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Java example source code file (CMAESOptimizerTest.java)

This example Java source code file (CMAESOptimizerTest.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, cigar, cigtab, cmaesoptimizer, dim, ellirotated, lambda, multivariatefunction, pointvaluepair, rastrigin, rosen, tablet, test, twoaxes, util

The CMAESOptimizerTest.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.Retry;
import org.apache.commons.math3.RetryRunner;
import org.apache.commons.math3.analysis.MultivariateFunction;
import org.apache.commons.math3.exception.NumberIsTooLargeException;
import org.apache.commons.math3.exception.NumberIsTooSmallException;
import org.apache.commons.math3.exception.DimensionMismatchException;
import org.apache.commons.math3.exception.NotPositiveException;
import org.apache.commons.math3.exception.OutOfRangeException;
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.random.MersenneTwister;
import org.apache.commons.math3.util.FastMath;
import org.junit.Assert;
import org.junit.Test;
import org.junit.runner.RunWith;

/**
 * Test for {@link CMAESOptimizer}.
 */
@Deprecated
@RunWith(RetryRunner.class)
public class CMAESOptimizerTest {

    static final int DIM = 13;
    static final int LAMBDA = 4 + (int)(3.*FastMath.log(DIM));

    @Test(expected = NumberIsTooLargeException.class)
    public void testInitOutofbounds1() {
        double[] startPoint = point(DIM,3);
        double[] insigma = point(DIM, 0.3);
        double[][] boundaries = boundaries(DIM,-1,2);
        PointValuePair expected =
            new PointValuePair(point(DIM,1.0),0.0);
        doTest(new Rosen(), startPoint, insigma, boundaries,
                GoalType.MINIMIZE, LAMBDA, true, 0, 1e-13,
                1e-13, 1e-6, 100000, expected);
    }
    @Test(expected = NumberIsTooSmallException.class)
    public void testInitOutofbounds2() {
        double[] startPoint = point(DIM, -2);
        double[] insigma = point(DIM, 0.3);
        double[][] boundaries = boundaries(DIM,-1,2);
        PointValuePair expected =
            new PointValuePair(point(DIM,1.0),0.0);
        doTest(new Rosen(), startPoint, insigma, boundaries,
                GoalType.MINIMIZE, LAMBDA, true, 0, 1e-13,
                1e-13, 1e-6, 100000, expected);
    }

    @Test(expected = DimensionMismatchException.class)
    public void testBoundariesDimensionMismatch() {
        double[] startPoint = point(DIM,0.5);
        double[] insigma = point(DIM, 0.3);
        double[][] boundaries = boundaries(DIM+1,-1,2);
        PointValuePair expected =
            new PointValuePair(point(DIM,1.0),0.0);
        doTest(new Rosen(), startPoint, insigma, boundaries,
                GoalType.MINIMIZE, LAMBDA, true, 0, 1e-13,
                1e-13, 1e-6, 100000, expected);
    }

    @Test(expected = NotPositiveException.class)
    public void testInputSigmaNegative() {
        double[] startPoint = point(DIM,0.5);
        double[] insigma = point(DIM,-0.5);
        double[][] boundaries = null;
        PointValuePair expected =
            new PointValuePair(point(DIM,1.0),0.0);
        doTest(new Rosen(), startPoint, insigma, boundaries,
                GoalType.MINIMIZE, LAMBDA, true, 0, 1e-13,
                1e-13, 1e-6, 100000, expected);
    }

    @Test(expected = OutOfRangeException.class)
    public void testInputSigmaOutOfRange() {
        double[] startPoint = point(DIM,0.5);
        double[] insigma = point(DIM, 1.1);
        double[][] boundaries = boundaries(DIM,-0.5,0.5);
        PointValuePair expected =
            new PointValuePair(point(DIM,1.0),0.0);
        doTest(new Rosen(), startPoint, insigma, boundaries,
                GoalType.MINIMIZE, LAMBDA, true, 0, 1e-13,
                1e-13, 1e-6, 100000, expected);
    }

