int i = 0; i < x.length; ++i) {
                y[i] = 0;
                for (int j = 0; j < x.length; ++j)
                    y[i] += basis[i][j] * x[j];
            }
            return y;
        }

        void GenBasis(int DIM) {
            if (basis != null ? basis.length == DIM : false)
                return;

            double sp;
            int i, j, k;

            /* generate orthogonal basis */
            basis = new double[DIM][DIM];
            for (i = 0; i < DIM; ++i) {
                /* sample components gaussian */
                for (j = 0; j < DIM; ++j)
                    basis[i][j] = rand.nextGaussian();
                /* substract projection of previous vectors */
                for (j = i - 1; j >= 0; --j) {
                    for (sp = 0., k = 0; k < DIM; ++k)
                        sp += basis[i][k] * basis[j][k]; /* scalar product */
                    for (k = 0; k < DIM; ++k)
                        basis[i][k] -= sp * basis[j][k]; /* substract */
                }
                /* normalize */
                for (sp = 0., k = 0; k < DIM; ++k)
                    sp += basis[i][k] * basis[i][k]; /* squared norm */
                for (k = 0; k < DIM; ++k)
                    basis[i][k] /= FastMath.sqrt(sp);
            }
        }
    }
}

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