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 */
017package org.apache.commons.math4.optim.nonlinear.scalar;
018
019import org.apache.commons.math4.analysis.MultivariateFunction;
020import org.apache.commons.math4.exception.DimensionMismatchException;
021import org.apache.commons.math4.exception.NumberIsTooSmallException;
022import org.apache.commons.math4.util.FastMath;
023import org.apache.commons.math4.util.MathUtils;
024
025/**
026 * <p>Adapter extending bounded {@link MultivariateFunction} to an unbouded
027 * domain using a penalty function.</p>
028 *
029 * <p>
030 * This adapter can be used to wrap functions subject to simple bounds on
031 * parameters so they can be used by optimizers that do <em>not</em> directly
032 * support simple bounds.
033 * </p>
034 * <p>
035 * The principle is that the user function that will be wrapped will see its
036 * parameters bounded as required, i.e when its {@code value} method is called
037 * with argument array {@code point}, the elements array will fulfill requirement
038 * {@code lower[i] <= point[i] <= upper[i]} for all i. Some of the components
039 * may be unbounded or bounded only on one side if the corresponding bound is
040 * set to an infinite value. The optimizer will not manage the user function by
041 * itself, but it will handle this adapter and it is this adapter that will take
042 * care the bounds are fulfilled. The adapter {@link #value(double[])} method will
043 * be called by the optimizer with unbound parameters, and the adapter will check
044 * if the parameters is within range or not. If it is in range, then the underlying
045 * user function will be called, and if it is not the value of a penalty function
046 * will be returned instead.
047 * </p>
048 * <p>
049 * This adapter is only a poor-man's solution to simple bounds optimization
050 * constraints that can be used with simple optimizers like
051 * {@link org.apache.commons.math4.optim.nonlinear.scalar.noderiv.SimplexOptimizer
052 * SimplexOptimizer}.
053 * A better solution is to use an optimizer that directly supports simple bounds like
054 * {@link org.apache.commons.math4.optim.nonlinear.scalar.noderiv.CMAESOptimizer
055 * CMAESOptimizer} or
056 * {@link org.apache.commons.math4.optim.nonlinear.scalar.noderiv.BOBYQAOptimizer
057 * BOBYQAOptimizer}.
058 * One caveat of this poor-man's solution is that if start point or start simplex
059 * is completely outside of the allowed range, only the penalty function is used,
060 * and the optimizer may converge without ever entering the range.
061 * </p>
062 *
063 * @see MultivariateFunctionMappingAdapter
064 *
065 * @since 3.0
066 */
067public class MultivariateFunctionPenaltyAdapter
068    implements MultivariateFunction {
069    /** Underlying bounded function. */
070    private final MultivariateFunction bounded;
071    /** Lower bounds. */
072    private final double[] lower;
073    /** Upper bounds. */
074    private final double[] upper;
075    /** Penalty offset. */
076    private final double offset;
077    /** Penalty scales. */
078    private final double[] scale;
079
080    /**
081     * Simple constructor.
082     * <p>
083     * When the optimizer provided points are out of range, the value of the
084     * penalty function will be used instead of the value of the underlying
085     * function. In order for this penalty to be effective in rejecting this
086     * point during the optimization process, the penalty function value should
087     * be defined with care. This value is computed as:
088     * <div style="white-space: pre"><code>
089     *   penalty(point) = offset + &sum;<sub>i</sub>[scale[i] * &radic;|point[i]-boundary[i]|]
090     * </code></div>
091     * where indices i correspond to all the components that violates their boundaries.
092     *
093     * <p>
094     * So when attempting a function minimization, offset should be larger than
095     * the maximum expected value of the underlying function and scale components
096     * should all be positive. When attempting a function maximization, offset
097     * should be lesser than the minimum expected value of the underlying function
098     * and scale components should all be negative.
099     * minimization, and lesser than the minimum expected value of the underlying
100     * function when attempting maximization.
101     * </p>
102     * <p>
103     * These choices for the penalty function have two properties. First, all out
104     * of range points will return a function value that is worse than the value
105     * returned by any in range point. Second, the penalty is worse for large
106     * boundaries violation than for small violations, so the optimizer has an hint
107     * about the direction in which it should search for acceptable points.
108     * </p>
109     * @param bounded bounded function
110     * @param lower lower bounds for each element of the input parameters array
111     * (some elements may be set to {@code Double.NEGATIVE_INFINITY} for
112     * unbounded values)
113     * @param upper upper bounds for each element of the input parameters array
114     * (some elements may be set to {@code Double.POSITIVE_INFINITY} for
115     * unbounded values)
116     * @param offset base offset of the penalty function
117     * @param scale scale of the penalty function
118     * @exception DimensionMismatchException if lower bounds, upper bounds and
119     * scales are not consistent, either according to dimension or to boundary
120     * values
121     */
122    public MultivariateFunctionPenaltyAdapter(final MultivariateFunction bounded,
123                                              final double[] lower, final double[] upper,
124                                              final double offset, final double[] scale) {
125
126        // safety checks
127        MathUtils.checkNotNull(lower);
128        MathUtils.checkNotNull(upper);
129        MathUtils.checkNotNull(scale);
130        if (lower.length != upper.length) {
131            throw new DimensionMismatchException(lower.length, upper.length);
132        }
133        if (lower.length != scale.length) {
134            throw new DimensionMismatchException(lower.length, scale.length);
135        }
136        for (int i = 0; i < lower.length; ++i) {
137            // note the following test is written in such a way it also fails for NaN
138            if (!(upper[i] >= lower[i])) {
139                throw new NumberIsTooSmallException(upper[i], lower[i], true);
140            }
141        }
142
143        this.bounded = bounded;
144        this.lower   = lower.clone();
145        this.upper   = upper.clone();
146        this.offset  = offset;
147        this.scale   = scale.clone();
148    }
149
150    /**
151     * Computes the underlying function value from an unbounded point.
152     * <p>
153     * This method simply returns the value of the underlying function
154     * if the unbounded point already fulfills the bounds, and compute
155     * a replacement value using the offset and scale if bounds are
156     * violated, without calling the function at all.
157     * </p>
158     * @param point unbounded point
159     * @return either underlying function value or penalty function value
160     */
161    @Override
162    public double value(double[] point) {
163
164        for (int i = 0; i < scale.length; ++i) {
165            if ((point[i] < lower[i]) || (point[i] > upper[i])) {
166                // bound violation starting at this component
167                double sum = 0;
168                for (int j = i; j < scale.length; ++j) {
169                    final double overshoot;
170                    if (point[j] < lower[j]) {
171                        overshoot = scale[j] * (lower[j] - point[j]);
172                    } else if (point[j] > upper[j]) {
173                        overshoot = scale[j] * (point[j] - upper[j]);
174                    } else {
175                        overshoot = 0;
176                    }
177                    sum += FastMath.sqrt(overshoot);
178                }
179                return offset + sum;
180            }
181        }
182
183        // all boundaries are fulfilled, we are in the expected
184        // domain of the underlying function
185        return bounded.value(point);
186    }
187}