    @Test(expected = DimensionMismatchException.class)
    public void testInputSigmaDimensionMismatch() {
        double[] startPoint = point(DIM,0.5);
        double[] insigma = point(DIM + 1, 0.5);
        double[][] boundaries = null;
        PointValuePair expected =
            new PointValuePair(point(DIM,1.0),0.0);
        doTest(new Rosen(), startPoint, insigma, boundaries,
                GoalType.MINIMIZE, LAMBDA, true, 0, 1e-13,
                1e-13, 1e-6, 100000, expected);
    }

    @Test
    @Retry(3)
    public void testRosen() {
        double[] startPoint = point(DIM,0.1);
        double[] insigma = point(DIM,0.1);
        double[][] boundaries = null;
        PointValuePair expected =
            new PointValuePair(point(DIM,1.0),0.0);
        doTest(new Rosen(), startPoint, insigma, boundaries,
                GoalType.MINIMIZE, LAMBDA, true, 0, 1e-13,
                1e-13, 1e-6, 100000, expected);
        doTest(new Rosen(), startPoint, insigma, boundaries,
                GoalType.MINIMIZE, LAMBDA, false, 0, 1e-13,
                1e-13, 1e-6, 100000, expected);
    }

    @Test
    @Retry(3)
    public void testMaximize() {
        double[] startPoint = point(DIM,1.0);
        double[] insigma = point(DIM,0.1);
        double[][] boundaries = null;
        PointValuePair expected =
            new PointValuePair(point(DIM,0.0),1.0);
        doTest(new MinusElli(), startPoint, insigma, boundaries,
                GoalType.MAXIMIZE, LAMBDA, true, 0, 1.0-1e-13,
                2e-10, 5e-6, 100000, expected);
        doTest(new MinusElli(), startPoint, insigma, boundaries,
                GoalType.MAXIMIZE, LAMBDA, false, 0, 1.0-1e-13,
                2e-10, 5e-6, 100000, expected);
        boundaries = boundaries(DIM,-0.3,0.3);
        startPoint = point(DIM,0.1);
        doTest(new MinusElli(), startPoint, insigma, boundaries,
                GoalType.MAXIMIZE, LAMBDA, true, 0, 1.0-1e-13,
                2e-10, 5e-6, 100000, expected);
    }

    @Test
    public void testEllipse() {
        double[] startPoint = point(DIM,1.0);
        double[] insigma = point(DIM,0.1);
        double[][] boundaries = null;
        PointValuePair expected =
            new PointValuePair(point(DIM,0.0),0.0);
        doTest(new Elli(), startPoint, insigma, boundaries,
                GoalType.MINIMIZE, LAMBDA, true, 0, 1e-13,
                1e-13, 1e-6, 100000, expected);
        doTest(new Elli(), startPoint, insigma, boundaries,
                GoalType.MINIMIZE, LAMBDA, false, 0, 1e-13,
                1e-13, 1e-6, 100000, expected);
    }

    @Test
    public void testElliRotated() {
        double[] startPoint = point(DIM,1.0);
        double[] insigma = point(DIM,0.1);
        double[][] boundaries = null;
        PointValuePair expected =
            new PointValuePair(point(DIM,0.0),0.0);
        doTest(new ElliRotated(), startPoint, insigma, boundaries,
                GoalType.MINIMIZE, LAMBDA, true, 0, 1e-13,
                1e-13, 1e-6, 100000, expected);
        doTest(new ElliRotated(), startPoint, insigma, boundaries,
                GoalType.MINIMIZE, LAMBDA, false, 0, 1e-13,
                1e-13, 1e-6, 100000, expected);
    }

    @Test
    public void testCigar() {
        double[] startPoint = point(DIM,1.0);
        double[] insigma = point(DIM,0.1);
        double[][] boundaries = null;
        PointValuePair expected =
            new PointValuePair(point(DIM,0.0),0.0);
        doTest(new Cigar(), startPoint, insigma, boundaries,
                GoalType.MINIMIZE, LAMBDA, true, 0, 1e-13,
                1e-13, 1e-6, 200000, expected);
        doTest(new Cigar(), startPoint, insigma, boundaries,
                GoalType.MINIMIZE, LAMBDA, false, 0, 1e-13,
                1e-13, 1e-6, 100000, expected);
    }

