SimplexOptimizer.java

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

import java.util.Comparator;

import org.apache.commons.math.analysis.MultivariateRealFunction;
import org.apache.commons.math.exception.MathUserException;
import org.apache.commons.math.exception.NullArgumentException;
import org.apache.commons.math.optimization.GoalType;
import org.apache.commons.math.optimization.ConvergenceChecker;
import org.apache.commons.math.optimization.RealPointValuePair;
import org.apache.commons.math.optimization.SimpleScalarValueChecker;
import org.apache.commons.math.optimization.MultivariateRealOptimizer;

/**
 * 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 {@link #setSimplex(AbstractSimplex) setSimplex} method <em>must</em>
 *  be called prior to calling the {@code optimize} method.
 * </p>
 * <p>
 *  Each call to {@link #optimize(int,MultivariateRealFunction,GoalType,double[])
 *  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>
 *  If {@link #setConvergenceChecker(ConvergenceChecker)} is not called,
 *  a default {@link SimpleScalarValueChecker} is used.
 * </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>
 *
 * @see AbstractSimplex
 * @version $Id$
 * @since 3.0
 */
public class SimplexOptimizer
    extends BaseAbstractScalarOptimizer<MultivariateRealFunction>
    implements MultivariateRealOptimizer {
    /** Simplex. */
    private AbstractSimplex simplex;

    /**
     * Default constructor.
     */
    public SimplexOptimizer() {
        setConvergenceChecker(new SimpleScalarValueChecker());
    }

    /**
     * @param rel Relative threshold.
     * @param abs Absolute threshold.
     */
    public SimplexOptimizer(double rel, double abs) {
        setConvergenceChecker(new SimpleScalarValueChecker(rel, abs));
    }

    /**
     * Set the simplex algorithm.
     *
     * @param simplex Simplex.
     */
    public void setSimplex(AbstractSimplex simplex) {
        this.simplex = simplex;
    }

    /** {@inheritDoc} */
    @Override
    protected RealPointValuePair doOptimize() throws MathUserException {
        if (simplex == null) {
            throw new NullArgumentException();
        }

        // Indirect call to "computeObjectiveValue" in order to update the
        // evaluations counter.
        final MultivariateRealFunction evalFunc
            = new MultivariateRealFunction() {
                public double value(double[] point) throws MathUserException {
                    return computeObjectiveValue(point);
                }
            };

        final boolean isMinim = getGoalType() == GoalType.MINIMIZE;
        final Comparator<RealPointValuePair> comparator
            = new Comparator<RealPointValuePair>() {
            public int compare(final RealPointValuePair o1,
                               final RealPointValuePair 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);

        RealPointValuePair[] previous = null;
        int iteration = 0;
        final ConvergenceChecker<RealPointValuePair> checker = getConvergenceChecker();
        while (true) {
            if (iteration > 0) {
                boolean converged = true;
                for (int i = 0; i < simplex.getSize(); i++) {
                    RealPointValuePair prev = previous[i];
                    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);
            ++iteration;
        }
    }
}