001/*
002 * Licensed to the Apache Software Foundation (ASF) under one or more
003 * contributor license agreements.  See the NOTICE file distributed with
004 * this work for additional information regarding copyright ownership.
005 * The ASF licenses this file to You under the Apache License, Version 2.0
006 * (the "License"); you may not use this file except in compliance with
007 * the License.  You may obtain a copy of the License at
008 *
009 *      http://www.apache.org/licenses/LICENSE-2.0
010 *
011 * Unless required by applicable law or agreed to in writing, software
012 * distributed under the License is distributed on an "AS IS" BASIS,
013 * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
014 * See the License for the specific language governing permissions and
015 * limitations under the License.
016 */
017
018package org.apache.commons.math3.optimization.direct;
019
020import org.apache.commons.math3.analysis.MultivariateFunction;
021import org.apache.commons.math3.exception.DimensionMismatchException;
022import org.apache.commons.math3.exception.NumberIsTooSmallException;
023import org.apache.commons.math3.util.FastMath;
024import org.apache.commons.math3.util.MathUtils;
025
026/**
027 * <p>Adapter extending bounded {@link MultivariateFunction} to an unbouded
028 * domain using a penalty function.</p>
029 *
030 * <p>
031 * This adapter can be used to wrap functions subject to simple bounds on
032 * parameters so they can be used by optimizers that do <em>not</em> directly
033 * support simple bounds.
034 * </p>
035 * <p>
036 * The principle is that the user function that will be wrapped will see its
037 * parameters bounded as required, i.e when its {@code value} method is called
038 * with argument array {@code point}, the elements array will fulfill requirement
039 * {@code lower[i] <= point[i] <= upper[i]} for all i. Some of the components
040 * may be unbounded or bounded only on one side if the corresponding bound is
041 * set to an infinite value. The optimizer will not manage the user function by
042 * itself, but it will handle this adapter and it is this adapter that will take
043 * care the bounds are fulfilled. The adapter {@link #value(double[])} method will
044 * be called by the optimizer with unbound parameters, and the adapter will check
045 * if the parameters is within range or not. If it is in range, then the underlying
046 * user function will be called, and if it is not the value of a penalty function
047 * will be returned instead.
048 * </p>
049 * <p>
050 * This adapter is only a poor man solution to simple bounds optimization constraints
051 * that can be used with simple optimizers like {@link SimplexOptimizer} with {@link
052 * NelderMeadSimplex} or {@link MultiDirectionalSimplex}. A better solution is to use
053 * an optimizer that directly supports simple bounds like {@link CMAESOptimizer} or
054 * {@link BOBYQAOptimizer}. One caveat of this poor man solution is that if start point
055 * or start simplex is completely outside of the allowed range, only the penalty function
056 * is used, and the optimizer may converge without ever entering the range.
057 * </p>
058 *
059 * @see MultivariateFunctionMappingAdapter
060 *
061 * @version $Id: MultivariateFunctionPenaltyAdapter.java 1422230 2012-12-15 12:11:13Z erans $
062 * @deprecated As of 3.1 (to be removed in 4.0).
063 * @since 3.0
064 */
065
066@Deprecated
067public class MultivariateFunctionPenaltyAdapter implements MultivariateFunction {
068
069    /** Underlying bounded function. */
070    private final MultivariateFunction bounded;
071
072    /** Lower bounds. */
073    private final double[] lower;
074
075    /** Upper bounds. */
076    private final double[] upper;
077
078    /** Penalty offset. */
079    private final double offset;
080
081    /** Penalty scales. */
082    private final double[] scale;
083
084    /** Simple constructor.
085     * <p>
086     * When the optimizer provided points are out of range, the value of the
087     * penalty function will be used instead of the value of the underlying
088     * function. In order for this penalty to be effective in rejecting this
089     * point during the optimization process, the penalty function value should
090     * be defined with care. This value is computed as:
091     * <pre>
092     *   penalty(point) = offset + &sum;<sub>i</sub>[scale[i] * &radic;|point[i]-boundary[i]|]
093     * </pre>
094     * where indices i correspond to all the components that violates their boundaries.
095     * </p>
096     * <p>
097     * So when attempting a function minimization, offset should be larger than
098     * the maximum expected value of the underlying function and scale components
099     * should all be positive. When attempting a function maximization, offset
100     * should be lesser than the minimum expected value of the underlying function
101     * and scale components should all be negative.
102     * minimization, and lesser than the minimum expected value of the underlying
103     * function when attempting maximization.
104     * </p>
105     * <p>
106     * These choices for the penalty function have two properties. First, all out
107     * of range points will return a function value that is worse than the value
108     * returned by any in range point. Second, the penalty is worse for large
109     * boundaries violation than for small violations, so the optimizer has an hint
110     * about the direction in which it should search for acceptable points.
111     * </p>
112     * @param bounded bounded function
113     * @param lower lower bounds for each element of the input parameters array
114     * (some elements may be set to {@code Double.NEGATIVE_INFINITY} for
115     * unbounded values)
116     * @param upper upper bounds for each element of the input parameters array
117     * (some elements may be set to {@code Double.POSITIVE_INFINITY} for
118     * unbounded values)
119     * @param offset base offset of the penalty function
120     * @param scale scale of the penalty function
121     * @exception DimensionMismatchException if lower bounds, upper bounds and
122     * scales are not consistent, either according to dimension or to bounadary
123     * values
124     */
125    public MultivariateFunctionPenaltyAdapter(final MultivariateFunction bounded,
126                                                  final double[] lower, final double[] upper,
127                                                  final double offset, final double[] scale) {
128
129        // safety checks
130        MathUtils.checkNotNull(lower);
131        MathUtils.checkNotNull(upper);
132        MathUtils.checkNotNull(scale);
133        if (lower.length != upper.length) {
134            throw new DimensionMismatchException(lower.length, upper.length);
135        }
136        if (lower.length != scale.length) {
137            throw new DimensionMismatchException(lower.length, scale.length);
138        }
139        for (int i = 0; i < lower.length; ++i) {
140            // note the following test is written in such a way it also fails for NaN
141            if (!(upper[i] >= lower[i])) {
142                throw new NumberIsTooSmallException(upper[i], lower[i], true);
143            }
144        }
145
146        this.bounded = bounded;
147        this.lower   = lower.clone();
148        this.upper   = upper.clone();
149        this.offset  = offset;
150        this.scale   = scale.clone();
151
152    }
153
154    /** Compute the underlying function value from an unbounded point.
155     * <p>
156     * This method simply returns the value of the underlying function
157     * if the unbounded point already fulfills the bounds, and compute
158     * a replacement value using the offset and scale if bounds are
159     * violated, without calling the function at all.
160     * </p>
161     * @param point unbounded point
162     * @return either underlying function value or penalty function value
163     */
164    public double value(double[] point) {
165
166        for (int i = 0; i < scale.length; ++i) {
167            if ((point[i] < lower[i]) || (point[i] > upper[i])) {
168                // bound violation starting at this component
169                double sum = 0;
170                for (int j = i; j < scale.length; ++j) {
171                    final double overshoot;
172                    if (point[j] < lower[j]) {
173                        overshoot = scale[j] * (lower[j] - point[j]);
174                    } else if (point[j] > upper[j]) {
175                        overshoot = scale[j] * (point[j] - upper[j]);
176                    } else {
177                        overshoot = 0;
178                    }
179                    sum += FastMath.sqrt(overshoot);
180                }
181                return offset + sum;
182            }
183        }
184
185        // all boundaries are fulfilled, we are in the expected
186        // domain of the underlying function
187        return bounded.value(point);
188
189    }
190
191}