    @Test
    public void testCigarWithBoundaries() {
        double[] startPoint = point(DIM,1.0);
        double[] insigma = point(DIM,0.1);
        double[][] boundaries = boundaries(DIM, -1e100, Double.POSITIVE_INFINITY);
        PointValuePair expected =
            new PointValuePair(point(DIM,0.0),0.0);
        doTest(new Cigar(), startPoint, insigma, boundaries,
                GoalType.MINIMIZE, LAMBDA, true, 0, 1e-13,
                1e-13, 1e-6, 200000, expected);
        doTest(new Cigar(), startPoint, insigma, boundaries,
                GoalType.MINIMIZE, LAMBDA, false, 0, 1e-13,
                1e-13, 1e-6, 100000, expected);
    }

    @Test
    public void testTwoAxes() {
        double[] startPoint = point(DIM,1.0);
        double[] insigma = point(DIM,0.1);
        double[][] boundaries = null;
        PointValuePair expected =
            new PointValuePair(point(DIM,0.0),0.0);
        doTest(new TwoAxes(), startPoint, insigma, boundaries,
                GoalType.MINIMIZE, 2*LAMBDA, true, 0, 1e-13,
                1e-13, 1e-6, 200000, expected);
        doTest(new TwoAxes(), startPoint, insigma, boundaries,
                GoalType.MINIMIZE, 2*LAMBDA, false, 0, 1e-13,
                1e-8, 1e-3, 200000, expected);
    }

    @Test
    public void testCigTab() {
        double[] startPoint = point(DIM,1.0);
        double[] insigma = point(DIM,0.3);
        double[][] boundaries = null;
        PointValuePair expected =
            new PointValuePair(point(DIM,0.0),0.0);
        doTest(new CigTab(), startPoint, insigma, boundaries,
                GoalType.MINIMIZE, LAMBDA, true, 0, 1e-13,
                1e-13, 5e-5, 100000, expected);
        doTest(new CigTab(), startPoint, insigma, boundaries,
                GoalType.MINIMIZE, LAMBDA, false, 0, 1e-13,
                1e-13, 5e-5, 100000, expected);
    }

    @Test
    public void testSphere() {
        double[] startPoint = point(DIM,1.0);
        double[] insigma = point(DIM,0.1);
        double[][] boundaries = null;
        PointValuePair expected =
            new PointValuePair(point(DIM,0.0),0.0);
        doTest(new Sphere(), startPoint, insigma, boundaries,
                GoalType.MINIMIZE, LAMBDA, true, 0, 1e-13,
                1e-13, 1e-6, 100000, expected);
        doTest(new Sphere(), startPoint, insigma, boundaries,
                GoalType.MINIMIZE, LAMBDA, false, 0, 1e-13,
                1e-13, 1e-6, 100000, expected);
    }

    @Test
    public void testTablet() {
        double[] startPoint = point(DIM,1.0);
        double[] insigma = point(DIM,0.1);
        double[][] boundaries = null;
        PointValuePair expected =
            new PointValuePair(point(DIM,0.0),0.0);
        doTest(new Tablet(), startPoint, insigma, boundaries,
                GoalType.MINIMIZE, LAMBDA, true, 0, 1e-13,
                1e-13, 1e-6, 100000, expected);
        doTest(new Tablet(), startPoint, insigma, boundaries,
                GoalType.MINIMIZE, LAMBDA, false, 0, 1e-13,
                1e-13, 1e-6, 100000, expected);
    }

    @Test
    public void testDiffPow() {
        double[] startPoint = point(DIM,1.0);
        double[] insigma = point(DIM,0.1);
        double[][] boundaries = null;
        PointValuePair expected =
            new PointValuePair(point(DIM,0.0),0.0);
        doTest(new DiffPow(), startPoint, insigma, boundaries,
                GoalType.MINIMIZE, 10, true, 0, 1e-13,
                1e-8, 1e-1, 100000, expected);
        doTest(new DiffPow(), startPoint, insigma, boundaries,
                GoalType.MINIMIZE, 10, false, 0, 1e-13,
                1e-8, 2e-1, 100000, expected);
    }

