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* 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 java.util.Comparator;
import org.apache.commons.math3.analysis.MultivariateFunction;
import org.apache.commons.math3.exception.NullArgumentException;
import org.apache.commons.math3.exception.MathUnsupportedOperationException;
import org.apache.commons.math3.exception.util.LocalizedFormats;
import org.apache.commons.math3.optim.nonlinear.scalar.GoalType;
import org.apache.commons.math3.optim.ConvergenceChecker;
import org.apache.commons.math3.optim.PointValuePair;
import org.apache.commons.math3.optim.SimpleValueChecker;
import org.apache.commons.math3.optim.OptimizationData;
import org.apache.commons.math3.optim.nonlinear.scalar.MultivariateOptimizer;
/**
* This class implements simplex-based direct search optimization.
*
* <p>
* Direct search methods only use objective function values, they do
* not need derivatives and don't either try to compute approximation
* of the derivatives. According to a 1996 paper by Margaret H. Wright
* (<a href="http://cm.bell-labs.com/cm/cs/doc/96/4-02.ps.gz">Direct
* Search Methods: Once Scorned, Now Respectable</a>), they are used
* when either the computation of the derivative is impossible (noisy
* functions, unpredictable discontinuities) or difficult (complexity,
* computation cost). In the first cases, rather than an optimum, a
* <em>not too bad</em> point is desired. In the latter cases, an
* optimum is desired but cannot be reasonably found. In all cases
* direct search methods can be useful.
* </p>
* <p>
* Simplex-based direct search methods are based on comparison of
* the objective function values at the vertices of a simplex (which is a
* set of n+1 points in dimension n) that is updated by the algorithms
* steps.
* <p>
* <p>
* The simplex update procedure ({@link NelderMeadSimplex} or
* {@link MultiDirectionalSimplex}) must be passed to the
* {@code optimize} method.
* </p>
* <p>
* Each call to {@code optimize} will re-use the start configuration of
* the current simplex and move it such that its first vertex is at the
* provided start point of the optimization.
* If the {@code optimize} method is called to solve a different problem
* and the number of parameters change, the simplex must be re-initialized
* to one with the appropriate dimensions.
* </p>
* <p>
* Convergence is checked by providing the <em>worst</em> points of
* previous and current simplex to the convergence checker, not the best
* ones.
* </p>
* <p>
* This simplex optimizer implementation does not directly support constrained
* optimization with simple bounds; so, for such optimizations, either a more
* dedicated algorithm must be used like
* {@link CMAESOptimizer} or {@link BOBYQAOptimizer}, or the objective
* function must be wrapped in an adapter like
* {@link org.apache.commons.math3.optim.nonlinear.scalar.MultivariateFunctionMappingAdapter
* MultivariateFunctionMappingAdapter} or
* {@link org.apache.commons.math3.optim.nonlinear.scalar.MultivariateFunctionPenaltyAdapter
* MultivariateFunctionPenaltyAdapter}.
* <br/>
* The call to {@link #optimize(OptimizationData[]) optimize} will throw
* {@link MathUnsupportedOperationException} if bounds are passed to it.
* </p>
*
* @since 3.0
*/
public class SimplexOptimizer extends MultivariateOptimizer {
/** Simplex update rule. */
private AbstractSimplex simplex;
/**
* @param checker Convergence checker.
*/
public SimplexOptimizer(ConvergenceChecker<PointValuePair> checker) {
super(checker);
}
/**
* @param rel Relative threshold.
* @param abs Absolute threshold.
*/
public SimplexOptimizer(double rel, double abs) {
this(new SimpleValueChecker(rel, abs));
}
/**
* {@inheritDoc}
*
* @param optData Optimization data. In addition to those documented in
* {@link MultivariateOptimizer#parseOptimizationData(OptimizationData[])
* MultivariateOptimizer}, this method will register the following data:
* <ul>
* <li>{@link AbstractSimplex}</li>
* </ul>
* @return {@inheritDoc}
*/
@Override
public PointValuePair optimize(OptimizationData... optData) {
// Set up base class and perform computation.
return super.optimize(optData);
}
/** {@inheritDoc} */
@Override
protected PointValuePair doOptimize() {
checkParameters();
// Indirect call to "computeObjectiveValue" in order to update the
// evaluations counter.
final MultivariateFunction evalFunc
= new MultivariateFunction() {
/** {@inheritDoc} */
public double value(double[] point) {
return computeObjectiveValue(point);
}
};
final boolean isMinim = getGoalType() == GoalType.MINIMIZE;
final Comparator<PointValuePair> comparator
= new Comparator<PointValuePair>() {
/** {@inheritDoc} */
public int compare(final PointValuePair o1,
final PointValuePair o2) {
final double v1 = o1.getValue();
final double v2 = o2.getValue();
return isMinim ? Double.compare(v1, v2) : Double.compare(v2, v1);
}
};
// Initialize search.
simplex.build(getStartPoint());
simplex.evaluate(evalFunc, comparator);
PointValuePair[] previous = null;
int iteration = 0;
final ConvergenceChecker<PointValuePair> checker = getConvergenceChecker();
while (true) {
if (getIterations() > 0) {
boolean converged = true;
for (int i = 0; i < simplex.getSize(); i++) {
PointValuePair prev = previous[i];
converged = converged &&
checker.converged(iteration, prev, simplex.getPoint(i));
}
if (converged) {
// We have found an optimum.
return simplex.getPoint(0);
}
}
// We still need to search.
previous = simplex.getPoints();
simplex.iterate(evalFunc, comparator);
incrementIterationCount();
}
}
/**
* Scans the list of (required and optional) optimization data that
* characterize the problem.
*
* @param optData Optimization data.
* The following data will be looked for:
* <ul>
* <li>{@link AbstractSimplex}</li>
* </ul>
*/
@Override
protected void parseOptimizationData(OptimizationData... optData) {
// Allow base class to register its own data.
super.parseOptimizationData(optData);
// The existing values (as set by the previous call) are reused if
// not provided in the argument list.
for (OptimizationData data : optData) {
if (data instanceof AbstractSimplex) {
simplex = (AbstractSimplex) data;
// If more data must be parsed, this statement _must_ be
// changed to "continue".
break;
}
}
}
/**
* @throws MathUnsupportedOperationException if bounds were passed to the
* {@link #optimize(OptimizationData[]) optimize} method.
* @throws NullArgumentException if no initial simplex was passed to the
* {@link #optimize(OptimizationData[]) optimize} method.
*/
private void checkParameters() {
if (simplex == null) {
throw new NullArgumentException();
}
if (getLowerBound() != null ||
getUpperBound() != null) {
throw new MathUnsupportedOperationException(LocalizedFormats.CONSTRAINT);
}
}
}