src/test/java/org/apache/commons/math3/optimization/direct/SimplexOptimizerMultiDirectionalTest.java

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package org.apache.commons.math3.optimization.direct;

import org.apache.commons.math3.analysis.MultivariateFunction;
import org.apache.commons.math3.optimization.GoalType;
import org.apache.commons.math3.optimization.PointValuePair;
import org.apache.commons.math3.optimization.SimpleValueChecker;
import org.apache.commons.math3.util.FastMath;
import org.junit.Assert;
import org.junit.Test;

@Deprecated
public class SimplexOptimizerMultiDirectionalTest {
    @Test
    public void testMinimize1() {
        SimplexOptimizer optimizer = new SimplexOptimizer(1e-11, 1e-30);
        optimizer.setSimplex(new MultiDirectionalSimplex(new double[] { 0.2, 0.2 }));
        final FourExtrema fourExtrema = new FourExtrema();

        final PointValuePair optimum
            = optimizer.optimize(200, fourExtrema, GoalType.MINIMIZE, new double[] { -3, 0 });
        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);
    }

    @Test
    public void testMinimize2() {
        SimplexOptimizer optimizer = new SimplexOptimizer(1e-11, 1e-30);
        optimizer.setSimplex(new MultiDirectionalSimplex(new double[] { 0.2, 0.2 }));
        final FourExtrema fourExtrema = new FourExtrema();

        final PointValuePair optimum
            =  optimizer.optimize(200, fourExtrema, GoalType.MINIMIZE, new double[] { 1, 0 });
        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);
    }

    @Test
    public void testMaximize1() {
        SimplexOptimizer optimizer = new SimplexOptimizer(1e-11, 1e-30);
        optimizer.setSimplex(new MultiDirectionalSimplex(new double[] { 0.2, 0.2 }));
        final FourExtrema fourExtrema = new FourExtrema();

        final PointValuePair optimum
            = optimizer.optimize(200, fourExtrema, GoalType.MAXIMIZE, new double[] { -3.0, 0.0 });
        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);
    }

    @Test
    public void testMaximize2() {
        SimplexOptimizer optimizer = new SimplexOptimizer(new SimpleValueChecker(1e-15, 1e-30));
        optimizer.setSimplex(new MultiDirectionalSimplex(new double[] { 0.2, 0.2 }));
        final FourExtrema fourExtrema = new FourExtrema();

        final PointValuePair optimum
            = optimizer.optimize(200, fourExtrema, GoalType.MAXIMIZE, new double[] { 1, 0 });
        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);
    }

    @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);
        optimizer.setSimplex(new MultiDirectionalSimplex(new double[][] {
                    { -1.2,  1.0 }, { 0.9, 1.2 } , {  3.5, -2.3 }
                }));
        PointValuePair optimum =
            optimizer.optimize(100, rosenbrock, GoalType.MINIMIZE, new double[] { -1.2, 1 });

        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);
        optimizer.setSimplex(new MultiDirectionalSimplex(4));
        PointValuePair optimum =
            optimizer.optimize(1000, powell, GoalType.MINIMIZE, new double[] { 3, -1, 0, 1 });
        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);
        optimizer.setSimplex(new MultiDirectionalSimplex(2));
        final Gaussian2D function = new Gaussian2D(0, 0, 1);
        PointValuePair estimate = optimizer.optimize(1000, function,
                                                         GoalType.MAXIMIZE, function.getMaximumPosition());
        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;
}