    @Test
    public void testSsDiffPow() {
        double[] startPoint = point(DIM,1.0);
        double[] insigma = point(DIM,0.1);
        double[][] boundaries = null;
        PointValuePair expected =
            new PointValuePair(point(DIM,0.0),0.0);
        doTest(new SsDiffPow(), startPoint, insigma, boundaries,
                GoalType.MINIMIZE, 10, true, 0, 1e-13,
                1e-4, 1e-1, 200000, expected);
        doTest(new SsDiffPow(), startPoint, insigma, boundaries,
                GoalType.MINIMIZE, 10, false, 0, 1e-13,
                1e-4, 1e-1, 200000, expected);
    }

    @Test
    public void testAckley() {
        double[] startPoint = point(DIM,1.0);
        double[] insigma = point(DIM,1.0);
        double[][] boundaries = null;
        PointValuePair expected =
            new PointValuePair(point(DIM,0.0),0.0);
        doTest(new Ackley(), startPoint, insigma, boundaries,
                GoalType.MINIMIZE, 2*LAMBDA, true, 0, 1e-13,
                1e-9, 1e-5, 100000, expected);
        doTest(new Ackley(), startPoint, insigma, boundaries,
                GoalType.MINIMIZE, 2*LAMBDA, false, 0, 1e-13,
                1e-9, 1e-5, 100000, expected);
    }

    @Test
    public void testRastrigin() {
        double[] startPoint = point(DIM,0.1);
        double[] insigma = point(DIM,0.1);
        double[][] boundaries = null;
        PointValuePair expected =
            new PointValuePair(point(DIM,0.0),0.0);
        doTest(new Rastrigin(), startPoint, insigma, boundaries,
                GoalType.MINIMIZE, (int)(200*FastMath.sqrt(DIM)), true, 0, 1e-13,
                1e-13, 1e-6, 200000, expected);
        doTest(new Rastrigin(), startPoint, insigma, boundaries,
                GoalType.MINIMIZE, (int)(200*FastMath.sqrt(DIM)), false, 0, 1e-13,
                1e-13, 1e-6, 200000, expected);
    }

    @Test
    public void testConstrainedRosen() {
        double[] startPoint = point(DIM, 0.1);
        double[] insigma = point(DIM, 0.1);
        double[][] boundaries = boundaries(DIM, -1, 2);
        PointValuePair expected =
            new PointValuePair(point(DIM,1.0),0.0);
        doTest(new Rosen(), startPoint, insigma, boundaries,
                GoalType.MINIMIZE, 2*LAMBDA, true, 0, 1e-13,
                1e-13, 1e-6, 100000, expected);
        doTest(new Rosen(), startPoint, insigma, boundaries,
                GoalType.MINIMIZE, 2*LAMBDA, false, 0, 1e-13,
                1e-13, 1e-6, 100000, expected);
    }

    @Test
    public void testDiagonalRosen() {
        double[] startPoint = point(DIM,0.1);
        double[] insigma = point(DIM,0.1);
        double[][] boundaries = null;
        PointValuePair expected =
            new PointValuePair(point(DIM,1.0),0.0);
        doTest(new Rosen(), startPoint, insigma, boundaries,
                GoalType.MINIMIZE, LAMBDA, false, 1, 1e-13,
                1e-10, 1e-4, 1000000, expected);
     }

    @Test
    public void testMath864() {
        final CMAESOptimizer optimizer = new CMAESOptimizer();
        final MultivariateFunction fitnessFunction = new MultivariateFunction() {
                public double value(double[] parameters) {
                    final double target = 1;
                    final double error = target - parameters[0];
                    return error * error;
                }
            };

        final double[] start = { 0 };
        final double[] lower = { -1e6 };
        final double[] upper = { 1.5 };
        final double[] result = optimizer.optimize(10000, fitnessFunction, GoalType.MINIMIZE,
                                                   start, lower, upper).getPoint();
        Assert.assertTrue("Out of bounds (" + result[0] + " > " + upper[0] + ")",
                          result[0] <= upper[0]);
    }

