org.apache.commons.math.optimization.direct.NelderMead Maven / Gradle / Ivy
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* http://www.apache.org/licenses/LICENSE-2.0
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package org.apache.commons.math.optimization.direct;
import java.util.Comparator;
import org.apache.commons.math.FunctionEvaluationException;
import org.apache.commons.math.optimization.OptimizationException;
import org.apache.commons.math.optimization.RealPointValuePair;
/**
* This class implements the Nelder-Mead direct search method.
*
* @version $Revision: 1070725 $ $Date: 2011-02-15 02:31:12 +0100 (mar. 15 févr. 2011) $
* @see MultiDirectional
* @since 1.2
*/
public class NelderMead extends DirectSearchOptimizer {
/** Reflection coefficient. */
private final double rho;
/** Expansion coefficient. */
private final double khi;
/** Contraction coefficient. */
private final double gamma;
/** Shrinkage coefficient. */
private final double sigma;
/** Build a Nelder-Mead optimizer with default coefficients.
* The default coefficients are 1.0 for rho, 2.0 for khi and 0.5
* for both gamma and sigma.
*/
public NelderMead() {
this.rho = 1.0;
this.khi = 2.0;
this.gamma = 0.5;
this.sigma = 0.5;
}
/** Build a Nelder-Mead optimizer with specified coefficients.
* @param rho reflection coefficient
* @param khi expansion coefficient
* @param gamma contraction coefficient
* @param sigma shrinkage coefficient
*/
public NelderMead(final double rho, final double khi,
final double gamma, final double sigma) {
this.rho = rho;
this.khi = khi;
this.gamma = gamma;
this.sigma = sigma;
}
/** {@inheritDoc} */
@Override
protected void iterateSimplex(final Comparator comparator)
throws FunctionEvaluationException, OptimizationException {
incrementIterationsCounter();
// the simplex has n+1 point if dimension is n
final int n = simplex.length - 1;
// interesting values
final RealPointValuePair best = simplex[0];
final RealPointValuePair secondBest = simplex[n-1];
final RealPointValuePair worst = simplex[n];
final double[] xWorst = worst.getPointRef();
// compute the centroid of the best vertices
// (dismissing the worst point at index n)
final double[] centroid = new double[n];
for (int i = 0; i < n; ++i) {
final double[] x = simplex[i].getPointRef();
for (int j = 0; j < n; ++j) {
centroid[j] += x[j];
}
}
final double scaling = 1.0 / n;
for (int j = 0; j < n; ++j) {
centroid[j] *= scaling;
}
// compute the reflection point
final double[] xR = new double[n];
for (int j = 0; j < n; ++j) {
xR[j] = centroid[j] + rho * (centroid[j] - xWorst[j]);
}
final RealPointValuePair reflected = new RealPointValuePair(xR, evaluate(xR), false);
if ((comparator.compare(best, reflected) <= 0) &&
(comparator.compare(reflected, secondBest) < 0)) {
// accept the reflected point
replaceWorstPoint(reflected, comparator);
} else if (comparator.compare(reflected, best) < 0) {
// compute the expansion point
final double[] xE = new double[n];
for (int j = 0; j < n; ++j) {
xE[j] = centroid[j] + khi * (xR[j] - centroid[j]);
}
final RealPointValuePair expanded = new RealPointValuePair(xE, evaluate(xE), false);
if (comparator.compare(expanded, reflected) < 0) {
// accept the expansion point
replaceWorstPoint(expanded, comparator);
} else {
// accept the reflected point
replaceWorstPoint(reflected, comparator);
}
} else {
if (comparator.compare(reflected, worst) < 0) {
// perform an outside contraction
final double[] xC = new double[n];
for (int j = 0; j < n; ++j) {
xC[j] = centroid[j] + gamma * (xR[j] - centroid[j]);
}
final RealPointValuePair outContracted = new RealPointValuePair(xC, evaluate(xC), false);
if (comparator.compare(outContracted, reflected) <= 0) {
// accept the contraction point
replaceWorstPoint(outContracted, comparator);
return;
}
} else {
// perform an inside contraction
final double[] xC = new double[n];
for (int j = 0; j < n; ++j) {
xC[j] = centroid[j] - gamma * (centroid[j] - xWorst[j]);
}
final RealPointValuePair inContracted = new RealPointValuePair(xC, evaluate(xC), false);
if (comparator.compare(inContracted, worst) < 0) {
// accept the contraction point
replaceWorstPoint(inContracted, comparator);
return;
}
}
// perform a shrink
final double[] xSmallest = simplex[0].getPointRef();
for (int i = 1; i < simplex.length; ++i) {
final double[] x = simplex[i].getPoint();
for (int j = 0; j < n; ++j) {
x[j] = xSmallest[j] + sigma * (x[j] - xSmallest[j]);
}
simplex[i] = new RealPointValuePair(x, Double.NaN, false);
}
evaluateSimplex(comparator);
}
}
}