    /**
     * Cf. MATH-867
     */
    @Test
    public void testFitAccuracyDependsOnBoundary() {
        final CMAESOptimizer optimizer = new CMAESOptimizer();
        final MultivariateFunction fitnessFunction = new MultivariateFunction() {
                public double value(double[] parameters) {
                    final double target = 11.1;
                    final double error = target - parameters[0];
                    return error * error;
                }
            };

        final double[] start = { 1 };

        // No bounds.
        PointValuePair result = optimizer.optimize(100000, fitnessFunction, GoalType.MINIMIZE,
                                                   start);
        final double resNoBound = result.getPoint()[0];

        // Optimum is near the lower bound.
        final double[] lower = { -20 };
        final double[] upper = { 5e16 };
        result = optimizer.optimize(100000, fitnessFunction, GoalType.MINIMIZE,
                                    start, lower, upper);
        final double resNearLo = result.getPoint()[0];

        // Optimum is near the upper bound.
        lower[0] = -5e16;
        upper[0] = 20;
        result = optimizer.optimize(100000, fitnessFunction, GoalType.MINIMIZE,
                                    start, lower, upper);
        final double resNearHi = result.getPoint()[0];

        // System.out.println("resNoBound=" + resNoBound +
        //                    " resNearLo=" + resNearLo +
        //                    " resNearHi=" + resNearHi);

        // The two values currently differ by a substantial amount, indicating that
        // the bounds definition can prevent reaching the optimum.
        Assert.assertEquals(resNoBound, resNearLo, 1e-3);
        Assert.assertEquals(resNoBound, resNearHi, 1e-3);
    }

    /**
     * @param func Function to optimize.
     * @param startPoint Starting point.
     * @param inSigma Individual input sigma.
     * @param boundaries Upper / lower point limit.
     * @param goal Minimization or maximization.
     * @param lambda Population size used for offspring.
     * @param isActive Covariance update mechanism.
     * @param diagonalOnly Simplified covariance update.
     * @param stopValue Termination criteria for optimization.
     * @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[] inSigma,
            double[][] boundaries,
            GoalType goal,
            int lambda,
            boolean isActive,
            int diagonalOnly,
            double stopValue,
            double fTol,
            double pointTol,
            int maxEvaluations,
            PointValuePair expected) {
        int dim = startPoint.length;
        // test diagonalOnly = 0 - slow but normally fewer feval#
        CMAESOptimizer optim = new CMAESOptimizer(30000, stopValue, isActive, diagonalOnly,
                                                  0, new MersenneTwister(), false, null);
        final double[] lB = boundaries == null ? null : boundaries[0];
        final double[] uB = boundaries == null ? null : boundaries[1];
        PointValuePair result = boundaries == null ?
            optim.optimize(maxEvaluations, func, goal,
                           new InitialGuess(startPoint),
                           new CMAESOptimizer.Sigma(inSigma),
                           new CMAESOptimizer.PopulationSize(lambda)) :
            optim.optimize(maxEvaluations, func, goal,
                           new InitialGuess(startPoint),
                           new SimpleBounds(lB, uB),
                           new CMAESOptimizer.Sigma(inSigma),
                           new CMAESOptimizer.PopulationSize(lambda));
        // System.out.println("sol=" + Arrays.toString(result.getPoint()));
        Assert.assertEquals(expected.getValue(), result.getValue(), fTol);
        for (int i = 0; i < dim; i++) {
            Assert.assertEquals(expected.getPoint()[i], result.getPoint()[i], pointTol);
        }
    }

    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 {

        public double value(double[] x) {
            return 1.0-(new Elli().value(x));
        }
    }

    private static class DiffPow implements MultivariateFunction {

        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.));
            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);
            }
        }
    }
}

Other Java examples (source code examples)

Here is a short list of links related to this Java CMAESOptimizerTest.java source code file:



my book on functional programming

 

new blog posts

 

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